HEAVY MESONS

A. I. Alikhanov

Submitted 1953 | SovietRxiv: ru-195301.44507 | Translated from Russian

Abstract

Research over the past two years has decisively changed the state of affairs and has not only shown that the heavy meson exists, but moreover has shown that there are charged heavy mesons of different masses and that, in addition, neutral heavy mesons also exist, likewise with different masses.

Full Text

HEAVY MESONS

A. I. Alikhanov

Beginning in 1946–1947, indications began to appear in the literature of the existence, among cosmic rays, of mesons heavier than the $\pi$-meson. These indications were obtained by various authors using different methods; however, for one reason or another, they could not be regarded as fully conclusive. Leprince-Ringuet$^1$ discovered in a Wilson chamber a single trajectory of a particle to which, from measurements of its momentum and energy and of the angle of emission of the $\delta$-electron knocked out by the particle along its path in the Wilson chamber, he ascribed a mass of $900\,m_e$. This single photograph met with objections in which it was pointed out that, by adopting extreme values of the errors, it was possible to identify this trajectory as the path of a proton.

Alikhanian, Alikhanov, and others$^2$ reported that in the mass spectrum of cosmic rays at an altitude of 3200 m, obtained with the aid of the first model of a mass spectrometer, there were, in addition to particles with masses of 200 and $350\,m_e$, charged particles with masses of about 600 and $1000\,m_e$. Although in this work the number of observed cases was large, doubts were nevertheless expressed by some authors as to the validity of these conclusions, on the grounds that under the experimental conditions the background could play a large role. More essential, however, was the fact that, as became clear later, $\pi$-mesons are nuclear-active particles and therefore can stop in filters at any values of the momenta and thus imitate particles of large masses. For the reasons indicated, more rigorous evidence for the existence of heavy mesons was necessary. Rochester and Butler$^3$, in a Wilson chamber, observed two cases of so-called $V$-shaped tracks, which could be interpreted as the decay in flight of charged (one case) and neutral (one case) heavy mesons.

Only two observed cases, the different explanation of each of them, and the possibility—admittedly with considerable stretching—of explaining them somehow otherwise, were the chief reasons that did not permit confidence in the correctness of these conclusions, especially since from 1947 to 1949 Butler and others, continuing work with the same chamber at sea level...

found not a single new case of this kind. Several observations in thick-layer photographic emulsions also led to similar conclusions. Thus, in 1949 Brown, Camerini, Powell^4 and others^4 discovered in a photographic emulsion sensitive to particles of all energies one case of the decay of a particle into three secondary particles. The mass of the decaying particle, determined from grain counts and range, proved to be about $1000\,m_e$, while the masses of the secondary particles were close to the mass of a $\pi$- or $\mu$-meson. The trajectories of the three scattered particles proved to lie in one plane, which was the most serious argument in favor of the proposed explanation. However, the observation of a single isolated case was not sufficient to regard the fact of the existence of such a meson as established, all the more so since the decay of a particle into three particles had not been observed by any other method. In the same year Alikhanian, Gurevich, and others^5 observed in photographic emulsion three cases which likewise could be explained only as decays after the stopping of heavy mesons. In all three cases, however, only one secondary particle was observed, and the masses of the decaying particles, determined from grain counts and range, proved to be different. Further searches for cases of decay into three particles were not crowned with success, which strengthened doubts as to the correctness of the interpretation of the single case of Brown and others.

Only a year later, in 1950, Gardiner^6 reported a case he had found of disintegration into three particles. The coplanarity of the paths of the three particles, after corrections were introduced for changes in the emulsion due to processing, was fulfilled with an accuracy of up to $2^\circ$. Determination of the mass of the decaying particle from the density of grains, however, gave a considerably smaller value of the mass than would follow from the assumption that the products of the decay were three $\pi$-mesons. The insufficiency of the number of observed cases in some works, and insufficiently stringent experimental conditions in others, for quite a long time did not make it possible to decide with complete certainty the question of the existence of heavy mesons.

The works of the last two years have decisively changed the situation and have not only shown that the heavy meson exists but, moreover, have shown that there are charged heavy mesons of different masses and that, in addition, there also exist neutral heavy mesons, likewise of different masses.

Alikhanov, Eliseev^7 and Alikhanian and others^8 considerably improved the mass-spectrometer method (Fig. 1), bringing the reliability of each observed trajectory practically to completeness. In this method, to determine the mass of a particle, the particle momentum is measured simultaneously from its deflection in a magnetic field and its range in absorbing filters placed in the path of the particle after its exit from the magnetic field.

The trajectory of the particle and its curvature in the magnetic field were recorded by means of ten layers of small-size counters. Ten coordinates of the trajectory gave two projections of the trajectory. In a constan-

in the magnet installed at sea level, the magnetic-field strength was about 5000 oersteds, while in the electromagnet installed at an altitude of 3200 m (Alagez) fields of up to 19,000 oersteds could be obtained. Control measurements carried out with the latter at almost complete absence of a magnetic field (200 oersteds), and intended to determine the spurious curvature of trajectories due to inaccuracies in the installation

Fig. 1.

Labels in the figure: Proportional counter II; Counter I.

of the counters, scattering in the walls of the counters, etc., showed that almost all particle trajectories satisfying a straight line in the projection along the direction of the magnetic field also satisfy a straight line in the projection perpendicular to the magnetic lines of force. In Fig. 2 is shown the spectrum of deviations (in numbers of counters) from a straight line in this projection for particles stopped in the filters.

In one case out of a hundred the spurious curvature of the trajectory of a particle stopped in the filter proved to be $0.1\ \mathrm{m}^{-1}$ (i.e. $\rho = 10\ \mathrm{m}$).

The system of absorbing filters was also improved. First of all, the absorbing filters were made of a material with a small atomic number—of graphite. Then they were interleaved with a large number of rows of counters, which had individual amplifying cells with neon bulbs, so that it was possible to determine through which particular counter of a layer the particle had passed. This made it possible to trace the trajectory of the particle also in the system of absorbing filters, and also, in favorable cases, to detect the occurrence of secondary particles. In a number of experiments the filter between the V and VI rows of counters was replaced by a proportional counter, which made it possible to measure also the ionizing power of the particle. The width of the mass line in such a method of mass measurement is determined by the error in determining the momentum due to the finite dimensions of the counters $\Delta p_g$, by the distortion of the curvature of the trajectory due to scattering in the counter walls $\Delta p_r$, by the error in determining the range of the particle due to the finite dimensions of the absorbing filters $\Delta R_g$, and by the error in determining the range due to range fluctuations resulting from fluctuations in energy loss during ionization braking—$\Delta R_f$.

Fig. 2.

Fig. 2.

The last error cannot be reduced arbitrarily, since range fluctuations are determined by the very mechanism of ionization braking; moreover, in filters made of heavy elements there are added range fluctuations $\Delta R_r$ due to the bypass factor associated with the scattering of the slowed particle in the Coulomb field of the nucleus. In a light substance (for example, graphite)

\[ \frac{\Delta R_r}{R} \sim 0,\qquad \frac{\Delta R_f}{R} \sim 4\text{--}5\%, \]

whereas in a heavy one (such as lead) there is added also

\[ \frac{\Delta R_r}{R} \sim 7.5\%. \]

The error in the curvature of the trajectory in the apparatus installed at an altitude of $3200\ \mathrm{m}$ is

\[ \frac{\Delta \rho}{\rho}=3.5\% \]

for $\rho = 1\ \mathrm{m}$ ($\mu$-mesons) and

\[ \frac{\Delta \rho}{\rho}=4.2\% \]

for $\rho = 2\ \mathrm{m}$ (for protons).

An indication of the resolving power of the spectrograph is provided by the region of the small-mass spectrum, where the mass lines of the $\mu$- and $\pi$-mesons (masses $215\,m_e$ and $270\,m_e$, respectively) are well separated (Fig. 3). In the same figure one can see the presence of a group of heavy mesons concentrated near mass values of 600 and $1000\,m_e$ $^{9}$. The hatched—

preserved sections correspond to particles with negative charge. The total number of mesons with masses $600\,m_e$ and $1000\,m_e$ in this experiment, under a $7$–$9$ cm layer of lead, proved to be equal to $10$–$15\%$ of the number of protons, with approximately equal numbers of both. Subsequently (in 1952) the region of the spectrum $400$—$1400$ was refined by Alikhanyan et al.$^{9}$ by increasing the number of measured tracks, and

Fig. 3

Fig. 3

distinct maxima were obtained for the separate lines $600$ and $1000\,m_e$. These data are shown in Fig. 4. The first maximum is located at the mass value $580\,m_e$, the second at the mass value $950\,m_e$. The experimental half-width of the $580$ line is $70\,m_e$, and that of the $950$ line is $110\,m_e$.

Many cases (about 40) of the appearance of secondary particles in filters were observed. Such an example, corresponding to a mass of $920\,m_e$, is shown in Fig. 1.

From the moment it was established that the $\pi$-meson interacts strongly with nuclei, decisive significance for the correct determination of the mass of other particles by the method of measuring momentum and range belongs to the evidence that the particle under study stopped in the filter owing to ionization energy losses.

Alikhanyan et al.$^{9,10,11}$ gave a number of such proofs. Briefly, they amount to the following:

1) Such a sharp grouping of particles around two mass values could not have been obtained if the particles stopped in the filters as a result of catastrophic processes.

2) The mean values of the momenta of particles of intermediate masses increase regularly with increasing particle range, which is likewise possible only in the case of ionization braking.

3) All particles of intermediate masses cover the momentum interval $2.8—4.5\cdot 10^8\ \text{eV}/c$. The number of particles with negative sign that stopped in the filters with momenta within the range $4.5—6.3\cdot 10^8\ \text{eV}/c$ is 10 times smaller than in the above-mentioned interval $2.8—4.5\cdot 10^8\ \text{eV}/c$.

Such a sharp difference in the number of particles stopped in two adjacent intervals would be impossible if the particles were stopped not because of ionizational slowing down, but as a result of nuclear interaction.

Fig. 4.
Vertical axis: Number of particles.
Horizontal axis: $m_e$.
Legend: 1, 2.

Fig. 5.
Vertical axis: Number of cases.
Horizontal axis: Magnitude of pulses in arbitrary units.
Curves: 1, 2.

4) Measurements of the ionizing ability of intermediate particles1 by means of proportional counters made it possible to use the second method of determining the mass of particles from momentum and ionizing ability—a determination no longer dependent on the mechanism by which the particle is stopped in the filters.

In Fig. 5 the ionization spectrum for the hard component of cosmic rays is shown, obtained with the aid of a proportional counter (for 14,829 particles). Curve 1 in Fig. 5 is the Landau ionization-fluctuation curve; curve 2 is experimental. The arrangement of the proportional counters is seen from Fig. 6.

Table I gives data for the mean ionizing ability of protons and mesons ($\mu$ and $\pi$) with various residual ranges (taking into account the thickness of the filter above the proportional counter and the thickness of its upper wall).

It is seen from the table that protons of all ranges have increased ionization in accordance with the residual range.

Coordinate counters

Transverse counters

Proportional counters

Filters

Capturing devices

Side counters

Fig. 6.

Table I

Kind of particles	Residual range in equivalent cm Pb: from	Residual range in equivalent cm Pb: to	Relative ionizing power: calculated	Relative ionizing power: experiment	Relative ionizing power: errors: statistical	Relative ionizing power: errors: calibration
Protons . . . . . . .	1.5	2.5	3.4	2.8	0.11	0.06
» . . . . . . .	2.5	3.5	2.7	2.35	0.08	0.05
» . . . . . . .	3.5	4.5	2.2	2	0.1	0.05
Mesons . . . . . . .	3	4.5	1.2	1.14	0.06	0.03
Penetrating . . . . .	14	—	1	—	—	0.03

In calculating the ratio of the mean ionization of soft protons and mesons to the ionization of hard mesons, a correction was taken into account for the increased ionizing power (because of its logarithmic increase) of very hard mesons, and a correction for the lengthening of the path due to oblique passage. Thus, column 5 of Table I gives the ratio of the ionizing power of the particles to the minimum ionization $I_{\min}$. The data for the intermediate particles—heavy mesons—are given in Tables II and III.

Table III gives, in the last three rows, the mean values of the masses of both groups of particles, obtained by three different methods: a) from momentum and range, b) from ionization and residual range, and c) from residual momentum and ionization. Within the limits of experimental errors, all three methods give an average mass of $700\,m_e$, which is what should be expected for two groups of equal intensity with masses $580$ and $950\,m_e$.

The mean ionizing power of the intermediate particles is twice the minimum ionization that $\pi$-mesons of such momenta should have, and therefore the possibility of explaining these two groups of particles by nonionizing stops of $\pi$-mesons is ruled out. This does not mean, however, that in some cases such an explanation cannot be valid. It is possible that cases 422, 426, 457, 431, and 527 (Table II) arose because of nonionizing stops of $\pi$-mesons.

The length of the mass spectrometer $(\sim 1\ \mathrm{m})$ leads to a lifetime of heavy mesons of the order of $5 \cdot 10^{-9}$ sec. The long lifetime of heavy mesons is one of the important

Table II

Plate No.	$p\cdot 10^{-8}_{\beta}/c$	Mean range	$M$ by range and impulse	Relative ioniz. ability	Plate No.	$p\cdot 10^{-8}_{\beta}/c$	Mean range	$M$ by range and impulse	Relative ioniz. ability
Minimal residual range $1.6\ \text{cm}$
325	−3.65	—	−1100	3.6	457	−4.30	—	−1400	0.8
338	−3.27	—	−940	2.3	468	2.73	—	720	1.6
338	−2.8	—	−800	2.2	517	3.09	—	880	3.7
351	3.50	—	1100	3.7	586	−2.0	—	−520	3.1
357	1.93	—	500	3.6	612	−3.03	—	−900	3.6
396	3.13	—	900	3.4	545	−2.3	—	−570	1.8
431	−3.94	—	−1280	1.6
$1.6\text{–}3\ \text{cm}$
328	2.84	3.78	620	1.17	423	−3.27	5.90	−585	1.44
333	−3.94	4.56	−920	1.72	425	−3.06	5.36	−565	3.04
335	4.50	4.67	1090	2.32	426	−3.38	6.18	−600	0.47
343	3.00	3.82	655	1.70	460	4.30	5.64	930	3.14
347	−3.16	4.60	−640	1.82	486	3.27	4.97	650	2.72
375	2.91	3.82	640	3.7	527	−3.19	4.96	−620	0.78
422	3.60	3.80	880	0.63	574	−3.60	4.80	−760	1.23
446	3.38	4.80	700	1.40	574	3.78	4.25	850	1.80
474	2.71	3.95	560	2.83	583	−3.42	4.3	−900	2.0
356	2.97	5.30	540	1.13	588	−3.24	3.0	−900	3.2
410	4.30	5.70	930	2.57

their features, which poses serious difficulties for theory.

Alikhanov and Eliseev$^{7}$ also found, at sea level, a small number (15) of tracks of intermediate particles; however, because of the smallness of the effect and the lower resolving power, although they did obtain a grouping of particles near the values 600 and $1000\,m_e$, it was not as distinct as was achieved at an altitude of $3200\ \text{m}$. Their data are of interest with respect to the dependence of the number of heavy mesons on altitude.

A. I. Alikhanov

Table III

	Interval of ranges in cm of lead	Interval of ranges in cm of lead	Interval of ranges in cm of lead	Interval of ranges in cm of lead
	1.6—3.5	3.6—4.8	4.8—6.4	3.6—6.4
Mean relative ionizing ability	2.7 ± 0.35	2.1 ± 0.31	1.7 ± 0.3	1.95 ± 0.2
Mean residual range	—	2.53	3.77	3.09
Mean total range	—	4.23	5.44	4.77
Mean momentum in eV/c · 10^-8	—	3.19	3.64	3.39
Mass from range and momentum in $m_e$	—	700	710	700
Mass from ionization and residual range in $m_e$	—	850 ± 300	790 ± 220	840 ± 200
Mass from ionization and residual momentum in $m_e$	—	740 ± 180	730 ± 110	740 ± 75

The number of heavy mesons stopped in the filters at an altitude of 3200 m is of the order of 0.1% of the number of particles in the entire flux of cosmic rays; at sea level this ratio under 10 cm Pb is equal to 0.015%, i.e., six times smaller than at the level of 3200 m. Thus the absolute change in the intensity of heavy mesons from sea level, taking into account the increase in the intensity of the cosmic-ray flux from sea level to an altitude of 3200 m, is approximately a factor of 10.

As was already said above, during two years of work with the Wilson chamber, Butler and others did not succeed in observing cases of particle decay similar to the two that he, together with Rochester, had discovered. In 1950, Andersen^12 and coworkers, having raised a Wilson chamber to an altitude of 3200 m, succeeded in observing 34 such cases. Like Rochester and Butler, Andersen and coworkers also note two types of V-shaped tracks.

The first type consists of the paths of two particles issuing from one point in the gas of the Wilson chamber, diverging at an acute angle from top to bottom and resembling an inverted letter $V$ (Fig. 7). According to Rochester and Butler and Andersen, these are cases of decay of a neutral particle moving from top to bottom. The second type (only 4 cases out of 34) consists of a sharp break in the trajectory of a particle moving vertically, and at the point of the break there is no trace of a recoil nucleus, which should have been observed if this break in the path had been caused by a collision of the particle with a nucleus. These cases are regarded as the decay of a charged particle into a charged and, at least, one neutral particle (Fig. 8).

Fig. 7.

Fig. 8.

Let us indicate here the considerations by which all authors were guided when considering such cases as the decay of a heavy meson. The simplest explanation of a sharp break in the trajectory as an act of scattering by a nucleus is rejected on the grounds that the momentum which is transferred to the nucleus in scattering is quite sufficient for the recoiling nucleus to leave a track in the gas of the chamber. Meanwhile, precisely those cases are selected in which no other tracks issue from the point of the break. The second possible explanation—the decay of a $\pi$- or $\mu$-meson—is excluded, since such momenta and angles between the primary and secondary particles cannot arise in $\pi$-$\mu$ and $\mu$-$e$ decays according to the decay schemes known to us. The projection of the momentum of the secondary particle onto the direction perpendicular to the direction of motion of the primary particle in $\pi$-$\mu$ decay cannot exceed $29\,M_e c$, and for $\mu$-$e$ decay, $55\,M_e c$. In addition, the probability of observing $\mu$-$e$ decay in the chamber is very small, since the lifetime of the $\mu$-meson is very large.

The Wilson chamber was controlled by means of a counter system constructed so as to register penetrating showers. In 12 cases, when the Wilson-chamber photograph made it possible to determine the point at which the penetrating shower arose, the plane passing through the $V$-shaped trajectory also contained this point. This circumstance is an indication that the neutral particle arose in one act with the penetrating shower and decays into two particles.

The angles of emission of the secondary particles in the decay of the neutral $V$-particle lie within the limits from $3.5$ to $126^\circ$. In most cases the ionizing power of the particles is equal or close to minimum, and the curvature of the path in the magnetic field was also, in most cases, measured inaccurately; therefore estimation of the mass of the secondary particles was difficult.

Only in one case was it possible, from the ionization and curvature of the path, to establish for one of the secondary particles that its mass lies within the limits between 150 and $350\,m_e$.

In three cases both secondary particles passed through a 2-centimeter lead plate located at the center of the chamber; moreover, despite their large momentum, they did not multiply in this plate. This indicates that the secondary particles are not electrons. Of ten cases of passage of secondary particles through the lead plate, in one case scattering through an angle of $35^\circ$ was observed, and in one case the particle caused a nuclear disintegration. Two nuclear interactions out of 10 possible correspond to an interaction cross section with lead of $\sim 10^{-24}\ \mathrm{cm}^2$; this indicates that at least one of the secondary particles is a nuclear-active particle, i.e. a $\pi$-meson or a proton. An estimate of the mass of the primary neutral particle did not give, and by the very nature of the initial data could not give, any definite value. From the distribution

decay points along the Wilson chamber, Andersen came to the conclusion that the lifetime of the neutral particles is $(3 \pm 2)10^{-10}$ sec. The few cases of the second kind (only four), i.e., cases of decay of a charged particle, of course give still fewer possibilities for judging the nature and masses of the primary and secondary particles. In one case the secondary particle traversed 2 cm of lead in the chamber and produced no multiplication, as would have been expected for an electron. Andersen’s estimate of the lifetime of charged particles, made from indirect considerations, was subsequently not confirmed.

The first data on the nature of the secondary particles and on the mass of the neutral $V$-particle were obtained in the work of Armenteros, Barker, Butler, Cachon, and Chapman $^{13}$ in 1951. Having raised the chamber to the Pic-du-Midi (2867 m), they succeeded, in four months of chamber operation, in observing 36 decays of neutral particles and 7 of charged ones. In some cases they succeeded, with a greater or lesser degree of certainty, in establishing the nature of the secondary particles. These results are given in Table IV.

Table IV

Positive particles	Number of cases	Negative particles	Number of cases
Identified protons	4	Identified mesons $(\pi$ or $\mu)$ . . . . . .	3
Particles with minimum ionization and with mass less than the proton mass	3	Particles with mass less than the proton mass . .	18
Particles that may be both protons and mesons . . . . .	12	Particles whose mass may be the mass of both a proton and a meson . .	8
Particles that may be protons according to the upper limit of the momentum . . . . . .	6

Of special interest are the four cases (see Table V) in which it was established that the secondary particles are protons. The authors believe that the decay of the neutral particle occurs into two particles, especially in view of the above-described result of Andersen, showing that the point of birth of the neutral $V$-particle apparently lies in the plane of the $V$-track. In such a case the decay scheme may be

\[ V_1^0 \to p + \pi^-, \]

and the value of the mass of the $V^0$-particle can be determined.

Table V

Case	1	2	3	4
Momentum of the positive particle (in $10^8$ eV/$c$) . . .	$2.1 \pm 0.2$	$5.2 \pm 0.7$	$3.8 \pm 0.5$	5
Momentum of the negative particle (in $10^8$ eV/$c$) . . .	2—5	$1.5 \pm 0.1$	$1.5 \pm 0.1$	$1.2 \pm 0.1$
Measured ionization of the positive particle . . .	10—15	3—4	4—6	3—4
Calculated ionization for a proton of the corresponding momentum . . .	12	3	5	3
Angle between the particles . . .	$31^\circ$	$50.5^\circ$	$76^\circ$	$50^\circ$
Mass $M$ of the particle in $m_e$ . .	$2400 \pm 150$	$2180 \pm 10$	$2220 \pm 20$	2200

Average of 4 values: $2250\,m_e$

Table V gives the initial experimental data and the results of the mass determinations.

The presence among the positive secondary particles of particles with mass less than the proton mass, which in any case was established in three cases, nevertheless compels one to introduce yet another type of decay. Presumably the authors introduce the decay scheme $V_2^0 \to \pi^+ + \pi^-$. In none of the three cases was it possible to establish even the upper limit of the mass of the negative particle. Moreover, the momentum of the negative particle also could not be established.

According to one of the photographs the mass of the $V_2^0$-particle proved to be $1400\text{—}1000\,m_e$, and according to another, $950\,m_e$. Thus, the authors come to the conclusion that there exist two different neutral particles: one with a mass greater than the proton mass, the other smaller.

Six cases of decay of charged particles did not make it possible to draw any conclusions about their mass. In three cases the secondary particle would have been negatively charged and apparently was a meson, and in one case it was positively charged and apparently could have been a proton.

Several Wilson-chamber photographs of particle decays were obtained by Bridge and Annis$^{14}$ and Thomson et al.$^{15}$. The first authors observed ten cases in all, of which four corresponded to the decay of a neutral particle and four to that of a charged one. Of these, only one case could be analyzed (the authors worked with a Wilson chamber without a magnetic field).

The trajectory of a particle, produced in a star and, after passing through an aluminum plate, having undergone a sharp break in the gas of the chamber (through an angle of $90^\circ$), then again entered the same plate, in which it once more underwent a sharp break, directing the particle downward. After passing through a series of lead and aluminum plates, the particle stopped in an aluminum (ninth) plate. The scattering, range, ionization, and strong interaction with aluminum (the above-mentioned sharp deflection of the particle on entering the aluminum plate) indicate that the secondary particle was a $\pi$-meson.

Assuming that the decay occurred into two particles—a charged $\pi$-meson and a neutral particle—the authors determined that the mass of the primary charged particle lies within the range $600$—$1200\,m_e$. Thompson et al. observed 9 cases of $V^0$-decay. In one of them it was possible to establish the nature of both particles and to measure their momenta. One of the particles—the positive one—proved to be a proton with momentum $0.75 \pm 0.1\ \text{MeV}/c$ and an ionizing power 2—4 times greater than minimum, while the other—the negative one—with momentum $0.24 \pm 0.02\ \text{MeV}/c$ and minimum ionization, was most probably a $\pi$-meson.

Hence the mass of the $V^0$-particle turns out to be $2165 \pm 20\,m_e$, and the decay energy $28 \pm 10\ \text{MeV}$. In one case, as also in the Manchester group of physicists, the positive particle definitely could not be interpreted as a proton: it had momentum $0.27 \pm 0.03\ \text{MeV}/c$ and minimum ionization and therefore could not be much heavier than a $\pi$-meson. The negative particle had momentum $1.3^{+1.0}_{-0.6}\ \text{MeV}/c$ and minimum ionization. Assuming that the negative particle also is a meson and that the decay occurred only into these two particles, the authors obtained the mass of a second kind of neutral particle $V^0_2 = 1020\,m_e$.

In 1951 the Manchester group, continuing the work, brought the number of observed cases of decay of neutral particles to 70 and analyzed them in detail. In this work${}^{16}$ the experimental arrangement used at an altitude of 2867 m above sea level was first described in detail.

In Fig. 9 are shown the arrangement and dimensions of the screens, the Wilson chamber, and the counters.

The chamber was in a magnetic field of strength 7500 oersteds. The counter system was adjusted to register penetrating showers. The total number of $V$-shaped tracks found (including those described in previous papers) is 105. Their angular distribution between the particles is presented in Fig. 10. Most of the tracks have angles up to $90^\circ$; the remaining part, on the contrary, is clustered near $180^\circ$.

According to the interpretation, already adopted in earlier works, of a $V$-track as the decay of a neutral particle, if its vertex is directed ...

approximately upward, or as the decay of a charged particle, if the $V$-track is oriented approximately perpendicular to the vertical,

Fig. 9.

Fig. 9.

then the first group corresponds to the decay of neutral particles, and the second group to that of charged ones. The sharp maximum at small angles

Fig. 10.

Fig. 10.

is due to an admixture of electron pairs, which in most cases could easily be excluded, since the angles between the pairs were $< 1^\circ$.

In this work the authors succeeded in finding four tracks of negative particles for which, from the ionizing power and momentum, it was possible to estimate the particle mass, just as in the preceding work it had been possible, from the same data, to establish for several positive particles that they are protons. The results are given in Table VI.

Table VI

Photograph No. . . .	3	7	65	86
Momenta $(10^8\ \mathrm{eV}/c)$	$1.05 \pm 0.05$	$0.8 \pm 0.04$	$0.78 \pm 0.14$	$0.74 \pm 0.04$
Measured ionization . . . . .	2–3	2–4	3–4	2.5–35
Mass $(\text{in } m_e)$ . . . .	270–430	210–380	290–370	230–330
Calculated ionization for a meson	2	2–7	2–8	3

In one case, direct evidence for the nature of the negative secondary particle was provided by the fact that this particle underwent decay. By all indications this was a $\pi$-$\mu$ decay, and consequently it was a $\pi$-particle. In those cases when the secondary particles passed through a lead plate in the chamber, no noticeable radiation losses were observed, which proves their non-electronic nature. On the other hand, in two cases a nuclear interaction in the plate was observed, which is characteristic of $\pi$-mesons and fast protons. There is substantial confidence that among the decay particles there are no neutral particles escaping observation. Direct proof that there are no neutral particles among the decay products is difficult to extract from these experiments, but in any case no indications to the contrary were obtained.

In two cases, when it was possible to make an assumption about the point of origin of the primary neutral particle and to carry out measurements, the plane passing through the $V$-shaped track contained the assumed point of origin of the primary particle with an accuracy of up to $5^\circ$. In addition, the sum of the projections of the momenta in the plane of the $V$-track in the direction perpendicular to the direction of flight of the primary particle turned out, within the accuracy of the errors, to be equal to zero, which also indicates the absence of a third particle among the decay products. Both cases considered belonged to $V_1^0$-particles.

Moreover, not a single case was found that would indicate the occurrence of a cascade shower in the lead plate in the chamber from the $\gamma$-rays of $\pi^0$-meson decay.

As the authors have already assumed in previous works, it is necessary to admit two decay schemes for the neutral $V^0$-particles, namely:

\[ V^0_1 \to p + \pi^- \]

and

\[ V^0_2 \to \pi^+ + \pi^-, \]

\[ V^0_2 \to \mu^+ + \mu^-, \]

if one assumes that the decay in all cases occurs into only two particles.

The decay in flight of a particle of mass $M$ into two particles is shown in Fig. 11: a) in the laboratory system and b) in the system associated

Fig. 11.

Fig. 11.

with the primary particle. If, in the system associated with the primary particle, a secondary particle is emitted with momentum $p^*$ at an angle $\Theta^*$ to the direction of motion of the primary particle, then the projection of this momentum onto the direction perpendicular to the direction of motion of the primary particle, $p^* \sin \Theta^*$, will be invariant. The probability that the value of this momentum projection will lie within the limits $p_T$ and $p_T + dp_T$ is equal to

\[ W(p_T)\,dp_T = \frac{p_T\,dp_T}{p^* \left(p^{*2} - p_T^2\right)^{1/2}} . \]

As is evident from this formula, the probability that $p_T$ is close to $p^*$ is very large.

The authors introduce the quantity

\[ \alpha=\frac{p_{+}\cos\Phi_{+}-p_{-}\cos\Phi_{-}} {p_{+}\cos\Phi_{+}+p_{-}\cos\Phi_{-}}, \]

where $p_{\pm}\cos\Phi_{\pm}$ are the projections of the momenta of the secondary particles onto the direction of motion of the primary particle,

\[ \alpha=\frac{p_{+}^{2}-p_{-}^{2}}{p^{2}} =\frac{m_{+}^{2}-m_{-}^{2}}{M^{2}} +2p^{*}\cos\Theta^{*}\left\{\frac{1}{M^{2}}+\frac{1}{p^{2}}\right\}^{1/2} = \]

\[ = \alpha_{0}+f\left(p\cos\Theta^{*}\right). \]

The mean value of $\alpha$ for a large number of cases will be equal to $\alpha_{0}$, since $f(p\cos\Theta^{*})$, for an equiprobable distribution of the directions of emission of the secondary particles in the system of the primary particle, is on average equal to zero. Using the value of $\alpha$, which depends only on the adopted decay scheme into two particles, one can preliminarily establish to which type of decay, i.e. to $V_{1}^{0}$ or $V_{2}^{0}$, the given case belongs. This was done for 29 cases. Figure 12 presents the distribution of the values of $\alpha$ as a function of $p$. The same figure also shows those cases for which the character of the decay was established directly, on the basis of identification of the decay particles by one or another direct determination of their nature.

Fig. 12.

Fig. 12.

As can be seen from Figure 12, the particles separated into two groups: 1) with the value $\alpha = 0.65 \pm 0.02$, and 2) with a value equal to $0.05 \pm 0.06$. The first group corresponds to the decay $V_1^0 \to p + \pi^-$, and the second to $V_2^0 \to \pi^+ + \pi^-$.

There is one case which, by direct determination of the nature of the secondary particles, corresponds to the decay $V_1^0$, while in Fig. 12 it falls in the group $V_2^0$, and one reverse case. Two points lay between the two values of $\alpha$. If, together with $\alpha$, one also uses the value $p_T$, which likewise depends only on the assumption that the decay occurs into two particles, then it is possible to check the correctness of assigning a given case to one or another type of $V$-particle decay. This check confirmed 16 cases of $V_1^0$ decay and 10 cases of $V_2^0$. The mean mass value of the $V_1^0$-particle corresponding to the value $\alpha = 0.65 \pm 0.02$ is equal to $M_1 = 2250 \pm 35m_e$, while the mean mass value of the $V_2^0$-particle corresponding to $\alpha$ equal to $0.05 \pm 0.06$ was $\sim 800\,m_e$.

Fig. 13.

Fig. 13.

In Fig. 13 the distribution of the values $p_T$ for $V_1^0$-tracks is presented. As was shown above, the theoretical distribution curve must have a maximum value at $p_T = p^*$. It is shown in Fig. 13 as a curve calculated under the assumption $M_1 = 2200\,m_e$ and the decay scheme

\[ V_1^0 \to p + \pi^- . \]

In Fig. 14 the same distribution of $p_T$ is given for $V_2^0$-tracks. The calculated curve was obtained under the assumption $M_2 \sim 800\,m_e$ and the decay scheme

\[ V_2^0 \to \pi^+ + \pi^- . \]

Fig. 14.

Fig. 14.

In both cases the experimental data are indeed grouped about $p_T$ values close to the largest values of $p_T$, and in general agree with the calculated curves, although for such a small

low statistics, all the conclusions, of course, cannot claim great reliability.

In order to determine more accurately the mass values, the authors selected 12 out of 16 cases for which they succeeded in carrying out the measurements accurately. They are given in Table VII, where the values are also given

Table VII

Values of the masses of 12 $V$-particles. The proton mass is $1836\,m_e$, the $\pi$-meson mass is $276\,m_e$

Catalog No.	$\alpha$	$p_T$ $(10^8\ \mathrm{eV}/c)$	Mass values $m_e$	Values $Q$, MeV
33	$-0.03$	0.78	$2277 \pm 40$	$82 \pm 20$
37	$+0.84$	0.94	$2228 \pm 40$	$58 \pm 20$
42	$+0.74$	1.00	$2186 \pm 20$	$37 \pm 10$
43 *)	$+0.50$	1.15	$2218 \pm 10$	$53 \pm 5$
47 *)	$+0.70$	1.31	$2228 \pm 10$	$53 \pm 5$
49	$+0.70$	0.82	$2160 \pm 20$	$24 \pm 10$
50	$+0.70$	0.92	$2183 \pm 20$	$36 \pm 10$
56 *)	$+0.53$	0.88	$2181 \pm 10$	$40 \pm 5$
85	$+0.67$	1.02	$2188 \pm 10$	$38 \pm 5$
88	$+0.76$	0.72	$2157 \pm 30$	$23 \pm 15$
92 *)	$+0.60$	0.81	$2169 \pm 10$	$29 \pm 5$
96	$+0.79$	0.97	$2256 \pm 50$	$72 \pm 25$

*) Cases with identified protons.

of the decay energy $Q_1=M_1-(m_+ + m_-)$. The mean value is $M_1=2203 \pm 12\,m_e$ and the mean value is $Q_1=46 \pm 6$ MeV. Likewise, from 10 cases of the second type they selected eight for a more accurate determination of the values $M_2$ and $Q_2$. They are given in Table VIII. The decay energy of the $V_2^0$-particles proved to be much greater than that of the $V_1^0$, $Q_2=122 \pm 13$ MeV, and $M_2=796 \pm 27m_e$, if the secondary particles are $\pi$-mesons, and, respectively, $Q_2=142 \pm 16$ MeV and $M_2=705 \pm 32m_e$, if the secondary particles are $\mu$-mesons. The authors themselves believe that the evidence they have presented for the existence of $V_1^0$-particles (heavier than the proton) is quite convincing, whereas for $V_2^0$-particles, lighter than the proton, it is less clear. The ratio

A. I. ALIKHANOV

Table VIII

Mass values of 8 $V_2^0$-particles

Catalog No.	$\alpha$	$p_T$, $10^8$ eV/$c$	Mass $m_e$	$Q$, MeV
5	$-0.07$	1.46	$796 \pm 130$	$122 \pm 65$
35	$+0.38$	1.56	$883 \pm 50$	$165 \pm 25$
38	$+0.33$	1.60	$872 \pm 50$	$160 \pm 25$
53	$-0.03$	1.66	$841 \pm 60$	$144 \pm 30$
63 *)	$-0.29$	1.46	$820 \pm 50$	$134 \pm 25$
66 *)	$+0.51$	1.03	$700 \pm 30$	$74 \pm 15$
69	$+0.07$	0.98	$673 \pm 100$ $\pm 50$	$61 \pm 50$ $\pm 25$
90 *)	$+0.05$	1.41	$785 \pm 30$	$116 \pm 15$

*) Cases in which it was established that both particles are lighter than the proton.

between the numbers of $V_1^0$- and $V_2^0$-particles, the authors obtained

\[ \frac{N_{V_1^0}}{N_{V_2^0}} = 1.6 \pm 0.5, \]

where, possibly, it will depend on the conditions of the experiment if the lifetimes of the particles differ. Some objections to the interpretation presented were raised by the Pasadena group of physicists. Leighton et al. pointed out the possibility of decay into three particles, and then the two types of decay could be explained by assuming the existence of only one neutral $V^0$-particle. Namely,

\[ V^0 = V_1^0 \to p + \pi^- + \pi^0, \]

\[ V^0 = V_2^0 \to n + \pi^- + \pi^+, \]

where $n$ is a neutron. The mass $M$ of the neutral particle is $\sim 2600m_e$. The difference in the values $Q_1$ and $Q_2$, which in this interpretation is apparent, can easily be explained by the fact that in the second case, when only two light particles out of the three are observed, the decay energy will be contained mainly in the kinetic energy of the light particles. However, a number of circumstances noted by the authors, including the absence in the experiment of any signs of a neutral $\pi^0$-meson, in their opinion,

makes the hypothesis of Leighton et al. rather unlikely. But, apart from differences in the interpretation of the experimental data, there are rather sharp contradictions between the Manchester and Pasadena groups in the experimental results themselves.

Thus, first of all, of 136 decays of $V^0$-particles, according to Leighton, Anderson, et al. $^{17,18}$, more than $80\%$ decay into a heavy positive and a light negative particle; moreover, the mass of the former sometimes turns out to be somewhat less than the proton mass $(1200—1500)m_e$. In one case the mass of the negative particle proved to be greater than $1100m_e$. Although the authors do not exclude cases of decay into two $\pi$-mesons $(V_2^0)$, they find that these are very rare.

In 88 cases in which it was possible to adopt the scheme $V_1^0 \to p+\pi^{-}$, the calculated values of the decay energy $Q_1$ turned out to lie within the limits from 10 to $100\,Mэв$, i.e. the authors definitely did not obtain a single value of the decay energy near $45\,Mэв$, as was mentioned above. The authors are even inclined to suppose that there are two discrete values of $Q_1$: one, $35 \pm 3\,Mэв$, and the other, $75 \pm 5\,Mэв$, but they also do not exclude the possibility of a continuous distribution of the values of $Q_1$.

On the other hand, in 55 cases in which it was possible to establish the place of origin of the particle, the plane passing through the $V$-shaped track contained the point of emission of the $V$-particle, and the sum of the momenta agreed with the scheme of decay into two particles.

At present the status of the question of neutral heavy mesons (although this term is hardly applicable to a particle having a mass $> M_p$) may be summarized as follows.

The existence of a neutral particle with a mass greater than the proton mass should be regarded as firmly established. The fact that it decays into two particles—a proton and a $\pi$-meson—though it cannot yet be considered definitively established, apparently is not now subject to serious disagreement, and most likely this is indeed so. The value of the decay energy, and consequently the exact value of the mass, cannot yet be regarded as established.

The lifetime of the $V^0$-particle, although estimated by Anderson, has the value $(3 \pm 2)\cdot 10^{-10}$ sec obtained by him, which cannot be considered accepted. The existence of a second $V_2^0$-particle with mass $\sim 800m_e$ has not been proved with the same certainty as $V_1^0$; however, there is no doubt that the single scheme $V_1^0 \to p+\pi^{-}$ does not explain all the observed cases. And since this is so, and if the scheme $V_1^0 \to p+\pi^{-}$ is accepted as occurring at least in some of the cases, and, consequently, the mass of the $V_1^0$-particle is of the order of $2200m_e$, then, in order to explain cases of decay distinct from $V_1^0$-decays, it is still necessary to admit the existence of a second neutral particle, decaying either according to a scheme similar to $V_2^0 \to \pi^{+}+\pi^{-}$ or $V_2^0 \to \pi^{+}+\pi^{-}+\pi^{0}$ and with a mass

$V_2^0$ particles, $\sim 800—900m_e$, or according to the scheme $V^0 \to n+\pi^+ + \pi^-$ and with a mass of the $V^0$ particle $\sim 2600m_e$.

The fact that the ratio

\[ \frac{N_{V_1^0}}{N_{V_2^0}} \]

differs sharply for the two groups of experimenters is possibly due to the fact that, because of the different lifetimes of these two kinds of particles, different experimental conditions had an effect.

With regard to charged $V$-particles, the results obtained by means of the Wilson chamber are considerably poorer quantitatively and less definite than the data obtained with the mass spectrometer of the Alagez group.

Greater successes were achieved by means of the photographic-plate method.

Apart from one case of the decay of a particle into three secondary particles, obtained by Powell et al. in 1949, and a second case obtained by Harding in 1950, in 1951 Powell et al. succeeded in finding a third case.^19 Coincident with their report was also a report by Hodgson^20 on a case observed by him of the decay of a heavy meson into three particles. The three cases of the decay of a heavy meson into three particles—two old and one new—were again analyzed and studied (Figs. 15, 16). The last proved especially successful, since, above all, the path length of the heavy meson in the emulsion was large—$2070\,\mu$.

Measurement of the multiple scattering of the particle in the material of the emulsion, as a function of its residual range, gave a mass value of $1015 \pm 280\,m_e$. Measurement of the grain density along the track (more precisely, the length of the gaps between grains) as a function of the range gave a mass value of $1000 \pm 180\,m_e$. From the point where the particle decayed there emerged three tracks, all of which left the emulsion; however, one of the secondary particles $(a)$ traversed a long path in the emulsion ($6.4$ mm). The other two left the emulsion after passing $120\,\mu$ $(b)$ and $490\,\mu$ $(c)$. All three tracks of the secondary particles proved to be coplanar to within $2^\circ$.

The long track $(a)$ made it possible to determine the mass of the secondary particle from scattering and grain density. It proved equal to $285 \pm 20\,m_e$, i.e. it corresponded to the mass of the $\pi$-meson. From the same measurements it followed that by the time the particle emerged from the emulsion it had practically lost almost all its energy and its residual range was equal to $400 \pm 200\,\mu$. This means that at birth the meson received an energy of $19 \pm 0.4$ MeV (which corresponds to a range of $6.8 \pm 0.2$ mm) and had a momentum of $75.4$ MeV/$c$. Knowing the momentum of particle $(a)$ and using the law of conservation of momentum, the momenta of particles $(b)$ and $(c)$ were found—$85.8 \pm 1$ MeV and $98.3 \pm 1$ MeV/$c$. Having the values of the momenta of particles $(b)$ and $(c)$ and having measured the grain density along their paths, the authors determined also the masses of these secondary particles. They proved to be $240 \pm 30\,m_e$

Fig. 15.

Fig. 16.

and $280 \pm 15\,m_e$, respectively. Thus, all three particles can with high probability be regarded as $\pi$-mesons. In this case the energy of particle $(a)$ is $19 \pm 0.4$ MeV, of particle $(b)$ is $24.2 \pm 2.0$ MeV, and of $(c)$ is $32 \pm 2.0$ MeV, while the total decay energy is $75.2 \pm 5.0$ MeV.

A similar analysis was also carried out for the two earlier cases. The results are given in Table IX.

Table IX

Kinetic energies of the secondary particles in MeV

Case	Particle $(a)$	Particle $(b)$	Particle $(c)$	Sum of kinetic energies
1	$1.04 \pm 0.1$	$31 \pm 4$	$33 \pm 4$	$65 \pm 8$
2	$50 \pm 7.5$	$13 \pm 2$	$22 \pm 3$	$85 \pm 15$
3	$19 \pm 0.4$	$24.2 \pm 2$	$32 \pm 2$	$75 \pm 5$
			Weighted mean	$73.5 \pm 4$
			Mass is equal to	$966 \pm 8\,m_e$

Assuming that in every case all the secondary particles are $\pi$-mesons, and using the precise value of the $\pi$-meson mass (according to Alvarez), the authors determined the decay energy for all three cases and, correspondingly, the mass of the heavy meson—the $\tau$-meson (Table X).

Table X

Absolute or relative values of the masses of the secondary particles

Case	Particle $(a)$	Particle $(b)$	Particle $(c)$
1	$274$*)	$280 \pm 30$	$1.02 \pm 12\%$
2	$1$	$1.10 \pm 15\%$	$1 \pm 10\%$
3	$285 \pm 20$	$0.88 \pm 11\%$	$1.03 \pm 5\%$

*) The nature of the particle was established exactly because it stopped in the emulsion and produced a star.

The exact establishment of the fact that all three secondary particles are $\pi$-mesons is a very important circumstance.

As is well established, $\pi$-mesons are strongly interacting particles; if the $\tau$-meson also is a particle interacting with nucleons, like the $\pi$-meson, then from the general principles of quantum mechanics it follows that the lifetime of a “system” of three strongly interacting particles must be very short. In fact, the lifetime of the $\tau$-meson is very large, which is an indication that $\tau$-mesons do not interact with nucleons as $\pi$-particles do. If even one of the three secondary particles were a weakly interacting particle, for example a $\mu$-meson, then this requirement on the lifetime and the nuclear properties of the $\tau$-meson would no longer apply.

From the data given in Table X it is seen that the masses of all three particles differ little from one another, in any case much less than the masses of $\pi$- and $\mu$-mesons differ. The masses of $\pi$- and $\mu$-mesons differ by $30\%$, whereas the experimental errors of the mass determinations are $\sim 10\%$.

In 1952 a group of Italian physicists—Ceccharelli et al.$^{22}$—found one very fortunate case of the decay of a $\tau$-meson, which made it possible to verify with great reliability the correctness of the three-$\pi$-meson decay scheme.

The path length of the $\tau$-meson in the photographic emulsion proved to be very large—$8000\,\mu$, which made it possible to determine the mass of the particle from the number of gaps between grains as a function of the range and from the value of the multiple-scattering parameter as a function of the range. The first method gave a mass value $940 \pm 140$, the second $995 \pm 150$, and the mean of these two measurements was $970 \pm 100\,m_e$.

The path lengths of two secondary particles also proved to be large—2600 and $2000\,\mu$, which made it possible, for these two particles, to determine the kinetic energy with good accuracy from the grain count, assuming that these particles are $\pi$- or $\mu$-mesons. Using the good accuracy with which the kinetic energy of one of the secondary particles could be determined, the known angles of emission of the three particles, and the conservation laws, the authors analyzed all possible combinations arising under one or another assumption about the nature of each of the secondary particles. The kinetic energy of the two remaining particles was calculated, assuming that the kinetic energy of one was known exactly. Table XI shows the results of this calculation.

As is seen from the table, only the first $(\pi,\ \pi,\ \pi)$ and the last $(\mu,\ \mu,\ \mu)$ schemes give agreement between the calculated and experimental data. However, the first scheme gives a mass value calculated from the masses and kinetic energies of the secondary particles equal to $990 \pm 15\,m_e$, while the last gives a value of $766\,m_e$, which is much lower than the value $970 \pm 100\,m_e$ obtained by direct determination of the mass.

Another type of decay of the heavy meson was described by O’Ceallaigh$^{21}$. Four cases were discovered in which the particle

...at the end of its range transforms into one charged particle and one or several invisible neutral particles. Two of these four cases, the most convincing ones, are described in detail below.

Table XI

Decay scheme	Decay scheme	Decay scheme	$E_a$	Theoretical	Theoretical	Experimental	Experimental
$a$	$b$	$c$	$E_a$	$E_b$	$E_c$	$E_b$	$E_c$
$\pi$	$\pi$	$\pi$	17.1	27.8	41.6	27.3	37
$\pi$	$\pi$	$\mu$	17.1	27.8	49.7	27.3	28.9
$\pi$	$\mu$	$\pi$	17.1	33.7	41.6	21.3	37
$\pi$	$\mu$	$\mu$	17.1	33.7	49.7	21.3	28.9
$\mu$	$\pi$	$\pi$	13.6	17.8	27.0	27.3	37
$\mu$	$\pi$	$\mu$	13.6	17.8	33.5	27.3	28.9
$\mu$	$\mu$	$\pi$	13.6	22.5	27	21.3	37
$\mu$	$\mu$	$\mu$	13.6	22.5	33.5	21.3	28.9

In appearance, these cases very much resemble the three cases of decay of a heavy meson described in the work of Alikhanian, Gurevich, and others in 1949 (Fig. 17). The advantage of the cases found by O’Ceallaigh is that: 1) the path length of the primary particle is large—in one case more than $4000\,\mu$, in the second $5800\,\mu$; 2) the emulsion was sensitive to particles of minimum ionization, which makes it possible to say exactly into how many charged particles the primary particle decayed, and, in a favorable case, to trace the fate of the secondary particle.

In the first case, determination of the mass of the primary particle (denoted by the letter $K_1$) from multiple scattering along the entire path of the particle gave the value $1260 \pm 290\,m_e$. Determination of the mass of this same particle from the length of the gaps between grains as a function of the residual range gave the mass value $1385 \pm 200\,m_e$.

Figure 18 gives the dependences of the number of gaps between grains of the emulsion on the residual range for a meson, a proton, and for the particle $K_1$. The average of these two determinations of the mass is $1320 \pm 170\,m_e$.

Exactly the same determinations of the mass of the primary particle in the second case (particle $K_2$) gave the value $1125 \pm 140\,m_e$.

Analysis of the secondary particles in these two cases led to the following result.

In the first case, the path length of the secondary particle was $2200\,\mu$, and the grain density $18.5 \pm 0.9$ per $50\,\mu$ of path length, whereas for this type of emulsion the minimum value of the grain density $g_{\min}$ is $17 \pm 0.8$. The mean deviation $\langle \Phi \rangle$ due to multiple scattering over $100\,\mu$ of path, according to the measurements, turned out to be equal to

Fig. 17.

0.10° ± 0.014°, whence $p\beta c = 250$ MeV. From this and from the grain density it follows that the particle had a mass less than $400\,m_e$ and a momentum of about $250$–$300$ MeV/$c$.

In the second case (Fig. 19) the nature of the secondary particle could be established unambiguously. It had a range in the emulsion of $1098\,\mu$ and at the end of its path underwent decay. Determination of its mass from scattering and from the number of grains and the range gave a mass value of $200$–$300\,m_e$.

$Graph of the number of grains per 100 microns of emulsion versus residual range in microns, with curves labeled $\mu$, $k$, and $p$.$

Fig. 18.

The last (tertiary) particle had a range in the emulsion of $150\,\mu$ and an ionizing power close to the minimum, and it was natural to regard it as an electron with an energy of about $10$ MeV. Thus, the secondary particle was most likely a $\mu$-meson, since up to now the $\beta$-decay of a $\pi$-meson has not yet been observed.

As a possible interpretation of the second case, one could put forward a more trivial explanation, namely as a somewhat unusual $(\pi \to \mu)$-decay. In the usual $(\pi \to \mu)$-decay the $\mu$-meson has a range of about $600\,\mu$, whereas in this case the range is much greater ($1028\,\mu$); therefore it is necessary to assume decay of the $\pi$-meson in flight. However, in such a case the $\mu$-meson would have to move in the direction of motion of the $\pi$-meson, while in fact it is, on the contrary, directed in the opposite direction. In addition, this explanation is contradicted by the determination of the mass of the primary particle, which, as has already been said, turned out to be much greater than the mass of the $\pi$-meson. The questions concerning the nature and number of neutral particles emitted in both these cases could not, of course, be decided unambiguously. It cannot be asserted with certainty that the particles $K_1$ and $K_2$ are of one and the same nature, although this

Fig. 19.

possibly, since the measured values of the masses are close to one another. If it is assumed that the particles $K_1$ and $K_2$ are of the same nature, then such a large difference in the energies of the secondary particles points directly to the fact that the decay occurs into one charged particle and two (or more) neutral ones.

The next important question—whether the $\tau$- and $K$-mesons are one and the same particles, but in individual cases decay differently—also has no definite answer.

Although there is a small difference in the magnitude of their masses, this difference lies entirely within the limits of error, especially if one compares the mass values obtained by direct determination by measuring the lengths of gaps, or by multiple scattering, which was the only possibility for the $K$-particle.

On the other hand, if the particles $K_1$, $K_2$, and $\tau$ are identical, then the spins of the $K$- and $\tau$-particles are equal. Since the spin of $\tau$ is integral, because $\tau$ decays into three $\pi$-mesons with integral spins, the simplest decay scheme will be $K \to \mu + \nu + \pi^0$, where $\mu$ and $\nu$ have half-integral spins, while $\pi^0$ has integral spin. This decay scheme, however, can only with difficulty be reconciled with the conservation laws for the particle $K_1$, since the secondary particle, if it is taken, as in the case of $K_2$, to be a $\mu$-meson, has a high energy—$182$ MeV. Adding to $182$ MeV the rest mass of the $\mu$-meson, the rest mass of the $\pi^0$-meson, and its kinetic energy, we find that, even under the assumption that the energy carried off by the neutrino is negligibly small, the mass of the particle $K_1$ is equal to $1160\,m_e$, which is greater than the exact mass of the $\tau$-meson $(966\,m_e)$. Of course, the initial number—the energy of the $\mu$-meson, $182$ MeV—is not determined so accurately that on this basis one could reject the idea that the particles $K$ and $\tau$ are identical. However, the second assumption, that the neutrino has carried away no appreciable energy, makes this whole point of view artificial. It should be said here that the decay cases observed by O’Ceallaigh are in essence very similar, both in appearance and in other features, to the so-called charged $V$-particles observed in a Wilson chamber.

Indeed, in the chamber decays of charged particles into one charged particle and an unknown number of neutral particles were also observed. Only, in contrast to the observations in the photoemulsion, in the chamber the decays occurred in flight. As is clear from the preceding, the mass of the charged $V$-particle is $\sim 1200\,m_e$. Below we shall clarify that analysis of cases of decay of charged $V$-particles also requires assuming a decay scheme into three particles—one charged and two neutral. As for the correspondence between the results described and the data of mass-spectrometric investigation, comparison is possible only for the values of the masses. The exact value of the mass obtained on the mass spectrometer for the group of heavy particles is $950 \pm 30\,m_e$, and therefore, with regard to the $K$- and $\tau$-particles, one may express the opinion that they are identical with the heavy group of mesons, discovered ...

irradiated in a mass spectrometer. In this light it is of interest here to compare data obtained by various methods concerning the lifetime of heavy mesons. As was already said above, the dimensions of the mass spectrometer require a lifetime $(2 \div 5)\cdot 10^{-9}$ sec. Powell also comes to the conclusion that the lifetime of $\tau$- and $K$-mesons is no less than $10^{-9}$ sec, on the basis of the following considerations. In the work of Camerini et al. it was found that the energy carried away by $\pi$-mesons in nuclear disintegration by a proton with energy $E$ (in the energy interval $2 \div 10$ Bev) is proportional to $E$. It is assumed that, in disintegration by protons with energy greater than $10$ Bev, the mesons carry away the same fraction of the energy, and that this energy is divided equally among $\pi$-mesons and $\tau$- and $K$-mesons. It is further assumed that the velocity spectrum and the angular distribution for $\tau$- and $K$-mesons in the center-of-inertia system are the same as for $\pi$-mesons. Knowing the energy distribution of fast protons and neutrons in cosmic rays at an altitude of $3200$ m, one can calculate the ratio between the number of $\tau$- and $K$-mesons and the number of $\pi$-mesons. According to this calculation it turns out to be $1/75$. In the experiment, however, under $30$ cm of lead, without any corrections for the fact that not all cases of $\tau$- and $K$-decay can be detected, this ratio was found to be $1/150$. If now one assumes that the lifetime of $\tau$- and $K$-mesons is $5\cdot 10^{-10}$ sec, then in matter of, say, density $8—9$, it turns out that only $5\%$ of the $\tau$- and $K$-mesons decay after stopping, while the rest decay in flight, i.e. they must be produced in numbers 20 times larger than in the above calculation. For a lifetime of $10^{-9}$ sec, already $25\%$ of the $\tau$- and $K$-mesons may have time to stop. This number will be greatly decreased further by nuclear collisions in the medium. Thus, the assumption of a short lifetime would make it necessary to ascribe too large a fraction of the energy to the production of $\tau$- and $K$-mesons in nuclear collisions of high energies.

Still more convincing considerations in favor of a long lifetime—greater than $10^{-9}$ sec—are adduced by Hertz et al.$^{23}$. Their photographic plates were irradiated under a thick layer of ice. It is assumed that $\tau$-mesons are produced with energies of the order of their rest energies, i.e. $500$ Mev. In that case the number of $\tau$-mesons able to stop in the photoemulsion will depend very strongly on the lifetime, since the particles, in order to stop in the emulsion, must lose almost completely their kinetic energy on the way to the emulsion; and this path (in ice) is great in length, and a considerable fraction of the $\tau$-mesons decay along this path. Moreover, $\tau$-mesons, if they are nuclear-active particles, will on this path to the photoemulsion undergo nuclear collisions and be absorbed.

Table XII gives the number of $\tau$-mesons born in the ice that is necessary in order that one of them be able to stop and decay in the photoemulsion and thus become observable.

HEAVY MESONS

Table XII

| Interaction cross section | $E$, MeV | \multicolumn{4}{c}{Lifetime in seconds} |
|---|---:|---:|---:|---:|---:|
| | | $10^{-7}$ | $10^{-8}$ | $10^{-9}$ | $10^{-10}$ |
| Small | 55 | 1.003 | 1.023 | 1.26 | 9.76 |
| Geometrical | 55 | 1.022 | 1.043 | 1.28 | 9.95 |
| Small | 500 | 1.068 | 1.93 | 713 | $3.4 \cdot 10^{28}$ |
| Geometrical | 500 | 6.68 | 12.1 | 4460 | $2.1 \cdot 10^{29}$ |

On the other hand, one can estimate the upper limit of the number of $\tau$-mesons decaying into a lepton per one case of a $\tau$-meson that has stopped in the emulsion. Indeed, if $\tau$-mesons disappear in large numbers owing to decay into a lepton, then, consequently, we should easily detect in the same photoemulsion cases of decay into a lepton. The calculated number of such cases of decay into a lepton in the photoemulsion per one stopped $\tau$-meson is given in Table XIII for $\tau$-mesons born with energy between 130 and 490 MeV.

Table XIII

	$10^{-8}$	$10^{-9}$	$10^{-10}$
Lifetime
Small interaction with nuclei	0.3	250	$2.2 \cdot 10^{29}$
Geometrical interaction cross section with nuclei	0.6	900	$1.3 \cdot 10^{30}$

According to the experiments of Herz et al., the upper limit of the number of cases of decay into a lepton in the same photoemulsion in which one case of stopping of a $\tau$-meson was found is two. Thus, according to Herz et al., even a lifetime of $10^{-9}$ sec is unacceptable; it must be considerably greater than this value. Data on the lifetime obtained from observations of the decay of charged $V$-particles in Wilson’s chamber likewise lead to a lifetime greater than $10^{-9}$ seconds.

Of particular interest are three photographs obtained by Leighton et al.$^{24}$. In two of them, cases of decay into a lepton, apparently of $\tau$-mesons, were obtained, and in one—a case of decay of a $K$-meson. One of the $\tau$-decays proved very convenient for analysis (Fig. 20). A particle with momentum $600 \pm 100$ MeV/$c$ entered the chamber from above, traversed the whole chamber, including a 2.5-cm lead plate, without noticeable scattering, and underwent decay into three particles in the lower

parts of the chamber. The three secondary particles had momenta $155 \pm 30$, $350 \pm 75$, and $210 \pm 50$ MeV/$c$. The law of conservation of charge and momentum was satisfied. Taking the secondary particles to be $\pi$-mesons, the authors obtained the mass of the primary particle as $975\,m_e$ and the decay energy as 75 MeV. The second photograph is similar to the first.

Since both $\tau$-mesons in the chamber traversed a long path (50 cm), their lifetime must be greater than $10^{-9}$ sec. In the third

Fig. 20.

photograph the track of the primary particle had a greatly increased ionization (6–10 times the minimum); its momentum was $185 \pm 20$ MeV/$c$, and its mass $1200 \pm 30\,m_e$. In the gas of the chamber the trajectory ended, and from this point there emerged, at an angle of $90^\circ$, the path of a secondary particle that had momentum $150 \pm 15$ MeV/$c$ and an ionizing power 1.2–1.6 times the minimum, which corresponds to a mass of $250 \pm 50\,m_e$. The secondary particle may be either a $\pi$- or a $\mu$-meson. Since, at a low velocity, the particle traversed a rather long path in the chamber, its lifetime should likewise be considered large. According to

in the opinion of Leighton et al., the flux of $\tau$- and $K$-particles is considerably larger than had seemed to be the case up to now, and greatly exceeds the flux of $V$-particles.

In 1952 the Manchester group published two papers concerning charged $V$-particles. The aim of these papers was to determine: a) the mass of the $V$-particles, b) the decay scheme, and c) the lifetime.

As will be seen below, not one of these problems could be solved completely, chiefly because of the paucity of the statistics. Since 1947 Butler et al.$^{25}$ had succeeded in accumulating twenty-two cases of decay of charged $V$-particles and four cases in which, from direct data on momentum and ionization, it was possible to establish that the particle is a heavy meson. These four cases are given in Table XIV.

Table XIV

Particle number	Sign	Momentum (in MeV/$c$)	Ionization (in units of minimum)	Mass interval (in $m_e$)
1	$-$	$160 \pm 10\%$	$6—10$	$900—1500$
2	$+$	$170 \pm 7\%$	$4—6$	$800—1000$
3	$+$	$170 \pm 10\%$	$5—7$	$900—1140$
4	$-$	$170 \pm 10\%$	$4—6$	$800—1020$

Attention is drawn to the extremely narrow interval of momenta $(160—170\ \mathrm{MeV}/c)$ in which these four cases are concentrated. Obviously, this is due to the experimental conditions, which only in this narrow interval of momenta make it possible reliably to distinguish heavy mesons from other particles. As in the analysis of $V^0$-particles, the authors constructed a plot of the distribution of 14 secondary particles according to the component of momentum in the direction perpendicular to the direction of motion of the primary $V^\pm$-particle, $p_T$ (Fig. 21). In the same figure is shown the theoretical distribution of $p_T$, calculated on the assumption that the decay of $V^\pm$-particles occurs into two particles. As was already said above, the distribution $p_T$

Fig. 21.

in this case is determined by the formula

\[ W(p_T)\,dp_T=-\frac{p_T}{p^*(p^{*2}-p_T^2)}\,dp_T, \]

where $p^*$ is the momentum of the secondary particle in the system associated with the primary particle, and is a constant quantity for all individual cases of decay. It depends only on the masses of the primary and of the two secondary particles and is related to $p_T$ by the formula

\[ p_T=p^*\sin\theta^*. \]

The maximum value is

\[ p_T=p^*. \]

The distribution in $p_T$ has a maximum at $p_T=p^*$. Taking the maximum value of $p_T$, obtained from measurements of fourteen cases and equal to $p_T=285\ \text{MeV}$, as $p^*$, the authors constructed the theoretical distribution of the number of secondary particles in $p_T$ for the two-particle decay scheme. It follows from the formula that this distribution has a maximum at the maximum value $p_T=p^*$ and, as is seen from the figure, does not agree with the experimental distribution.

From this the authors conclude that the two-particle decay scheme is untenable, and that either the decay proceeds into a larger number of particles, say three, or the charged $V^\pm$-particles are inhomogeneous in mass or in type of decay. It is natural to assume that charged $V^\pm$- and $K$-particles are identical particles. Both, in decay, emit one secondary charged particle, and both, apparently, decay with the emission of two secondary neutral particles.

In those cases in which the mass of the primary $V^\pm$-particle could be estimated from ionization and momentum, it proved not to differ greatly from the estimate of the mass of the $K$-particles. Thus, in one case, from the ionizing power (about twice minimum) and the momentum $(4.1\pm0.4\ \text{MeV}/c)$, the mass of the primary particle was found to be $1100\,m_e$, and if the maximum possible values of the ionization are taken, the upper limit of the mass will be $(1580\pm160)\,m_e$. In the second case the upper limit of the mass turned out to be $(1600\pm160)\,m_e$. In one case Bridge and Annis, as described above, also obtained a value of the mass within the limits $600\text{—}1200\,m_e$. Thus admitting that the $V^\pm$- and $K$-particles are identical still does not accomplish very much. Since the value of the mass of the $K$-particles was obtained with greater accuracy, it becomes possible to establish the maximum total mass of the neutral particles. This estimate is given in Table XV.

Table XV

Possible values of $(m_2 + m_3)$ for $K$- and $V^\pm$-particles

$M$ in $m_e$	Mass of the secondary charged particle equal to $210\,m_e$	Mass of the secondary charged particle equal to $210\,m_e$	Mass of the secondary charged particle equal to $210\,m_e$	Mass of the secondary charged particle equal to $210\,m_e$	Mass of the secondary charged particle equal to $210\,m_e$
	1000	1100	1200	1300	1400
$m_2 + m_3$ for $p^* = 250\ \text{MeV}/c$ . . . .	—	245	425	570	700
$m_2 + m_3$ for $p^* = 300\ \text{MeV}/c$ . . . .	—	—	—	330	506

From this table it is seen that the maximum value of the mass of the neutral particle, if it is assumed that in some cases the decay proceeds into two particles according to the scheme

\[ V^\pm = \mu^\pm + V_2^0, \]

can be $700\,m_e$, in the case when the maximum value of the momentum of the $\mu$-meson produced in the decay does not exceed

Fig. 22.

Fig. 22.

in the center-of-inertia system $250\ \text{MeV}/c$, and the mass of the primary particle is not less than $1400\,m_e$. Thus, this scheme too, even for some cases, appears unlikely. On the other hand, the authors have dis-

discovered one case very similar precisely to this decay scheme. This case is shown in Fig. 22. The particle, along the path $AB$, entered a lead plate and, emerging from it at point $C$, underwent a sharp kink—decay—at point $D$. The secondary particle, as follows from the ionization and momentum, has a mass less than $(200 \pm 50)m_e$. At a distance of $1.25$ cm from point $D$, from point $F$ there emerges a $V$-shaped track corresponding to a $V^0$-particle. Since the branches of the $V$-shaped track are short, no conclusions could be drawn about the nature of the secondary particles and, consequently, no choice could be made between $V^0_1$- and $V^0_2$-particles. The plane of this $V$-shaped track passes through point $D$. Simultaneously with the first particle, a second also enters the lead plate (along the path $IK$) and at point $O$ causes a nuclear disintegration, creating two charged secondary particles. The plane of the $V$-track also passes through point $O$. As a result, two possible interpretations of this photograph arise.

The first interpretation is as follows: the charged $V^{\pm}$-particle underwent decay at point $D$ into a meson and a $V^0$-particle, which in turn decayed and produced the $V$-track. The momentum of the primary charged particle is large $(1—2\ \text{Bev}/c)$, the momentum of the secondary charged particle is small $(73 \pm 20\ \text{Mev}/c)$, and if the decay occurred into two particles, then, indeed, the neutral particle must be heavy. The mass of the primary charged particle under these assumptions turns out to lie within the limits $1100—1500\,m_e$. The second interpretation amounts to the fact that the $V^0$-track accidentally coincided with the $V^{\pm}$-track, and that the $V^0$-particle in fact arose at point $O$, which also lies in the plane of the $V$-shaped track.

Two attempts were made to estimate the lifetime of the particles. Let us dwell on the one that gave more definite results. This work was carried out with a large Wilson chamber—54 cm long and 54 cm wide—installed at an altitude of 3580 m.

The authors, Astbury et al.$^{26}$, expected, thanks to the large dimensions of the chamber, to obtain more quickly an appreciable number of photographs of interest to them and, moreover, if the decay path length is comparable with $0.5$ m, to obtain a picture of the distribution of decay points along the length of the chamber. In the course of one year of operation of the chamber they discovered 40 kinks of trajectories in the chamber gas. These 40 photographs were interpreted as follows:

Interpretation	Number
decays $V^{\pm}$	13
» $\pi \to \mu$	13
» $\mu \to e$	1
elastic scatterings	3
indeterminate	10

In four cases out of 13, the masses of the primary particles were estimated from ionization and momentum; values of $(630—1420)\,m_e$, $(550—4200)\,m_e$, $(690—1570)\,m_e$, and $<1490\,m_e$ were obtained. In this case (which does not coincide with the four enumerated above) the mass of the secondary particle was established within the limits $200—330\,m_e$. The lifetime of the $V^{\pm}$-particles was estimated as follows. The path length of each particle in the chamber up to its decay was measured. The path length that the particle would have traversed if it had not decayed, $L$, was measured. The flight times corresponding to these lengths in the rest frame of the moving particle, $t$ and $l$, are connected by the relation

\[ l = \frac{p}{M}ct, \]

where $p$ and $M$ are the momentum and mass of the particle. For all 13 particles the mass was taken to be $1200\,m_e$; Table XVI gives the results of the calculations.

Table XVI

$N$	$l$ (cm)	$L$ (cm)	$\dfrac{p}{M}$	$t$ ($10^{-10}$ sec.)	$T$ ($10^{-10}$ sec.)	$\dfrac{t}{T}$
1	6,5	21	1,3	1,7	5,4	0,31
2	13	33	0,47	9,2	23,4	0,39
3	10	22	0,4	8,3	18,3	0,45
4	8	10,5	0,8	3,3	6,8	0,48
5	13	19	0,7	6,2	9	0,69
6	38,3	60,5	0,53	24,1	38	0,63
7	11,1	15	1,6	2,3	3,1	0,74
8	20,2	41	0,7	10,4	21,2	0,49
9	9,6	30	0,7	4,9	15,2	0,32
10	33,7	44,5	16	6,9	9,1	0,76
11	8	18,5	0,7	4,1	9,5	0,43
12	6,6	26	0,5	4,5	17,7	0,25
13	22,2	43,5	1,3	5,7	11,2	0,51

The average of all $\dfrac{t}{T}$ is equal to 0.5, as should be the case when the decay path length is much greater than the mean time

the time of flight $\overline{T}$ through the chamber. The mean time of flight $\overline{T}$ lies within the limits

\[ (7<\overline{T}<14)\cdot 10^{-10}\ \text{sec}. \]

Thus, the lifetime of the $V^\pm$-particles is $>10^{-9}$ sec, in good agreement with the results of the mass spectrometer.

It is noteworthy that, along with thirteen cases of $V^\pm$-decay, the authors observed 13 $\pi$-$\mu$ decays. If the lifetime of the $V^\pm$-particle is $\sim \frac{1}{5}$ of the lifetime of the $\pi$-particle, then the number of $V^\pm$-particles will amount to $\sim \frac{1}{5}$ of the number of $\pi$-mesons. The same authors, continuing the work in 1953, registered two cases of decay of slow $V^\pm$-particles and thereby refined the lifetime of the $V^\pm$-particles. It proved to be close to $10^{-8}$ sec.

If the heavy mesons with mass about $1000\,m_e$ were discovered by different methods and by different authors, then, with respect to mesons of intermediate mass—about $600\,m_e$—for a long time the mass-spectrometer data remained the only ones, as a result of which doubts arose as to the correctness of the mass-spectrometer data.

Meanwhile, Alikhanyan and Kharitonov$^{27}$, continuing measurements on a mass spectrometer equipped with two proportional counters, separated these two groups of heavy mesons according to ionizing power. The ionizing power was measured for 87 particles, of which 30 particles had mass $580\,m_e$ and 57 particles mass $950\,m_e$. Of the total number of 87 particles, data simultaneously from counter No. 1 and counter No. 2 are available for only 26. For all the others, data were obtained only from counter No. 2. The results are given in Table XVII.

From this table it is seen that the ionizing power of the heavy mesons of both groups: 1) is noticeably greater than the ionizing power of $\mu$-mesons of the corresponding momenta, 2) is less than the ionizing power of $\mu$-protons of the same ranges, 3) is greater for the group of heavy mesons (mass $1000\,m_e$) than for the group of light ones (mass $600\,m_e$), 4) varies in accordance with the range.

As was to be expected, according to counter No. 1 the ionizing power of the heavy mesons is less than according to counter No. 2, but it is again greater (for both groups) than the ionizing power of $\mu$-mesons of the same momenta. Fig. 23 gives the differential spectrum of 54 intermediate particles recorded in the range interval from $3.5\div 4$ to $5.5\div 6$ Pb.

For comparison, the same figure shows the ionization spectra for protons of the same range interval and for mesons: 1—heavy mesons, 2—mesons, 3—protons.

HEAVY MESONS

Table XVII

Type of particles	Residual range (in cm), from	Residual range (in cm), to	Number of particles	Relative ionizing power, calculated	Relative ionizing power, $H$	Relative ionizing power, experimental	Errors, statistical	Errors, graduations
By counter No. 2
Intermediate heavy	0	1.5	12	—	—	3.50	0.46	0.10
Same	1.5	2.5	13	—	—	2.52	0.31	0.08
Same	2.5	3.5	23	—	—	1.90	0.18	0.06
Same	3.5	4.5	9	—	—	1.88	0.28	0.06
Intermediate light	0	1.5	4	—	—	2.4	0.6	0.1
Same	1.5	2.5	4	—	—	2.5	0.6	0.1
Same	2.5	3.5	16	—	—	1.62	0.18	0.05
Same	3.5	4.5	6	—	—	1.25	0.23	0.04
Mesons	3.5	4.5	167	1.23	0.02	1.25	0.04	0.04
Mesons with momenta $(2.8 \div 4.8)\,10^8$ eV/s	—	—	104	1.01	—	1.06	0.05	0.03
Protons	2.5	3.5	191	2.7	—	2.50	0.08	0.08
Protons	3.5	4.5	115	2.2	—	2.12	0.09	0.06
By counter No. 1
Mesons with momenta $(2.8 \div 4.8)\,10^8$ eV/s	—	—	104	1.01	—	0.92	0.05	0.03
Mesons	4.5	6.0	62	1.15	0.02	1.07	0.07	0.03
For the series in which both counters operated
Intermediate heavy: by counter No. 1	3.0	6.0	15	—	—	1.74	0.20	0.05
Intermediate heavy: by counter No. 2	1.5	4.5	15	—	—	1.96	0.23	0.06
Intermediate light: by counter No. 1	3.0	6.0	11	—	—	1.21	0.16	0.04
Intermediate light: by counter No. 2	1.5	4.5	11	—	—	1.87	0.25	0.06

For protons, the percentage of cases in which the ionization exceeds by two times the most probable (for protons) ionization is $14 \pm 3.5\%$. For heavy mesons (of both groups) this percentage is $12 \pm 4\%$; consequently, the increased ionizing power of these particles is not associated with an admixture of a separate group of strongly ionizing particles among the particles with minimum ionization.

Likewise, no difference was found between the ionizing power of heavy mesons of different signs.

Fig. 23.

As is known, in measurements of the ionizing power of monoenergetic particles by means of a proportional counter, the obtained ionization values are distributed according to an asymmetric fluctuation curve, the so-called Landau distribution curve.

In the case when $N$ such measurements have been made, where $N$ is a large number, the value of the most probable ionizing power of particles of the given kind can be determined from the position of the maximum of the Landau distribution curve. However, when $N$ is not large, the most reliable value of the probable ionization, and with the smallest error, can be determined in the following way. Suppose that $N$ values of the quantity $\Delta_0$ have been obtained: $\Delta_1, \Delta_2, \ldots, \Delta_N$. The probability density, for the true value $\Delta_0$, of having the given set of readings $\Delta_1, \Delta_2, \ldots, \Delta_N$ is equal to

\[ F(\Delta_1,\Delta_2,\ldots,\Delta_N,\Delta_0)\sim \varphi_1(\Delta_1-\Delta_0)\varphi(\Delta_2-\Delta_0)\ldots \varphi(\Delta_N-\Delta_0), \]

where $\varphi(\Delta_i-\Delta_0)$ is the Landau distribution for the given proportional counter, i.e., the probability density of obtaining, in a measurement of $\Delta$, the value $\Delta_i$ when the true value of $\Delta$ is equal to $\Delta_0$. Since $\varphi(\Delta_i-\Delta_0)$ is a function of the differences $\Delta-\Delta_0$, and not of the values $\Delta$ and $\Delta_0$ themselves, the variables $\Delta$ and $\Delta_0$ are equivalent, and if we fix the given

$\Delta_i$, then $\varphi(\Delta_i-\Delta_0)$ will be the probability, for the given value $\Delta_i$, of having the value $\Delta_0$.

Then $F(\Delta_1,\Delta_2,\ldots,\Delta_N,\Delta_0)\,d\Delta_0$ can also be spoken of as the probability, for the given set of values $\Delta_i$, of having the value $\Delta_0$.

Thus, by the usual method of finding the mean, we have:

\[ \overline{\Delta_0}= \frac{ \displaystyle \int_{-\infty}^{+\infty} F(\Delta_1,\Delta_2,\ldots,\Delta_N,\Delta_0)\Delta_0\,d\Delta_0 }{ \displaystyle \int_{-\infty}^{+\infty} F(\Delta_1,\Delta_2,\ldots,\Delta_N,\Delta_0)\,d\Delta_0 } = \]

\[ = \frac{ \displaystyle \int_{-\infty}^{+\infty} \varphi(\Delta_1-\Delta_0)\varphi(\Delta_2-\Delta_0)\ldots \varphi(\Delta_N-\Delta_0)\Delta_0\,d\Delta_0 }{ \displaystyle \int_{-\infty}^{+\infty} \varphi(\Delta_1-\Delta_0)\varphi(\Delta_2-\Delta_0)\ldots \varphi(\Delta_N-\Delta_0)\,d\Delta_0 }. \]

Using this method of processing the experimental data, the probability-distribution curves for the mass values determined from momentum and ionization were calculated for both groups of heavy mesons. These curves (Fig. 24) were obtained from the experimental values for the “light” and “heavy” groups.

Thus, the two groups of heavy mesons were also separated by ionization measurements. The group of mesons with mass $\sim 600\,m_e$ was obtained more clearly than before. Alikhanov and Eliseev, continuing their measurements at sea level, increased the resolving power of the mass spectrometer by reducing the thickness of the absorbing filters. The total number of intermediate mesons observed by them was 30, and the grouping around the mass value $600\,m_e$ was obtained distinctly.

The first data on mesons with mass $580\,m_e$, obtained by a method different from the mass-spectrometer method, were obtained by Leighton et al. In a Wilson chamber, along with two $\tau$-mesons, which we have already discussed, they found three tracks with mass values lying in the interval $400—650\,m_e$. The momenta of these three particles were equal to $180\pm20$, $100\pm15$, $135\pm15$ MeV/$c$, and the ionizations to $2—3$, $3—6$, and $4—8$ minimum ionizations, respectively. These numbers indicate mass values of $550\pm150\,m_e$, $450\pm150\,m_e$, and $750\pm150\,m_e$.

Danich, Locke, and Yekutieli$^{28}$ reported the possible existence of a neutral meson of such mass, with a very short ($\sim 10^{-14}$ sec.) lifetime. The basis for making this suggestion was the following observation. In one of the nuclear disintegrations, two shower particles were emitted from the nucleus in the form of

pairs with an opening angle of $4^\circ$, and this pair had an angle of $150^\circ$ with respect to the vertical. Although this case was obtained at an altitude of $22000$ m, nevertheless even at this altitude it is very unlikely that the primary particle was traveling practically from below upward. Therefore the authors believe that the pair was emitted in a direction opposite to the direction of the primary particle that caused this splitting. The emission of shower

Fig. 24.

Fig. 24.

particles backward by such a narrow pair seems very unlikely, especially since, from measurements of grain density and multiple scattering, it was found that these two particles are $\pi$-mesons with rather close energies: $76 \pm 5$ and $117 \pm 10$ MeV. The authors suppose that these $\pi$-mesons resulted from the decay of a neutral, very short-lived meson $\zeta^0$ according to the scheme

\[ \zeta^0 \to \pi^+ + \pi^- + Q. \]

The value of the decay energy $Q$ for this case turned out to be equal to $2$ MeV.

Subsequently the authors examined a large number of stars in order to find similar cases, and in their search they were guided by the following requirements: a) the star must contain two $\pi$-mesons with an emission angle greater than $90^\circ$ with respect to the direction of the primary particle that caused the disintegration; b) the star must contain two $\pi$-mesons with energies less than $30$ MeV, independently of their emission angle.

For the eight cases found, the values of the decay energies $Q$ were calculated under the assumption that the pair of $\pi$-mesons was produced as the result of the decay in flight of a $\zeta^0$-meson. In six cases the values of $Q$, within the limits of experimental error, were close and of the order of $3$ MeV. Two cases gave different values—$10$ MeV and $19$ MeV.

The authors also gave a number of additional arguments in favor of their hypothesis, based on the fact that the probability of emission of pairs of $\pi$-mesons in nuclear disintegrations with an angle of divergence between them of $5$—$15^\circ$ is much greater than follows from the normal statistical theory for independent emission of $\pi$-mesons. The correlated emission of pairs of $\pi$-mesons, however, may be caused by another reason. Since $\pi$-mesons are strongly interacting particles, the nuclear forces acting between them at the moment of production may alter the random angular distribution in the center-of-inertia system.

Quite recently, new data have been obtained confirming the existence of charged mesons with mass $580\,m_e$. At the Copenhagen conference in July 1952, Powell${}^{29}$ reported five mesons found in photoemulsion among the products of nuclear disintegrations caused by high-energy particles, whose mass proved to be $535 \pm 35\,m_e$. The mass of the particles was apparently determined from the grain density and multiple scattering, and this accuracy was achieved because the tracks in the emulsion were very long. In one of the five cases the track of a particle in the emulsion underwent a kink of $1^\circ$. Measurements of the characteristics of the particle track after the kink indicate a mass of $280\,m_e$. This case is therefore regarded as the decay in flight of a particle of mass $535 \pm 35$ (called a $\zeta$-meson):

\[ \zeta^{\pm} \to \pi^{+} + \pi^{0}. \]

Since no change in the velocity of the particle after the kink was observed, the value of the decay energy is taken to be very small—$1$ MeV.

In addition, Powell reported that two more cases had been found of $K$-mesons with mass $1080 \pm 100\,m_e$, decaying into a $\mu$-meson and a neutral particle. The kinetic energy of the $\mu$-mesons from the decay was, in these two cases, also different from the first two cases—in one $6.9$, and in the other $34$ MeV. Thus, for

For $K$-mesons one should adopt a decay scheme into three (or four) particles:

\[ K \to \mu + 2\nu, \]

\[ K \to \mu + \nu + \pi^0, \]

\[ K \to \mu + \nu + \pi^0 + \pi^0. \]

Finally, Powell also reported a new heavy meson, named the $\chi$-meson. Three cases of the decay of the particle into a $\pi$-meson were observed, and in all three cases the energy of the $\pi$-meson was the same. The mass of these three particles is

\[ 1470 \pm 100\, m_e. \]

The decay scheme of the $\chi$-meson, in view of the fact that the $\pi$-meson, the product of its decay, always had one and the same energy, must be

\[ \chi^{\pm} \to \pi^{\pm} + N^0, \]

where $N^0$ is a heavy neutral particle.

Its mass can be determined from the energy of the $\pi$-meson, equal to

\[ 110 \pm 10\ \text{Mev}, \]

and from the mass of the primary particle. It proves to be equal to

\[ 890 \pm 100\, m_e \]

and, consequently, the $N^0$-particle may be a neutral analogue of the $\tau$-meson and, possibly, coincides with the $V^0_2$-particle.

Let us now try to form an idea of which heavy mesons have recently had their existence established, or reported provisionally (Table XVIII).

The data presented in Table XVIII are not established with equal firmness. In particular, this applies to the $\zeta$-mesons, whose existence still requires proof.

In conclusion, let us dwell on the works in which the first data were obtained on the processes of production of heavy mesons. This important question has until now been studied only with the aid of photographic emulsions.

For several years a large group of Bristol physicists carried out a systematic study of the so-called stars, i.e. nuclear disintegrations arising in photographic emulsions. This study became especially fruitful when photographic emulsions sensitive to particles of all velocities, up to relativistic ones, began to be used, and when the technique of measuring the mean angle of multiple scattering $\bar{\alpha}$, suitable for carrying out mass measurements, was applied. Measurement of the scattering parameter $\bar{\alpha}$ on

Table XVIII

Name	Mass in $m_e$	Methods by which existence was established	Decay scheme	Decay energy in $Mev$	Spin	Lifetime
$\zeta^{\pm}$	$580 \pm 50$	mass spectrometer	—	—	integer	$>5 \div 2 \cdot 10^{-9}$ sec.
$\zeta^{\pm}$	$580 \pm 150$	Wilson chamber	—	—	integer	$>10^{-9}$ sec.
$\zeta^{\pm}$	$535 \pm 35$	photoemulsion	$\pi^{\pm}+\pi^{0}$	$1$	integer	$>10^{-10}$ sec.
$\zeta^{0}$	$556 \pm 4$	photoemulsion	$\pi^{+}+\pi^{-}$	$2$	integer	$\sim 10^{-14}$ sec.
$\tau$	$950 \pm 70$	mass spectrometer	—	—	integer	$>5—2 \cdot 10^{-9}$
$\tau$	$977 \pm 5$	photoemulsion	$\pi^{\pm}+\pi^{+}+\pi^{-}$	$77 \pm 4$	integer	$>10^{-9}$ sec.
$\tau$	$975$	Wilson chamber	—	$75$	integer	$>10^{-9}$ sec.
$\nu^{\pm}$ $K$	$1080 \pm 100$	Wilson chamber	decays into three or more particles	—	—	$\sim 10^{-8}$ sec.
$\nu^{\pm}$ $K$	$1080 \pm 200$	photoemulsion	decays into three or more particles	—	—	$>10^{-9}$ sec.
$\chi^{\pm}$	$1450 \pm 100$	photoemulsion	$\pi^{\pm}+N^{0}$	$150 \pm 10$	integer	$>5 \cdot 10^{-10}$ sec.
$V_{2}^{0}=N^{0}?$	$800—1000$	Wilson chamber	—	$120$	—	$10^{-9}—10^{-10}$
$V_{1}^{0}$	$2200 \pm 12$	Wilson chamber	$p^{+}+\pi^{-}$	$46$ $\dfrac{35}{75}$	half-integer	$10^{-9}—10^{-10}$

per unit length of path makes it possible to determine the quantity $\dfrac{p\beta}{z}$ for the corresponding particle and is equivalent to measuring the curvature of the particle path in a magnetic field in a Wilson chamber and in a mass spectrometer, but with an accuracy inferior to that of the latter methods. Measurement of the grain density $g$ is equivalent to measuring the ionization in a Wilson chamber; however, the accuracy with which the value of the particle velocity is thereby obtained is much higher than can be obtained in a Wilson chamber.

Thus, simultaneous measurement of $\bar{\alpha}$ and $g$ for a particle makes it possible to determine the mass and energy of the particle in those cases where it is possible to measure $\bar{\alpha}$ accurately; and this is possible for tracks having a great length in the emulsion.

For the analysis of the composition of stars, such measurements had to be carried out for a large number of particles entering into the stars, and therefore the success of the investigation depended on such an improvement of the measurement technique as would permit them to be carried out in short times. These improvements are described in the paper by Powell et al. (UFN, vol. 43, issue 1).

The authors succeeded, for very long paths, in measuring such small values of $\alpha$ (over 100 microns of path length) as $0.001^\circ$.

In analyzing the particles of stars, Camerini, Perkins et al.^30 classify the tracks as follows:

1) Shower particles. They are characterized by a low grain density (fewer than 16 grains per $50\,\mu$); the corresponding ionization is less than 1.4 times the minimum. These are $\pi$-mesons with energy greater than 80 MeV and protons with energy greater than 500 MeV. The number of shower particles in a star is denoted by $n_s$.

2) Grey tracks. They are characterized by a grain density from 16 to 80 per $50\,\mu$ of path. They correspond to protons with energy from 25 to 500 MeV. Their number in a star is denoted by $N_g$.

3) Black tracks. They are characterized by a grain density greater than 80 per $50\,\mu$. They are produced by protons with energy less than 25 MeV. They are denoted by $N_b$. The sum $N_b + N_g$ is denoted by $N_h$; a star is characterized by the expression $N_h + n_s$, with a sign indicating the nature of the primary particle. Stars with $n_s \geqslant 2$ are called showers.

The scale of the work carried out can be seen from the fact that $87\ \mathrm{cm}^3$ of emulsion were examined and 15,300 stars, i.e. nuclear disintegrations, were observed.

Analysis of the stars showed that $\pi$-mesons and protons and, correspondingly, $\pi^0$-mesons and neutrons are emitted in stars.

In this work, for a certain number of stars the energy of the primary particles was measured up to $10 \cdot 10^9$ eV.

The main conclusion reached by the authors amounts to the fact that primary particles with energy up to 10 BeV, in the disintegration of nuclei, create only $\pi$-mesons and do not create heavy mesons.

In the next work, by Daniel et al.^31, with the aid of certain new methods the authors succeeded in analyzing the composition of secondary particles of stars generated by particles with still higher energies.

The dependence of the grain density on $p\beta$ has the character shown in Fig. 25. The grain density decreases with increasing $p\beta$, has a fairly broad minimum near the value $500$ Mev, and then increases by $10\%$ and thereafter does not change. Since it was possible,

Fig. 25.

stars were selected in which the primary particle had $\dfrac{p\beta}{\mu c} > 10$ and a range in the emulsion $> 4$ mm. Measurements of these tracks made it possible to determine the grain density for the ultrarelativistic region $(g_0)$ with an accuracy of $2.5\%$. Having selected stars in which the primary particles had energies greater than $5$ Bev and less than $50$ Bev, i.e., an average energy $\sim 15$ Bev, the authors found that the secondary particles in the stars are mainly $\pi$-mesons and protons, and that the number of heavy mesons, if they are present at all, is small in comparison with the number of $\pi$-mesons.

The authors were able to distinguish the next energy stage of the primary particles by considering a special kind of shower, the so-called “jets.” “Jets” are disintegrations in which the secondary particles with relativistic ionization are directed forward along the direction of the primary particle in a narrow cone, the number of gray or black tracks in them being small or equal to zero. Examples of such jets are shown in Fig. 26.

The energy of the primary particle in these cases can be determined approximately from the relation

\[ \tilde{\gamma}_p = \frac{2}{\eta^2}, \]

where $\tilde{\gamma}_p$ is the energy of the primary particle in proton masses, and $\eta$ is the mean angle of divergence of the shower. The selected jets corresponded

energies of the primary particles $>50\ \text{BeV}$ and an average energy $\sim 500\ \text{BeV}$. Among the secondary particles of these stars there proved to be many heavy mesons with an average mass $\sim 1300 m_e$.

Fig. 26.

In Figs. 27a and 27b, $p\beta$ and $g^*$ are given for the secondary particles of stars formed by primary particles with energies:

a) $E = 10\text{–}50\ \text{BeV}, \quad \bar E = 30\ \text{BeV};$

and

b) $E > 50\ \text{BeV}, \quad \bar E = 300\ \text{BeV}.$

These figures show the calculated curves for $\pi$- and $K$-mesons, and protons, and from them it is evident that the larger the energy

Figure 27a.

Fig. 27a.

Figure 27b.

Fig. 27b.

primary particles, the larger the percentage of $K$-particles formed in stars.

If one restricts oneself only to $\pi$-mesons and $K$-mesons and protons with ionizing ability greater than 1.2 minimum (and such are the conditions of observation in some other methods, for example in the mass-spectrometer method), then at an average energy of the primary particles of $30$ Bev per $3\pi$-meson there is 1 meson with mass $520 \pm 70\,m_e$, 1 meson with mass $\sim 1300\,m_e$, and 2 protons, while at $3000$ Bev there is not a single $\pi$-meson, 4 $K$-mesons and 2 protons.

The authors give the ratio between the number of $\pi$- and $K$-mesons, trying, as far as possible, to take both of them fully into account.

Table XIX gives their data for different energies of the primary particles and for different intervals $p\beta$ of the secondary particles.

Table XIX

| Mean energy of primary particles | \multicolumn{4}{c}{$p\beta \leqslant 1$ Bev} | \multicolumn{4}{c}{$p\beta \leqslant 7$ Bev} |
|---|---:|---:|---:|---:|---:|---:|---:|---:|
| | $N_K$ | $N_\pi$ | $N_p$ | $N_K/N_\pi$ | $N_K$ | $N_\pi$ | $N_p$ | $N_K/N_\pi$ |
| $E > 50$ Bev
$\bar E \sim 300$ » | 6 | 14 | 1 | 0.43 | 15 | 37 | 6 | 0.4 |
| $E > 50$ Bev
$\bar E \sim 500$ » | 6 | 11 | 1 | 0.36 | 8 | 22 | 4 | 0.36 |
| $E = 10\text{--}50$ Bev
$\bar E \sim 30$ Bev | 2 | 11 | 3 | 0.18 | 3 | 19 | 3 | 0.16 |

According to the new data, also in the region of lower primary-particle energies the fraction of heavy mesons is quite appreciable and not as small as was reported in the first works. Namely, according to these data, secondary particles with energies $>1.1$ Bev are produced in the following ratios (Table XX).

Table XX

Energy of the primary particle	$0\text{--}10$ Bev	$10\text{--}50$ Bev	$50$ Bev
$N_{\kappa}/N_{\pi}$ . . . . . . . . . .	0.05	0.10	0.5
$N_{\xi}/N_{\pi}$ . . . . . . . . . .	0.03	0.04	0.10

In conclusion it should be noted that the question of exactly which of the heavy mesons is produced in stars has not been resolved. Apparently the Bristol group has grounds for believing that the $\chi$-meson is produced, and not the $K$-meson.

However, in the few obtained photographs of stars in which slow heavy mesons were born, the values of the mass of the heavy meson in two cases are, with high probability, smaller than the mass of the $\chi$-meson.

Two such photographs were obtained by the Italian physicists Levi-Setti and Tomasini $^{32}$, and one by a group of Norwegian authors—Isachsen et al. $^{33}$.

In the photographs of the first authors, the heavy meson, having been born in a star, after a path of $4500\,\mu$ in the photographic emulsion underwent decay into a charged particle (the $K$-decay type). The mass, determined from the frequency of gaps between grains and the range, and also from the scattering parameter and the range, proved to be $1040 \pm 90\,m_e$, i.e., definitely smaller than the mass of the $\chi$-meson.

Similarly, in the Norwegian authors’ work, a slow heavy meson, born in a star, stopped in the photographic emulsion and underwent decay, emitting also one secondary particle—apparently a $\mu$-meson. The path length of the heavy meson was $14\,000\,\mu$, and the mass, determined by the same methods, proved to be $940 \pm 140\,m_e$.

Levi-Setti and Tomasini discovered one more case of the birth of a heavy meson in a star, but in this case its mass proved already to be considerably larger, namely $1380 \pm 210\,m_e$, i.e., much closer to the mass of the $\chi$-meson. Finally, a case of the birth in a star of a $\tau$-meson has been noted.

Among all heavy mesons, apparently, a special place should be assigned to $V_1^0$-particles, which have a mass greater than that of the proton. It can hardly be assumed that a $V_1^0$-particle can, even in some cases, decay according to a scheme in which there would be no nucleon (i.e., proton), for example, into two heavy mesons. The existence of such a decay mechanism would lead to the instability of nuclear matter. It is natural to regard the $V_1^0$-particle as a certain excited state of the neutron and, thus, to assign it to the class of nucleons. Accordingly, the spin of $V_1^0$-particles must be half-integral. Confirmation of this point of view is provided by several observations in which, apparently, it proved possible to detect a $V_1^0$-particle in a nucleus.

The first such observation was made by Danysz and Pniewski $^{34}$ in photographic emulsion (Fig. 28).

From star $A$, with a very large number of outgoing particles (the splitting of a silver or bromine nucleus took place), there emerged one strongly ionizing particle $(f)$, which was a nucleus with charge about 5. After traversing $60\,\mu$ in the photographic emulsion, this particle stopped, and in

at the end of the track a new star $(B)$ arose, consisting of four tracks. Of these four tracks, track (3) is of particular significance, having a low grain density corresponding to a high particle velocity. If this track is taken to be the track of a proton, then its energy

Fig. 28.

Fig. 28.

will be equal to $82$ Mev. The sum of the kinetic energies of the particles emitted in the second star is $140$ Mev. It is difficult to suppose that a nucleus—a fragment—having received such a high excitation in the process of splitting that produced the first star, would have retained this excitation for a time of $3 \cdot 10^{-12}$ sec. up to the moment of its stopping.

It is more natural to suppose that the $V_1^0$-particle exists not only in the free state, but also in the bound state within the nucleus. In a nuclear fragment, during the process of splitting, one of the nucleons could pass into an excited state, i.e. into a $V_1^0$-particle, which, being unstable also in the nucleus, underwent decay after the fragment stopped.

An analogous case was observed by Krouser and Morell ${}^{35}$. The case they observed is interesting in that from a nuclear fragment (an $\alpha$-particle or a lithium nucleus), at the point where it stopped, a $\pi$-meson and a proton were emitted, and the sum of the kinetic energies of the particles was $\sim 46$ MeV, in close agreement with the decay energy of $V_1^0$-particles.

Tidman and others ${}^{36}$ also found a case of decay of a nuclear fragment with a large release of energy. In their case the energy emitted in the decay of the nucleus-fragment was 50–70 MeV.

In connection with all that has been said, the question naturally arises: is there not also a charged unstable particle, similar to the $V_1^0$-particle, i.e. an excited proton? Some indication of this has appeared recently. Bonetti et al. ${}^{37}$ succeeded, in a photographic emulsion, in detecting an extremely long track—15,000 $\mu$—of a particle which, on stopping, emitted a light particle. The track of the secondary particle was very short (120 $\mu$), and therefore the secondary particle could not be identified with certainty. It was only possible to assert that it is not an electron. The mass of the primary particle, determined by the scattering method, proved to be $2500 \pm 345\,m_e$.

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Submission history

[v1] 1953

Case	1	2	3	4
Momentum of the positive particle (in \(10^8\) eV/\(c\)) . . .	\(2.1 \pm 0.2\)	\(5.2 \pm 0.7\)	\(3.8 \pm 0.5\)	5
Momentum of the negative particle (in \(10^8\) eV/\(c\)) . . .	2—5	\(1.5 \pm 0.1\)	\(1.5 \pm 0.1\)	\(1.2 \pm 0.1\)
Measured ionization of the positive particle . . .	10—15	3—4	4—6	3—4
Calculated ionization for a proton of the corresponding momentum . . .	12	3	5	3
Angle between the particles . . .	\(31^\circ\)	\(50.5^\circ\)	\(76^\circ\)	\(50^\circ\)
Mass \(M\) of the particle in \(m_e\) . .	\(2400 \pm 150\)	\(2180 \pm 10\)	\(2220 \pm 20\)	2200

Catalog No.	\(\alpha\)	\(p_T\) \((10^8\ \mathrm{eV}/c)\)	Mass values \(m_e\)	Values \(Q\), MeV
33	\(-0.03\)	0.78	\(2277 \pm 40\)	\(82 \pm 20\)
37	\(+0.84\)	0.94	\(2228 \pm 40\)	\(58 \pm 20\)
42	\(+0.74\)	1.00	\(2186 \pm 20\)	\(37 \pm 10\)
43 *)	\(+0.50\)	1.15	\(2218 \pm 10\)	\(53 \pm 5\)
47 *)	\(+0.70\)	1.31	\(2228 \pm 10\)	\(53 \pm 5\)
49	\(+0.70\)	0.82	\(2160 \pm 20\)	\(24 \pm 10\)
50	\(+0.70\)	0.92	\(2183 \pm 20\)	\(36 \pm 10\)
56 *)	\(+0.53\)	0.88	\(2181 \pm 10\)	\(40 \pm 5\)
85	\(+0.67\)	1.02	\(2188 \pm 10\)	\(38 \pm 5\)
88	\(+0.76\)	0.72	\(2157 \pm 30\)	\(23 \pm 15\)
92 *)	\(+0.60\)	0.81	\(2169 \pm 10\)	\(29 \pm 5\)
96	\(+0.79\)	0.97	\(2256 \pm 50\)	\(72 \pm 25\)

Catalog No.	\(\alpha\)	\(p_T\), \(10^8\) eV/\(c\)	Mass \(m_e\)	\(Q\), MeV
5	\(-0.07\)	1.46	\(796 \pm 130\)	\(122 \pm 65\)
35	\(+0.38\)	1.56	\(883 \pm 50\)	\(165 \pm 25\)
38	\(+0.33\)	1.60	\(872 \pm 50\)	\(160 \pm 25\)
53	\(-0.03\)	1.66	\(841 \pm 60\)	\(144 \pm 30\)
63 *)	\(-0.29\)	1.46	\(820 \pm 50\)	\(134 \pm 25\)
66 *)	\(+0.51\)	1.03	\(700 \pm 30\)	\(74 \pm 15\)
69	\(+0.07\)	0.98	\(673 \pm 100\) \(\pm 50\)	\(61 \pm 50\) \(\pm 25\)
90 *)	\(+0.05\)	1.41	\(785 \pm 30\)	\(116 \pm 15\)

Case	Particle \((a)\)	Particle \((b)\)	Particle \((c)\)	Sum of kinetic energies
1	\(1.04 \pm 0.1\)	\(31 \pm 4\)	\(33 \pm 4\)	\(65 \pm 8\)
2	\(50 \pm 7.5\)	\(13 \pm 2\)	\(22 \pm 3\)	\(85 \pm 15\)
3	\(19 \pm 0.4\)	\(24.2 \pm 2\)	\(32 \pm 2\)	\(75 \pm 5\)
			Weighted mean	\(73.5 \pm 4\)
			Mass is equal to	\(966 \pm 8\,m_e\)

Case	Particle \((a)\)	Particle \((b)\)	Particle \((c)\)
1	\(274\)*)	\(280 \pm 30\)	\(1.02 \pm 12\%\)
2	\(1\)	\(1.10 \pm 15\%\)	\(1 \pm 10\%\)
3	\(285 \pm 20\)	\(0.88 \pm 11\%\)	\(1.03 \pm 5\%\)

Abstract

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HEAVY MESONS

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HEAVY MESONS

Plate No.	\(p\cdot 10^{-8}_{\beta}/c\)	Mean range	\(M\) by range and impulse	Relative ioniz. ability	Plate No.	\(p\cdot 10^{-8}_{\beta}/c\)	Mean range	\(M\) by range and impulse	Relative ioniz. ability
Minimal residual range \(1.6\ \text{cm}\)
325	−3.65	—	−1100	3.6	457	−4.30	—	−1400	0.8
338	−3.27	—	−940	2.3	468	2.73	—	720	1.6
338	−2.8	—	−800	2.2	517	3.09	—	880	3.7
351	3.50	—	1100	3.7	586	−2.0	—	−520	3.1
357	1.93	—	500	3.6	612	−3.03	—	−900	3.6
396	3.13	—	900	3.4	545	−2.3	—	−570	1.8
431	−3.94	—	−1280	1.6
\(1.6\text{–}3\ \text{cm}\)
328	2.84	3.78	620	1.17	423	−3.27	5.90	−585	1.44
333	−3.94	4.56	−920	1.72	425	−3.06	5.36	−565	3.04
335	4.50	4.67	1090	2.32	426	−3.38	6.18	−600	0.47
343	3.00	3.82	655	1.70	460	4.30	5.64	930	3.14
347	−3.16	4.60	−640	1.82	486	3.27	4.97	650	2.72
375	2.91	3.82	640	3.7	527	−3.19	4.96	−620	0.78
422	3.60	3.80	880	0.63	574	−3.60	4.80	−760	1.23
446	3.38	4.80	700	1.40	574	3.78	4.25	850	1.80
474	2.71	3.95	560	2.83	583	−3.42	4.3	−900	2.0
356	2.97	5.30	540	1.13	588	−3.24	3.0	−900	3.2
410	4.30	5.70	930	2.57

Positive particles	Number of cases	Negative particles	Number of cases
Identified protons	4	Identified mesons \((\pi\) or \(\mu)\) . . . . . .	3
Particles with minimum ionization and with mass less than the proton mass	3	Particles with mass less than the proton mass . .	18
Particles that may be both protons and mesons . . . . .	12	Particles whose mass may be the mass of both a proton and a meson . .	8
Particles that may be protons according to the upper limit of the momentum . . . . . .	6

Photograph No. . . .	3	7	65	86
Momenta \((10^8\ \mathrm{eV}/c)\)	\(1.05 \pm 0.05\)	\(0.8 \pm 0.04\)	\(0.78 \pm 0.14\)	\(0.74 \pm 0.04\)
Measured ionization . . . . .	2–3	2–4	3–4	2.5–35
Mass \((\text{in } m_e)\) . . . .	270–430	210–380	290–370	230–330
Calculated ionization for a meson	2	2–7	2–8	3

Decay scheme	Decay scheme	Decay scheme	\(E_a\)	Theoretical	Theoretical	Experimental	Experimental
\(a\)	\(b\)	\(c\)	\(E_a\)	\(E_b\)	\(E_c\)	\(E_b\)	\(E_c\)
\(\pi\)	\(\pi\)	\(\pi\)	17.1	27.8	41.6	27.3	37
\(\pi\)	\(\pi\)	\(\mu\)	17.1	27.8	49.7	27.3	28.9
\(\pi\)	\(\mu\)	\(\pi\)	17.1	33.7	41.6	21.3	37
\(\pi\)	\(\mu\)	\(\mu\)	17.1	33.7	49.7	21.3	28.9
\(\mu\)	\(\pi\)	\(\pi\)	13.6	17.8	27.0	27.3	37
\(\mu\)	\(\pi\)	\(\mu\)	13.6	17.8	33.5	27.3	28.9
\(\mu\)	\(\mu\)	\(\pi\)	13.6	22.5	27	21.3	37
\(\mu\)	\(\mu\)	\(\mu\)	13.6	22.5	33.5	21.3	28.9

Particle number	Sign	Momentum (in MeV/\(c\))	Ionization (in units of minimum)	Mass interval (in \(m_e\))
1	\(-\)	\(160 \pm 10\%\)	\(6—10\)	\(900—1500\)
2	\(+\)	\(170 \pm 7\%\)	\(4—6\)	\(800—1000\)
3	\(+\)	\(170 \pm 10\%\)	\(5—7\)	\(900—1140\)
4	\(-\)	\(170 \pm 10\%\)	\(4—6\)	\(800—1020\)

Interpretation	Number
decays \(V^{\pm}\)	13
» \(\pi \to \mu\)	13
» \(\mu \to e\)	1
elastic scatterings	3
indeterminate	10

Name	Mass in \(m_e\)	Methods by which existence was established	Decay scheme	Decay energy in \(Mev\)	Spin	Lifetime
\(\zeta^{\pm}\)	\(580 \pm 50\)	mass spectrometer	—	—	integer	\(>5 \div 2 \cdot 10^{-9}\) sec.
\(\zeta^{\pm}\)	\(580 \pm 150\)	Wilson chamber	—	—	integer	\(>10^{-9}\) sec.
\(\zeta^{\pm}\)	\(535 \pm 35\)	photoemulsion	\(\pi^{\pm}+\pi^{0}\)	\(1\)	integer	\(>10^{-10}\) sec.
\(\zeta^{0}\)	\(556 \pm 4\)	photoemulsion	\(\pi^{+}+\pi^{-}\)	\(2\)	integer	\(\sim 10^{-14}\) sec.
\(\tau\)	\(950 \pm 70\)	mass spectrometer	—	—	integer	\(>5—2 \cdot 10^{-9}\)
\(\tau\)	\(977 \pm 5\)	photoemulsion	\(\pi^{\pm}+\pi^{+}+\pi^{-}\)	\(77 \pm 4\)	integer	\(>10^{-9}\) sec.
\(\tau\)	\(975\)	Wilson chamber	—	\(75\)	integer	\(>10^{-9}\) sec.
\(\nu^{\pm}\) \(K\)	\(1080 \pm 100\)	Wilson chamber	decays into three or more particles	—	—	\(\sim 10^{-8}\) sec.
\(\nu^{\pm}\) \(K\)	\(1080 \pm 200\)	photoemulsion	decays into three or more particles	—	—	\(>10^{-9}\) sec.
\(\chi^{\pm}\)	\(1450 \pm 100\)	photoemulsion	\(\pi^{\pm}+N^{0}\)	\(150 \pm 10\)	integer	\(>5 \cdot 10^{-10}\) sec.
\(V_{2}^{0}=N^{0}?\)	\(800—1000\)	Wilson chamber	—	\(120\)	—	\(10^{-9}—10^{-10}\)
\(V_{1}^{0}\)	\(2200 \pm 12\)	Wilson chamber	\(p^{+}+\pi^{-}\)	\(46\) \(\dfrac{35}{75}\)	half-integer	\(10^{-9}—10^{-10}\)

Energy of the primary particle	\(0\text{--}10\) Bev	\(10\text{--}50\) Bev	\(50\) Bev
\(N_{\kappa}/N_{\pi}\) . . . . . . . . . .	0.05	0.10	0.5
\(N_{\xi}/N_{\pi}\) . . . . . . . . . .	0.03	0.04	0.10