$K$- and $\tau$-Particles

A report has recently been published on the observation in photographic emulsions of cosmic particles with mass $\sim 1200\,m_e$ ($K$-particles); new confirmations have also been obtained of the existence of $\tau$-mesons (mass $\sim 1000\,m_e$).

In the studies Ilford G-5 photographic emulsions of thickness $400\,\mu$ were used. The plates were exposed at an altitude of $3300\,m$ (Jungfrau), under $30\,cm$ of Pb.

$K$-particles

The author1 studied the energy distribution of electrons arising in the decay of $\mu$-mesons ($\mu \to e$ decay). In one case the energy of the decay electron proved to be anomalously large, equal to $\sim 240$ MeV. This prompted the author to study this decay event in detail and to make a special measurement of the particle masses.

Figure 1 presents a microphotograph of the decay: the primary particle $K_1$ comes to rest in the emulsion; at the point where it stops (point $P$), the track of a weakly ionizing particle begins. The length of the track of the primary particle in the emulsion is more than $4000\,\mu$. To determine the mass, the mean angles of multiple scattering and the range–grain-density relation were measured as functions of the residual range of the particle. Determination of the mass from these

Fig. 1.

data was carried out by various independent methods developed earlier[^2][^3][^4]. The mean value of the mass proved to be

\[ m_{K_1} = (1320 \pm 170)\,m_e . \]

The secondary, weakly ionizing particle leaves in the emulsion a track 2200 μ long. The grain density and the value of \(p\beta\) (estimated from the mean angle of multiple scattering) are such that the particle should be assigned a mass smaller than \(400\,m_e\).

Another case of decay of a heavy particle is shown in the microphotograph of Fig. 2. Here two successive decays are observed at point \(P\) and at point \(Q\). At first sight it might appear that this is an ordinary \(\pi \to \mu \to e\) decay. As is known, in the decay of a stopped \(\pi\)-meson a \(\mu\)-meson with a range \(\sim 590\) μ is produced. The measured range, however, proved to be 1098 μ. The assumption that a \(\pi\)-meson decays in flight here is unlikely, since the decay \(\mu\)-meson flies out almost in the opposite direction.

Therefore the author specially measured the masses of the primary and secondary particles (by the same methods as in the first case). The length of the track of the primary particle in the emulsion is \(\sim 5800\) μ, and its mass proved to be

\[ m_{K_2} = (1125 \pm 140)\,m_e . \]

The mass of the secondary particle is \(200\)—\(300\,m_e\), i.e. it is either a \(\pi\)- or a \(\mu\)-meson; it is more probable, however, that the secondary particle is a \(\mu\)-meson, since at the end of its range (point \(Q\)) it gives a decay particle—most likely an electron; the emission of electrons directly in the decay of \(\pi\)-mesons has not been observed anywhere.

The accuracy of the mass determinations is insufficient for asserting that in both cases considered there is decay of heavy particles of identical mass, i.e. that \(m_{K_1}=m_{K_2}\). If the particles \(K_1\) and \(K_2\) are identical, then their decay must be accompanied by the emission of at least two neutral particles (since the energy of the decay \(\mu\)-mesons is different in the two cases). If, however, \(K_1\) and \(K_2\) are different, then it is possible that the \(K\)-decay is accompanied by the emission of a single neutral particle; then its mass can be readily estimated, knowing the mass and momentum of the charged particles. For the case \(K_2\) the mass of the neutral particle proves to be \(900 \pm 130\,m_e\). In the case \(K_1\) the uncertainty in determining the momentum of the secondary particle is so large that the data do not contradict the emission of any of the neutral particles \(\nu\) (neutrino), \(\pi^0\), or \(V_0\) \((800\,m_e)\).

The inaccuracy of the mass determinations is such that it is also impossible to assert categorically that the mass of the \(K\)-particles is not equal to the mass of the \(\tau\)-meson (see below). The experimental data, nevertheless, apparently contradict the assumption of equality of these masses.

In addition to the cases \(K_1\) and \(K_2\), two more \(K\)-particles were observed, but their masses could not be accurately estimated because of unfavorable geometrical conditions.

To clarify the nature and to determine accurately the mass of the \(K\)-particles, further investigations are necessary.

\(\tau\)-meson

In 1949 and 1950 cases were first described[^5][^6] in which a charged cosmic particle with mass \(\sim 1000\,m_e\) stops in a photographic emulsion and decays into three charged particles, most probably \(\pi\)-mesons.

Recent works[^7][^8] give new evidence for the existence of such heavy particles (the so-called \(\tau\)-mesons).

Fig. 2.

In the microphotograph of Fig. 3 a case described in paper \(^{7}\) is shown. The primary particle \(\tau\) stops at the point \(P\). From this point the tracks of three new particles \(a, b, c\) diverge; the ends of the tracks are outside the emulsion.

The length of the track of the primary particle \(\tau\) in the emulsion is \(2070\,\mu\). Its mass, determined from measurements of the mean angles of multiple scattering as a function of the residual range, proved to be equal to \((1015 \pm 280)m_e\). A more exact value of the mass, \((1000 \pm 180)m_e\), was obtained by using measurements of the gaps between the grains of the emulsion.

The lengths of the tracks of the secondary particles \(a, b, c\) in the emulsion are \(6400\,\mu\), \(120\,\mu\), and \(490\,\mu\), respectively. As in the preceding papers, the initial directions of motion of the secondary particles were collinear within the experimental errors; therefore with high probability one may consider that the three observed particles are the only decay products of the \(\tau\)-meson. The authors succeeded in estimating the kinetic energies of the secondary particles and, hence, independently—the mass of the primary \(\tau\)-meson.

The great length of the track \(a\) made it possible to estimate the mass of the particle (from the grain density and the scattering parameter), which proved to be \((285 \pm 20)m_e\). Most probably this is a \(\pi\)-meson. Its energy was determined by the following method:

the mean scattering angles and the grain density were measured for different sections along the trajectory \(a\); from comparison of these data with similar data for \(\mu\)-mesons and protons it was possible to conclude that the range of the particle outside the emulsion is about \(400\,\mu\), and consequently its total range is \((6800 \pm 200)\,\mu\).

Using the range–energy relation for protons \(^{9,10}\), it was easy to determine the energy of a particle with mass \(274m_e\) (the most exact value of the mass of the \(\tau\)-meson) having a range of \(6800\,\mu\). The value obtained for the energy was \((19.0 \pm 0.4)\) MeV, which corresponds to a momentum of \(75.4\,\dfrac{\text{MeV}}{c}\).

The momenta of the particles \(b\) and \(c\) are determined from the condition that the sum of the momenta of all three particles is zero. The momentum of \(b\) is \((85.8 \pm 1)\,\dfrac{\text{MeV}}{c}\), the momentum of \(c\) is \((98.3 \pm 1)\,\dfrac{\text{MeV}}{c}\). From the momenta and the grain density of the trajectory, the masses of the particles were estimated as \(m_b = (240 \pm 30)m_e\) and \(m_c = (280 \pm 15)m_e\).

The authors indicate that the conditions of observation of track \(b\) are such that the value \(m_b\) should be considered underestimated and, consequently, the value of the mass obtained agrees with the idea that the primary particle decays into three \(\pi\)-mesons.

An independent determination of the relative magnitude of the masses of the secondary particles on the basis of measurements of the angles between the trajectories and of the grain density also led to the conclusion that they are equal within the errors of measurement.

The kinetic energies of \(b\) and \(c\) (determined from the momentum and mass) are \((24.2 \pm 2.0)\) MeV and \((32.0 \pm 2.0)\) MeV, respectively, and the total energy of the three emitted particles is \((75.2 \pm 5.0)\) MeV.

The results of determining the kinetic energies of the secondary particles are collected in the table (see p. 136).

Here cases 1 and 2 are taken from papers \(^{5,6}\), but recalculated with account of the more exact value \(m_{\pi} = 274m_e\).

The mass of the primary particle, estimated on the basis of the adopted scheme of decay into three \(\pi\)-mesons and the obtained value of their total kinetic energy \((73.5 \pm 4)\) MeV, is equal to \(m_{\tau} = (966 \pm 8)m_e\).

The same value of the total kinetic energy of the secondary particles \((73.5 \pm 7)\) MeV and of the mass \(m_{\tau}\) was obtained in the last paper \(^{8}\).

Fig. 3.

The entire body of the data presented confirms the stated point of view on the nature of the decay. It cannot, however, be asserted categorically that no neutrino or weak $\gamma$-radiation arises in the decay.

Total kinetic energy (in MeV) of the decay particles
(it is assumed that all three particles are $\pi$-mesons)

energy. A neutrino with an energy of 10 MeV would cause a deviation from the coplanarity of the tracks of the three charged particles by $\sim 3^\circ$, which is within the limits of accuracy of the angle measurements in the experiments.

In papers$^{1,7}$ four $K$-particles and one $\tau$-meson were recorded in the same emulsion volume in which 750 $\pi$-mesons were recorded. Consequently,

\[ \frac{N_{K,\tau}}{N_\pi} = \frac{1}{150}, \]

where $N_{K,\tau}$ is the total number of $K$- and $\tau$-particles, and $N_\pi$ is the number of $\pi$-particles.

In the same laboratory, Camerini et al.$^{11}$ showed that in nuclear reactions caused by protons with energy $E$ in the interval 2–10 Bev, the amount of energy released in the form of $\pi$-mesons is approximately proportional to $E$.

Let us assume, first, that at proton energies $E > 10$ Bev the same fraction of energy goes into the formation of $\pi$-mesons and that, in addition to $\pi$-mesons, $K$-, $\tau$-mesons are also produced; second, that the proton energy is distributed among $\pi$-particles, on the one hand, and $K$-, $\tau$-particles, on the other; third, that in the center-of-inertia system of the interacting nuclear particles the produced $K$- and $\tau$-particles have a distribution in velocities and angles similar to that found for $\pi$-mesons; knowing the energy distribution of fast protons and neutrons at a given altitude ($\sim 3300$ m), one may calculate the expected ratio

\[ \frac{N_{K,\tau}}{N_\pi}. \]

It turns out to be equal to

\[ \frac{1}{75}, \]

i.e. a quantity of the same order as that observed. (The discrepancy by a factor of two with the observed ratio can quite well be explained by the fact that $K$-particles are very difficult to identify against the background of $\mu$-mesons, which are almost a thousand times more numerous; some $K$-particles, therefore, may escape observation.)

The authors regard this as confirmation of the hypothesis that, in nuclear transformations caused by nucleons with energy $>10$ Bev, a significant part of the energy goes into the formation of $K$- and $\tau$-particles.

From the postulated distribution in velocities and in the number of observed events in the experiment with \(K\)- and \(\tau\)-particles (5 particles), the conclusion is drawn that their lifetime is not less than \(10^{-9}\) sec.

As to the sign of the charge of the \(K\)- and \(\tau\)-particles, no conclusion can yet be drawn.

Obviously, the frequency of registration of \(K\)- and \(\tau\)-particles should increase at high altitudes, where there is a larger number of protons and neutrons with energies \(\gg 10\) Bev; it is worthwhile to carry out observations at low latitudes (less than \(40^\circ\)), since the background from extraneous particles generated by protons of lower energies is reduced there (at low latitudes, owing to the Earth’s magnetic field, protons with energies greater than \(\sim 5\) Bev enter the atmosphere).

In Refs. \(^{6,8}\) the plates were exposed under ice, and the author of Ref. \(^{8}\) considers that, among hydrogen-containing substances, a larger yield of \(\tau\)-particles is observed than from other elements.

At the present time, apparently, the existence of cosmic particles with mass \(\sim 1000\,m_e\), decaying into three charged particles (apparently \(\pi\)-mesons), may be regarded as established. For a comprehensive study of the nature of these heavy particles, further investigations are necessary.

As for \(K\)-particles, the data obtained on their existence should be regarded as preliminary, requiring confirmation and refinement.

M. D.

CITED LITERATURE

1. O’Ceallaigh C., Phil. Mag. 42, 1032 (1951).
2. Hodgson, Phil. Mag. 41, 725 (1950).
3. Menon and Rochat; reference in \(^{1}\) to unpublished work.
4. Perkins, cf. Lattes, Occhialini and Powell, Proc. Phys. Soc. 61, 178 (1948).
5. Brown, Camerini, Fowler, Muirhead, Powell and Ritson, Nature, 163, 82 (1949).
6. Harding, Phil. Mag. 41, 405 (1950).
7. Fowler, Menon, Powell and Rochat, Phil. Mag. 42, 1040 (1951).
8. Hodgson, Phil. Mag. 42, 1060 (1951).
9. Lattes, Fowler and Cuer, Proc. Phys. Soc. 59, 883 (1947).
10. Brander, Smith, Barkas and Bishop, Phys. Rev. 77, 462 (1950).
11. Camerini et al., 1951; reference in \(^{7}\) to unpublished work.