Vol. 21, No. 11 (1965)
1965, 116 (11): 1831-1872. doi: 10.7498/aps.21.1831
This paper intends to give a comprehensive survey of the development in the experimental study of "elementary particles" during the last four or five years. However, the most part of the paper has been devoted to the strongly interacting particles, bringing into discussion only a few problems concerning the weak interaction. The main reason for doing so is this: It is in the area of the strongly interacting particles that there has been in these years a rapid and large accumulation of newly discovered facts, that is, the resonant states of particles, quickly bringing the total number of particles from about 30 to about 100; moreover, in the corresponding theoretical aspect, there is also up to now a more or less successful development, that is, the SU(3) classification scheme as proposed from the symmetry of strong interaction. Simply because of these new developments, we are now more than ever certain that the so-called elementary particles are not elementary but composite, i.e. having internal structure (at least as far as the strongly interacting particles are concerned). This point has been discussed in some detail in the "Introduction". The paper then summari2es and discusses seven groups of experiments which have been performed in the last four or five years and are considered as more important in the field of "elementary particles", four groups being concerned with the strong interaction while three groups with the weak interaction. After this, discussion has been concentrated on the recent development of the strongly interacting particles, on the status of statistics before and after 1960, and on the physical meaning of the particle classification, etc. It is hoped that this will provide a physical background for discussing the classification schemes of SU(3) and the Regge trajectories. Finally, in discussing the two classification schemes, particularly the SU(3) scheme, effort has been made to explain with as much clarity as possible the physical background and the conjecture made, the mathematical basis, the theoretical results, and comparison with experiment. Comparison with experiment shows that the Regge trajectory scheme is not at all as satisfactory as the SU(3) scheme, this being naturally related with the serious difficulty as revealed by experiment (cf. Section II.3) of the theory of Regge poles. It is hoped that this paper may present a general picture of the recent development of "elementary particles", probably showing what problems have become clear and what still have not, and may possibly indicate the direction of future experimental research.
This short paper studies the motion of the poles in the first and the second sheets of the scattering amplitude in the Lee model as the coupling constant g2 changes. It is proved that, with or without the left hand cut, with or without the inelastic cut, the theory does not permit the occurrence of poles in the second sheet representing resonances unless the CDD poles are introduced for the inverse amplitude.When the left hand cut is present and the CDD poles are introduced, a pole representing resonance may slip across the normal cut (near the right threshold) into the first sheet as the coupling constant g2 increases. But before this occurs, another pole slips into the first sheet across the left hand cut (near the left threshold). Motion of poles in the two sheets is plotted for one such special case.When the left hand cut is absent and the CDD poles are not yet introduced, it is pointed out that no passage of poles of one sheet into another sheet is possible so long as g2>0. When the CDD poles are introduced, such passage becomes possible. It is shown that if a pole in the second sheet slips across the normal cut on increasing g2 beyond a certain value g12>0, then before g2 reaches this value, another pole enters the first sheet at-∞. Needless to say, poles entering from the left usually provide ghosts.These general features are believed to hold for field-theoretical models in general.
1965, 116 (11): 1889-1896. doi: 10.7498/aps.21.1889
Basing on the dispersion relation, an approximate method is suggested to obtain the scattering amplitudes. In principle we can apply this method to the study of the amplitude behaviour of low and high energy scattering. For high energy π±p, K±p, pp, and pp scattering, the primary comparison with experiments is made by two parameters. It is found that the theory agrees with experiments.
From the requirements of analyticity and unitarity, the resonance behaviours of the partial wave amplitudes for π-π scattering are discussed in general. The theory involves a function F(l)I)(v), which indicates deviation from the Breit-Wigner type resonance formula. When F(l)I)(v)=1, the amplitude has exactly the Breit-Wigner form. Further investigation shows that the function F(l)I)(v) in general deviates from 1. By use of the ND-1 method, the crossing symmetry and the ρ- and f0-bootstrap approximation, by comparing with the integral expression of the partial wave amplitude for the interval -90 are calculated. The method takes into account both the contributions of the inelastic process and the dispersion integral of the negative interval. The calculation gives v(R1)=6.4,Г1=0.12 for the J=1, I=1 state and v(R2)=20, Г2=0.016 for the J=2, I=0 state. These results correspond to a mass of 762 MeV and a half-width of about 45 MeV for the ρ meson, and a mass of 1283 MeV for the f0 meson. They are in good agreement with recent experimental data.