A consideration of the two-channel problem consisting of 7777 and TTOO in the J p = 1"*, T = 1 state leads to interesting effects in the process 77 + 7r-77 + a). 1 One finds that a peak will occur in the iroo effective mass at 1200-1300 MeV. This is near the observed J3-meson mass. There has been some doubt in the past as to whether the 1220-MeV TTCO bump was a bona fide resonance, due to a variety of ways of producing such a bump kinematically. 2 This paper presents another "kinematic" effect leading to a TTOJ enhancement around 1220 MeV.
The antiproton-nucleon system at rest and its annihilation are discussed. Final states of two mesons, of many mesons with all but one in a vector resonance, and of two vector resonances are the main concern, al though the decay to lepton pairs and other properties of the ;p-nucleon system are also considered. The basic assumptions are that annihilations proceed mainly through an intermediate vector meson (^^i decay) or pseudoscalar meson p5o decay) and also that SU{3) symmetry is vaUd for obtaining unknown coupling constants. The unknown parameters in the SU(3) couplings are determined by fitting to experiment, with the following interesting results: gpNN^gwNN and gn*NN^-'2girNNi where ry* refers to the 960-MeV rjirir resonance, and the above coupling constants for the p and со are the sum of the уц and a^vq^ coefficients. gpNN'^gaNN at 52= -4mjv^ is shown to be consistent with nuclear-force calculations around ?^=0, and the above value for g,*^-j^helps explain the rapid increase with energy of the proton Compton-scattering cross section. The SU(3) EBV interaction is determined from the rates for ^^i annihilations of pp to ir^ifir^, тг^тГ, K'^K", and K\K2, the VVP coupling from w -> Зтг and ф -^ Зтг, and the BBP interaction from the ^SQ decays of pp to K^R*, pYy and />V. We discuss briefly the relation of the SU{S) coupUngs determined here and the results of broken SU{6) and U{12). In particular, we show that d/f^l for BBV at §2= ~4m^, in contradiction to the value | given by SU{6) and U{X2); we also conclude that the d/f ratio is not constant for the BBV coupling. A table of relative rates and graphs of expected mass spectra are given for final states consisting of a vector resonance plus pseudoscalar meson, and a comparison with the available experi mental evidence is made. The approximate agreement expected is observed. The discussion of the vectorvector final states leads to the prediction that Т(рр-^р^р^)^Т{рр->са^оз^), and we also determine that (pp -»e'^e~)/(pp ->• ir+TT") »2X 10-5. Finally we conclude that the assumptions made are thus far consistent with experiment. ^ The proposition that the deuteron ought to be regarded as a bound state of proton and neutron has had public debate. See S. Weinberg, Phys. Rev. 137, B672 (1965).
We derive an integral equation which should describe, to a good approximation, the results of any theory of the K and rj 3ir decays. We show that present experimental information implies that one subtraction in this equation is not enough; instead, we find that two subtractions are necessary in order for the equation to describe experiment correctly. We then observe the striking fact that for the weak (K) and electromagnetic (rj) decay processes leading to a 3ir final state, the subtraction constants are identical, up to an over-all normalization. A short discussion of the possible significance of this is given, although no definite conclusions are reached. Our analysis confirms the suggestion that mr final-state interactions will appear only in quadratic terms in the 3-?r final state.
A set of axioms and a formalism is presented for handling units and dimensions. Using the axioms, one form of the II theorem is proved simply and rigorously; also, two often debated questions are given definitive answers, both in the affirmative: (1) Are transcendental functions of a dimensional quantity legitimate? (2) Are the laws of physics always expressible in a form invariant under transformations of units?
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