Fixed angle behavior in four point dual models. I. Absolutely convergent series of beta functions
Syracuse Univ., N. Y. Dept. of Physics. Tata Inst. of Fundamental, Bombay (India), C Gardiner · 1973
The large s fixed angle asymptotic behavior of scattering amplitudes of the form 44 T(s,t,u) = A(s,t) + A(s,u) + A(u,t) 00 with A(s,t) = I Ch B[h-a(s), h-a(t)] h=0 is studied.We find that the asymptotic behavior is determined 00 by the function F(z) = I Chz.h h=0 If F(z) is entire, the Veneziano fixed angle behavior is preserved.If F(z) is singular at z=A, A real and larger than one, a different, but still exponentially damped, fixed angle behavior is produced around the forward and backward regions.If X=l, we find power law behavior, or asymptotic behavior that decreases faster than any power of s, but slower than any exponential.This behavior is found to be a slowly varying function of scattering angle, and is therefore probably unphysical.We find, in particular, that the models of Mandelstam and Frampton have power law fixed angle behavior with the power independent of angle.The same is true of the model at Gervaisand Neveu, unless their choice ao=-i: is made.We consider there- fore, that the first two of these models are unacceptable physically.The model of Neveu and Schwarz, however, does have the usual Veneziano fixed angle behavior.-We also comment on the work of Ellis and Freund, pointing out that their statement that linearly-ris ing trajectories necessarily give rise to exponentially damped transverse momentum distributions must be incorrect, the models of Mandelstam, etc. being counterexamples.