Upper bounds on the elastic differential cross section

Abstract

We derive improved axiomatic upper bounds on the elastic unpolarized differential cross section, dσ dΩ , at high energies for the scattering of particles with arbitrary spin. We prove that dσ dω ⩽ s→∞ σ el 4φ {(L+1) 2[P L(cos θ)] 2+sin 2θ[P L′(cos θ)] 2} with L= 1 2 S t o In s σ el ), where s and t are, respectively, the squares of the c.m. energy and the c.m. momentum transfer; θ is the c.m. scattering angle. Further t o , is the mass of the lowest mass state that couples to the crossed t-channel (being equal to twice the pion mass for ππ and πN scattering). This result has the following important consequences: 1. (i) for forward scattering, dσ dt t=0 ⩽ s→∞ σ el 4t 0 In s σ el 2 2. (ii) for fixed θ ≠ 0, π, dσ dω (s;cosθ) ⩽ s→∞ 1 4φ 2 s t 0 σ el sinθ In s σ el and 3. (iii) for fixed negative t, dσ dω (s,t) ⩽ s→∞ 1 8φ t 0 s −t σ el In s σ el We also give an upper bound on differential cross section involving the diffraction peak width but not having an explicit ln s dependence.