Upper bounds on the Elastic differential cross section

Singh, Virendra ; Roy, S. M. (1970) Upper bounds on the Elastic differential cross section Annals of Physics, 57 (2). pp. 461-480. ISSN 0003-4916

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0003-4916(70)90361-1


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→∝σel/4φ {(L+1)2[PL(cos θ)]2 + sin2θ[PL'(cos θ)]2} with L=½ √S/t0In s/σel), 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 √t0 , 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→∝ σel/4t0[ In (s/σel)]22. (ii) for fixed θ ≢ 0, π (dσ/dω (s;cosθ) ≤s→∝ 1/4φ2√s/t0 σel/sinθ In) s/σel and 3. (iii) for fixed negative t,dσ/dω (s;t) ≤s→∝ 1/8φ√t0 s/√ −tσel In (s/σel)We also give an upper bound on differential cross section involving the diffraction peak width but not having an explicit ln s dependence.

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