An upper bound on the total inelastic cross section as a function of the total cross section

Tai Tsun Wu,André Martin,Virendra Singh,Shasanka Mohan Roy

doi:10.1103/physrevd.84.025012

Abstract

Recently, Andr\'e Martin has proved a rigorous upper bound on the inelastic cross section${\ensuremath{\sigma}}_{\mathrm{inel}}$ at high energy, which is one-fourth of the known Froissart-Martin-Lukaszuk upper bound on ${\ensuremath{\sigma}}_{\mathrm{tot}}$. Here, we obtain an upper bound on ${\ensuremath{\sigma}}_{\mathrm{inel}}$ in terms of ${\ensuremath{\sigma}}_{\mathrm{tot}}$ and show that the Martin bound on ${\ensuremath{\sigma}}_{\mathrm{inel}}$ is improved significantly with this added information.

Highlights

The total cross-section σt√ot(s) for two particles to go to anything at c.m. energy s must obey the FroissartMartin bound, σtot(s) ≤s→∞ C [ln(s/s0)]2 (1)proved at first from the Mandelstam representation by Froissart [1] and later from the basic principles of axiomatic field theory by Martin [2]
The Froissart-Martin bound has been seminal both to the development of the field of high energy theorems in axiomatic field theoryand to that of phenomenological models leading to accurate predictions of total and elastic cross sections before their experimental measurem ents [7]
M.) has recently obtained a bound on the total inelastic cross section at high energy [8], σinel(s) ≤s→∞ π/t0 [ln(s/s0)]2, (4)

Summary

Introduction

The total cross-section σt√ot(s) for two particles to go to anything at c.m. energy s must obey the FroissartMartin bound, σtot(s) ≤s→∞ C [ln(s/s0)]2. The Froissart-Martin bound has been seminal both to the development of the field of high energy theorems in axiomatic field theory (see e.g. the review [6])and to that of phenomenological models leading to accurate predictions of total and elastic cross sections before their experimental measurem ents [7]. M.) has recently obtained a bound on the total inelastic cross section at high energy [8], σinel(s) ≤s→∞ π/t0 [ln(s/s0)]2,. The present paper is inspired by Martin’s bound on the inelastic cross-section. Maximizing wth respect to σtot we get the factor 1/4 announced at the beginning of this paper,i.e. In Sec. 2 we summarise our notations and recall the basic results from axiomatic field theory. Bounds on energy averages will be considered later to avoid this restriction

Basic Results from Axiomatic Field Theory

Variational Bound on Inelastic Cross-section in terms of Total Cross-section

Conclusion