# Froissart bound on inelastic cross section without unknown constants

Martin, André ; Roy, S. M. (2015) Froissart bound on inelastic cross section without unknown constants Physical Review D - Particles, Fields, Gravitation and Cosmology, 91 (7). Article ID 076006. ISSN 1550-7998

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Related URL: http://dx.doi.org/10.1103/PhysRevD.91.076006

## Abstract

Assuming that axiomatic local field theory results hold for hadron scattering, André Martin and S. M. Roy recently obtained absolute bounds on the D wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section σinel which is one-fourth of the corresponding upper bound on σtot, and Wu, Martin, Roy and Singh improved the bound by adding the constraint of a given σtot. Here we use unitarity and analyticity to determine, without any high-energy approximation, upper bounds on energy-averaged inelastic cross sections in terms of low-energy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms, together with the Martin-Roy absolute bounds on pion-pion D waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. For example, for π0π0 scattering, defining σinel=σtot(σπ0π0π0π0+σπ0π0π+π), we show that for c.m. energy s, σ¯inel(s,)ssdsσinel(s)/s'2(π/4)(mπ)2[ln(s/s1)+(1/2)lnln(s/s1)+1]2 where 1/s1=34π2πm2π. This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor s1 is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic π0π0 cross section has a bound of the same form with 1/s1 replaced by 1/s2=2/s1.

Item Type: Article Copyright of this article belongs to The American Physical Society. 99292 26 Feb 2016 09:23 26 Feb 2016 11:20

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