Universal Rise of Hadronic Total Cross Sections based on Forward pi p and pbarp(pp) Scatterings

TL;DR

This paper empirically investigates the universal rise of hadronic total cross sections at high energies, focusing on pi p scattering, and finds results supporting the hypothesis that different hadronic processes share a common growth rate.

Contribution

It provides an empirical determination of the coefficient B for pi p scattering, supporting the universality of the total cross section rise across different hadronic interactions.

Findings

Derived B(pi p) = 0.311 ± 0.044 mb, consistent with other hadronic processes.

Supports the universality hypothesis of total cross section growth.

Uses finite-energy sum rules and data fitting to constrain high-energy behavior.

Abstract

Recently there are several evidences of the increase of the total cross section sigma(tot) to be log2 s consistent with the Froissart unitarity bound, and the COMPETE collaborations in the PDG have further assumed sigma(tot) = B log2(s/s0) to extend its universal rise with a common value of B for all the hadronic scatterings. However, there is no rigorous proof yet based only on QCD. Therefore, it is worthwhile to prove this universal rise of sigma(tot) even empirically. In this letter we attempt to obtain the value of B for pi p scattering, B(pi p), with reasonable accuracy by taking into account the rich pi p data in all the energy regions. We use the finite-energy sum rule(FESR) expressed in terms of the pi p scattering data in the low and intermediate energies as a constraint between high-energy parameters. We then have searched for the simultaneous best fit to the sigma(tot) and rho ratios, the ratios of the real to imaginary parts of the forward scattering amplitudes. The lower energy data are included in the integral of FESR, the more precisely determined is the non-leading term such as log s, and then helps to determine the leading terms like log2 s. We have derived the value of B(pi p) as B(pi p)=0.311 +- 0.044mb. This value is to be compared with the value of B for pbarp,pp scattering, B(pp), in our previous analysis[11], B(pp)=0.289 +- 0.023mb. Thus, our result appears to support the universality hypothesis.