The elastic differential pp cross-section at 13 TeV: an empirical model analysis

Simone Pacetti,A.H Chan,K.K Phua,Giulia Pancheri,Yogendra N Srivastava,W.Y Wang,Agnes Grau,C.H Oh,S.C.C Ng,A Yang

doi:10.1051/epjconf/201920606003

Abstract

We discuss the differential elastic pp cross-section data measured at 13 TeV, through the Coulomb Nuclear Interference region until past the dip. We show that data are consistent with the asymptotic predictions from an empirical model and examine the presence of a zero for the real part of the elastic amplitude near the Coulomb region, well before the dip.

Highlights

The TOTEM group has produced a remarkably precise determination of the proton-proton elastic nuclear amplitude at LHC energies [1,2,3,4]
The unexpectedly low value of ρ ∼ (0.9 ÷ 0.1) measured by TOTEM at 13 TeV, have pointed to a possible “anomaly”: If the Froissart limit is saturated, that is if σtot (s) ∼ L2(s) for large L >> 1, where L = ln(s/so), Khuri-Kinoshita theorem[6] forces ρ(s) ∼ π/L(s)
We assume s0 = 1 GeV 2, in the analysis presented here, following the old convention of early asymptotic particle physics and the scale here is not a free parameter

Summary

Introduction

The TOTEM group has produced a remarkably precise determination of the proton-proton elastic nuclear amplitude at LHC energies [1,2,3,4]. Through the Coulomb nuclear interference (CNI) at very small momentum transfer, TOTEM has reported direct measurements of the ρ parameter We have data for the modulus (through the elastic differential cross-section) and the phase (through CNI) of the near forward nuclear amplitude. The unexpectedly low value of ρ ∼ (0.9 ÷ 0.1) measured by TOTEM at 13 TeV, have pointed to a possible “anomaly”: If the Froissart limit is saturated, that is if σtot (s) ∼ L2(s) for large L >> 1, where L = ln(s/so), Khuri-Kinoshita theorem[6] forces ρ(s) ∼ π/L(s). The old debate has been considerably fuelled by the recent TOTEM data

The asymptotic empirical model for the differential elastic cross-section

The Coulomb interference region

The structure outside the Coulomb region

The total cross-sections

Acnowledgments and conclusions