Pomeron pole plus grey disk model: real parts, inelastic cross sections and LHC data

Abstract

I propose a two component analytic formula $F(s,t)=F^{(1)}(s,t)+F^{(2)}(s,t)$ for $(ab\to ab)+(a\bar{b}\to a\bar{b})$ scattering at energies $\ge 100GeV$ ,where $s,t$ denote squares of c.m. energy and momentum transfer.It saturates the Froissart-Martin bound and obeys Auberson-Kinoshita-Martin (AKM) \cite{AKM1971} scaling. I choose $Im{F}^{(1)}(s,0)+Im{F}^{(2)}(s,0)$ as given by Particle Data Group (PDG) fits to total cross sections. The PDG formula is extended to non-zero momentum transfers using partial waves of $Im{F}^{(1)}$ and $Im{F}^{(2)}$ motivated by Pomeron pole and 'grey disk' amplitudes . $ReF(s,t)$ is deduced from real analyticity: I prove that $ReF(s,t)/ImF(s,0)\to (\pi /\ln s)d/d\tau (\tau ImF(s,t)/ImF(s,0))$ for $s\to \infty$ with $\tau =t(lns{)}^2$ fixed, and apply it to $F^{(2)}$.Using also the forward slope fit by Schegelsky-Ryskin , the model gives real parts,differential cross sections for $(-t)<.3Ge{V}^2$, and inelastic cross sections in good agreement with data at $546GeV,1.8TeV,7TeV$ and $8TeV$. It predicts for inelastic cross sections for $pp$ or $\bar{p}p$, ${\sigma }_{inel}=72.7\pm 1.0mb$ at $7TeV$ and $74.2\pm 1.0mb$ at $8TeV$ in agreement with $pp$ Totem experimental values $73.1\pm 1.3mb$ and $74.7\pm 1.7mb$ respectively, and with Atlas values $71.3\pm 0.9mb$ and $71.7\pm 0.7mb$ respectively. The predictions at $546GeV$ and $1800GeV$ also agree with $\bar{p}p$ experimental results of Abe et al \cite{Abe} at $546GeV$ and $1800GeV$. The model yields for $\sqrt{s}>0.5TeV$, with PDG2013 total cross sections , and Schegelsky-Ryskin slopes as input, ${\sigma }_{inel}(s)=22.6+.034lns+.158(lns{)}^{2}mb,and{\sigma }_{inel}/{\sigma }_{tot}\to 0.56,s\to \infty ,$ where $s$ is in $Ge{V}^2$

Comments: 6 pages, 5 figures, 2 tables