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

Abstract

AbstractI propose a two component analytic formula F(s,t)=F(1)(s,t)+F(2)(s,t) for (ab→ab)+(ab¯→ab¯) scattering at energies ≥100 GeV, where s,t denote squares of c.m. energy and momentum transfer. It saturates the Froissart–Martin bound and obeys Auberson–Kinoshita–Martin (AKM) [1,2] scaling. I choose ImF(1)(s,0)+ImF(2)(s,0) as given by Particle Data Group (PDG) fits [3,4] to total cross sections, corresponding to simple and triple poles in angular momentum plane. The PDG formula is extended to non-zero momentum transfers using partial waves of ImF(1) and ImF(2) motivated by Pomeron pole and ‘grey disk’ amplitudes and constrained by inelastic unitarity. ReF(s,t) is deduced from real analyticity: I prove that ReF(s,t)/ImF(s,0)→(π/ln⁡s)d/dτ(τImF(s,t)/ImF(s,0)) for s→∞ with τ=t(lns)2 fixed, and apply it to F(2). Using also the forward slope fit by Schegelsky–Ryskin [5], the model gives real parts, differential cross sections for (−t)<.3 GeV2, and inelastic cross sections in good agreement with data at 546 GeV, 1.8 TeV, 7 TeV and 8 TeV. It predicts for inelastic cross sections for pp or p¯p, σinel=72.7±1.0 mb at 7 TeV and 74.2±1.0 mb at 8 TeV in agreement with pp Totem [7–10] experimental values 73.1±1.3 mb and 74.7±1.7 mb respectively, and with Atlas [12–15] values 71.3±0.9 mb and 71.7±0.7 mb respectively. The predictions σinel=48.1±0.7 mb at 546 GeV and 58.5±0.8 mb at 1800 GeV also agree with p¯p experimental results of Abe et al. [47] 48.4±.98 mb at 546 GeV and 60.3±2.4 mb at 1800 GeV. The model yields for s>0.5 TeV, with PDG2013 [4] total cross sections, and Schegelsky–Ryskin slopes [5] as input, σinel(s)=22.6+.034lns+.158(lns)2 mb, and σinel/σtot→0.56, s→∞, where s is in GeV2 units. Continuation to positive t indicates an ‘effective’ t-channel singularity at ∼(1.5 GeV)2, and suggests that usual Froissart–Martin bounds are quantitatively weak as they only assume absence of singularities upto 4mπ2