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 → ab) + (a b bar → a b bar) 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 Im^{F (1)} (s , 0) + Im^{F (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 Im^{F (1)} and Im^{F (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 bar p, σ_inel = 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 σ_inel = 48.1 ± 0.7 mb at 546 GeV and 58.5 ± 0.8 mb at 1800 GeV also agree with p bar 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, σ_inel (s) = 22.6 + . 034 lns + . 158^{(lns) 2} mb, and σ_inel /σ_tot → 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 4m_π²