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

Article history: Received 18 June 2016 Received in revised form 2 November 2016 Accepted 15 November 2016 Available online 18 November 2016 Editor: J.-P. Blaizot I propose a two component analytic formula F (s, t) = F (1)(s, t) + F (2)(s, t) for (ab → ab) + (ab̄ → ab̄) 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 (τ ImF (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 p̄p, 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 p̄p 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 4mπ . © 2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.