Multiple Hard Partonic Collisions with Correlations in Proton-Proton Scattering

TL;DR

The paper addresses unitarity tensions in modeling multiple hard partonic collisions by introducing correlations in the impact-parameter space using gluon GPD-derived overlap functions and sigma_eff constraints. It develops an analytic framework to include double and higher-order partonic correlations through parameters like $\eta_4(s)$ (and $\eta_6$, $\eta_8$, etc.), deriving corrected expressions for the inelastic hard-dijet profile function. Numerical studies show that modest correlations bring the hard contribution into better agreement with expectations for the total inelastic pp cross section at LHC energies, particularly for a fixed $p_t^c$ around 2.5 GeV. The work also discusses tests of the impact-parameter dependence of correlations and outlines paths to refine the approach with more data, aiming to improve simulations and our understanding of the proton’s transverse structure. Overall, incorporating correlations provides a more consistent, data-driven description of multi-parton scattering relevant for high-energy collider phenomenology.

Abstract

We propose a simple method for incorporating correlations into the impact parameter space description of multiple (semi-)hard partonic collisions in high energy hadron-hadron scattering. The perturbative QCD input is the standard factorization theorem for inclusive dijet production with a lower cutoff on transverse momentum. The width of the transverse distribution of hard partons is fixed by parameterizations of the two-gluon form factor. We then reconstruct the hard contribution to the total inelastic profile function and obtain corrections due to correlations to the more commonly used eikonal description. Estimates of the size of double correlation corrections are based on the rate of double collisions measured at the Tevatron. We find that, if typical values for the lower transverse momentum cutoff are used in the calculation of the inclusive hard dijet cross section, then the correlation corrections are necessary for maintaining consistency with expectations for the total inelastic proton-proton cross section at LHC energies.

Figures (11)

• Figure 1: Schematic depiction of a double hard collision. A disconnected pair of partons from each proton collide to produce a pair of high transverse momentum dijets.
• Figure 2: Momentum labels for $pp$ scattering.
• Figure 3: Graphical representation of the term in the series for uncorrelated scattering --- the first three terms in the second line of Eq. (\ref{['eq:profile']}), assuming no correlations. Spectator partons are not shown.
• Figure 4: Graphical representation of the extra contribution $(-1 /2) \eta_4(s) \chi_2(s,b;p_t^c)^2$ due to double partonic correlations in Eq. (\ref{['eq:doublecorr']}).
• Figure 5: Graphical representation of the extra contribution to the $n=3$ term of Eq. (\ref{['eq:profile']}) due to double partonic correlations.