Scale Factor in Double Parton Collisions and Parton Densities in Transverse Space

TL;DR

This work analyzes double parton scattering and the scale factor $σ_{eff}$ as a probe of transverse parton distributions. It adopts a correlated multi-parton density framework distinguishing valence and sea/gluon partons, deriving expressions for the double scattering cross section via geometric coefficients $Θ^{ij}_{kl}$. The study predicts nonuniversal $σ_{eff}$ across final states and finds energy-dependent variations from Tevatron to LHC, with robustness to PDF choice. The results suggest measuring $σ_{eff}$ in different channels can constrain the proton's 3D transverse structure and the correlations among partons in transverse space.

Abstract

The scale factor $σ_{eff}$, which characterizes double parton collisions in high energy hadron interactions, is a direct manifestation of the distribution of the interacting partons in transverse space, in such a way that different distributions give rise to different values of $σ_{eff}$ in different double parton collision processes. We work out the value of the scale factor in a few reactions of interest, in a correlated model of the multi-parton density of the proton recently proposed.

Figures (2)

• Figure 1: $\sigma_{eff}$ as a function of the c.m. energy in various processes in $pp$ collisions.
• Figure 2: $\sigma_{eff}$ as a function of the c.m. energy in various processes in $p{\bar{p}}$ collisions.