Proton Structure in Transverse Space and the Effective Cross Section

TL;DR

The paper investigates how the proton’s transverse structure affects double parton scattering by focusing on the effective cross section $σ_{eff}$. It first analyzes the uncorrelated multiparton framework and shows that naive predictions overestimate $σ_{eff}$, motivating a correlated two-scale model that ties gluon/sea transverse size to the valence-quark configuration. This correlation lowers $σ_{eff}$ to values closer to experimental data and yields a testable prediction for the triple-scattering factor $τ$. The work underscores the importance of transverse-space correlations in hadron structure and their impact on multi-parton processes, with mild energy dependence and concrete experimental tests proposed through $τ$ measurements.

Abstract

The observation of double parton collisions by CDF has provided the first direct information on the structure of the proton in transverse space. The actual quantity which has been measured is the `effective cross section' $σ_{eff}$, which is related to the transverse size of the region where hard interactions are localized. The actual value which has been measured is sizably smaller than naively expected and it is an indication of important correlation effects in the many-body parton distribution of the proton. We discuss the problem pointing out a possible source of correlations in the proton structure, which could have a significant effect on the value of $σ_{eff}$.

Figures (2)

• Figure 1: $\sigma_S$, $\sigma_H$ and $\sigma_{eff}$ in the simplest uncorrelated case. The two curves for $\sigma_H$ and $\sigma_{eff}$ refer to the two different choices made for $f({\bf b})$, a gaussian (higher curve) and a sphere (lower curve).
• Figure 2: $\sigma_S$, $\sigma_H$ and $\sigma_{eff}$ when taking for $f({\bf r})$ a sphere a) or a gaussian b). The lower curves for $\sigma_H$ and $\sigma_{eff}$ refer to the correlated many-body parton distribution, the higher curves to the uncorrelated ones.