Analytical asymptotics for hard diffraction

TL;DR

This paper derives an analytical expression for the gap distribution in hard diffraction, linking it to a classical probabilistic process involving color dipole branchings, and highlights the role of multiple dipole interactions.

Contribution

It provides a novel probabilistic formulation of the diffractive cross section, enabling parameter-free analytical solutions for the gap distribution in high-energy scattering.

Findings

Asymptotic solutions relate to a classical stochastic process.

The dipole participation distribution is proportional to 1/[k(k-1)].

The approach simplifies the Kovchegov-Levin equation analysis.

Abstract

We show that the cross section for diffractive dissociation of a small onium off a large nucleus at total rapidity $Y$ and requiring a minimum rapidity gap $Y_{\text{gap}}$ can be identified, in a well-defined parametric limit, with a simple classical observable on the stochastic process representing the evolution of the state of the onium, as its rapidity increases, in the form of color dipole branchings: It formally coincides with twice the probability that an even number of these dipoles effectively participate in the scattering, when viewed in a frame in which the onium is evolved to the rapidity $Y-Y_{\text{gap}}$. Consequently, finding asymptotic solutions to the Kovchegov-Levin equation, which rules the $Y$-dependence of the diffractive cross section, boils down to solving a probabilistic problem. Such a formulation authorizes the derivation of a parameter-free analytical expression for the gap distribution. Interestingly enough, events in which many dipoles interact simultaneously play an important role, since the distribution of the number $k$ of dipoles participating in the interaction turns out to be proportional to $1/[k(k-1)]$.