# Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC

## TL;DR

This paper calculates the direct component of forward dijet production in ultra-peripheral Pb-Pb collisions at the LHC using a framework that interpolates between the Color Glass Condensate and high energy factorization, highlighting the sensitivity to the less-known Weizs"acker-Williams gluon distribution.

## Contribution

It introduces a formalism that interpolates between the CGC and $k_T$ factorization for dijet production, and uses this to analyze the sensitivity to the WW gluon distribution in ultra-peripheral collisions.

## Key findings

- Saturation effects are weak, reaching about 20% at low $p_T$ cuts.
- The WW gluon distribution can be derived from the dipole gluon density fitted to HERA data.
- LO collinear factorization with nuclear shadowing predicts similar effects.

## Abstract

Using the framework that interpolates between the leading power limit of the Color Glass Condensate and the High Energy (or $k_{T}$) factorization we calculate the direct component of the forward dijet production in ultra-peripheral $\mathrm{Pb}$-$\mathrm{Pb}$ collisions at CM energy $5.1\,\mathrm{TeV}$ per nucleon pair. The formalism is applicable when the average transverse momentum of the dijet system $P_{T}$ is much bigger than the saturation scale $Q_{s}$, $P_{T}\gg Q_{s}$, while the imbalance of the dijet system can be arbitrary. The cross section is uniquely sensitive to the Weizs\"acker-Williams (WW) unintegrated gluon distribution, which is far less known from experimental data than the most common dipole gluon distribution appearing in inclusive small-$x$ processes. We have calculated cross sections and nuclear modification ratios using WW gluon distribution obtained from the dipole gluon density through the Gaussian approximation. The dipole gluon distribution used to get WW was fitted to the inclusive HERA data with the nonlinear extension of unified BFKL+DGLAP evolution equation. The saturation effects are visible but rather weak for realistic $p_{T}$ cut on the dijet system, reaching about $20\%$ with the cut as low as $6\,\mathrm{GeV}$. We find that the LO collinear factorization with nuclear leading twist shadowing predicts quite similar effects.