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

TL;DR

The paper addresses how nonlinear QCD saturation manifests in forward dijet production in ultra-peripheral heavy-ion collisions at the LHC, by evaluating the Weizsäcker-Williams unintegrated gluon distribution. It employs the ITMD framework to interpolate between high-energy factorization and CGC, using WW UGDs derived from KS dipole UGDs via Gaussian approximation, and includes Sudakov resummation. The results show saturation effects of up to about 20% at low jet pT and demonstrate that saturation-induced suppression is similar in shape to leading-twist nuclear shadowing in pT spectra, with differences mainly in x-dependence and Δφ behavior. The study provides a practical MC-based approach to constrain WW UGDs and highlights centrality and angular correlations as promising observables to disentangle nonlinear 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 Weizsäcker-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.

Figures (9)

• Figure 1: The Weizsacker-Williams (WW) unintegrated gluon distributions for proton and lead obtained from the KS dipole distributions Kutak:2012rf. The top row compares the WW distribution for lead with the dipole distribution for two values of $x$. The middle row shows the WW distributions for proton and lead as a function of $k_T$ for two values of $x$. Finally, the bottom row shows the WW distributions for proton and lead as a function of $x$ for two values of $k_T$.
• Figure 2: The longitudinal fractions probed within the kinematic cuts for different $p_{T}$ cuts: top left $p_{T0}=25\,\mathrm{GeV}$, top right $p_{T0}=10\,\mathrm{GeV}$, bottom left $p_{T0}=6\,\mathrm{GeV}$. In bottom right plot we show the distribution of collision energy of $\gamma A$ system.
• Figure 3: Transverse momentum spectra for leading (left column) and sub-leading (right column) jets. The bottom row shows the effect of the Sudakov resummation model. For comparison we show the results from the LO collinear factorization using nuclear PDFs with the leading twist shadowing (no additional effects are included in this LO calculation thus the spectra for leading and subleading jet are identical).
• Figure 4: Phase space coverage in $p_{T}$ and the longitudinal fraction $\log x$ probed in the nucleus for leading (left) and sub-leading (right) jets.
• Figure 5: Differential cross sections in the azimuthal angle between the jets with (right) and without (left) Sudakov resummation model.