Low-$x$ improved TMD approach to the lepto- and hadroproduction of a heavy-quark pair

TL;DR

The work extends the ITMD factorization framework to forward heavy-quark pair production in both DIS and proton-nucleus collisions at small $x$, incorporating nonzero quark mass and photon virtuality. It shows that new contributions arise from gluons not fully linearly polarized, with $H^{h}$ terms generally non-negligible and saturations effects playing a key role; ITMD reduces to TMD or HEF in appropriate limits. A comparison with ITMD* reveals that neglecting $H^{h}$ can be acceptable only in limited kinematic regimes, and longitudinal-photon channels can exhibit large deviations. The study also highlights fundamental limitations of the diagrammatic approach for multi-scale processes, guiding future efforts to automate hard-factor calculations and extend ITMD to more complex final states.

Abstract

We study lepto- and hadroproduction of a heavy-quark pair in the ITMD factorization framework for dilute-dense collisions. Due to the presence of a nonzero quark mass and/or nonzero photon virtuality, new contributions appear compared to the cases of photo- and hadroproduction of dijets, for which the ITMD framework was originally derived. The extra terms are sensitive to gluons that are not fully linearly polarized. At small $x$ those gluons emerge only when saturation effects are taken into account, and in a proper way. As a result, in linear small-$x$ frameworks where gluon are fully linearly polarized, such contributions are absent. We show however that they are not always negligible, even for large gluon transverse momentum, due to the behavior of the off-shell hard factors.

Figures (5)

• Figure 4.1: Ratio of the $\gamma^{*}_{{ T}}A\to Q\bar{Q}X$ cross sections calculated in the ITMD* and ITMD frameworks, as a function of the angle $\alpha$ between the transverse momenta of the heavy quarks. Gluon TMDs are numerically evaluated in the McLerran-Venugopalan (MV) model MV, and evolved towards lower values of $x$ with the JIMWLK equations.
• Figure 4.2: Ratio of the $\gamma^{*}_{{ L}}A\to Q\bar{Q}X$ cross sections calculated in the ITMD* and ITMD frameworks, as a function of the angle $\alpha$ between the transverse momenta of the heavy quarks. Gluon TMDs are numerically evaluated in the MV model, and evolved towards lower values of $x$ with the JIMWLK equations.
• Figure 4.3: Ratio of the $\gamma^{*}_{{ L}}A\to Q\bar{Q}X$ and $\gamma^{*}_{{ T}}A\to Q\bar{Q}X$ cross sections, calculated in the ITMD framework and as a function of the angle $\alpha$ between the transverse momenta of the heavy quarks. Gluon TMDs are numerically evaluated in the MV model, and evolved towards lower values of $x$ with the JIMWLK equations.
• Figure 4.4: Ratio of the $pA\to Q\bar{Q}X$ cross sections calculated in the ITMD* and ITMD frameworks, as a function of the angle $\alpha$ between the transverse momenta of the heavy quarks. Gluon TMDs are numerically evaluated in the MV model, and evolved towards lower values of $x$ with the JIMWLK equations.
• Figure 5.1: The two Feynman diagrams contributing to the heavy-quark pair photoproduction cross section.