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

Tolga Altinoluk,Cyrille Marquet,Pieter Taels

doi:10.1007/jhep06(2021)085

Abstract

We study the 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. These extra terms are sensitive to gluons that are not fully linearly polarized. At small x, those gluons emerge only when all saturation effects are carefully taken into account. Therefore, the resulting contributions are absent in linear small-x frameworks, where gluons are fully linearly polarized. We show, however, that even for large gluon transverse momentum, these contributions are not always negligible, due to the behavior of the off-shell hard factors.

Highlights

Heavy-quark pair production in deep-inelastic scatteringThe differential cross section for the process e( ) + A(pA) → e( ) + Q(k1) + Q(k2) + X is given by: dσ A dxB dQ2 d3 k1 d3 k2
All those distributions share a common perturbative tail known as the unintegrated gluon distribution (UGD), and the difference between them shows up at low values of kt = |k|, where a single distribution ceases to be sufficient
At small x, one may write F(c), H(c) = (1/π)Fg/A+O(Q2s/k2) where Fg/A is the UGD; the difference between the gluon TMDs is due to a resummation of non-linear corrections, called leadingtwist saturation effects as they are not suppressed by powers of P2

Summary

Heavy-quark pair production in deep-inelastic scattering

The differential cross section for the process e( ) + A(pA) → e( ) + Q(k1) + Q(k2) + X is given by: dσ A dxB dQ2 d3 k1 d3 k2. Where z = k1+/q+ and z = k2+/q+ are the longitudinal momentum fractions of the virtual photon carried by the (anti)quark. Used to extract the correlation limit (or TMD limit) by requiring k P. used to extract the correlation limit (or TMD limit) by requiring k P In this limit, the virtual photon-nucleus cross sections from eq (2.1) are found to be [11, 26,27,28]: dσγT∗ ;LA d3k1d3k2. All dependence on the intrinsic momentum k is absorbed into FWW and HWW, and the hard parts that appear in eq (2.4) are given by:. Explicit expressions for FWW and HWW (as well as for the other TMDs that we shall encounter below) in the McLerran-Venugopalan (MV) [30,31,32] model are given in [10, 11], along with their evaluation from simulations of the Jalilian-Marian-Iancu-McLerranWeigert-Leonidov-Kovner (JIMWLK) [33,34,35,36,37,38,39] equation

Reintroducing higher kinematical twists

Forward heavy-quark pair production in proton-nucleus scattering

On the diagrammatic approach to ITMD and its limitations

Conclusions