Glauber quark and gluon contributions to quark energy loss at next-to-leading order and next-to-leading twist

Abstract

The higher-twist formalism is used at $O({\alpha }_s^2)$ to compute all possible medium-induced single-scattering emission kernels for an incoming highly energetic and virtual quark traversing the nuclear environment. The effects of the heavy-quark mass scale are taken into account [Phys. Rev. C 94, 054902 (2016)] both in the initial state as well as in the final state, along with interactions involving both in-medium Glauber gluons and quarks [Nucl. Phys. A 793, 128 (2007)], as well as coherence effects [Phys. Rev. C 105, 024908 (2022)]. As this study is a continuation of our work on medium-induced photon production [Phys. Rev. C 112, 025204 (2025)], the general factorization procedure for $e$-$A$ deep-inelastic scattering is still used. An incoming quark energy loss in the nuclear medium yields four possible scattering kernels $K_i$ with the following final states: (i) $q+g$, (ii) $g+g$, (iii) $q+{\bar{q}}^{\prime }$, where the quark $q$ may have a flavor different from the antiquark ${\bar{q}}^{\prime }$, and (iv) $q+q^{\prime }$, where, again, $q$ may have a flavor different from $q^{\prime }$. The collisional kernels include full phase factors from all non-vanishing diagrams and complete first-order derivative in the longitudinal direction ($k^{-}$) as well as second-order derivative in the transverse momentum ($k_{\perp }$) gradient expansion. Furthermore, in-medium parton distribution functions and the related jet transport coefficients have a hard transverse-momentum dependence (of the emitted quark or gluon) present within the phase factor.

Comments: 66 pages, 23 figures, single column; Updated introduction and discussion; Matched to published version [Phys. Rev. C 113, 055207 (2026)]