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

The higher-twist formalism is used at O ( α 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 [] both in the initial state as well as in the final state, along with interactions involving both in-medium Glauber gluons and quarks [], as well as coherence effects []. As this study is a continuation of our work on medium-induced photon production [], 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 ; and (iii) q + q ¯ ′ , where the quark q may have a flavor different from the antiquark q ¯ ′ ; and (iv) q + q ′ , where, again, q may have a flavor different from q ′ . The collisional kernels include full phase factors from all nonvanishing diagrams and complete first-order derivative in the longitudinal direction ( k − ) as well as second-order derivative in the transverse momentum ( k ⊥ ) 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.