Calculating hard probe radiative energy loss beyond the soft-gluon approximation: Examining the approximation validity

Abstract

The soft-gluon approximation, which implies that radiated gluon carries away a small fraction of initial parton's energy, is a commonly used assumption in calculating radiative energy loss of high momentum partons traversing QGP created at RHIC and LHC. While soft-gluon approximation is convenient, different theoretical approaches reported significant radiative energy loss of high p ⊥ partons, thereby questioning its validity. To address this issue, we relaxed the soft-gluon approximation within DGLV formalism. The obtained analytical expressions are quite distinct compared to the soft-gluon case. However, numerical results for the first order in opacity fractional energy loss lead to small differences in predictions for the two cases. The difference in the predicted number of radiated gluons is also small. Moreover, the effect on these two variables has an opposite sign, which when combined results in almost overlapping suppression predictions. Therefore, our results imply that, contrary to the commonly held doubts, the soft-gluon approximation in practice works surprisingly well in DGLV formalism. Finally, we also discuss generalizing this relaxation in the dynamical QCD medium, which suggests a more general applicability of the conclusions obtained here. PACS numbers: 12.38.Mh; 24.85.+p; arXiv:1804.07593v2 [nucl-th]

Testing the Reliability of the Soft-Gluon Approximation for High p⊥ Particles

“…In this section we outline the features of the DGLV formalism, the assumptions used in the beyond soft-gluon (bsg) calculations [11], as well as the definition of an observable for which we generated the predictions. The DGLV formalism [12] considers a finite size, optically thin QCD medium, consisting of static scattering centers, so that the jet-medium interactions are described by static color-screened Yukawa potential given by Eq.…”

“…(5) from [13], whereas gluons in a finite temperature QGP are considered to be transversely polarized with an effective mass equal to m g = µ/ √ 2 (µ is Debye mass), as obtained in [14]. We applied the following assumptions in calculating 11 Feynman diagrams (for more details see [11]) for the gluon-jet bsg approximation: (1) that initial gluon propagates along the longitudinal axis consistently for all diagrams; (2) the soft-rescattering (eikonal) approximation and (3) the first order in opacity approximation.…”

“…However, the approximation clearly breaks-down for intermediate momentum range (5 < p ⊥ < 10 GeV), where the experimental data are most abundant and with the smallest error bars; and primarily for the gluon-jets, as due to the color factor of 9/4, gluons lose significantly more energy compared to the quarks. This questioned the applicability of the soft-gluon approximation (sga), which we addressed in [11] for the gluon-jet radiative energy loss within the DGLV [12] formalism to the 1st order in opacity, by allowing x to acquire a finite value, and discussed its implications when recoiling of the medium constituents is taken into account. Note that, in these proceedings, only the main results are presented, while for more details, we refer the reader to [11].…”

“…This questioned the applicability of the soft-gluon approximation (sga), which we addressed in [11] for the gluon-jet radiative energy loss within the DGLV [12] formalism to the 1st order in opacity, by allowing x to acquire a finite value, and discussed its implications when recoiling of the medium constituents is taken into account. Note that, in these proceedings, only the main results are presented, while for more details, we refer the reader to [11].…”

Quark branching in QCD matter to any order in opacity beyond the soft gluon emission limit

“…This evaluation of the numerator algebra also applies to the single-Born amplitude R C 1 Eq. (40) and in general to the rescattering of the radiated gluon. Using the averaging Eq.…”