Non-Abelian energy loss in cold nuclear matter

TL;DR

This work develops a reaction-operator, opacity-expansion framework to compute non-Abelian medium-induced gluon radiation in cold nuclear matter, deriving all-orders BG and initial-state radiation spectra and clarifying their distinct LPM-like interference patterns. It demonstrates that initial-state energy loss scales linearly with the in-medium path length $L$ and can dominate over final-state loss in cold nuclei, whereas final-state loss remains strongly suppressed in cold matter. Numerical results at first order in opacity show sizable IS energy loss for realistic cold-nucleus parameters, while BG tracks the expected linear path-length dependence and FS remains suppressed. These results refine pQCD phenomenology for $p+A$ and $A+A$ collisions, and suggest potential implications for backward-rapidities and the broader treatment of hard processes in nuclear environments.

Abstract

We use a formal recurrence relation approach to multiple parton scattering to find the complete solution to the problem of medium-induced gluon emission from partons propagating in cold nuclear matter. The differential bremsstrahlung spectrum, where Landau-Pomeranchuk-Migdal destructive interference effects are fully accounted for, is calculated for three different cases: (1) a generalization of the incoherent Bertsch-Gunion solution for asymptotic on-shell jets, (2) initial-state energy loss of incoming jets that undergo hard scattering and (3) final-state energy loss of jets that emerge out of a hard scatter. Our analytic solutions are given as an infinite opacity series, which represents a cluster expansion of the sequential multiple scattering. These new solutions allow, for the first time, direct comparison between initial- and final-state energy loss in cold nuclei. We demonstrate that, contrary to the naive assumption, energy loss in cold nuclear matter can be large. Numerical results to first order in opacity show that, in the limit of large jet energies, initial- and final-state energy losses exhibit different path length dependences, linear versus quadratic, in contrast to earlier findings. In addition, in this asymptotic limit, initial-state energy loss is considerably larger than final-state energy loss. These new results have significant implications for heavy ion phenomenology in both p+A and A+A reactions.

Figures (9)

• Figure 1: (Color online) Three distinct cases of medium-induced bremsstrahlung are illustrated: 1) Bertsch-Gunion case of $t=-\infty, t = + \infty$ on-shell jets; 2) initial-state energy loss in the nucleus followed by a large $Q^2$ process, resulting in the production of high-$p_T$ or high-$E_T$ particles and jets; 3) final-state energy loss in the nucleus, after a hard scatter.
• Figure 2: (Color online) Representation of the reaction operator for an arbitrary propagating system of partons. Three different cuts, corresponding to the relevant single-Born and double-Born interactions, are shown.
• Figure 3: Diagrammatic representation of the sum of amplitudes generated by the direct single-Born scattering $\hat{D}_i {\cal A}$.
• Figure 4: Diagrammatic representation of the sum of amplitudes generated by the virtual double-Born scattering $\hat{V}_i {\cal A}$.
• Figure 5: (Color online) Fractional energy loss for massless quark jets versus the jet energy, $E_{\rm jet}$, in cold nuclear matter of length $L= 5$ fm. Two different sets of typical momentum transfer per scattering and gluon mean free path have been used for comparison: $(\mu, \lambda_g) = (0.35$ GeV$, 1$ fm$)$ and $(\mu, \lambda_g) = (0.7$ GeV$, 4$ fm$)$.