Radiative energy loss and $p_{\perp}$-broadening of high energy partons in nuclei

TL;DR

This work shows that for high-energy partons traversing nuclear matter, both radiative energy loss and transverse momentum broadening scale with the path length in a diffusion-like framework based on Glauber multiple scattering. A central, model-independent result ties the two observables via -dE/dz = (αs Nc/8) p⊥W^2, while the detailed L-dependence emerges from the transport coefficient tilde v and the scale μ^2/λ. By connecting the broadening to the gluon distribution xG(x, μ^2) and to phenomenological parameters like λLQS^2, the authors provide a tractable way to estimate energy loss and broadening in cold and hot nuclear matter and to assess potential signals of quark-gluon plasma formation. The analysis emphasizes that hot matter can significantly enhance both effects, offering a potential diagnostic for plasma formation in heavy-ion collisions.

Abstract

The medium-induced $p_{\perp}$-broadening and induced gluon radiation spectrum of a high energy quark or gluon traversing a large nucleus is studied. Multiple scattering of the high energy parton in the nucleus is treated in the Glauber approximation. We show that -dE/dz, the radiative energy loss of the parton per unit length, grows as L, the length of the nuclear matter, as does the characteristic transverse momentum squared of the parton $p_{\perp W}^2$. We find dE/dz = (1/8)α_s N_c $p_{\perp W}^2$ holds independent of the details of the parton-nucleon scatterings so long as L is large. Numerical estimates suggest that $p_{\perp}$-broadening and energy loss may be significantly enhanced in hot matter as compared to cold matter, thus making the study of such quantities a possible signal for quark-gluon plasma formation.

Figures (2)

• Figure 1: Basic quark-nucleon scattering amplitude.
• Figure 2: Diagrammatic representation of the cross section (B.1).