Universality (beyond leading log) of soft radiative corrections to $\hat{q}$ in $p_{\perp }$ broadening and energy loss

Abstract

It has been known for many years that soft radiation can give potentially large double-logarithm corrections to $p_{\perp }$ broadening of a high-energy particle traveling through QCD matter, but that this soft radiation correction can be absorbed into an effective value ${\hat{q}}_{\mathrm{eff}}$ for the medium $p_{\perp }$-broadening parameter $\hat{q}$. Here "soft" means high energy compared to medium scales but soft compared to the original high-energy particle traveling through the medium. A similar situation arises in the case of soft corrections to hard splitting of a high-energy particle, such as hard $g\to gg$, where double logarithms can also be absorbed using the same effective ${\hat{q}}_{\mathrm{eff}}$. In this paper, I study whether the same holds true for potentially large, subleading, *single*-logarthim corrections. The correspondence is more indirect for single logarithms, but I show (in the large-$N_{\mathrm{c}}$ limit) that single logarithms from soft radiation in the case of $p_{\perp }$ broadening also determine the single logarithms from soft radiative corrections to hard $g\to gg$ splitting. Along the way, there is an interesting variation of the original BDMPS-Z calculation of splitting rates in the $\hat{q}$ approximation. I also discuss how, for soft-radiative corrections to hard splitting processes, there are two different types of "${\hat{q}}_{\mathrm{eff}}$" that come into play, which differ by "$i\pi$" terms that multiply single logarithms.

arXiv comment35 pages, 13 figures [only minor change from v2 (fixed a figure reference)]

References in corpus (28)

• Radiative energy loss and $p_{\perp }$-broadening of high energy partons in nuclei
• Radiative energy loss of high energy quarks and gluons in a finite volume quark-gluon plasma
• Fully quantum treatment of the Landau--Pomeranchuk--Migdal effect in QED and QCD
• Radiative energy loss of high energy quarks in finite-size nuclear matter and quark-gluon plasma
• Photon and Gluon Emission in Relativistic Plasmas
• Calculating the Jet Quenching Parameter from AdS/CFT
• Medium-induced radiative energy loss; equivalence between the BDMPS and Zakharov formalisms
• Wilson loops in heavy ion collisions and their calculation in AdS/CFT
• O(g) plasma effects in jet quenching
• The Landau-Pomeranchuk-Migdal effect in QED
• Radiative pT-broadening of high-energy quarks and gluons in QCD matter
• Renormalization of the jet-quenching parameter
• Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium
• QCD Splitting/Joining Functions at Finite Temperature in the Deep LPM Regime
• Ab Initio Coupling of Jets to Collective Flow in the Opacity Expansion Approach
• Gauge invariant definition of the jet quenching parameter
• The non-linear evolution of jet quenching
• The LPM effect in sequential bremsstrahlung
• Improved opacity expansion for medium-induced parton splitting
• The LPM effect in sequential bremsstrahlung 2: factorization
• Radiative energy loss and radiative p_T-broadening of high-energy partons in QCD matter
• The LPM effect in sequential bremsstrahlung: nearly complete results for QCD
• Non-perturbative determination of collisional broadening and medium induced radiation in QCD plasmas
• High-energy gluon bremsstrahlung in a finite medium: harmonic oscillator versus single scattering approximation
• The LPM effect in sequential bremsstrahlung: dimensional regularization
• In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers
• The nonperturbative contribution to asymptotic masses
• Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parameters $\hat{q}$

Cited by in corpus (7)

• The ALICE experiment: a journey through QCD
• Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma
• The LPM Effect in sequential bremsstrahlung: $1/N_c^2$ corrections
• Dark sector searches with high-intensity positron beams in the CERN North Area
• Transport properties of the QCD medium
• Anomalous dimension of transverse momentum broadening in planar $\mathcal{N}=4$ SYM
• Universality aspects of quantum corrections to transverse momentum broadening in QCD media