Multiparticle potentials from lightlike Wilson lines in quark-gluon plasmas: A generalized relation of in-medium splitting rates to jet-quenching parameters q^

Abstract

A powerful historical insight about the theory of in-medium showering in QCD backgrounds was that splitting rates can be related to a parameterq that characterizes the rate of transversemomentum kicks to a high-energy particle from the medium. Another powerful insight was that q can be defined (with caveats) even when the medium is strongly coupled, using long, narrow Wilson loops whose two long edges are light-like Wilson lines. The medium effects for the original calculations of in-medium splitting rates can be formulated in terms of 3-body imaginary-valued "potentials" that are defined with three long, light-like Wilson lines. Corrections due to overlap of two consecutive splittings can be calculated using similarly defined 4-body potentials. I give a simple argument for how such N -body potentials can be determined in the appropriate limit just from knowledge of the values ofq for different color representations. For N > 3, the N -body potentials have non-trivial color structure, which will complicate calculations of overlap corrections outside of the large-N c or soft bremsstrahlung limits.

Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N=3 via the SU(Arnold1 2019Phys. Rev. DSelf Cite120100View full textAdd to dashboardCite

“…(This high-energy approximation has the same technical caveats, reviewed in ref. [16], as most all other applications ofq.) Above, the b i are the transverse positions of the high-energy particles during any particular stage of the evolution.q i represents the value ofq for the i-th particle.q ij represents the value ofq for the color representation corresponding to the combined color representation of particles i and j.…”

“…In more detail, ref. [16] discusses how the potential energy for the Schrödinger-like evolution equation can be defined in terms of multi-particle Wilson loops involving lightlike Wilson lines. These are generalizations of the 2-particle Wilson loops that were introduced by Liu, Rajagopal, and Wiedemann [17,18] as a way to define the medium parametersq R for strongly-interacting plasmas.…”

“…In this paper, we start from the result of ref. [16] that the multi-particle potentials that are needed for the calculations represented by fig. 1b are harmonic oscillator potentials that can be written in terms ofq as…”

“…Ref. [16] discusses why the color structure of the n-particle potential (1.1) is trivial for n=3 because overall color conservation then impliesq 12 =q 3 and permutations. But the color structure is not trivial for n=4, which is needed for evolution of the shaded part of fig.…”

“…Though Casimir scaling ofq has long been known through next-to-leading order for weakly-coupled plasmas [19], we are unaware of a previous argument for Casimir scaling in applications to finite-N c strongly-coupled plasmas (again subject to the technical caveats of theq approximation reviewed in ref. [16]).…”