Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parameters $\hat{q}$

Abstract

A powerful historical insight about the theory of in-medium showering in QCD backgrounds was that splitting rates can be related to a parameter $\hat{q}$ that characterizes the rate of transverse-momentum kicks to a high-energy particle from the medium. Another powerful insight was that $\hat{q}$ 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 of $\hat{q}$ 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.

20 pages, 8 figures. Difference from v2: correction (which does not propagate) to eq. (2.16)

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• The LPM effect in sequential bremsstrahlung: nearly complete results for QCD
• Universality (beyond leading log) of soft radiative corrections to $\hat{q}$ in $p_{\perp }$ broadening and energy loss
• The LPM effect in sequential bremsstrahlung: from large-N QCD to N=3 via the SU(N) analog of Wigner 6-j symbols
• The LPM Effect in sequential bremsstrahlung: $1/N_c^2$ corrections
• System of evolution equations for quark and gluon jet quenching with broadening
• The LPM effect in sequential bremsstrahlung: incorporation of "instantaneous'' interactions for QCD
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution