Abstract
We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with Lévy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient \( \hat{q} \) and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.
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Caucal, P., Mehtar-Tani, Y. Universality aspects of quantum corrections to transverse momentum broadening in QCD media. J. High Energ. Phys. 2022, 23 (2022). https://doi.org/10.1007/JHEP09(2022)023
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DOI: https://doi.org/10.1007/JHEP09(2022)023