Momentum broadening in weakly coupled quark-gluon plasma (with a view to finding the quasiparticles within liquid quark-gluon plasma)

We calculate P (k⊥), the probability distribution for an energetic parton that propagates for a distance L through a medium without radiating to pick up transverse momentum k⊥, for a medium consisting of weakly coupled quark-gluon plasma. We use full or HTL self-energies in appropriate regimes, resumming each in order to find the leading large-L behavior. The jet quenching parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \widehat{q} $\end{document} is the second moment of P (k⊥), and we compare our results to other determinations of this quantity in the literature, although we emphasize the importance of looking at P (k⊥) in its entirety. We compare our results for P (k⊥) in weakly coupled quark-gluon plasma to expectations from holographic calculations that assume a plasma that is strongly coupled at all length scales. We find that the shape of P (k⊥) at modest k⊥ may not be very different in weakly coupled and strongly coupled plasmas, but we find that P (k⊥) must be parametrically larger in a weakly coupled plasma than in a strongly coupled plasma — at large enough k⊥. This means that by looking for rare (but not exponentially rare) large-angle deflections of the jet resulting from a parton produced initially back-to-back with a hard photon, experimentalists can find the weakly coupled short-distance quark and gluon quasiparticles within the strongly coupled liquid quark-gluon plasma produced in heavy ion collisions, much as Rutherford found nuclei within atoms or Friedman, Kendall and Taylor found quarks within nucleons.