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

We calculate P(k(perpendicular to)), the probability distribution for an energetic parton that propagates for a distance L through a medium without radiating to pick up transverse momentum k(perpendicular to), 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 (q) over cap is the second moment of P(k(perpendicular to)), and we compare our results to other determinations of this quantity in the literature, although we emphasize the importance of looking at P(k(perpendicular to)) in its entirety. We compare our results for P(k(perpendicular to)) 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(perpendicular to)) at modest k(perpendicular to) may not be very different in weakly coupled and strongly coupled plasmas, but we find that P(k(perpendicular to)) must be parametrically larger in a weakly coupled plasma than in a strongly coupled plasma at large enough k(perpendicular to). 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.