Jet rates in the hard scattering process at finite temperature

Abstract

We compute the cross-section of the hadronic jets arising from the quark antiquark pair which are produced from a hard photons (of 4-momentum $q$) in the plasma, predominantly consisting of thermalised quarks and gluons. The quark antiquark pair is hard and scattered off the heat bath to form jets, while the gluons being soft get thermalised in the heat bath. The infrared divergences cancel in the observable cross-section to $\alpha_s$ order, which includes the process of emission and absorption of real gluons. Since the massless quark antiquark pair is hard the Compton scattering processes are absent in the heat bath and it renders an uncancelled collinear divergent piece in the cross-section. We regularize it by eliminating the collinear region from the phase space and write it in terms of jet parameters. The temperature dependent part of the jet cross-section is regular at large ${\sqrt{q^2}\over T}$ and vanishes when ${\sqrt{q^2}\over T}\to \infty$. Since jets carry the thermal signature of the hot plasma the jet production rate can be used as a thermometer of the heat bath.