Jet quenching parameter in an expanding QCD plasma

Abstract

We present a new definition of the jet quenching parameterq in a weakly-coupled quark-gluon plasma undergoing boost-invariant longitudinal expansion. We propose a boost-invariant definition ofq, which is proportional to the broadening of the angular variables η (the pseudo-rapidity) and φ (the azimuthal angle). We furthermore consider radiative corrections toq and find potentially large corrections enhanced by a double logarithm like the case of a static medium. But unlike for the static medium, these corrections are now local in (proper) time.

Radiative Contribution to p⊥ Broadening of Fast Partons in a Quark–Gluon Plasma

“…As in [13], we take α s = 1/3 at the vertex of the q → qg transition. Also, like in [13], we regularize the 1/∆z divergence in (19) by truncating the integration at ∆z min = 1/m with m = 300 MeV. In (19)-(21) we integrate over x from x min = m q /E up to x max = 1 − m g /E (recall that we define x as x q ; in terms of x g , our integration region corresponds to the variation of x g from m g /E to 1 − m q /E).…”

“…However, one should bear in mind that this conclusion may depend on the value of the I 1 term, which requires the ∆z-regularization. To understand the sensitivity of the results to the lower limit of the ∆z-integration in (19), we have performed calculations for ∆z min = 1/m with m = 600 MeV. In this case I 1 becomes bigger by a factor of ∼ 2.5(2) for RHIC(LHC).…”

“…The integrand in the formula (19) for I 1 behaves as 1/∆z for ∆z → 0, which leads to the logarithmic divergence of I 1 . In the LCPI approach it is assumed that the typical |z 2 − z 1 | (i.e., the formation length L f ) is bigger than the correlation radius of the medium.…”

“…For the QGP it is the Debye radius. For this reason, it is reasonable to regularize the integration over ∆z taking the lower limit in (19) at ∆z ∼ 1/m D . This prescription was used in [13] in calculating with a logarithmic accuracy the analogue of our contribution I 1 .…”

“…This is the purpose of the present paper. The case of the expanding QGP has been addressed previously in [19]. But there the effect of the Glauber factors has not been accounted for.…”