Abstract
QCD jets produced in heavy-ion collisions at LHC or RHIC energies partially evolve inside the produced hot and dense quark gluon plasma, offering unique opportunities to study QCD splitting processes in different backgrounds. Induced (modified) splittings are expected to be the most relevant mechanism driving the modifications of in-medium jets compared to vacuum jets for a wide sets of observables. Although color coherence among different emitters has been identified as an essential mechanism in studies of the QCD antenna radiation, it is usually neglected in the multi-gluon medium-induced cascade. This independent gluon emission approximation can be analytically proved to be valid in the limit of very large media, but corrections or modifications to it have not been computed before in the context of the evolution (or rate) equation describing the gluon cascade. We propose a modified evolution equation that includes corrections due to the interference of subsequent emitters. In order to do so, we first compute a modified splitting kernel following the usual procedure of factorizing it from the subsequent Brownian motion. The calculation is performed in the two-gluon configuration with no overlapping formation times, that is expected to provide the first correction to the completely independent picture.
Highlights
The goal of the present paper is to go beyond this approximation, taking into account the first correction to the completely independent subsequent gluon emission and to propose a modification of the rate equations that takes into account color coherence
But below the critical frequency, ω ωc ∼ qL2, with a typical formation time tf (ω) = 2ω/k2, where k is the transverse momentum of the gluon, L the medium length, μ the Debye screening mass and qthe averaged square transverse momentum acquired by a particle propagating in the medium during a time t, i.e. k2 = qt
Θ(z − x) − K z, xp+0 ; t D(x, k, t). This is the well-known rate equation taking into account multiple soft medium-induced gluon production derived in [11, 37]. It has a very simple interpretation: the O(αs0) term corresponds to the broadening in momentum space occurring between in-medium splittings; the first term at αs order corresponds to the production of a gluon with energy fraction x and momentum k from a parton of the same kinematics enhanced by a 1 z factor; and the last term corresponds to a gluon with momentum fraction x and transverse momentum k being displaced to another energy and momentum mode via a splitting inside the medium, such that the creation and annihilation rates are balanced — and probability is conserved
Summary
We briefly review the main results from [9, 11], where the double-differential medium-induced gluon emission spectrum was computed and simplified in order to provide a probabilistic picture for the production of medium-induced radiation.
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