Mapping collinear in-medium parton splittings

Self Cite

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.

Section: Jhep05(2021)148mentioning

confidence: 99%

“…Here the emission angle depends on the transverse momenta variables only through the relative transverse momentum between the two outgoing states Q and is fixed by the kinematics of the emission process, as considered in the previous section. It is explicitly given by [47] θ(Q, z, p…”

Section: Introducing Color Coherence Effects Into the Rate Equationmentioning

confidence: 99%

A modified in-medium evolution equation with color coherence

Barata

Domínguez

Salgado

et al. 2021

Self Cite

“…where n = p/E, see [18,22]. The last term in this product is simply the Fourier transform of the vacuum propagator.…”

Section: Jhep11(2021)125mentioning

confidence: 99%

“…where α can be α em or α s depending on the process, and P (z) is the relevant Altarelli-Parisi splitting function. Then one can write the full spectrum on the form [22]…”

Section: Emission Spectramentioning

confidence: 99%

“…Previous studies of such processes focused mostly on a hard photon splitting into a quark-antiquark pair [18,22] and invoked the large-N c approximation to obtain analytical formulas. In this work, we consider three generic QCD splitting processes that involve up to eight correlated Wilson lines in the fundamental representation, in the case of gluon splitting into two daughter gluons.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Wilson line correlators beyond the large-Nc

Isaksen

Tywoniuk

2021

Self Cite

We study hard 1 → 2 final-state parton splittings in the medium, and put special emphasis on calculating the Wilson line correlators that appear in these calculations. As partons go through the medium their color continuously rotates, an effect that is encapsulated in a Wilson line along their trajectory. When calculating observables, one typically has to calculate traces of two or more medium-averaged Wilson lines. These are usually dealt with in the literature by invoking the large-Nc limit, but exact calculations have been lacking in many cases. In our work, we show how correlators of multiple Wilson lines appear, and develop a method to calculate them numerically to all orders in Nc. Initially, we focus on the trace of four Wilson lines, which we develop a differential equation for. We will then generalize this calculation to a product of an arbitrary number of Wilson lines, and show how to do the exact calculation numerically, and even analytically in the large-Nc limit. Color sub-leading corrections, that are suppressed with a factor $$ {N}_c^{-2} $$ N c − 2 relative to the leading scaling, are calculated explicitly for the four-point correlator and we discuss how to extend this method to the general case. These results are relevant for high-pT jet processes and initial stage physics at the LHC.

The medium-modified $$ g\to c\overline{c} $$ splitting function in the BDMPS-Z formalism

Attems

Brewer

Innocenti

et al. 2023

The formalism of Baier-Dokshitzer-Mueller-Peigné-Schiff and Zakharov determines the modifications of parton splittings in the QCD plasma that arise from medium-induced gluon radiation. Here, we study medium-modifications of the gluon splitting into a quark-anti-quark pair in this BDMPS-Z formalism. We derive a compact path-integral formulation that resums effects from an arbitrary number of interactions with the medium to leading order in the $$ 1/{N}_c^2 $$ 1 / N c 2 expansion. Analyses in the N = 1 opacity and the saddle point approximations reveal two phenomena: a medium-induced momentum broadening of the relative quark-anti-quark pair momentum that increases the invariant mass of quark-anti-quark pairs, and a medium-enhanced production of such pairs. We note that both effects are numerically sizeable if the average momentum transfer from the medium is comparable to the quark mass. In ultra-relativistic heavy-ion collisions, this condition is satisfied for charm quarks. We therefore focus our numerical analysis on the medium modification of $$ g\to c\overline{c} $$ g → c c ¯ , although our derivation applies equally well to $$ g\to b\overline{b} $$ g → b b ¯ and to gluons splitting into light-flavoured quark-anti-quark pairs.