The radiation pattern of a QCD antenna in a dilute medium

Abstract

Radiative interferences in the multi-parton shower is the building block of QCD jet physics in vacuum. The presence of a hot medium made of quarks and gluons is expected to alter this interference pattern. To study these effects, we derive the gluon emission spectrum off a color-correlated quark-antiquark pair (antenna) traversing a colored medium to first order in the medium density. The resulting induced gluon distribution is found to be governed by the hardest scale of the problem. In our setup, this can either be the inverse antenna transverse size, r −1 ⊥ , or the scale related to the transverse color correlation length in the medium, which is given by the Debye mass m D . This emerging scale opens the angular phase space of emissions off the antenna compared to the vacuum case and gives rise to a typical transverse momentum of the medium-induced emitted gluons, k 2 ⊥ med ∼ max(r. Above the hard scale interference effects suppress the spectrum resulting in the restoration of vacuum coherence.

Jet coherence in QCD media: the antenna radiation spectrum

“…(4.2). It is nevertheless important to point out that the above considerations imply on the other hand that the interferences are instrumental at short timescales, t < t d , and in particular in the regime where t d > L. In this case, the interferences are weakly suppressed and decoherence is partial, see [25][26][27].…”

“…In order to study the importance of these radiative interferences, lately the gluon emission spectrum off a time-like quark-antiquark (qq) antenna was calculated. In [25,26] we considered an antenna traversing a relatively thin medium, i.e., assuming only one scattering in the medium background potential. In [27], on the other hand, we resummed multiple scatterings in the limit of soft gluon emission.…”

“…eq. (4.16), while a complete and detailed discussion of the emerging physical picture is presented in [26,28], see also [29] for a complementary discussion. The paper is structured as follows.…”

“…However, such a unified approach is missing to date. Only recently were both coherence effects considered together in the context of antenna radiation in medium [25][26][27][28][29].…”

“…As in our previous works [25][26][27], we shall proceed in the framework of the classical YangMills (CYM) equations, applicable for soft gluon radiation off an energetic charge [24]. First, let us recall the amplitude of emitting a gluon with momentum k ≡ (ω, k), given by the standard reduction formula,…”