Parton energy loss due to synchrotron-like gluon emission

We develop a quasiclassical theory of the synchrotron-like gluon radiation. Our calculations show that the parton energy loss due to the synchrotron gluon emission may be important in the jet quenching phenomenon if the plasma instabilities generate a sufficiently strong chromomagnetic field. Our gluon spectrum disagrees with that obtained by Shuryak and Zahed within the Schwinger’s proper time method. 1. The hydrodynamic description [1] of the RHIC hadron spectra at low pT gives strong evidence for the thermalization of the produced hot quark-gluon plasma (QGP) at the time scale τ0 ∼ 1 fm. The early thermalization provides a serious challenge for the perturbative approach based on the Boltzmann equation with the binary and the 2 ↔ 3 processes [2]. The fast thermalization can probably be explained if the plasma is strongly coupled [3]. A promising possibility of speeding the equilibration in a weakly coupled plasma scenario is connected with plasma instabilities [4, 5, 6, 7, 8]. One of the potentially important instabilities is the Weibel [9] instability which occurs for the anisotropic plasma distribution. In the QGP produced in AA-collisions the initial parton distribution has pz ≪ pT [2]. In this case the Weibel instability can generate considerable (predominantly transverse) chromomagnetic field which bends the parton trajectories and leads eventually to isotropization of the parton distribution [5, 7, 8]. Also, the generated chromomagnetic field may be important for explanation of the anomalously small plasma viscosity [10] and the longitudinal broadening of the jet cone (the ridge effect) [11]. In the scenario with generation of the chromomagnetic field an interesting question arises on the effect of the chromomagnetic field on the jet quenching due to the synchrotron-like gluon emission from fast partons. Evidently the available analyses of the jet quenching, based on the idea of the induced gluon emission due to multiple scattering [12, 13, 14, 15, 16], become inappropriate if the contribution of this mechanism to the parton energy loss is comparable to that from the ordinary multiple scattering. It is clear that in this case both these mechanism must be treated on an even footing. As a first step in understanding the role of the chromomagnetic field in the parton energy loss it would be interesting to calculate the purely synchrotron induced gluon radiation neglecting the interference between the two mechanisms. It requires a formalism for the synchrotron radiation in QCD. In the present paper we develop a semiclassical approach to the synchrotron gluon radiation and give a qualitative estimate of the parton energy loss in the QGP produced