Nonlinear dynamics of soft boson collective excitations in hot QCD plasma III: Bremsstrahlung and energy losses

Abstract

Within of the framework of semiclassical approximation a general formalism for deriving an effective current generating bremsstrahlung of arbitrary number of soft gluons (longitudinal or transverse ones) in scattering of higher-energy parton off thermal parton in hot quark-gluon plasma with subsequent extension to two and more scatterers, is obtained. For the case of static color centers an expression for energy loss induced by usual bremsstrahlung of lowestorder with allowance for an effective temperature-induced gluon mass and finite mass of the projectile (heavy quark), is derived. The detailed analysis of contribution to radiation energy loss associated with existence of effective three-gluon vertex induced by hot QCD medium, is performed. It is shown that in general, the bremsstrahlung associated with this vertex have no sharp direction (as in the case of usual bremsstrahlung) and therefore here, we can expect an absence of suppression effect due to multiple scattering. For the case of two color static scattering centers it was shown that the problem of calculation of bremsstrahlung induced by four-gluon hard thermal loop (HTL) vertex correction can be reduced to the problem of the calculation of bremsstrahlung induced by three-gluon HTL correction. It was shown that for limiting value of soft gluon occupation number N k ∼ 1/α s all higher processes of bremsstrahlung of arbitrary number of soft gluons become of the same order in coupling, and the problem of resummation of all relevant contributions to radiation energy loss of fast parton, arises. An explicit expression for matrix element of two soft gluon bremsstrahlung in small angles approximation is obtained. *

Nonlinear dynamics of soft fermion excitations in hot QCD plasma II: Soft-quark–hard-particle scattering and energy losses

“…Here we use a simpler approach to calculation of effective currents and sources suggested in our previous works [1,6,8,9]. It is based on the fact that by virtue of the structure of the right-hand sides of Eqs.…”

The equations of motion for a classical color particle in background non-Abelian bosonic and fermionic fields

“…It turns out more simple to restrict ourselves to consideration of the solutions of equations only for the θ i (t) and θ †i (t) charges, and reproduce the usual charge Q a with the help of the relation (2.3). Thus, if we define the solutions in the 6 It is easy to verify that in this case we correctly reproduce unusual form of density matrix (1.8) when it is considered that for fully unpolarized state of a particle, the standard relation is hold [16] …”

“…It is this spinor 6 that appears in equations (1.6) and (1.7). Similar equations can be written for color charges θ †i and Q a .…”

“…Thus instead of (1.4) we have the following generalized equations for the Grassman color charges: 6) and similar, instead of the Wong equation (1.5) now we have the generalized Wong equation…”

“…Putting into consideration the Grassmann color charges of a hard particle on an equal footing with the usual color charge 1 , enables us to introduce so-called color (Grassmann valued) source of a spin-1/2 hard particle along with classical color current. We add this Grassmann source to the right-hand side of the Dirac equation for soft fermion field just as we add the usual color current of the hard particle to the right-hand side of the Yang-Mills equation for soft boson field [6]. This allowed us to obtain a closed self-consistent description of nonlinear interaction dynamics of soft and hard excitations of the hot QCD plasma both Fermi and Bose statistics (within the framework of semiclassical approximation).…”