Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses

TL;DR

This paper develops a semiclassical framework for calculating soft quark and gluon bremsstrahlung in hot QCD plasma, deriving explicit formulas for energy losses and proposing a method to determine color factors in scattering processes.

Contribution

It introduces an effective method for calculating bremsstrahlung of soft excitations and extends the dynamical equations for Grassmann color charges to include higher-order terms.

Findings

Explicit formulas for energy losses due to soft quark and gluon bremsstrahlung.

A new method for determining color factors in scattering probabilities.

Extension of dynamical equations for Grassmann color charges to higher orders.

Abstract

In general line with our early works [Yu.A. Markov, M.A. Markova, Nucl. Phys. A770 (2006) 162; 784 (2007) 443] within the framework of a semiclassical approximation the general theory of calculation of effective currents and sources generating bremsstrahlung of an arbitrary number of soft quarks and soft gluons at collision of a high-energy color-charged particle with thermal partons in a hot quark-gluon plasma, is developed. For the case of one- and two-scattering thermal partons with radiation of one or two soft excitations, the effective currents and sources are calculated in an explicit form. In the model case of `frozen' medium, approximate expressions for energy losses induced by the most simple processes of bremsstrahlung of soft quark and soft gluon, are derived. On the basis of a conception of the mutual cancellation of singularities in the sum of so-called `diagonal' and `off-diagonal' contributions to the energy losses, an effective method of determining color factors in scattering probabilities, containing the initial values of Grassmann color charges, is suggested. The dynamical equations for Grassmann color charges of hard particle used by us early are proved to be insufficient for investigation of the higher radiative processes. It is shown that for correct description of these processes the given equations should be supplemented successively with the higher-order terms in powers of the soft fermionic field.