Nonlinear Dynamics of Soft Fermion Excitations in Hot QCD Plasma: Soft-Quark Bremsstrahlung and Energy Losses

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. *

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

“…. , N The equations of motion for Grassmann and usual color charges, (1.4) and (1.5), have been used in our two papers [4,5] in the study of the scattering processes of hard color-charged particles off soft gluon and quark-antiquark fields. These soft fields are induced by thermal fluctuations in a hot quark-gluon plasma.…”

“…Furthermore, χ α is a c -number spinor describing spin state of a particle. In the papers [4,5], this spinor was considered as independent of time. The minimal information about this spinor we shall need in the present work, is its connection with the density matrix for completely unpolarized state of the particle.…”

“…Aside from the generalized equations of motion for the color charges in [4,5], new gaugecovariant additional color currents and sources generated by a moving color particle, which should be added to the right-hand side of the proper field equations, have been suggested. In this case only we are able to calculate complete and gauge-covariant expressions for effective currents and sources generating the scattering processes of soft quark excitations off hard thermal particles in a hot QCD plasma.…”

“…In this case only we are able to calculate complete and gauge-covariant expressions for effective currents and sources generating the scattering processes of soft quark excitations off hard thermal particles in a hot QCD plasma. For convenience of the further references, the list of all additional color currents and sources obtained in the papers [4,5] is given in Appendix A.…”

“…Unfortunately, these additional color currents and sources have been derived in the works [4,5] mainly from heuristic reasoning, practically without any connection with dynamical equations (1.6) and (1.7). Here, we would like to have some systematic procedure, which would 2 Since in [4] we were interested in the case of ultrarelativistic particles, in the expression for ̺(E, v) the term proportional to m/E was dropped.…”