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

In general line with our first work [Yu.A. Markov, M.A. Markova, Nucl. Phys. A 770 (2006) 162] within the framework of semiclassical approximation a general theory for the scattering processes of soft (anti)quark excitations off hard thermal particles in hot QCD-medium is thoroughly considered. The dynamical equations describing evolution for the usual classical color charge $Q^a(t)$ and Grassmann color charges $\theta^i(t), \theta^{\dagger i}(t)$ of hard particle taking into account the soft fermion degree of freedom of the system are suggested. On the basis of these equations and the Blaizot-Iancu equations iterative procedure of calculation of effective currents and sources generating the scattering processes under consideration is defined and their form up to third order in powers of free soft quark field, soft gluon one, and initial values of the color charges of hard particle is explicitly calculated. With use of the generalized Tsytovich principle a connection between matrix elements of the scattering processes and the effective currents and sources is established. In the context of the effective theory suggested for soft and hard fermion excitations new mechanisms of energy losses of high-energy parton propagating through QCD-medium are considered.Comment: 85 pages, 15 figures, added new appendix A, section 10 is removed, mistakes, and typing errors are corrected. Version to appear in Nucl. Phys.

Nonlinear dynamics of soft fermion excitations in hot QCD plasma I: soft-quark - soft-gluon scattering

Within the framework of the hard thermal loop effective theory we derive a system of Boltzmann-like kinetic equations taking into account the simplest processes of nonlinear interaction of soft fermionic and bosonic QCD plasma excitations: elastic scattering of soft-(anti)quark excitations off soft-gluon and soft-quark excitations, pair production of soft quark-antiquark excitations, annihilation into two soft-gluon excitations. The matrix elements of these processes to leading order in the coupling constant $g$ are obtained. The iterative method of calculation of the matrix elements for the higher processes of soft-mode interactions is proposed. The most general expression for the emitted radiant power induced by the effective currents and effective sources in a quark-gluon plasma (QGP) taking into account an existence of fermion sector of plasma excitations is defined. The explicit form of the linearized Boltzmann equation accounting for scattering of color(less) plasminos off color(less) plasmons is written out.Comment: 54 pages, 5 EPS figures, some important changes in sections 2,5,7,8. Introduction and conclusion are expanded. The version accepted for the publication in Nucl. Phys.

Nonlinear dynamics of soft boson excitations in hot QCD plasma I: plasmon-plasmon scattering

On the basis of pure gauge sector of Blaizot-Iancu equation, we derive kinetic equation of Boltzmann type, taking into account 2n+2-colorless plasmon decay processes, n=1,2,.... Using so-called Tsytovich correspondence principle, a direct connection between matrix elements of the plasmon decay processes and certain effective current, generating these processes, is established. The procedure of calculation of matrix element for simplest four-plasmon decay is considered comprehensively. The limiting value of the plasmon occupation number (~ 1/g^2, where g is a strong coupling) wherein all plasmon decays with n >= 1, contribute to the right-hand side of the Boltzmann equation, is defined. The iterative method of calculation of matrix elements for higher decay processes (n > 1), is proposed, and a problem of their gauge-invariance is discussed. Proceed from the general reasons the problem of extension of suggested approach to the case of color plasmons, is considered. The explicit form of linearized Boltzmann equation for color plasmons is written out, and it is shown that this equation covariantly conserves the color current, resulting from color-plasmon number density.Comment: 41 pages, LaTeX, 2 figures in P

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

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 lowest-order 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 $N_{\bf k}\sim 1/\alpha_s$ 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.Comment: 68 pages, 9 EPS figures; added new sections 8, 10 and reference