Nonlinear dynamics of soft boson collective excitations in hot QCD plasma II: plasmon-hard-particle scattering and energy losses

Abstract

In a general line with our first work [1], within hard thermal loop (HTL) approximation a general theory of the scattering for an arbitrary number of colorless plasmons off hard thermal particles of hot QCD-medium is considered. Using generalized Tsytovich correspondence principle, a connection between matrix elements of the scattering processes and a certain effective current, generating these processes is established. The iterative procedure of calculation of these matrix elements is defined, and a problem of their gaugeinvariance is discussed. An application of developed theory to a problem of calculating energy losses of energetic color particle propagating through QCD-medium is considered. It is shown that for limiting value of the plasmon occupation number (∼ 1/g 2 , where g is a strong coupling) energy losses caused by spontaneous scattering process of energetic particle off soft-gluon waves is of the same order in the coupling as other known losses type: collision and radiation ones. The Fokker-Planck equation, describing decceleration (acceleration) and diffusion in momentum space of beam of energetic color particles scattering off soft excitations of quark-gluon plasma (QGP), is derived. *

Heavy ion event generator HYDJET++ (HYDrodynamics plus JETs)

“…The model simplification is that the collisional energy loss due to scatterings with low momentum transfer (resulting mainly from the interactions with plasma collective modes or colour background fields, see for recent developments [53][54][55][56][57][58][59][60][61] and references therein) is not considered here. Note, however, that in the majority of estimations, the latter process does not contribute much to the total collisional loss in comparison with the high-momentum scattering (due to absence of the large factor ∼ ln (E/µ D )), and in numerical computations it can be effectively "absorbed" by means of redefinition of minimum momentum transfer t min ∼ µ 2 D in (2).…”

Nonlinear Dynamics of Soft Boson Excitations in Hot QCD Plasma. I. Plasmon–Plasmon Scattering

“…The examples considered above suggest that a color structure of the effective amplitudes * ˜ (s) entirely coincides with a color structure of the usual s-gluon HTL amplitudes, 5 derived by Braaten and Pisarski [24] for an arbitrary number of external soft-gluon legs. Besides, by direct calculation it can be shown that an effective subamplitude (7.13) satisfies two relations which hold for usual five-gluon HTL amplitude, namely * ˜…”

“…For a sufficiently large intensity of plasma excitations (exact estimations will be given in Sect. 6 of this paper and in [5]), the processes of a first type can play the same important role in the dynamics of a system as the second ones and even become dominant. Under this condition, plasma may be considered as involving two interacting subsystems: the subsystem of hard thermal gluons and the subsystem of soft plasmons, which exchange energy among themselves.…”

“…By direct algebraic transformations, using the Jacobi identity for structure constants and relations (5.12) and (5.13), it can be represented in the form of an expansion in terms of six independent combinations of a product of three structure constants, which we have chosen as follows Here, as in basis (7.9), we fixed the first and the last color indices. The expansion * ˜ (5) in terms of a basis (7.11) ) represent a generalized decay and regenerating rates of color plasmons, respectively. These rates can be formally represented like a colorless case in the form of functional expansion in powers of the number density of color plasmons…”

On the fluctuation–dissipation theorem for soft fermionic excitations in a hot QCD plasma

“…Thus, setting into consideration the integration over the Grassmann color charges enables us to automatize fully the procedure of calculation of various color factors which appear when doing the determination of the scattering probabilities involving hard and soft fermionic excitations. In doing so, we practically achieve here, perfect analogy with the purely bosonic case [30].…”