Impact of off-shell dynamics on the transport properties and the dynamical evolution of charm quarks at RHIC and LHC temperatures
Maria Lucia Sambataro, Salvatore Plumari, Vincenzo Greco
Abstract
Abstract We evaluate drag and diffusion transport coefficients comparing a quasi-particle approximation with on-shell constituents of the QGP medium and a dynamical quasi-particles model with off-shell bulk medium at finite temperature T. We study the effects of the width $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> of the particles of the bulk medium on the charm quark transport properties exploring the range where $$\gamma < M_{q,g}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo><</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . We find that off-shell effects are in general quite moderate and can induce a reduction of the drag coefficient at low momenta that disappear already at moderate momenta, $$p \gtrsim $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>≳</mml:mo> </mml:mrow> </mml:math> 2–3 GeV. We also observe a moderate reduction of the breaking of the fluctuation–dissipation theorem (FDT) at finite momenta. Moreover, we have performed a first study of the dynamical evolution of HQ elastic energy loss in a bulk medium at fixed temperature extending the Boltzmann (BM) collision integral to include off-shell dynamics. A comparison among the Langevin dynamics, the BM collisional integral with on-shell and the BM extension to off-shell dynamics shows that the evolution of charm energy when off-shell effects are included remain quite similar to the case of the on-shell BM collision integral.