Heavy-flavor in-medium momentum evolution: Langevin versus Boltzmann approach

Abstract

The propagation of heavy quarks in the quark-gluon plasma (QGP) has been often treated within the framework of the Langevin equation (LV), i.e. assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass mD. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked (mD ∼ = T ) or the mass to temperature ratio is quite large (MHQ/T > ∼ 8 − 10) there are significant differences in the evolution of the p−spectra and consequently on nuclear modification factor RAA(pT ). However for charm quark we find that very similar RAA(pT ) between the LV and BM can be obtained, but with a modified diffusion coefficient by about ∼ 15 − 50% depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by a single heavy quarks we see that at temperatures T > ∼ 250 MeV the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultra-relativistic heavy-ion collisions. Finally, we have shown the possible impact of this study on RAA(pT ) and v2(pT ) for a realistic simulation of relativistic HIC. For larger mD the elliptic flow can be about 50% larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of RAA(pT ) and v2(pT ). 24.85.+p; 05.20.Dd; 12.38.Mh PACS

Heavy-flavor production and medium properties in high-energy nuclear collisions --What next?

“…For bottom quarks the Fokker Planck and the Boltzmann approach yield almost identical results. For the charm quarks differences between both approaches have been reported [135] what should be investigated in detail in near future.…”

“…In the last years, several groups have advanced approaches, which study the interaction of heavy quarks in an expanding QGP [61,[89][90][91][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144]. These approaches are either based on a Fokker-Planck equation or on the use of the full Boltzmann collision kernel to describe the collisions of heavy quarks with the partons of the QGP.…”

Heavy quark dynamics in the QGP: Towards a solution of theRAAandν2puzzle

“…The comparison between LV and BM approach has been thoroughly studied in these references [15,16] where it is shown that for charm quark the results that one gets using the Fokker-Planck approach deviate significantly from those obtained using the Boltzmann approach and such a deviation significantly depends on the the values of the Debye screening mass, whereas for bottom quarks the FP is a very good approximation. We considered in references [15,16] three values of m D : 0.4 GeV, 0.83 GeV and 1.6 GeV. Here we have not considered a fixed value of the Debye screening mass but a value which depends on the temperature according to m D = gT .…”

“…The two key observables related to HQ that have been measured in experiments are the nuclear suppression factor R AA and the elliptic flow v 2 [3][4][5]. Several theoretical efforts have been made to study the R AA and the v 2 measured in experiments within the Fokker Planck (FP) approach [6-9, 11, 12] and the relativistic Boltzmann approach (BM) [13][14][15][16]. However all the approaches show some difficulties to describe both the nuclear modification factor and the elliptic flow simultaneously.…”

Impact of momentum space anisotropy on heavy quark dynamics in a QGP medium

“…To address this, one requires to describe the dynamics of the HQs propagating through the QGP. Therefore, one can explore the physics of the HQ transport [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] in the QGP medium as follows.The non-equilibrated HQs can travel in the equilibrated QGP medium, and one has to deal the problem within the framework of Langevin dynamics [22]. This is to say that the HQs perform random motion in the equilibrated QGP.…”