Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann

Understand

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 $m_D$.
• 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 ($m_D\cong T $) or the mass to temperature ratio is quite large ($M_{HQ}/T \gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra and consequently on nuclear modification factor $R_{AA}(p_T)$.