Heavy quark dynamics in a strongly magnetized quark-gluon plasma

Abstract

We evaluate the heavy quark momentum diffusion coefficients in a hot magnetized medium for the most general scenario of any arbitrary values of the external magnetic field, thereby extending our previous Lowest Landau Level (LLL) approximated result. We choose to work with the systematic way of incorporating the effect of the magnetic field, by using the effective gluon and quark propagators, generalized for a hot and magnetized medium. To get gauge independent analytic form factors valid through all Landau levels, we apply the Hard Thermal Loop (HTL) technique for the resummed effective gluon propagator. The derived effective HTL gluon propagator and the generalized version of Schwinger quark propagator subsequently allows us to analytically evaluate the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Within the static limit we also explore another way of incorporating the effect of the magnetic field, i.e. through the magnetized medium modified Debye mass and compare the results to justify the need for structural changes.

Heavy quark dynamics in a strongly magnetized medium

“…In this proceeding we will just sketch the basic steps. For the detailed calculation with explicit expression for each step (both for B = 0 and B 0 case) interested readers can look up in Ref [9]. The scattering rate can be effectively expressed in terms of the cut/imaginary part of the HQ self energy Σ(P) [10] as :…”

“…with q f being the fermionic charge for flavor f and K ≡ (K , k ⊥ ) as the fermionic four momentum (Details about these notations can be found in Ref [9]).…”

“…Also Π µν (Q) is the gluon self energy in a strongly magnetized medium (within LLL and HTL approximation) : a combination of the eB independent pure glue contribution Π g µν and eB dependent fermionic loop contribution Π s µν . Again, for the details about the construction of the tensor structure and the notations of ūµ , nν , g µν ⊥ , Π s µν , Π g µν etc., interested readers can look up in Refs [9,13]. So, using Eqs.…”

“…The final expressions for both the cases are given in Ref. [9]. Finally to reach the relatively well known static limit results for the momentum diffusion coefficients, one can take the ⃗ v → 0 limit in our general expressions.…”

Nonlinear effective dynamics of a Brownian particle in magnetized plasma

“…Second, the noise would obey a non-Gaussian distribution, and might be coloured as well, which requires to go beyond (1.2). Third, isotropy would be broken by an external field, such as in magnetized thermal medium [7,8]. Then, beyond linear level, dynamics of transverse and longitudinal modes (with respect to external field) would get mixed.…”