Chirality dependence in charge and heat transport in thermal QCD

Abstract

As the strength of the magnetic field ($B$) becomes weak, novel phenomena, similar to the Hall effect in condensed matter physics, emerges both in charge and heat transport in a thermal QCD medium with a finite quark chemical potential ($\ensuremath{\mu}$). So we have calculated the transport coefficients in a kinetic theory within a quasiparticle framework, wherein we compute the effective mass of quarks for the aforesaid medium in a weak magnetic field (B) limit ($|eB|\ensuremath{\ll}{T}^{2}$; $T$ is temperature) by the perturbative thermal QCD up to one loop, which depends on $T$ and $B$ differently to left-handed (L) and right-handed (R) chiral modes of quarks, lifting the prevalent degeneracy in L and R modes in strong magnetic field limit ($|eB|\ensuremath{\gg}{T}^{2}$). Another implication of weak $B$ is that the transport coefficients assume a tensorial structure: The diagonal elements represent the usual (electrical and thermal) conductivities (${\ensuremath{\sigma}}_{\text{Ohmic}}$ and ${\ensuremath{\kappa}}_{0}$ as the coefficients of charge and heat transport, respectively) and the off-diagonal elements denote their Hall counterparts (${\ensuremath{\sigma}}_{\text{Hall}}$ and ${\ensuremath{\kappa}}_{1}$, respectively). It is found in charge transport that the magnetic field acts on L and R modes of the Ohmic part of electrical conductivity in an opposite manner, viz. ${\ensuremath{\sigma}}_{\text{Ohmic}}$ for L mode decreases and for R mode, increases with $B$ whereas the Hall-part ${\ensuremath{\sigma}}_{\text{Hall}}$ for both L and R modes always increases with $B$. In heat transport too, the effect of the magnetic field on the usual thermal conductivity (${\ensuremath{\kappa}}_{0}$) and Hall-type coefficient (${\ensuremath{\kappa}}_{1}$) in both modes is identical to the above-mentioned effect of $B$ on charge transport coefficients. We have then derived some coefficients from the above transport coefficients, namely Knudsen number ($\mathrm{\ensuremath{\Omega}}$ is the ratio of the mean-free path to the length scale of the system) and Lorenz number in Wiedemann-Franz law. The effect of $B$ on $\mathrm{\ensuremath{\Omega}}$ either with ${\ensuremath{\kappa}}_{0}$ or with ${\ensuremath{\kappa}}_{1}$ for both modes is identical to the behavior of ${\ensuremath{\kappa}}_{0}$ and ${\ensuremath{\kappa}}_{1}$ with $B$. The value of $\mathrm{\ensuremath{\Omega}}$ is always less than unity for the entire temperature range, validating our calculations. Lorenz number (${\ensuremath{\kappa}}_{0}/{\ensuremath{\sigma}}_{\text{Ohmic}}T$) and Hall-Lorenz number (${\ensuremath{\kappa}}_{1}/{\ensuremath{\sigma}}_{\text{Hall}}T$) for L mode increases and for R mode decreases with magnetic field. It also does not remain constant with temperature hence violating the Wiedemann-Franz law.