Impact of magnetic field on shear viscosity of quark matter in Nambu-Jona-Lasinio model

We have investigated the shear viscosity of quark matter in the presence of a strong uniform magnetic field background in which the Nambu-Jona-Lasinio model has been considered to describe the magnetothermodynamical properties of the medium. In the presence of magnetic field, the shear viscosity coefficient gets split into different components because of anisotropy in tangential stress of the fluid. Four different components can be merged to two components in the strong field limit, at which the collisional width of the quark becomes much lower than its synchrotron frequency. A simplified contact diagram of quark-quark interaction can estimate a small collisional width, for which the strong field limit expressions are exactly applicable, although for the Relativistic Heavy Ion Collider or LHC matter, one can expect a large thermal width, for which generalized four-component viscosities are necessary. We have explored all these different possible cases in the thermodynamical framework of the Nambu-Jona-Lasinio model.