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Shear Viscosity of hadronic matter at finite temperature and magnetic field

We calculate the transport coefficient of hadronic matter in the presence of temperature and magnetic field using the linear sigma model. In the relaxation time approximation, we estimate the shear viscosity over entropy density $η/s$. The point-like interaction rates of hadrons are evaluated through the $S$-matrix approach in the presence of a magnetic field to obtain the temperature and magnetic field-dependent relaxation time. We observe that the transport coefficients are anisotropic in the presence of the magnetic field. We calculate the temperature and magnetic field-dependent anisotropic shear viscosity coefficients by incorporating the estimated relaxation time. The value of viscosity over entropy density is lower in the presence of a magnetic field than the value of it in a thermal medium. The behavior of the perpendicular components of the shear-viscous coefficient is also discussed. We consider the temperature-dependent hadron masses from mean-field effects in this work.