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Interacting hadron resonance gas model in magnetic field and the fluctuations of conserved charges

In this paper we discuss the interacting hadron resonance gas model in presence of a constant external magnetic field. The short range repulsive interaction between hadrons are accounted through van der Waals excluded volume correction to the ideal gas pressure. Here we take the sizes of hadrons as $r_π$ (pion radius) $= 0$ fm, $r_K$ (kaon radius) $= 0.35$ fm, $r_m$ (all other meson radii) $= 0.3$ fm and $r_b$ (baryon radii) $= 0.5$ fm. We analyse the effect of uniform background magnetic field on the thermodynamic properties of interacting hadron gas. We especially discuss the effect of interactions on the behaviour of magnetization of low temperature hadronic matter. The vacuum terms have been regularized using magnetic field independent regularization scheme. We find that the magnetization of hadronic matter is positive which implies that the low temperature hadronic matter is paramagnetic. We further find that the repulsive interactions have very negligible effect on the overall magnetization of the hadronic matter and the paramagnetic property of the hadronic phase remains unchanged. We have also investigated the effects of short range repulsive interactions as well as the magnetic field on the baryon and electric charge number susceptibilities of hadronic matter within the ambit of excluded volume hadron resonance gas model.