Rotational susceptibility of a hot and dense hadronic matter: A possible probe of QCD phase transition

We study the effect of rotation and the consequent angular momentum fluctuations in a hadron resonance gas produced in ultra-relativistic heavy ion collisions. The rotational susceptibilities ($\chi_{\rm \omega}$, $\chi^{2}_{\rm \omega}$, etc.), which quantify how much the system responds to a small angular velocity, are estimated for the first time, considering that these can be valuable indicators of the QCD phase transition. The higher-order rotational susceptibilities and their ratios are estimated in the presence and absence of baryon chemical potential ($\mu_{\rm B}$) in the system. The effect of particle spin ($s$) and rotational chemical potential ($\omega$) on the fluctuation of the angular momentum is studied. To consider a more realistic scenario, the effect of interactions between hadrons is taken into account by considering van der Waals-like interactions, which include both attractive and repulsive interactions. A phase transition, absent in an ideal hadron gas model, can be observed in an interacting hadron gas model.