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We explore the properties of neutral mesons within the context of a chirallyimbalanced medium, employing the two-flavor Nambu--Jona-Lasinio model. Thetemperature dependence of the constituent quark mass at finite values of thechiral chemical potential (CCP) demonstrates the well-established phenomena ofchiral catalysis at lower temperatures and inverse chiral catalysis at highertemperatures. The polarization functions in both the scalar ($\sigma$) andpseudo-scalar ($\pi^0$) channels have been evaluated using real time formalismof thermal field theory. These have been used to determine the masses andspectral functions of $ \sigma $ and $ \pi $ mesons. Detailed investigation ofthe analytic structure of the imaginary part of the polarization function for$\sigma$ and $\pi$ mesons results in the emergence of non-trivial Landau cutcontributions due to the presence of chiral imbalance. The multiple solutionsfor the mass of the $\pi$ meson for specific values of CCP have been analysedon the basis of their residue at the pole. Furthermore, we have observed abruptchanges in the masses of both scalar and pseudo-scalar mesons at finite CCPvalues, particularly at higher temperatures. A decreasing trend in the Motttransition temperature is seen with the increase in CCP.

The mass and spectral function of scalar and pseudoscalar mesons in a hot and chirally imbalanced medium using the two-flavor NJL model