We explore the properties of neutral mesons within the context of a chirally imbalanced medium, employing the two-flavor Nambu–Jona-Lasinio model. The temperature dependence of the constituent quark mass at finite values of the chiral chemical potential (CCP) demonstrates the well-established phenomena of chiral catalysis at lower temperatures and inverse chiral catalysis at higher temperatures. The polarization functions in both the scalar (σ) and pseudoscalar (π0) channels have been evaluated using the real-time formalism of thermal field theory. These have been used to determine the masses and spectral functions of σ and π mesons. Detailed investigation of the analytic structure of the imaginary part of the polarization function for σ and π mesons results in the emergence of nontrivial Landau-cut contributions due to the presence of chiral imbalance. The multiple solutions for the mass of the π meson for specific values of CCP have been analyzed on the basis of their residue at the pole. Furthermore, we have observed abrupt changes in the masses of both scalar and pseudoscalar mesons at finite CCP values, particularly at higher temperatures. A decreasing trend in the Mott transition temperature is seen with the increase in CCP. Published by the American Physical Society 2024
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