Production of $K^{+}{K}^{-}$ Pairs Through Decay of $\ddot{I}•$ Meson

Abstract

We develop a theoretical framework for the production of $K^{+}{K}^{-}$ pairs through the decay of $\ddot{I}•$ mesons produced from a thermal background, based on the Nambu-Jona-Lasinio (NJL) model. The differential production rate of $K^{+}{K}^{-}$ is related to the self-energy of the $\ddot{I}•$ meson, incorporating the contributions of the quark loop at leading order and the kaon loop at next-to-leading order in the $1/N_c$ expansion. We numerically evaluate the invariant mass spectrum of the $K^{+}{K}^{-}$ pair both in vacuum and at finite temperature. The inclusion of the kaon loop results in a finite width of the spectrum, improving agreement with experimental data. We also investigate the spin alignment of the $\ddot{I}•$ meson induced by its motion relative to the thermal background. In the NJL model with only chiral condensates, we find that deviations from the unpolarized limit of 1/3 are negligible.

15 pages, 11 figures