Signatures of Odd-Parity $s$-wave $\Xi^*$ States in Femtoscopic Correlation Functions

Abstract

We investigate the $\Xi^*$ resonances within the molecular picture, where these states are dynamically generated as poles in the unitarized scattering amplitudes arising from the coupled-channel interactions of $K^{*-} \Lambda$, $K^{*-} \Sigma^0$, $\rho^- \Xi^0$, $\overline{K}{}^{*0} \Sigma^-$, $\rho^0 \Xi^-$, $\omega \Xi^-$, and $\phi \Xi^-$. The interaction kernel is derived from the local hidden gauge formalism, while the unitarization procedure employs a hybrid method that combines cutoff and dimensional regularizations in the evaluation of the loop function. From a detailed spectroscopic analysis, we identify two $S = -2$ baryon states whose properties are compatible with some of the $\Xi^*$ resonances listed in the Review of Particle Physics. To explore their possible experimental signatures, we compute the femtoscopic correlation functions for all the vector-baryon pairs considered in the present study, using realistic estimates of production weights and varying source sizes $R = 1, 1.1, 1.2, 1.3, 1.5$ fm.