Impact of Finite Volume on Kaon, Antikaon, and φ Meson Masses and Decay Widths in Asymmetric Strange Hadronic Matter

In the present work, we investigate the impact of finite volume on the in-medium properties of kaons ($K<^>+$, $K<^>0$), antikaons ($K<^>-$, $\bar{K<^>0}$), and $\phi$ mesons in the isospin asymmetric strange hadronic medium at finite density and temperature. We use the chiral SU(3) hadronic mean-field model, which accounts for the interactions between baryons through the exchange of scalar ($\sigma , \zeta , \delta$) and vector ($\omega$, $\rho$, $\phi$) fields. To investigate the effects of finite volume, we apply the multiple reflection expansion technique for calculations of the density of states. At high baryon density, an increase of the isospsin asymmetry of the medium from zero to a finite value is found to impact the nonstrange scalar field $\sigma$ more than the strange scalar field $\zeta$, whereas the opposite is the case as a function of the strangeness fraction of the medium. For example, in an infinite nuclear medium at $\rho _B = 4\rho _0$, for an increase of isospin asymmetry from zero to ${\sim}0.3$, the magnitudes of the scalar fields $\sigma$ and $\zeta$ increase by ${\sim}3.0$% and ${\sim}0.1$%, respectively. On the other hand, for a symmetric medium, an increase of $f_s$ from 0 to 0.5 leads to an increase in the magnitude of $\sigma$ by ${\sim}0.4$% and a decrease in $\zeta$ by ${\sim}16$%. We use the medium-modified masses of kaons and antikaons calculated using the chiral SU(3) model to obtain the masses and decay widths of $\phi$ mesons in the finite volume hadronic medium. To obtain the masses and decay widths of $\phi$ mesons, an effective Lagrangian approach with $\phi$K$\bar{K}$ interactions at the one-loop level is used in the present work. We obtain the effective masses and decay widths in the finite volume matter for a spherical geometry of a medium with Neumann and Dirichlet boundary conditions as well as for a cubic geometry. At baryon density 4$\rho _0$, the Dirichlet boundary conditions with spherical geometry of the medium leads to changes of ${\sim}4$%, ${\sim}3$%, and ${\sim}0.6$% in the effective masses of the K, $\bar{K}$, and $\phi$ mesons, as the system size decreases from $R = \infty$ to 2 fm in a symmetric nuclear medium.