$φ$ meson in nuclear matter and atomic nuclei

Abstract: The properties (masses and decay widths) of the $\phi$ meson are investigated in nuclear matter from the $\phi$ meson self-energy, using the tree-level $\phi K\bar{K}$ Lagrangian, and, incorporating in-medium masses of (anti)kaons calculated within the quark meson coupling (QMC) model. These mass shifts and decay widths are incorporated in the Breit-Wigner spectral function of the $\phi$ meson to calculate the production cross-section of $\phi$ in asymmetric nuclear matter. Considerable modifications to the production cross-section are observed at normal nuclear matter density, driven by the in-medium mass reduction and the increase in the decay width of $\phi$ meson. The potential experienced by $\phi$ meson in nuclear matter is used to study the possibility of formation of the $\phi$ mesic bound state with atomic nuclei. We explore the potential formation of $\phi$-mesic bound states in ${\rm{^{4}He}}$, ${\rm{^{12}C}}$, ${\rm{^{16}O}}$, ${\rm{^{40}Ca}}$, ${\rm{^{90}Zr}}$, ${\rm{^{197}Au}}$ and ${\rm{^{208}Pb}}$ nuclei by investigating their binding energies and absorption widths based on the corresponding $\phi$-nucleus potentials. Our study shows shallow bound states with the light nuclei and deeply bound states in heavy nuclei. Among the investigated nuclei, a particularly distinct signal for a $\phi$-mesic bound state is identified in ${\rm{^{16}O}}$, suggesting its potential experimental observability. The work provides valuable insights into $\phi$ meson interactions in infinite nuclear matter and the potential formation of exotic $\phi$-mesic nuclear states, offering promising probes for strongly interacting matter in the upcoming experiments at J-PARC, JLab, and ${\rm{\bar{P}}ANDA}$@FAIR physics program.