Exploring the photoproduction of \(\rho \) and \(\phi \) in hadronic heavy-ion collisions

Significant enhancements of J/\(\psi \) production have been observed by various experiments at RHIC and LHC for very low transverse momenta in peripheral heavy-ion collisions, which has ignited a surge of investigations into photon-induced processes in hadronic heavy-ion collisions (HHICs). Within this wave of research enthusiasm, the search for more photon induced products in HHICs becomes paramount. In this paper, we perform the calculation of the \(\rho \) and \(\phi \) production resulting from photon-nucleus interactions in HHICs, which are crucial probes for studying the properties of quark-gluon plasma (QGP) in HHICs. Our study reveals that, in comparison to hadronic production, the photon-induced production of \(\rho \) and \(\phi \) does not reach the same level of significance as that observed in J/\(\psi \) production. Nevertheless, it remains substantial, especially in peripheral collisions, holding great promise for experimental verification in the imminent future.