$\phi$ and $J/\psi$ Production in Proton-Proton Scattering through Hadronic Molecules

This study estimates the contributions of hidden-strangeness hadronic molecular states ($N(2080)3/2^-$, $N(2270)3/2^-$) to $\phi$ production and hidden-charm $P_c$ states to $J/\psi$ production in $pp$ collisions. The calculated cross-sections reach $\sim 10~\mu b$ for $pp\to pp\phi$ and $\sim 0.1~nb$ for $pp\to pp J/\psi$ at energies $\sim 2$~GeV above threshold. We also compute the spin density matrix element $\rho_{00}$ and the decay angular distributions for $\phi\to K^+K^-$ and $J/\psi\to\mu^+\mu^-$. To support future experiments, we conduct Monte Carlo simulations for the four-body final states of $pp\to ppK^+K^-$ and $pp\to pp\mu^+\mu^-$. The resulting lab-frame distributions are expected to inform detector design at facilities like the High-Intensity heavy-ion Accelerator Facility (HIAF) and the proposed Chinese Advanced Nuclear Physics Research Facility (CNUF), enabling more precise measurements and tighter theoretical constraints. Furthermore, to explain the STAR collaboration's result on $\phi$ meson spin alignment in heavy-ion collisions, we propose a novel mechanism involving hidden-strangeness molecular states, testable with future high-statistics $pp\to pp\phi$ data.