$φ$ and $J/ψ$ Production in Proton-Proton Scattering through Hadronic Molecules

Abstract

This study estimates the contributions of hidden-strangeness hadronic molecular states ($N(2080)3/2^-$, $N(2270)3/2^-$) to $φ$ production and hidden-charm $P_c$ states to $J/ψ$ production in $pp$ collisions. The calculated cross-sections reach $\sim 10~μb$ for $pp\to ppφ$ and $\sim 0.1~nb$ for $pp\to pp J/ψ$ at energies $\sim 2$~GeV above threshold. We also compute the spin density matrix element $ρ_{00}$ and the decay angular distributions for $φ\to K^+K^-$ and $J/ψ\toμ^+μ^-$. To support future experiments, we conduct Monte Carlo simulations for the four-body final states of $pp\to ppK^+K^-$ and $pp\to ppμ^+μ^-$. 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 $φ$ meson spin alignment in heavy-ion collisions, we propose a novel mechanism involving hidden-strangeness molecular states, testable with future high-statistics $pp\to ppφ$ data.

Figures (15)

• Figure 1: Generic structures of the $\phi$ and $J/\psi$ production in proton-proton scattering within hadronic molecular picture. Time proceeds from left to right.
• Figure 2: Total cross sections obtained by our model and simply estimation of the contribution of the proton, where the blue dashed line and red dot-dashed line corresponding to the solution A and B listed in Tab. \ref{['tab_couplings']}, while the black solid line and the gray dotted line corresponding to the $(g_{\phi NN},\kappa_{\phi}) = (-0.4,-0.5)$ and $(g_{\phi NN},\kappa_{\phi}) = (-0.4,-4.0)$ case based on Ref. Tsushima:2003fs.
• Figure 3: Total cross sections and the single molecular state $N(2080)3/2^-$ or $N(2270)3/2^-$ contribution to the cross section. Where the blue dashed line and red dot-dashed line notably the same as its in Fig.\ref{['Total1']}, while the cyan large-dashed line, green solid line, orange dotted line and purple large-dotted line corresponding to the contribution from $N(2080)3/2^-$ in solution A, $N(2270)3/2^-$ in solution A, $N(2080)3/2^-$ in solution B, and $N(2270)3/2^-$ in solution B, respectively. Solutions A and B are based on Tab. \ref{['tab_couplings']}.
• Figure 4: Differential cross section with the angle of outgoing $\phi$ meson $\theta_\phi$ in the center-of-mass frame at the center-of-mass energy $W=4.38$ GeV. Where the blue dashed line and the red dot-dashed line correspond to the solutions A and B obtained by our model.
• Figure 5: Contribution from different terms individually while the assumption decay widths are equal, re-normalized to $\sigma^{3/2^-}_{g_1}$. Where the gray baseline, cyan dashed line, magenta large-dashed line, black solid line, blue dot-dashed line, and red dotted line correspond to the contribution from $g_1$, $g_2$, and $g_3$ of $J^P = 3/2^-$ and $5/2^-$, respectively.