Indication of a p-$\phi$ bound state from a correlation function analysis

The existence of a nucleon-$\phi$ (N-$\phi$) bound state has been subject of theoretical and experimental investigations for decades. In this letter, indication of a \pphi bound state is found, using for the first time two-particle correlation functions as alternative to invariant mass spectra. Newly available lattice calculations for the spin 3/2 \Nphi interaction by the HAL QCD collaboration are used to constrain the spin 1/2 counterpart from the fit of the experimental \pphi correlation function measured by ALICE. The corresponding scattering length and effective range are $f_0^{(1/2)}=\left(-1.54^{+0.53}_{-0.53}(\mathrm{stat.})^{+0.16}_{-0.09}(\mathrm{syst.})+i\cdot0.00^{+0.35}_{-0.00}(\mathrm{stat.})^{+0.16}_{-0.00}(\mathrm{syst.})\right)$~fm and $d_0^{(1/2)}=\left(0.39^{+0.09}_{-0.09}(\mathrm{stat.})^{+0.02}_{-0.03}(\mathrm{syst.})+i\cdot0.00^{+0.00}_{-0.04}(\mathrm{stat.})^{+0.00}_{-0.02}(\mathrm{syst.})\right)$~fm, respectively. The results imply the appearance of a \pphi bound state with an estimated binding energy in the range of $12.8-56.1$ MeV.