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 $f_0^{(1\mathrm{/}2)}=(-1.54_{-0.53}^{+0.53}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}{)}_{-0.09}^{+0.16}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})+i\cdot 0.00_{-0.00}^{+0.35}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}{)}_{-0.00}^{+0.16}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}))$~fm and $d_0^{(1\mathrm{/}2)}=(0.39_{-0.09}^{+0.09}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}{)}_{-0.03}^{+0.02}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})+i\cdot 0.00_{-0.04}^{+0.00}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}{)}_{-0.02}^{+0.00}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}))$~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.