  We propose a resolution of the discrepancy between the proton yield predicted
by the statistical hadronization approach and data on hadron production in
ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix
formulation of statistical mechanics to include pion-nucleon interactions, we
reexamine their contribution to the proton yield, taking resonance widths and
the presence of nonresonant correlations into account. The effect of
multi-pion-nucleon interactions is estimated using lattice QCD results on the
baryon-charge susceptibility. We show that a consistent implementation of these
features in the statistical hadronization model, leads to a reduction of the
predicted proton yield, which then quantitatively matches data of the ALICE
collaboration for Pb-Pb collisions at the LHC.
