  The origin of the observed Band-like photon spectrum in short gamma-ray
bursts (sGRBs) is a long-standing mystery. We carry out the first general
relativistic magnetohydrodynamic simulation of a sGRB jet with initial
magnetization $\sigma_0 = 150$ in dynamical ejecta from a binary merger. From
this simulation, we identify regions along the jet of efficient energy
dissipation due to magnetic reconnection and collisionless sub-shocks. Taking
into account electron and proton acceleration processes, we solve for the first
time the coupled transport equations for photons, electrons, protons,
neutrinos, and intermediate particles species up to close to the photosphere
(i.e., up to $1 \times 10^{12}$ cm), accounting for all relevant radiative and
cooling processes. We find that the subphotospheric multi-messenger signals
carry strong signatures of the hadronic interactions and their resulting
particle cascades. Importantly, the spectral energy distribution of photons is
significantly distorted with respect to the Wien one, commonly assumed below
the photosphere. Our findings suggest that the bulk of the non-thermal photon
spectrum observed in sGRBs can stem from hadronic processes, occurring below
the photosphere and previously neglected, with an accompanying energy flux of
neutrinos peaking in the GeV energy range.
