A bound on the nucleon Druck-term from chiral EFT in curved space-time and mechanical stability conditions

Using dispersive representations of the nucleon gravitational form factors, the results for their absorptive parts from chiral effective field theory in curved space-time, and the mechanical stability conditions, we obtain a model independent inequality for the value of the gravitational $D(t)$ form factor at zero momentum transfer (Druck-term). In particular, the obtained inequality leads to a conservative bound on the Druck-term in the chiral limit $D \leq -0.95(9)$. This bound implies the restriction on the low-energy constant $c_8$ of the effective chiral action for nucleons and pions in the presence of an external gravitational field, $c_8\leq -1.1(1)$ GeV$^{-1}$. For the physical pion mass we obtain a model independent bound $D\leq -0.20(2)$.