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≤−0.95(9). This bound implies the restriction on the low-energy constant c8 of the effective chiral action for nucleons and pions in the presence of an external gravitational field, c8≤−1.1(1) GeV−1. For the physical pion mass we obtain a model independent bound D≤−0.20(2).