Quantum corrections to gravitational potential of scalarized neutron star binary

We investigate the long-distance, low-energy, leading quantum corrections to gravitational potential for scalarized neutron star (NS) binary systems, by treating general relativity as an effective field theory. We neglect the extended scales of two star components and treat them as heavy point particles, which gravitationally interact with each other via the exchanges of both gravitons and scalar particles, because of the settled scalar configurations inside the stars. Accordingly, the gravitational potential includes both Newtonian potential and scalar-modified Newtonian-like part. We, in the non-relativistic limit, calculate the non-analytic corrections to the modified gravitational potential directly from the sum of all exchanges of both gravitons and scalar particles to one-loop order. The appropriate vertex rules are extracted from the effective Lagrangian. Our calculations demonstrate that either the graviton exchanges or the exchanges of scalar particles contribute to both classical relativistic corrections and quantum corrections to the gravitational potential of the scalarized NS binaries.