Scattering of fermions in the Yukawa theory coupled to Unimodular Gravity

Understand

We compute the lowest order gravitational UV divergent radiative corrections to the S matrix element of the $fermion + fermion\rightarrow fermion + fermion$ scattering process in the massive Yukawa theory, coupled either to Unimodular Gravity or to General Relativity.

• We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contribution in Dimensional Regularization.
• This is a nontrivial result, since in the classical action of Unimodular Gravity coupled to the Yukawa theory, the graviton field does not couple neither to the mass operator nor to the Yukawa operator.
• This is unlike the General Relativity case.