We compute the lowest order gravitational UV

divergent radiative corrections to the S matrix element of

the fermion + fermion → 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. The agreement found points in the direction

that Unimodular Gravity and General Relativity give rise to

the same quantum theory when coupled to matter, as long as

the Cosmological Constant vanishes. Along the way we have

come across another unexpected cancellation of UV divergences

for both Unimodular Gravity and General Relativity,

resulting in the UV finiteness of the one-loop and κy^2 order

of the vertex involving two fermions and one graviton only.

# Scattering of fermions in the Yukawa theory coupled to Unimodular Gravity

2018, March 10

Eur. Phys. J. C (2018) 78:236