Scattering of fermions in the Yukawa theory coupled to Unimodular Gravity

2018, March 10
S. Gonzalez-Martin and C.P. Martin
Eur. Phys. J. C (2018) 78:236
  s10052-018-5734-z-1.pdf

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.