Scattering of fermions in the Yukawa theory coupled to Unimodular Gravity

Abstract

We compute the lowest order gravitational UV divergent radiative corrections to the S matrix element of the $fermion+fermion\to fermion+fermion$ 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 $\kappa g^2$ order of the vertex involving two fermions and one graviton only.

arXiv comment21 pages, 12 figures

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• Unimodular Gravity vs General Relativity: A status report
• Gravity with more or less gauging
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Effective action for the Yukawa model in curved spacetime
• Can quantum fluctuations differentiate between standard and unimodular gravity?
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