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Scattering of fermions in the Yukawa theory coupled to unimodular gravity

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González Martín, S. and Pérez Martín, Carmelo (2018) Scattering of fermions in the Yukawa theory coupled to unimodular gravity. European physical journal C, 78 (3). ISSN 1434-6044

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Official URL: http://doi.org/10.1140/epjc/s10052-018-5734-z




Abstract

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.


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© The Author(s) 2018. We are grateful to E. Álvarez for illuminating discussions. This work has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grants Agreement No. 674896 and No. 690575. We also have been partially supported by the Spanish MINECO through Grants FPA2014-54154-P and FPA2016-78645-P, COST actions MP1405 (Quantum Structure of Spacetime) and COST MP1210 (The string theory Universe). S.G.-M. acknowledge the support of the Spanish Research Agency (Agencia Estatal de Investigación) through the Grant IFT Centro de Excelencia Severo Ochoa SEV-2016- 0597.

Uncontrolled Keywords:Cosmological constant.
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:47510
Deposited On:18 May 2018 08:02
Last Modified:18 May 2018 08:11

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