Unimodular gravity and general relativity UV divergent contributions to the scattering of massive scalar particles

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We work out the one-loop and order κ 2m2 φ UV divergent contributions, coming from Unimodular Gravity and General Relativity, to the S matrix element of the scattering process φ+φ → φ+φ in a λφ4 theory with mass mφ . We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contributions in Dimension Regularization. This seems to be at odds with the known result that in a multiplicative MS dimensional regularization scheme the General Relativity corrections, in the de Donder gauge, to the beta function βλ of the λ coupling do not vanish, whereas the Unimodular Gravity corrections, in a certain gauge, do vanish. Actually, we show that the UV divergent contributions to the 1PI Feynman diagrams which give rise to those non-vanishing corrections to βλ do not contribute to the UV divergent behaviour of the S matrix element of φ + φ → φ + φ and this shows that any physical consequence –such existence of asymptotic freedom due to gravitational interactions– drawn from the value of βλ is not physically meaningful.
© 2018 IOP Publishing Ltd and Sissa Medialab. We are grateful to E. Alvarez 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 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 SEV2016-0597.
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