Unimodular Gravity and General Relativity UV divergent contributions to the scattering of massive scalar particles

We work out the one-loop and order kappa M-2(phi)2 UV divergent contributions, coming from Unimodular Gravity and General Relativity, to the S matrix element of the scattering process phi + phi -> phi + phi in a lambda phi(4) theory with mass m(phi). 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 beta(lambda) of the lambda 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 beta(lambda) do not contribute to the UV divergent behaviour of the S matrix element of phi + phi -> phi + phi and this shows that any physical consequence - such existence of asymptotic freedom due to gravitational interactions - drawn from the value of beta(lambda) is not physically meaningful.