Carlos M. Nieto

We explore a simple parameterization of new physics that results in an ultraviolet complete gauge-quark sector of the Standard Model. Specifically, we add an antiscreening contribution to the beta functions of the gauge couplings and a flavor-independent, antiscreening contribution to the beta functions of the Yukawa couplings. These two free parameters give rise to an intricate web of Renormalization Group fixed points. Their predictive power extends to the flavor structure and mixing patterns, which we investigate to demonstrate that some of the free parameters of the Standard Model could be determined by the Renormalization Group flow.

A bstract: Asymptotically safe extensions of the Standard Model have been searched for by adding vector-like fermions charged under the Standard Model gauge group and having Yukawa-like interactions with new scalar fields. Here we study the corresponding renormalization group β -functions to next and next-to-next to leading order in the perturbative expansion, varying the number of extra fermions and the representations they carry. We test the fixed points of the β -functions against various criteria of perturbativity to single out those that are potentially viable. We show that all the candidate ultraviolet fixed points are unphysical for these models: either they are unstable under radiative corrections, or they cannot be matched to the Standard Model at low energies.

We discuss various realizations of the Weyl group in the background field expansion of quantum gravity, in the presence of a cutoff, as required in applications of the functional renormalization group. To study the background dependence, special attention is given to split gauge transformations, which act on the background field and fluctuation keeping the total metric unchanged. The results generalize previous works on global and local scale transformations.