Carlos M. Nieto: In search of a UV completion of the Standard Model
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. We study the corresponding renormalization group $\beta$-functions to the 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 $\beta$-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.