TeV-scale scalar leptoquarks motivated by B anomalies improve Yukawa unification in SO(10) GUT

Abstract

It is common practice to explain deviations between data and Standard-Model (SM) predictions by postulating new particles at the TeV scale ad-hoc. This approach becomes much more convincing, if one successfully embeds the postulated particles into a UV completion which addresses other conceptual or phenomenological shortcomings of the SM. We present a study of an SO(10) grand unified theory which contains scalar leptoquark fields employed to explain the ``flavour anomalies'' in $b\rightarrow s$ and $b\rightarrow c$ decays. We find that the additional degrees of freedom improve the renormalization-group (RG) evolution of the SM parameters. In particular, the light leptoquarks modify the RG evolution of the Yukawa couplings such that successful bottom-tau unification becomes possible in a minimal SO(10) GUT with only a $126$-plet coupling to fermions. If we amend the Yukawa interaction of the minimal one-generation model with a second fermion multiplet and small flavor-violating terms, we find the flavour violation in the leptoquark couplings growing with the RG evolution while it stays small in the Yukawa interaction of the SM Higgs boson. By employing mass splittings among the members of the $126$-plet one can increase the effect and obtain large flavor violation in leptoquark couplings from tiny perturbations at the GUT scale, because the flavour-conserving limit is an unstable initial condition for the RG equations.