Abstract
We provide a combined explanation of the increasingly tantalizing B-meson anomalies, both in {R}_{K^{left(ast right)}} and {R}_{D^{left(ast right)}} , in the Pati-Salam model with minimal matter content. This well-known model, based on the gauge group SU(4)LC × SU(2)L × SU(2)R, naturally contains a variety of scalar leptoquarks with related and restricted couplings. In particular we show that the seesaw-motivated scalar leptoquark within the representation ( overline{mathbf{10}} ,3,1) and its right-handed parity partner ( overline{mathbf{10}} ,1,3) can solve both anomalies while making testable predictions for related observables such as B → Kνν and B → Kμτ. The solution of the {R}_{K^{left(ast right)}} anomaly alone can be related to a type-II seesaw neutrino mass structure. Explaining also {R}_{D^{left(ast right)}} requires the existence of a light right-handed neutrino, which constrains the UV structure of the model.
Highlights
Parametrized by the double ratio RK(∗) between the μ and e channels, relative to the SM
The effective-field-theory (EFT) scale involved is rather low at Λ 3.4 TeV [20] — in that the effective operator 2/(3.4 TeV)2 significantly improves the fit [21] — and a number of related observables pose stringent constraints; one of the most important observables here is B → Kνν because the involved quark-level transition b → sνν is often related to the same new physics that contributes to the anomalous b → cτ ν by SU(2)L invariance
Since the anomalies point at new physics in the TeV range, such a light PS gauge boson would conflict with experiments involving first-generation fermions, for instance KL → e±μ∓, which exclude PS scales lower than ∼ 1000 TeV [32,33,34,35]
Summary
The Pati-Salam model is based on the gauge group SU(4)LC × SU(2)L × SU(2)R [41], where colour and lepton number are unified in a single SU(4)LC factor. For the Dirac mass matrices of down quarks with charged leptons, and up quarks with Dirac neutrinos The latter relation will be broken by the seesaw mechanism, as discussed below, leaving md = m as a PS prediction. If this is the only PS-breaking VEV, it needs to be above ∼ 1000 TeV to satisfy constraints on KL → e±μ∓ induced by the heavy. Assuming that δ1 is the only PS-breaking VEV, our PS setup brings both type I and II seesaw contributions to the light Majorana neutrino masses, similar to standard left-right models [64]: Mν = MνI + MνII. This will be postponed to the sections (sections 4 and 5)
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