Addressing the ${\mathbf{R}}_{D^{(\ast )}}$ anomalies with an ${\mathbf{S}}_1$ leptoquark from $\mathbf{SO}(10)$ grand unification

Abstract

Motivated by the $R_{D^{(\ast )}}$ anomalies, we investigate an $\mathrm{SO}(10)$ grand unification scenario where a charge $-1/3$ scalar leptoquark ($S_1$) remains as the only new physics candidate at the TeV scale. This leptoquark along with the Standard Model (SM) Higgs doublet originates from the same 10-dimensional real scalar multiplet in the $\mathrm{SO}(10)$ grand unification framework taking its mass close to the electroweak scale. We explicitly show how the gauge coupling unification is achieved with only one intermediate symmetry-breaking scale at which the Pati-Salam gauge group is broken into the SM group. We investigate the phenomenological implications of our scenario and show that an $S_1$ with a specific Yukawa texture can explain the $R_{D^{(\ast )}}$ anomalies. We perform a multiparameter scan considering the relevant flavour constraints on $R_{D^{(\ast )}}$, $F_L(D^{\ast })$, $P_{\tau }(D^{\ast })$ and $R_{K^{(\ast )}}^{\nu \nu }$ as well as the constraint coming from the $Z\to \tau \tau$ decay and the latest $\tau \tau$ resonance search data at the LHC. Our analysis shows that a single leptoquark solution to the observed $R_{D^{(\ast )}}$ anomalies with $S_1$ is still a viable solution.

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