Carlini et al. (2023)

# Resolving RDsubscript𝑅𝐷R\_{D} and RD∗subscript𝑅superscript𝐷R\_{D^{\*}} Anomalies in Adjoint SU(5)

A. Ismael1,2 and S. Khalil21Physics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.
2Center for Fundamental Physics, Zewail City of Science and
Technology, 6th of October City, Giza 12578, Egypt.

###### Abstract

We investigate the RDsubscript𝑅𝐷R\_{D} and RD∗subscript𝑅superscript𝐷R\_{D^{\*}} anomalies in the context of non-minimal S​U​(5)𝑆𝑈5SU(5), where Higgs sector is extended by
adjoint 45-dimensional multiplet. One of the light spectrum of this model could be the scalar triplet leptoquark that is contained in this multiplet.
We demonstrate that this particular scalar leptogquark mediation of the transition b→c​τ​ν→𝑏𝑐𝜏𝜈b\\to c\\tau\\nu is capable of simultaneously accounting for both RDsubscript𝑅𝐷R\_{D} and RD∗subscript𝑅superscript𝐷R\_{D^{\*}} anomalies. We further emphasize that another Yukawa coupling controls its contribution to b→s​ℓ+​ℓ−→𝑏𝑠superscriptℓsuperscriptℓb\\to s\\ell^{+}\\ell^{-}, ensuring that RKsubscript𝑅𝐾R\_{K} and RK∗subscript𝑅superscript𝐾R\_{K^{\*}} remain consistent with the standard model predictions.

## I Introduction

Semileptonic decays B→{D,D∗}​τ​ν→𝐵𝐷superscript𝐷𝜏𝜈B\\to\\{D,D^{\*}\\}\\tau\\nu have received a lot of attention in recent years because they provide a good opportunity to test the Standard Model (SM) and look for possible new physics beyond. Recent intriguing measurements of RD,D∗subscript𝑅𝐷superscript𝐷R\_{D,D^{\*}} by BaBar \[ [2](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib2 ""), [3](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib3 "")\], Belle \[ [4](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib4 ""), [5](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib5 ""), [6](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib6 ""), [7](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib7 "")\], and LHCb collaborations \[ [8](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib8 "")\] are significant hints of new physics that violate lepton flavor universality. The ratios RD,D∗subscript𝑅𝐷superscript𝐷R\_{D,D^{\*}} are defined by

|     |     |     |     |
| --- | --- | --- | --- |
|  | RD∗,D≡B​R​(Bq→{D∗,D}​τ​ν)B​R​(Bq→{D∗,D}​l​ν),subscript𝑅superscript𝐷𝐷𝐵𝑅→subscript𝐵𝑞superscript𝐷𝐷𝜏𝜈𝐵𝑅→subscript𝐵𝑞superscript𝐷𝐷𝑙𝜈\\displaystyle R\_{D^{\*},D}\\equiv\\frac{BR(B\_{q}\\rightarrow\\{D^{\*},D\\}\\tau\\nu)}{BR(B\_{q}\\rightarrow\\{D^{\*},D\\}l\\nu)}\\,, |  | (1) |

where l=e,μ𝑙𝑒𝜇l=e,\\mu. The current experimental averages of RDsubscript𝑅𝐷R\_{D} and
RD∗subscript𝑅superscript𝐷R\_{D^{\*}} are given by \[ [9](https://ar5iv.labs.arxiv.org/html/2301.02226#bib.bib9 "")\]

|     |     |     |     |     |
| --- | --- | --- | --- | --- |
|  | RDsubscript𝑅𝐷\\displaystyle R\_{D} | =0.339±0.026±0.014,absentplus-or-minus0.3390.0260.014\\displaystyle=0.339\\pm 0.026\\pm 0.014\\,, |  | (2) |
|  | RD∗subscript𝑅superscript𝐷\\displayst

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