transitions in the standard model effective field theory

Quan-Yi Hu; Xin-Qiang Li; Ya-Dong Yang

doi:10.1140/epjc/s10052-019-6766-8

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2019) 79: 264
https://doi.org/10.1140/epjc/s10052-019-6766-8

Regular Article - Theoretical Physics

${b\rightarrow c\tau \nu }$ transitions in the standard model effective field theory

Quan-Yi Hu, Xin-Qiang Li^* and Ya-Dong Yang

Key Laboratory of Quark and Lepton Physics (MOE), Institute of Particle Physics, Central China Normal University, Wuhan, 430079, Hubei, China

^* e-mail: xqli@mail.ccnu.edu.cn

Received: 19 November 2018
Accepted: 8 March 2019
Published online: 22 March 2019

Abstract

The $R(D^{(*)})$ anomalies observed in $B\rightarrow D^{(*)}\tau \nu$ decays have attracted much attention in recent years. In this paper, we study the $B\rightarrow D^{(*)}\tau \nu$ , $\Lambda _b\rightarrow \Lambda _c\tau \nu$ , $B_c\rightarrow (J/\psi ,\,\eta _c)\tau \nu$ , $B\rightarrow X_c\tau \nu$ , and $B_c\rightarrow \tau \nu$ decays, all being mediated by the same quark-level $b\rightarrow c\tau \nu$ transition, in the Standard Model Effective Field Theory. The most relevant dimension-six operators for these processes are $Q_{lq}^{(3)}$ , $Q_{ledq}$ , $Q^{(1)}_{lequ}$ , and $Q^{(3)}_{lequ}$ in the Warsaw basis. Evolution of the corresponding Wilson coefficients from the new physics scale $\Lambda =1$ TeV down to the characteristic scale $\mu _b\simeq m_b$ is performed at three-loop in QCD and one-loop in EW/QED. It is found that, after taking into account the constraint ${{\mathcal {B}}}(B_c\rightarrow \tau \nu )\lesssim 10\%$ , a single $\left[ C_{lq}^{(3)}\right] _{3323}(\Lambda )$ or $\left[ C^{(3)}_{lequ}\right] _{3332}(\Lambda )$ can still be used to resolve the $R(D^{(*)})$ anomalies at $1\sigma$ , while a single $\left[ C^{(1)}_{lequ}\right] _{3332}(\Lambda )$ is already ruled out by the measured $R(D^{(*)})$ at more than $3\sigma$ . By minimizing the $\chi ^2(C_i)$ function constructed based on the current data on R(D), $$R(D^*)$$ , $P_\tau (D^*)$ , $R(J/\psi )$ , and $$R(X_c)$$ , we obtain eleven most trustworthy scenarios, each of which can provide a good explanation of the $R(D^{(*)})$ anomalies at $1\sigma$ . To further discriminate these different scenarios, we predict thirty-one observables associated with the processes considered under each NP scenario. It is found that most of the scenarios can be differentiated from each other by using these observables and their correlations.