$b\to c\tau \nu$ Transitions in the Standard Model Effective Field Theory

Abstract

The $R(D^{(\ast )})$ anomalies observed in $B\to D^{(\ast )}\tau \nu$ decays have attracted much attention in recent years. In this paper, we study the $B\to D^{(\ast )}\tau \nu$, ${\Lambda }_b\to {\Lambda }_c\tau \nu$, $B_c\to (J/\psi ,{\eta }_c)\tau \nu$, $B\to X_c\tau \nu$, and $B_c\to \tau \nu$ decays, all being mediated by the same quark-level $b\to c\tau \nu$ transition, in the Standard Model Effective Field Theory. The most relevant dimension-six operators for these processes are $Q_{lq}^{(3)}$, $Q_{ledq}$, $Q_{lequ}^{(1)}$, and $Q_{lequ}^{(3)}$ 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 $\mathcal{B}(B_c\to \tau \nu )\lesssim 10\%$, a single ${\left[C_{lq}^{(3)}\right]}_{3323}(\Lambda )$ or ${\left[C_{lequ}^{(3)}\right]}_{3332}(\Lambda )$ can still be used to resolve the $R(D^{(\ast )})$ anomalies at $1\sigma$, while a single ${\left[C_{lequ}^{(1)}\right]}_{3332}(\Lambda )$ is already ruled out by the measured $R(D^{(\ast )})$ at more than $3\sigma$. By minimizing the ${\chi }^2(C_i)$ function constructed based on the current data on $R(D)$, $R(D^{\ast })$, $P_{\tau }(D^{\ast })$, $R(J/\psi )$, and $R(X_c)$, we obtain eleven most trustworthy scenarios, each of which can provide a good explanation of the $R(D^{(\ast )})$ 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.

43 pages, 3 figures and 5 tables; references updated and more discussions added, final version to be published in the journal

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• Implication of $R_{D^{(\ast )}}$ anomalies on semileptonic decays of ${\Sigma }_b$ and ${\Omega }_b$ baryons
• Signatures of complex new physics in $b\to c\tau \bar{\nu }$ transitions
• Mapping out the Space for New Physics with Leptonic and Semileptonic $B_{(c)}$ Decays
• Implication of $b\to c\tau \nu$ flavor anomalies on $B_s\to D_s^{\ast }\tau \nu$ decay observables
• Scrutinizing New Physics in Semi-leptonic $B_c\to J/\psi \tau \nu$ Decay
• New physics footprints in the angular distribution of $B_s\to D_s^{\ast }(\to D_s\gamma ,D_s\pi )\tau \nu$ decays
• $D^{\ast }$ Polarization as an Additional Constraint on New Physics in the $b\to c\tau {\bar{\nu }}_{\tau }$ Transition
• Probing new physics in semileptonic ${\Sigma }_b$ and ${\Omega }_b$ decays
• Probing New Physics Signals with Symmetry-Restored Yukawa Textures
• New physics contributions to moments of inclusive $b\to c$ semileptonic decays
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• $R_{K^{(\ast )}}$ from RPV-SUSY sneutrinos
• Investigating the effect of $U_1$ vector leptoquark on $b\to u\tau \bar{\nu }$ mediated $B$ decays
• $B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau },{\rho }^{-}{\nu }_{\tau },{\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decays with visible final-state kinematics
• Impact of $b\to c$ measurements on ${\Lambda }_b\to p\tau \bar{\nu }$ decay in $U_1$ leptoquark model
• Lepton Flavor Violating $B\to K_2^{\ast }(1430){\mu }^{\pm }{\tau }^{\mp }$ Decays
• Fingerprinting the presence of extra scalars in the $h\to Vf{f}^{\prime }$ forward-backward asymmetry
• ${\eta }_c$ leading-twist distribution amplitude and the $B_c\to {\eta }_c\ell {\bar{\nu }}_{\ell }$ semileptonic decays using QCD Sum Rules
• Lepton Universality Violation by Kaluza-Klein Neutrinos in $b\to sll$ transition