We extend our general framework for semileptonic decay, originally introduced in N. Penalva et al. [Phys. Rev. D 100, 113007 (2019)], with the addition of new physics (NP) tensor terms. In this way, all the NP effective Hamiltonians that are considered in lepton flavor universality violation (LFUV) studies have now been included. Those are left and right vector and scalar NP Hamiltonians and the NP tensor one. Besides, we now also give general expressions that allow for complex Wilson coefficients. The scheme developed is totally general and it can be applied to any charged current semileptonic decay, involving any quark flavors or initial and final hadron states. We show that all the hadronic input, including NP effects, can be parametrized in terms of 16 Lorentz scalar structure functions, constructed out of the NP complex Wilson coefficients and the genuine hadronic responses, with the latter determined by the matrix elements of the involved hadron operators. In the second part of this work, we use this formalism to obtain the complete NP effects in the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\tau {\overline{\nu }}_{\tau }$ semileptonic decay, where LFUV, if finally confirmed, is also expected to be seen. We stress the relevance of the center of mass (CM) $d^2\mathrm{\Gamma }/(d\omega d\cos {\theta }_{\ell })$ and laboratory (LAB) $d^2\mathrm{\Gamma }/(d\omega d{E}_{\ell })$ differential decay widths, with $\omega$ the product of the hadron four-velocities, ${\theta }_{\ell }$ the angle made by the three-momenta of the charged lepton and the final hadron in the $W^{-}$ CM frame and $E_{\ell }$ the charged lepton energy in the decaying hadron rest frame. While models with very different strengths in the NP terms give the same differential $d\mathrm{\Gamma }/d\omega$ and total decay widths for this decay, they predict very different numerical results for some of the $\cos {\theta }_{\ell }$ and $E_{\ell }$ coefficient-functions that determine the above two distributions. Thus, the combined analysis of the CM $d^2\mathrm{\Gamma }/(d\omega d\cos {\theta }_{\ell })$ and LAB $d^2\mathrm{\Gamma }/(d\omega d{E}_{\ell })$ differential decay widths will help clarifying what kind of NP is a better candidate in order to explain LFUV.

• Received 17 April 2020
• Accepted 4 June 2020

DOI:https://doi.org/10.1103/PhysRevD.101.113004

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society