Addressing the $R_{\tau /\mu ,e}\left(D^{(\ast )}\right)$ puzzle through New Physics four-fermion operators and their impact on ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ decay

Abstract

The Lepton Flavor Universality ratio $R_{\tau /\mu ,e}\left(D^{(\ast )}\right)$ poses a challenge to the Standard Model (SM), as B-factory experiments, BaBar, Belle, and the LHCb show $3.31\sigma$ deviations from their theoretical predictions. Utilizing the latest HFLAV averages and incorporating the branching ratio constraints $60\%$, $30\%$ and $10\%$ from the lifetime of the $B_c$ meson, we determine the values of the Wilson coefficients (WCs) for different New Physics (NP) four-fermion operator with specific Lorentz structures. Our analysis finds that the WC scenario $\left(C_{S_L},C_{S_R}\right)$ is the most probable, the maximum pull from the SM, and strongly influenced by branching ratio constraints. Furthermore, we identify three degenerate solutions involving $C_{V_L}$, $C_{V_L}^{\prime }$, $C_{V_L}^{\prime \prime }$, and $C_{S_R}^{\prime \prime }$ as the second most probable NP scenarios. We then studied the influence of these NP operators on various physical observables in ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ decay by using the Lattice QCD form factors. Our results highlighted $C_{S_L}^{\prime \prime }$, $C_{S_R}$, $C_T$, $\left(C_{S_L},C_{S_R}\right)$, $\left(C_{S_R},C_T\right)$, and the three degenerate scenarios involving $\left(C_{S_L},C_T\right)$, $\left(C_{S_L}^{\prime },C_T^{\prime }\right)$ and $\left(C_{S_L}^{\prime \prime },C_T^{\prime \prime }\right)$ as strong indicators of NP. The correlation of different physical observables shows a direct correlation between $d\Gamma /d{q}^2$ and $P_L^{\tau }$ for WC $\left(C_{S_L},C_{S_R}\right)$; and between $A_{FB}$ and $P_L^{{\Lambda }_c}$ for three degenerate WCs involving $\left(C_{S_L},C_T\right)$. We hope that the measurements of these observables in ongoing and future experiments will help us scrutinize these constraints on the various NP couplings.

35 pages, 9 figures

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