Investigation of Effects of New Physics in ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ Decay

Abstract

Recent experimental results of $\mathcal{R}(D^{(\ast )})$ deviate from the standard model (SM) by $3.1\sigma$, suggesting a new physics (NP) that affects the $b\to c\tau {\bar{\nu }}_{\tau }$ transition. Motivated by this, we investigate the possible NP effects in the ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ decay. For this purpose, assuming the neutrinos are left-handed, we calculate in detail the helicity amplitudes of ${\Lambda }_b\to {\Lambda }_c\ell {\bar{\nu }}_{\ell }$ decays with all possible four-fermion operators. Within the latest results of ${\Lambda }_b\to {\Lambda }_c$ form factors from lattice QCD calculations, we study these decays in a model-independent manner. The differential and total branching fractions and other observables are calculated. In SM, we obtain the ratio $\mathcal{R}({\Lambda }_c)=0.33\pm 0.01$. Supposing that NP only affects the third generation fermions, we present the correlations among $\mathcal{R}(D)$, $\mathcal{R}(D^{\ast })$ and $\mathcal{R}({\Lambda }_c)$. We perform a minimum ${\chi }^2$ fit of the wilson coefficient of each operator to the latest experimental data of different observables. It is found that the left-handed scalar operator ${\mathcal{O}}_{SL}$ affects the branching fraction remarkably, and the ratio $\mathcal{R}({\Lambda }_c)$ can be enhanced by $30\%$. For other operators, the ratio amounts to $0.38\pm 0.02$, which is larger than prediction of SM by $20\%$. Using the fitted values of the wilson coefficients of the single NP operators, we also give a prognosis for the physical observables of ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$. Furthermore, we also study the effects of three typical NP models on ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$. We hope our results can be tested in the current LHCb experiment and the future high energy experiments.

Comments: 24 pages,8 figures