The Angular Observables of ${\Lambda }_b\to {\Lambda }_c(\to {\Lambda }^0{\pi }^{+}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$ within the Paradigm of FCCC Anomalies

Abstract

We present a global analysis of the current $B$-meson flavor anomalies and extend it to the baryonic sector through the decay ${\Lambda }_b^0\to {\Lambda }_c^{+}(\to {\Lambda }^0{\pi }^{+}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$. The lepton flavor universality ratios $R_{\tau /(\mu ,e)}(D^{(\ast )})$, measured by BaBar, Belle, and LHCb, exhibit a combined $3.8\sigma$ deviation from Standard Model (SM) predictions. Using the latest HFLAV averages and $B_c$-lifetime constraints, $\mathcal{B}(B_c\to \tau \nu )<60\%,30\%,10\%$, found new physics (NP) solutions to the cascade decay ${\Lambda }_b^0\to {\Lambda }_c^{+}(\to {\Lambda }^0{\pi }^{+}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$. The scenario $(C_{V_L},C_{S_R})$ emerges as the most favored NP solution, largest pull from the SM and insensitive to branching-ratio constraints; followed by $C_{V_L}$ case. We study the impact of NP operators on a complete set of angular observables on the five-fold ${\Lambda }_b$ decay using Lattice-QCD form factors and find that the scenarios $(\Re [C_{S_L}=4C_T],\Im [C_{S_L}=4C_T])$ and $(C_{S_L},C_{S_R})$ generate the largest deviations from the SM predictions. In particular, the observables ${\mathcal{K}}_{1c}$, ${\mathcal{K}}_{2ss}$, ${\mathcal{K}}_{2cc}$, and ${\mathcal{K}}_{4s}$ show the highest sensitivity to NP effects. The correlation analysis reveals the $(\Re [C_{S_L}=4C_T],\Im [C_{S_L}=4C_T])$ scenario exhibits inverse correlations among ${\mathcal{K}}_{1c}$ and ${\mathcal{K}}_{2ss,2cc,4s}$ and direct correlations between ${\mathcal{K}}_{2ss}$ and ${\mathcal{K}}_{2cc,4s}$, pointing to a possible CP-violating phase, while the $(C_{S_L},C_{S_R})$ scenario displays complementary behavior consistent with CP-conserving dynamics. These results establish baryonic semileptonic decays as a powerful and independent probe of the $R_{\tau /(\mu ,e)}(D^{(\ast )})$ anomalies, with future measurements providing critical tests of the underlying NP structure.

23 pages, 5 figures and accepted for publication in EPJC

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