A comprehensive study of $\Lambda_c^- \to \Lambda (\to p \pi) \mu^- \bar \nu_{\mu}$ incorporating SMEFT implications and right-handed neutrino

Abstract

We present a comprehensive analysis of the decay $\Lambda_c^- \to \Lambda(\to p\pi)\,\mu^- \bar\nu_\mu$ within a model-independent effective field theory framework. Previous studies have been restricted to the three-body decay $\Lambda_c^+ \to \Lambda \mu^+ \nu_\mu$ and considered only left-handed neutrinos within the Low-Energy Effective Theory (LEFT). In this work, we extend the analysis to the complete four-body angular distribution for the first time, incorporating the indirect constraints implied by the Standard Model Effective Field Theory (SMEFT) on the LEFT Wilson coefficients. We also include the effects of right-handed neutrino (RHN) operators, enabling a unified treatment of both left- and right-handed neutrino interactions in the $c \to s \mu \nu_\mu$ transition. Using the global bounds derived from LEFT observables and their SMEFT correlations, we study the impact of allowed new-physics scenarios on a variety of observables, including differential decay rates, forward-backward asymmetries, polarization asymmetries of the final-state hadron and lepton, and the angular coefficients (${\cal M}_0$ to ${\cal M}_9$) in the 4-body angular distribution. Our analysis reveals significant deviations from the Standard Model in the observables $\mathcal{P}^\Lambda_L$ and ${\cal M}_1$ for $C^V_{RL}$ and $C^V_{RR}$, and striking $T$-odd effects in ${\cal M}_7$ for complex $C^V_{RL}$. These features provide sensitive probes of vector-type new physics, such as leptoquark or right-handed current models. The predicted patterns can be tested in forthcoming measurements at BESIII, LHCb, and Belle II, where polarization-sensitive observables in $\Lambda_c$ decays are becoming experimentally accessible.