Angular Observables in the ${\Lambda }_b\to \Lambda \nu \bar{\nu }$ Decay

Abstract

We study the rare decay ${\Lambda }_b\to \Lambda (\to p{\pi }^{-})\nu \bar{\nu }$ of polarized ${\Lambda }_b$ baryons produced at the $Z$ pole. We find that the differential decay distribution is characterized by five independent angular observables, four of which require initial ${\Lambda }_b$ polarization. While standard observables in mesonic $b\to s\nu \bar{\nu }$ decays ($B\to K^{(\ast )}\nu \bar{\nu }$, $B_s\to \varphi \nu \bar{\nu }$) probe only two combinations of short-distance Wilson coefficients, $|C_L+C_R|$ and $|C_L-C_R|$, the angular observables in ${\Lambda }_b\to \Lambda (\to p{\pi }^{-})\nu \bar{\nu }$ provide access to the orthogonal combinations $|C_R{|}^2-|C_L{|}^2$ and $\text{Im}(C_L{C}_R^{\ast })$. In particular, we identify a $T$-odd CP asymmetry, $A_5$, that directly probes CP-violating phases in the short-distance effective Hamiltonian. We present Standard Model predictions for the branching ratio and all angular observables using lattice QCD form factors, and evaluate the projected new physics sensitivity at the FCC-ee. Our results demonstrate that baryonic angular observables are essential for resolving parameter degeneracies and for completely characterizing the chiral and CP structure of possible new physics in $b\to s\nu \bar{\nu }$ transitions.

42 pages, 8 figures