$c \to u \nu {\bar \nu}$ transitions of $B_c$ mesons: 331 model facing Standard Model null tests

TL;DR

This paper investigates rare $c o u u \bar \nu$ decays of $B_c$ mesons, analyzing their suppression in the Standard Model and potential enhancements in new physics scenarios, especially within the 331 model, to identify possible null tests of the Standard Model.

Contribution

It provides the first detailed analysis of $B_c \to B^{(*)+} \nu \bar \nu$ decays within SMEFT and the 331 model, highlighting potential large enhancements over Standard Model predictions.

Findings

Standard Model predicts extremely small branching ratios (~10^{-16}) for these decays.

New physics, especially the 331 model, can enhance branching ratios up to ~10^{-6}.

Correlations exist between $B_c$ decay channels and other rare meson decays in the 331 model.

Abstract

The Glashow-Iliopoulos-Maiani mechanism is extremely efficient to suppress the flavour-changing neutral current decays of charmed hadrons induced by the $c \to u$ transitions, making such processes particularly sensitive to phenomena beyond the Standard Model. In particular, $c \to u$ decays with a neutrino pair in the final state are theoretically appealing due to the small long-distance contributions. Moreover, in the framework of the Standard Model Effective Field Theory (SMEFT), the $SU(2)_L$ invariance allows to relate the Wilson coefficients in the effective Hamiltonian governing the $c \to u \nu {\bar \nu}$ decays to the coefficients in the $c \to u \ell^+ \ell^-$ Hamiltonian. We analyze the $B_c \to B^{(*)+} \nu {\bar \nu}$ decays, for which branching fractions of at most ${\cal O}(10^{-16})$ are predicted in the Standard Model including short- and long-distance contributions, so small that they can be considered as null tests. Using SMEFT and the relation to the $c \to u \ell^+ \ell^-$ processes we study the largest enhancement achievable in generic new physics scenarios. Then we focus on a particular extension of the Standard Model, the 331 model. SMEFT relations and the connection with $c \to u \ell^+ \ell^-$ imply that ${\cal B}(B_c \to B^{(*)+} \nu {\bar \nu})$ could even reach ${\cal O}(10^{-6})$, an extremely large enhancement. A less pronounced effect is found in the 331 model, with ${\cal O}(10^{-11})$ predicted branching fractions. Within the 331 model correlations exist among the $B_c \to B^{(*)+}\nu \bar \nu$ and $K\to \pi \nu \bar \nu$, $B\to (X_s, K, K^*) \nu \bar \nu$ channels.