Connecting $b\to s\ell\ell$ with $b\to s\nu\bar\nu$ and $s\to d\nu\bar\nu$

Abstract

We discuss the consequences of deviations from the Standard Model observed in $b\to s\mu^+\mu^-$ transitions for flavour-changing neutral-current processes involving down-type quarks and neutrinos. We work within an effective field theory approach respecting the SM gauge symmetry, including right-handed currents, a flavour structure based on approximate U(2) symmetry, and assuming only SM-like light neutrinos. We discuss correlations among $B\to h_s\nu\bar\nu$ ($h_s=K,K^*,X_s$), $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$ branching ratios in the case of linear Minimal Flavour Violation and in a more general framework.