A Dispersive Look at Rare $B$-meson Semileptonic Decays

Rare semileptonic $b \to s$ flavour-changing neutral current transitions provide stringent tests of the Standard Model. Their interpretation is limited by hadronic uncertainties, notably the $B \to K^{(*)}$ and $B_s \to \phi$ form factors (FFs) and the matrix elements of four-quark operators. We perform a global analysis of $b \to s \ell^+\ell^-$ transitions taking these uncertainties fully into account, determining the FFs through the Dispersive Matrix method and comparing a setup based solely on lattice QCD (LQCD) with one that also includes light-cone sum-rule (LCSR) inputs at low $q^2$. Compared to the case where both input are taken into account, using only LQCD substantially enlarges the FF uncertainties at large recoil. Combined with the latest LHCb and CMS angular measurements sensitive to strong phases, our global fit yields strengthened evidence in favour of long-distance hadronic effects rather than a short-distance shift in $C_9$. We further present new SM predictions for the theoretically clean $b \to s \nu\bar\nu$ modes, which depend only on local FFs, and a New Physics analysis of these transitions in the Weak Effective Theory, discussing their impact on the interpretation of the recent Belle~II measurement and on the available experimental upper bounds.