Rare b decays - theory overview

Highly suppressed in the Standard Model (SM), rare $B$-meson decays offer precise observables critical for new physics searches, yet pose significant theoretical challenges. Effective field theory (EFT) methods enable us to analyze amplitude factorization and explore power-suppressed contributions. For $B_q \to \gamma\gamma$ decays, we incorporate power corrections from diverse sources and find these corrections to be substantial. A physically motivated hard-collinear assignment for internal quark lines in long-distance quark-loop contributions introduces a novel soft function. Renormalization group (RG) evolution reveals its momentum-space argument is non-positive definite, and its asymptotic behavior ensures factorization of this contribution. Numerically, this effect significantly impacts mixing-induced $CP$ violation. For exclusive $B \to \{K, \pi\}\ell^+\ell^-$ decays with an energetic light meson in the final state, we present the first next-to-leading-order (NLO) calculation of weak annihilation corrections. This fills a critical gap in the QCD corrections to hadronic operator matrix elements, and we demonstrate that one-loop corrections notably impact direct $CP$ and isospin asymmetries in $B \to \pi\ell^+\ell^-$ decays. For pure leptonic decays, power-enhanced structure-dependent QED corrections are mandatory for $B \to \mu^+\mu^-$ calculations, yet negligible for $B \to \tau^+\tau^-$ due to the absence of logarithmic enhancement. In two-body nonleptonic decays, power-suppressed weak annihilation contributions play an important phenomenological role, but hard gluon exchange processes suffer from endpoint singularities. Previously neglected hard-collinear gluon exchange diagrams hold the potential to cancel these singularities, warranting further study. In pure annihilation decays, quark-loop diagrams contribute comparably to leading-order terms and significantly modify predicted $CP$-violating observables.