High Luminosity LHC data collected by CMS experiment -- an excellent ground for the search of Rare Radiative $B_s^0$ meson decays: A Review

Abstract

The High-Luminosity Large Hadron Collider (HL-LHC) provides unprecedented opportunities to study rare radiative decays in the flavor sector, particularly with the CMS experiment. This review focuses on the search for the challenging decay $B_s^0 \to \mu^+ \mu^- \gamma$, a flavor-changing neutral current process forbidden at tree level in the Standard Model. These decays probe Wilson coefficients C7, C9, and C10, which connect short-distance electroweak dynamics with long-distance hadronic effects. The main experimental difficulty is reconstructing low-pT photons (2-20 GeV) under extreme pile-up conditions ( ~ 60). We argue that collider data naturally live on curved statistical manifolds shaped by conservation laws, detector geometry, and kinematic constraints. The Fisher-Rao information metric captures this structure, suggesting that curvature-aware analysis methods may enhance sensitivity beyond traditional approaches. We outline a framework that links collider data hierarchies, information geometry, and quantum machine learning as a pathway for future searches for rare radiative B_s^0 decays at the HL-LHC.