Exploring Lepton Flavour with $b$-hadron Decays at LHCb: Universality Tests and Searches for Violation

The flavour sector of the Standard Model (SM) exhibits striking hierarchies whose origin remain unexplained, making precision flavour physics a powerful probe of physics beyond the SM. In particular, tests of lepton-flavour universality (LFU) and charged lepton–flavour violation (cLFV) in flavour-changing neutral currents processes offer exceptionally clean and sensitive avenues for discovering new physics (NP), as the SM contributions for these observables are theoretically well controlled. These proceedings present a series of recent measurements from the LHCb experiment based on the full Run 1 and Run 2 datasets of $9 \, \textrm{fb}^{-1}$ of $pp$ collisions. These include LFU tests in rare $b \rightarrow s \ell^{+} \ell^{-}$ transitions for previously unmeasured $B$-decays, including $B^{0}_{s} \rightarrow \phi(1020) \ell^{+} \ell^{-}$ and $B^{+} \to K^{+} \pi^{-} \pi^{+} \ell^{+} \ell^{-}$ decays, as well as in previously unexplored kinematic region using $B^{+} \to K^{+} \ell^{+} \ell^{-}$ decays. These analyses achieve improved precision and include first observations of the $B^{0}_{s} \rightarrow \phi(1020) e^{+} e^{-}$ and $B^{+} \to K^{+} \pi^{-} \pi^{+} e^{+} e^{-}$ decays, as well as the most precise determination of $R_{K}$ at high di-lepton invariant mass. All LFU measurements are consistent with the SM expectation within uncertainties. In addition, LHCb reports the world’s most stringent limits on cLFV in $b \to s \tau e$ transitions through the search for $B \to K^* \tau^{\pm}e^{\mp}$ decays, superseding previous constraints. Together, these results demonstrate the breadth and sensitivity of LHCb’s flavour- physics programme. With the onset of Run 3 and its upgraded trigger and higher luminosity, LHCb is poised to deliver an expanded set of precision tests and searches that will continue placing stringent constraints of NP models.