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
$B^{0}_{s} \rightarrow \phi(1020) e^{+} e^{-}$ and $B^{+} \to K^{+} \pi^{-} \pi^{+} e^{+} e^{-}$, as well as the most precise determination of $R_{K}$ at high dilepton 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 addressing the flavour problem.