Probing flavoured Axions in the Tail of $B_q \to \mu^+\mu^-$

We discuss how LHC di-muon data collected to study B$_{q}$ → μμ can be used to constrain light particles with flavour-violating couplings to b-quarks. Focussing on the case of a flavoured QCD axion, a, we compute the decay rates for B$_{q}$ → μμa and the SM background process B$_{q}$ → μμγ near the kinematic endpoint. These rates depend on non-perturbative B$_{q}$ → γ$^{(*)}$ form factors with on- or off-shell photons. The off-shell form factors — relevant for generic searches for beyond-the-SM particles — are discussed in full generality and computed with QCD sum rules for the first time. This includes an extension to the low-lying resonance region using a multiple subtracted dispersion relation. With these results, we analyse available LHCb data to obtain the sensitivity on B$_{q}$ → μμa at present and future runs. We find that the full LHCb dataset alone will allow to probe axion-coupling scales of the order of 10$^{6}$ GeV for both b → d and b → s transitions. As a spin-off application of the off-shell form factors we further analyse the case of light, Beyond the Standard Model, vectors.