Flavoured axions in the tail of Bq → µ +µ − and B → γ ∗ form factors

We discuss how LHC di-muon data collected to study Bq → 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 Bq → µµa and the SM background process Bq → µµγ near the kinematic endpoint. These rates depend on non-perturbative Bq → 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 Bq → 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 106 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.