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We discuss how LHC di-muon data collected to study $B_q \to \mu\mu$ can beused to constrain light particles with flavour-violating couplings to$b$-quarks. Focussing on the case of a flavoured QCD axion, $a$, we compute thedecay rates for $B_q \to \mu \mu a$ and the SM background process $B_q \to \mu\mu \gamma$ near the kinematic endpoint. These rates depend on non-perturbative$B_q \to \gamma^{(*)}$ form factors with on- or off-shell photons. Theoff-shell form factors -- relevant for generic searches for beyond-the-SMparticles -- are discussed in full generality and computed with QCD sum rulesfor the first time. With these results, we analyse available LHCb data toobtain the sensitivity on $B_q \to \mu \mu a$ at present and future runs. Wefind that the full LHCb dataset alone will allow to probe axion-coupling scalesof the order of $10^6$ GeV for both $b\to d$ and $b \to s$ transitions.

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