The QCD axion, colour-mediated neutrino masses, and $B^+→ K^+ + Eₘᵢₛₛ$ anomaly

Motivated by the recent Belle II result indicating a 2.7\,σ excess of B⁺→ K⁺ + Eₘᵢₛₛ events compared to the Standard Model (SM) prediction for B⁺ → K⁺ νν̄, we explore an explanation to this anomaly based on a KSVZ-type QCD axion model featuring a Peccei-Quinn (PQ) symmetry breaking at high-scale, that can provide a solution to the strong CP problem with dark matter relic abundance. The model contains a PQ-charged scalar} leptoquark which can interact with the SM quarks only via mass-mixing of the latter with vector-like quarks. The mixing between SM and vector-like quarks is determined by the PQ mass scales and can explain the excess B⁺→ K⁺ + Eₘᵢₛₛ events while respecting other flavour constraints. The same PQ-charged scalar leptoquarks and vector-like quarks also mediate the two-loop radiative neutrino masses.