B → K+ axionlike particles: Effective versus UV-complete models and enhanced two-loop contributions

An axionlike particle a (ALP) can explain the excess of B → K+ invisible events at Belle II. However, many analyses of ALP scenarios are oversimplified. We revisit the B → Ka transition rate in a popular minimal and UV complete model with two Higgs doublets (2HDM) and a complex singlet [Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model]. To this end we compare our results with previous studies which derived the ¯bsa vertex from the ¯bsA vertex, where A is the heavy pseudoscalar of the 2HDM, in terms of an a − A mixing angle. We find this approach to work only at the leading one-loop order, while it fails at the two-loop level. Furthermore, while an approximate Z₂ symmetry suppresses the leading-order amplitude by a factor of 1= tan β, which is the ratio of the two vacuum expectation values of the Higgs doublets, we find the two-loop contribution unsuppressed and phenomenologically relevant for tan β ≳ 5. We determine the allowed parameter space and underline the importance of better searches for ϒ → γ+ invisible and for a possible excess in B → Kμ⁺þμ⁻. We further study the low-energy axion effective theory which leads to a divergent and basis-dependent amplitude. As a conceptual result, we clarify the ambiguities and identify which low-energy framework is consistent with the DFSZ model.