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Probing an intrinsically flavorful ALP via tau-lepton flavor physics

Any axionlike particle (ALP) intrinsically possesses flavorful couplings to the standard model (SM) fermions arising as a consequence of the right-handed flavor rotation within the SM. In this paper we discuss this intrinsically flavored ALP, and explore the correlation of a minimal set of the couplings in a view of coherence in flavor physics observables. We focus particularly on the tau-lepton flavor violation (LFV). The ALP is assumed to be tau-philic on a current-eigenstate basis, a la Pecci-Quinn. The ALP has the intrinsic flavorful coupling structure for fermions, which allows coupling also to muon and electron only in a right-handed specific manner. Several LFV processes are generated including radiative tau decays and also anomalous magnetic moments of electron and muon. We first pay attention to two separated limits: electron scenario with the ALP coupled to tau which mixes only with right-handed electron, and muon scenario as the muonic counterpart of the electron scenario. It turns out that those scenarios are highly constrained by experimental limits, to require a mu or electron - tau flipped feature in the mass eigenbasis when coupled to the ALP. We then examine a hybrid scenario, and find a fully viable parameter space on the ALP mass-photon coupling plane, which limits the ALP mass to be (1.7 - 10) GeV and the ALP decay constant $f_a$ to be (12.8 - 67.9) GeV. We find that the same-sign multilepton signal at Belle II is a smoking-gun to probe the present ALP signal, and the polarization asymmetry in LFV radiative $τ$ decay is a punchline, which definitely predicts preference of the right-handed polarization, in sharp contrast to the SM plus massive Dirac neutrinos having the highly left-handed preference, and also other light-new physics candidates. Possible model-building to underlie the present third-generation specific ALP is also briefly addressed.