Abstract
Because the Peccei-Quinn (PQ) symmetry has to be anomalous to solve the strong CP puzzle, some colored and chiral fermions have to transform non-trivially under this symmetry. But when the SM fermions are charged, as in the PQ or DFSZ models, this symmetry ends up entangled with the SM global symmetries, baryon (B) and lepton (L) numbers. This raises several questions addressed in this paper. First, the compatibility of axion models with some explicit B and/or L violating effects is analyzed, including those arising from seesaw mechanisms, electroweak instanton interactions, or explicit B and L violating effective operators. Second, how many of these effects can be simultaneously present is quantified, along with the consequences for the axion mass and vacuum alignment if too many of them are introduced. Finally, large classes of B and/or L violating interactions without impact on axion phenomenology are identified, like for example the various implementations of the type I and II seesaw mechanisms in the DFSZ context.
Highlights
Even if the simplest axion models introduced more than 40 years ago have been ruled out, axions still remain one of the best solutions for the strong CP problem of the Standard Model (SM)
IV, we investigate the impact of baryon number violation on axion models and explore what would happen if further explicit B- and/or L-violating interactions were introduced in the theory
Show that axion phenomenology is essentially unaffected by neutrino masses, we review three realizations
Summary
Even if the simplest axion models introduced more than 40 years ago have been ruled out, axions still remain one of the best solutions for the strong CP problem of the Standard Model (SM). In a previous study [9], we have described that, for this class of models, the fermion charges are necessarily ambiguous because of the presence of the accidental Uð1Þ symmetries of the SM, corresponding to the conserved baryon (B) and lepton (L) numbers Though this ambiguity was found to have no impact on the low-energy phenomenology, it raises several questions that we want to address in the present paper. We will see that the fermion charges for all PQ and DFSZ-like models based on the same Yukawa couplings, whether with a seesaw mechanism of type I or II or with some (limited) B violation, are equivalent Despite their very different appearance in terms of effective interactions, those models cannot be distinguished at low energy.
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