Flavored Peccei-Quinn symmetries in the minimal ν DFSZ model

We consider a Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion model extended with two right-handed neutrino fields to realize the minimal type-I seesaw. In this <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ν</a:mi> <a:mi>DFSZ</a:mi> </a:math> scheme we systematically determine the simplest quark and lepton flavor patterns compatible with masses, mixing, and charge-parity violation data, realized by flavored U(1) Peccei-Quinn (PQ) symmetries. We discuss axion dark matter production in pre- and postinflationary cosmology in this context, and predictions for the axion couplings to photons and fermions. In particular, helioscopes and haloscopes are able to probe our models via their distinct axion-to-photon couplings, while in the quark sector the most stringent constraints on axion-fermion couplings are set by <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>K</c:mi> <c:mo>+</c:mo> </c:msup> <c:mo stretchy="false">→</c:mo> <c:msup> <c:mi>π</c:mi> <c:mo>+</c:mo> </c:msup> <c:mo>+</c:mo> <c:mi>a</c:mi> </c:math> . Flavor-violating constraints in the lepton sector are not as relevant as those stemming from red giants and star cooling SN1987a that restrict the diagonal <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>e</f:mi> <f:mi>e</f:mi> </f:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>μ</h:mi> <h:mi>μ</h:mi> </h:math> axion couplings to charged leptons, respectively. We also obtain axion mass bounds for the most interesting models and discuss how minimal flavored PQ symmetries provide a natural framework to suppress flavor-violating couplings.