Flavored Peccei-Quinn symmetries in the minimal $ν$DFSZ model

TL;DR

The paper addresses the flavor puzzle and the strong CP problem by embedding a flavored PQ symmetry into a minimal νDFSZ framework that realizes a type-I seesaw with two right-handed neutrinos, yielding one massless light neutrino. It systematically Classifies maximally restrictive quark and lepton textures compatible with data, resulting in 88 viable models, and derives their axion phenomenology, including DM production via misalignment and model-dependent axion–photon couplings governed by $g_{a\gamma\gamma} = \frac{\alpha}{2\pi f_a}\left[\frac{E}{N} - 1.92(4)\right]$. The analysis shows how domain-wall problems are avoided for $N_{DW}=1$ in the cubic model, and how flavor-violating axion couplings to fermions are naturally suppressed by decoupled states, leading to robust constraints from $K^+ \rightarrow \pi^+ a$ and stellar cooling bounds. The results provide testable links between axion searches (helioscopes, haloscopes) and flavor/neutrino data, offering a natural framework that ties together flavor structure, neutrino masses, dark matter, and CP violation with upcoming experimental prospects.

Abstract

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 $ν$DFSZ 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 post-inflationary 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 $K^+ \rightarrow π^+ + a$. Flavor-violating constraints in the lepton sector are not as relevant as those stemming from star cooling that restrict the diagonal $ee$ and $μμ$ axion couplings to charged leptons. 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.

Figures (3)

• Figure 2: Axion-to-photon coupling $|g_{a \gamma \gamma}|$ versus axion mass $m_a$ (bottom axis) and decay constant $f_a$ (top axis). Colored solid lines indicate $E/N$ values for the different models identified in Sec. \ref{['sec:symmetries']} (see Table \ref{['tab:EN']}). The yellow shaded region refers to the usual QCD axion window DiLuzio:2016sbl. Current constraints from helioscopes like CAST CAST:2017uph exclude the light-gray shaded region, while haloscopes like ADMX ADMX:2018ghoADMX:2019uokADMX:2021nhd, RBF DePanfilis:1987dk, CAPP CAPP:2020utb and HAYSTAC HAYSTAC:2020kwv, rule out the black region. Projected sensitivities of IAXO Shilon_2013, ADMX Stern:2016bbw, MADMAX Beurthey:2020yuq and ALPHA ALPHA:2022rxj are indicated by the dashed gray, dashed black, short-dash black (dark-gray shaded region) and dotted (light-gray shaded region) contours, respectively. To the right of the black vertical line, axion DM is under-abundant. In the left region $\Omega h^2_a = 0.12$, for the pre-inflationary case featuring the misalignment mechanism.
• Figure 3: Vector flavor-violating axion-quark couplings $|\mathbf{C}^V_{\alpha\beta}|$, versus $m_a$ (bottom axis) and $f_a$ (top axis). We present the most restricted couplings $\alpha \beta = ds$ ($uc$) [$ct$], indicated by horizontal green (orange) [blue] lines, for models featuring $N_{\text{DW}} =1$ (see Table \ref{['tab:quarkcharges']} and Sec. \ref{['sec:axiondarkmatter']}). The dashed part of the lines are currently excluded by the red (purple) [magenta] oblique bound from $K^+ \rightarrow \pi^+ + a$ ($D^+ \rightarrow \pi^+ + a$) [$K^+ \rightarrow \pi^+ + a$ (loop)] MartinCamalich:2020dfeAlonso-Alvarez:2023wig (see Table \ref{['tab:QuarkConstraints']} and text for details). Future experimental sensitivities are indicated by oblique dash-dotted lines. SN1987a excludes the purple shaded region Carenza:2019pxu. In the gray shaded region axion DM is underabundant, while in the white region $\Omega h^2_a = 0.12$, for the pre-inflationary case. Considering the post-inflationary scenario for $N_{\text{DW}} =1$ the axion mass is restricted to the white region to the right of the vertical dotted black line where $\Omega h^2_a = 0.12$Buschmann:2021sdqGorghetto:2020qwsKlaer:2017ondKawasaki:2014sqa.
• Figure 4: Axial diagonal axion-lepton couplings $|\mathbf{C}^A_{\alpha\alpha}|$, versus $m_a$ (bottom axis) and $f_a$ (top axis). We present the most restricted couplings $\alpha \alpha = ee$ ($\mu\mu$), indicated by horizontal green (blue) lines, for the lepton model $\text{L}_{10}^{\tau,\text{NO}}$ with $N_{\text{DW}} =1$ (see Table \ref{['tab:leptoncharges']} and Sec. \ref{['sec:axiondarkmatter']}). The dashed part of these lines are currently excluded by the red [purple] oblique bound from Red Giants Capozzi:2020cbuBottaro:2023gep [Star Cooling (SN1987$_a\mu\mu$) MartinCamalich:2020dfeAlonso-Alvarez:2023wig]. We also indicate via an orange oblique line the constraint on the $ee$ coupling stemming from Star Cooling White Dwarfs (WDs) MartinCamalich:2020dfeAlonso-Alvarez:2023wig (see Table \ref{['tab:LeptonConstraints']} and main text for details). The horizontal lines correspond to the $|\mathbf{C}^A_{\alpha\alpha}|$ values for the indicated $\tan \beta$. The remaining elements follow the color code of Fig. \ref{['fig:quarks']}.