Axion and neutrino physics in a $U(1)$-enhanced supersymmetric model

Motivated by the flavored Peccei-Quinn symmetry for unifying the flavor physics and string theory, we construct an explicit model by introducing a $U(1)$ symmetry such that the $U(1{)}_X-[\text{gravity}{]}^2$ anomaly-free condition together with the standard model flavor structure demands additional sterile neutrinos as well as no axionic domain-wall problem. Such additional sterile neutrinos play the role of realizing baryogenesis via a new Affleck-Dine leptogenesis. We provide grounds for interpreting the $U(1{)}_X$ symmetry as a fundamental symmetry of nature. The model will resolve rather recent but fast-growing issues in astroparticle physics, including leptonic mixings and $CP$ violation in neutrino oscillation, high-energy neutrinos, QCD axions, and axion cooling of stars. The QCD axion decay constant, through its connection to the astrophysical constraints of stellar evolution and the SM fermion masses, is shown to be fixed at $F_A={1.30}_{-0.54}^{+0.66}\times 10^9\mathrm{GeV}$ (consequently, its mass is $m_a=4.34_{-1.49}^{+3.37}\mathrm{meV}$ and the axion-photon coupling is $|g_{a\gamma \gamma }|={1.30}_{-0.45}^{+1.01}\times {10}^{-12}{\mathrm{GeV}}^{-1}$). Interestingly enough, we show that neutrino oscillations at low energies could be connected to astronomical-scale baseline neutrino oscillations. The model predicts the nonobservational neutrinoless double beta ($0\nu \beta \beta$) decay rate as well as a remarkable pattern between the leptonic Dirac $CP$ phase (${\delta }_{CP}$) and the atmospheric mixing angle (${\theta }_{23}$); e.g., ${\delta }_{CP}\simeq 220°–240°$, 120°–140° for ${\theta }_{23}=42.3°$ for normal mass ordering, and ${\delta }_{CP}\simeq 283°$, 250°, 100°, 70° for ${\theta }_{23}=49.5°$ for the inverted one. We stress that future measurements on the ${\theta }_{23}$, $0\nu \beta \beta$ decay rate, the sum of active neutrino masses, the track-to-shower ratio of a cosmic neutrino, astrophysical constraints on axions, QCD axion mass, and the axion-photon coupling are of importance to test the model in the near future.

Figure 1

Plot of $(g_{a\gamma \gamma }/m_a{)}^2$ versus $E/N$ for $z=0.56$. The gray-band represents the experimentally excluded bound $(g_{a\gamma \gamma }/m_a{)}^2\le 1.44\times {10}^{-19}{\mathrm{GeV}}^{-2}{\mathrm{eV}}^{-2}$ from ADMX [62]. Here the dotted-black, dashed-blue, and solid-red lines stand for $(g_{a\gamma \gamma }/m_a{)}^2=1.435\times {10}^{-19}{\mathrm{GeV}}^{-2}{\mathrm{eV}}^{-2}$ for $E/N=0$, $2.120\times {10}^{-20}{\mathrm{GeV}}^{-2}{\mathrm{eV}}^{-2}$ for $E/N=8/3$, and $9.010\times {10}^{-20}{\mathrm{GeV}}^{-2}{\mathrm{eV}}^{-2}$ for $E/N=14/39$, respectively. See more various supersymmetric and no-supersymmetric KSVZ and DFSZ-type models varying the parameter $E/N$ in Ref. [64].

Figure 2

Plot of $|g_{a\gamma \gamma }|$ versus $m_a$ for KSVZ (black dotted line), DFSZ (blue dashed line) and our model (red solid line) in terms of $E/N=0$, $8/3$ and $14/39$, respectively. Here the horizontal dotted line stands for the upper bound $|g_{a\gamma \gamma }|\lesssim 6.6\times {10}^{-11}{\mathrm{GeV}}^{-1}$ which is from globular-cluster stars [31]. And the black bar corresponding to $m_a\lesssim 16\mathrm{meV}$ is the constraint derived from the measured duration of the neutrino signal of the supernova SN1987A [31]. In particular, in the model, for $F_A=1.30_{-0.54}^{+0.66}\times 10^9\mathrm{GeV}$, we obtain $m_a=4.34_{-1.49}^{+3.37}\mathrm{meV}$ and $|g_{a\gamma \gamma }|=1.30_{-0.45}^{+1.01}\times {10}^{-12}{\mathrm{GeV}}^{-1}$, which corresponds to the yellow band.

Figure 3

For NO, the left plot shows predictions of ${\delta }_{CP}$ as a function of ${\theta }_{23}$, while the right plot shows predictions of $\sum _i{m}_{{\nu }_i}$ in terms of ${\theta }_{23}$. Here, the red crosses and blue dots correspond to $\mathrm{\Delta }{m}_1^2=\mathrm{\Delta }{m}_2^2=2.7\times {10}^{-15}{\mathrm{eV}}^2<\mathrm{\Delta }{m}_3^2=5\times {10}^{-15}{\mathrm{eV}}^2$ and $\mathrm{\Delta }{m}_1^2=\mathrm{\Delta }{m}_2^2=\mathrm{\Delta }{m}_3^2=5\times {10}^{-15}{\mathrm{eV}}^2$, respectively. In both plots, the vertical dotted lines indicate the best-fit value for NO, and in the right plot the horizontal dotted line shows the cosmological bounds $\sum _i{m}_{{\nu }_i}<0.194\mathrm{eV}$ at 95% CL [18].

Figure 4

For IO, the left plot shows predictions of ${\delta }_{CP}$ as a function of ${\theta }_{23}$, while the right plot shows predictions of $\sum _i{m}_{{\nu }_i}$ in terms of ${\theta }_{23}$. Here, the red asters and black stars correspond to $\mathrm{\Delta }{m}_1^2=\mathrm{\Delta }{m}_2^2={10}^{-14}{\mathrm{eV}}^2>\mathrm{\Delta }{m}_3^2=5.5\times {10}^{-15}{\mathrm{eV}}^2$ and $\mathrm{\Delta }{m}_1^2=\mathrm{\Delta }{m}_2^2=\mathrm{\Delta }{m}_3^2=5\times {10}^{-15}{\mathrm{eV}}^2$, respectively. In both plots, the vertical dotted lines indicate the best-fit value for IO, and in the right plot the horizontal dotted line shows the cosmological bounds $\sum _i{m}_{{\nu }_i}<0.194\mathrm{eV}$ at 95% CL [18].

Figure 5

Plots of the track-to-shower ratio $N_T/N_S$ as a function of $L({\log }_{10}[\text{path length}/10\mathrm{kpc}])$ for NO with $\mathrm{\Delta }{m}_1^2=\mathrm{\Delta }{m}_2^2=2.7\times {10}^{-15}{\mathrm{eV}}^2<\mathrm{\Delta }{m}_3^2=5.0\times {10}^{-15}{\mathrm{eV}}^2$, and for IO with $\mathrm{\Delta }{m}_3^2=5.5\times {10}^{-15}{\mathrm{eV}}^2<\mathrm{\Delta }{m}_1^2=\mathrm{\Delta }{m}_2^2={10}^{-14}{\mathrm{eV}}^2$. Each panel corresponds to the specific initial flavor composition (${\varphi }_e^0:{\varphi }_{\mu }^0:{\varphi }_{\tau }^0$) at the source. For three neutrino mixing angles and Dirac-type $CP$ phase, we take the global fit results at $1\sigma$ [67]. Red and blue curved lines correspond to normal and inverted neutrino mass orderings, respectively, for $\omega =2.2$, whereas light red and light blue regions represent the corresponding results for $\omega =1.8-2.6$. Gray shaded regions represent the forbidden bound from $N_T/N_S={0.18}_{-0.05}^{+0.13}$ in Ref. [77].