CERN Accelerating science

Left panel: regions of $M_2$, $M_3$, $M_X$ as functions of $M_1$ allowed by gauge unification; Right panel: prediction of proton lifetime as functions of $M_1$, with exclusion upper bound of Super-K and future sensitivity of Hyper-K indicated.

Left panel: regions of $M_2$, $M_3$, $M_X$ as functions of $M_1$ allowed by gauge unification; Right panel: prediction of proton lifetime as functions of $M_1$, with exclusion upper bound of Super-K and future sensitivity of Hyper-K indicated.

The RG running of gauge couplings in the breaking chain $SO(10) \to G_3 \to G_2 \to G_1 \to G_{\rm SM}$. BP1 with the first and second lowest intermediate scales are fixed at $M_1 = 2 \times 10^{13}$~GeV and $M_2 = 5 \times 10^{13}$~GeV, the remaining scales $M_3$ and $M_X$, as well as gauge couplings $\alpha_{2R}$, are determined by the gauge unification at $M_X$.

Two-dimensional correlations between theory inputs (left two panels) and predicted observables (right two panels) for $\chi^2<100$ for $\theta_{23}\leq 45^{\circ}$. Consistency with gauge unification is not considered.

The predicted observables (top left two panels), the effective neutrino mass prediction (top right panel) and two-dimensional correlations between theory inputs (bottom panels) for $\chi^2<10$ and $\theta_{23}\leq 45^{\circ}$. Consistency with gauge unification is considered.

The predicted observables (top left two panels), the effective neutrino mass prediction (top right panel) and two-dimensional correlations between theory inputs (bottom panels) for $\chi^2<10$ and $\theta_{23}\geq 45^{\circ}$. Consistency with gauge unification is considered.

The top (bottom) left and centre panels are the two-dimensional correlations between predicted observables for $\chi^2<10$ and $\theta_{23}\leq 45^{\circ}$ ($\theta_{23}\geq 45^{\circ}$). The top (bottom) rightmost panel shows the predictions for the effective neutrino mass for $\theta_{23}\leq 45^{\circ}$ ($\theta_{23}\geq 45^{\circ}$). The colour of the points denotes the ratio of the predicted baryon-to-photon ratio to the experimentally observed best-fit value as measured using CMB data $\eta_B^{\rm CMB} = 6.15 \times 10^{-10}$ \cite{Planck:2015fie}. Consistency with gauge unification is considered. In the leftmost plots, the dashed line labels the sensitivity of the next generation experiments on $0\nu \beta \beta$ decay.

Gravitational wave spectrum predicted from the model. Breaking of the intermediate symmetry $G_1 \equiv SU(3)_c\times SU(2)_L \times SU(2)_R \times U(1)_X$ generates cosmic strings with tension $\mu$. The lower bound to the GW spectrum for the benchmark point we considered earlier (red lines) is $G \mu = 2.68 \times 10^{-11}$ corresponding to $M_1 \simeq 2\times 10^{13}$~GeV. The GW spectrums of these two bounds are shown in dashed and solid curves, respectively.

Comparison between SGWB signals produced by cosmic strings with $G\mu$ from $10^{-11}$ to $10^{-9}$ the possible $1\sigma$ and $2\sigma$ regions hinted by EPTA, PPTA, IPTA and NANOGrav. The SGWB signal has been fitted for three frequencies: 2.4 nHz, 5.4 nHz and 12 nHz. The simulation shows that the signal is compatible with all experiments at $2\sigma$. The orange star indicates the prediction of $(\gamma, A)$ in BP1.

Left: Blown-up image of the nHz region of the gravitational waves spectrum of the benchmark point and the upper bound. This is compared with the region of EPTA, IPTA, PPTA and NANOGrav consistent with the observation of an SGWB. Right: Proton decay lifetime compared with the region of M1 consistent with NANOGrav12.5, we can see that there is a region of the parameter space which can be tested by Hyper-K, which is consistent with NANOGrav. The orange star indicates BP1.

Comparison between the results of our scan and NANOGrav12.5 bound. The yellow shaded region includes all the values of $M_1$ consistent with NANOGrav. Applying the perturbativity ansatz, i.e., $M_1>M_{N_3}$, we can see how most of the points in our scan are consistent with NANOGrav. The first octant of lepton mixing angle $\theta_{23}$ is considered.