Cornering the revamped BMV model with neutrino oscillation data

Using the latest global determination of neutrino oscillation parameters from~\cite{deSalas:2017kay} we examine the status of the simplest revamped version of the BMV (Babu-Ma-Valle) model, proposed in~\cite{Morisi:2013qna}. The model predicts a striking correlation between the"poorly determined"atmospheric angle $\theta_{23}$ and CP phase $\delta_{CP}$, leading to either maximal CP violation or none, depending on the preferred $\theta_{23}$ octants. We determine the allowed BMV parameter regions and compare with the general three-neutrino oscillation scenario. We show that in the BMV model the higher octant is possible only at $99\%$ C.L., a stronger rejection than found in the general case. By performing quantitative simulations of forthcoming DUNE and T2HK experiments, using only the four"well-measured"oscillation parameters and the indication for normal mass ordering, we also map out the potential of these experiments to corner the model. The resulting global sensitivities are given in a robust form, that holds irrespective of the true values of the oscillation parameters.


Present status of oscillation parameters
Upscaled version of T2K with the same baseline of 295 km but with a much larger detector of 560 kt fiducial mass.
A beam of 7.5 MW corresponding to a POT of 1.53 × 10 22 1 year of ν and 3 yrs. ofν run was assumes.
A4 symmetry and BMV model: brief overview Babu,Ma,Valle: Phys. Lett. B552, 207 (2003) Requires the existence of extra heavy fermions and three scalars χ i , i = 1, 2, 3, all of them belonging to A4 triplets representation and coupled through standard Yukawa interactions.
After breaking the A4 at high energy, Translates into zero-th order neutrino mixing matrix, Revamped A4 symmetry and BMV model: brief overview Morisi, Forero, Romao, and Valle: PRD88, 016003 (2013) A single flavon scalar ξ is added to break the remnant symmetry in A4 and the charged fermion mass matrix is changed slightly, , and β is a small complex parameter.
The mixing matrix gets modified to, where the pre-factor U † δ (β) characterizes the revamping and generates a nonzero reactor mixing angle.
The mixing angles are extracted from from this modified mixing matrix and the phase of the complex coupling of flavon β becomes the source of CP violation.
Revamped A4 symmetry and BMV model: brief overview...(cont.) Morisi, Forero, Romao, and Valle: PRD88, 016003 (2013) The revamped model shows the theoretical correlation between the flavon coupling (β) and the solar angle θ13 and also between the CP phase and the atmospheric angle θ23.
We wanted to extend on this study by testing the model in DUNE and T2HK and doing a χ 2 level analysis for excluding the model. Numerical procedure (using GLoBES) n is the total number of bins and ξa and ξ b denote the pulls due to systematic errors.
We simulate the true dataset x i using GLoBES (by considering the present BF parameters) and get the test dataset from the value of oscillation parameters predicted by the model.
χ 2 total is minimized over the free oscillation parameters (θ23, θ13, θ12, and δ CP ) predicted by the model Allowed region in δ CP (test)-sin 2 θ 23 (test) plane Normal ordering is preferred and inverted ordering is only allowed at 99% C.L.
For normal ordering, preferred solution indicates to the lower octant and maximal CP violation.
Capability to reconstruct the CP phase Sensitivity of DUNE, T2HK to the model: a fit-independent approach For each δ CP (true)-sin 2 θ 23 (true), all the test parameters were marginalized over their allowed range.
Regions within the black contour correspond to 90% CL of the present best fit.
Sensitivity of DUNE, T2HK to the model: a fit-independent approach...(cont.) At 4σ DUNE can exclude, the regions corresponding to sin 2 θ 23 0.59 and 0.44 without much dependence on δ CP T2HK can exclude more regions for its higher statistics.
Current BF values of θ 23 and δ CP are also discarded at 4σ.

Conclusion
We have focused on the sharp correlation between θ 23 and δ CP predicted in the model.
We showed the allowed regions in this parameter space and compare it with the standard global fits.
We showed how the ability to reconstruct the CP phase and the atmospheric angle gets significantly affected Finally we have also presented the capability of the experiment to exclude the model in a fit independent way.