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Register a new userHigh scale mixing relations as a natural explanation for large neutrino mixing
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The origin of small mixing among the quarks and a large mixing among the neutrinos has been an open question in particle physics. In order to answer this question, we postulate general relations among the quarks and the leptonic mixing angles at a high scale, which could be the scale of Grand Unified Theories. The central idea of these relations is that the quark and the leptonic mixing angles can be unified at some high scale either due to some quark-lepton symmetry or some other underlying mechanism and as a consequence, the mixing angles of the leptonic sector are proportional to that of the quark sector. We investigate the phenomenology of the possible relations where the leptonic mixing angles are proportional to the quark mixing angles at the unification scale by taking into account the latest experimental constraints from the neutrino sector. These relations are able to explain the pattern of leptonic mixing at the low scale and thereby hint that these relations could be possible signatures of a quark-lepton symmetry or some other underlying quark-lepton mixing unification mechanism at some high scale linked to Grand Unified Theories.
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With the latest results of a large mixing angle $theta_{13}$ for neutrinos by the T2K, MINOS and Double Chooz experiments, we find that the self-complementarity (SC) relations agree with the data in some angle-phase parametrizations of the lepton mixing matrix. There are three kinds of self-complementarity relations: (1) $vartheta_i+vartheta_j=vartheta_k=45^circ$; (2) $vartheta_i+vartheta_j=vartheta_k$; (3) $vartheta_i+vartheta_j=45^circ$ (where $i$, $j$, $k$ denote the mixing angles in the angle-phase parametrizations). We present a detailed study on the self-complementarity relations in nine different angle-phase parametrizations, and also examine the explicit expressions in reparametrization-invariant form, as well as their deviations from global fit. These self-complementarity relations may lead to new perspective on the mixing pattern of neutrinos.
Starting with high scale mixing unification hypothesis, we investigate the renormalization group evolution of mixing parameters and masses for Dirac type neutrinos. Following this hypothesis, the PMNS mixing angles and phase are taken to be identical to the CKM ones at a unifying high scale. Then, they are evolved to a low scale using renormalization-group equations. The notable feature of this hypothesis is that renormalization group evolution with quasi-degenerate mass pattern can explain largeness of leptonic mixing angles even for Dirac neutrinos. The renormalization group evolution naturally results in a non-zero and small value of leptonic mixing angle $theta_{13}$. One of the important predictions of this work is that the mixing angle $theta_{23}$ is non-maximal and lies only in the second octant. We also derive constraints on the allowed parameter range for the SUSY breaking and unification scales for which this hypothesis works. The results are novel and can be tested by present and future experiments.
We investigate the renormalization group evolution of masses and mixing angles of Majorana neutrinos under the `High Scale Mixing Unification hypothesis. Assuming the unification of quark-lepton mixing angles at a high scale, we show that all the experimentally observed neutrino oscillation parameters can be obtained, within 3-$sigma$ range, through the running of corresponding renormalization group equations provided neutrinos have same CP parity and are quasi-degenerate. One of the novel results of our analysis is that $theta_{23}$ turns out to be non-maximal and lies in the second octant. Furthermore, we derive new constraints on the allowed parameter space for the unification scale, SUSY breaking scale and $tan beta$, for which the `High Scale Mixing Unification hypothesis works.
The latest experimental progress have established three kinds of neutrino oscillations with three mixing angles measured to rather high precision. There is still one parameter, i.e., the CP violating phase, missing in the neutrino mixing matrix. It is shown that a replay between different parametrizations of the mixing matrix can determine the full neutrino mixing matrix together with the CP violating phase. From the maximal CP violation observed in the original Kobayashi-Maskawa (KM) scheme of quark mixing matrix, we make an Ansatz of maximal CP violation in the neutrino mixing matrix. This leads to the prediction of all nine elements of the neutrino mixing matrix and also a remarkable prediction of the CP violating phase $delta_{rm CK}=(85.48^{+4.67(+12.87)}_{-1.80(-4.90)})^circ$ within $1sigma (3sigma)$ range from available experimental information. We also predict the three angles of the unitarity triangle corresponding to the quark sector for confronting with the CP-violation related measurements.
We investigate the consequences of $mu-tau$ reflection symmetry in presence of a light sterile neutrino for the $3+1$ neutrino mixing scheme. We discuss the implications of total $mu-tau$ reflection symmetry as well partial $mu-tau$ reflection symmetry. For the total $mu-tau$ reflection symmetry we find values of $theta_{23}$ and $delta$ remains confined near $pi/4$ and $pm pi/2$ respectively. The current allowed region for $theta_{23}$ and $delta$ in case of inverted hierarchy lies outside the area preferred by the total $mu-tau$ reflection symmetry. However, interesting predictions on the neutrino mixing angles and Dirac CP violating phases are obtained considering partial $mu-tau$ reflection symmetry. We obtain predictive correlations between the neutrino mixing angle $theta_{23}$ and Dirac CP phase $delta$ and study the testability of these correlations at the future long baseline experiment DUNE. We find that while the imposition of $mu-tau$ reflection symmetry in the first column admit both normal and inverted neutrino mass hierarchy, demanding $mu-tau$ reflection symmetry for the second column excludes the inverted hierarchy. Interestingly, the sterile mixing angle $theta_{34}$ gets tightly constrained considering the $mu-tau$ reflection symmetry in the fourth column. We also study consequences of $mu-tau$ reflection symmetry for the Majorana phases and neutrinoless double beta decay.
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