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Register a new userCorrections to Tri-bimaximal Neutrino Mixing: Renormalization and Planck Scale Effects
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We study corrections to tri-bimaximal (TBM) neutrino mixing from renormalization group (RG) running and from Planck scale effects. We show that while the RG effects are negligible in the standard model (SM), for quasi-degenerate neutrinos and large $tanbeta$ in the minimal supersymmetric standard model (MSSM) all three mixing angles may change significantly. In both these cases, the direction of the modification of $theta_{12}$ is fixed, while that of $theta_{23}$ is determined by the neutrino mass ordering. The Planck scale effects can also change $theta_{12}$ up to a few degrees in either direction for quasi-degenerate neutrinos. These effects may dominate over the RG effects in the SM, and in the MSSM with small $tan beta$. The usual constraints on neutrino masses, Majorana phases or $tan beta$ stemming from RG running arguments can then be relaxed. We quantify the extent of Planck effects on the mixing angles in terms of mismatch phases which break the symmetries leading to TBM. In particular, we show that when the mismatch phases vanish, the mixing angles are not affected in spite of the Planck scale contribution. Similar statements may be made for $mu$-$tau$ symmetric mass matrices.
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We propose an extension of tri-bimaximal mixing to include a non-zero reactor angle $theta_{13}$ while maintaining the tri-bimaximal predictions for the atmospheric angle $theta_{23}=45^o$ and solar angle $theta_{12}=35^o$. We show how such tri-bimaximal-reactor mixing can arise at leading order from the(type I) see-saw mechanism with partially constrained sequential dominance. Partially constrained sequential dominance can be realized in GUT models with a non-Abelian discrete family symmetry, such as $A_4$, spontaneously broken by flavons with a particular vacuum alignment.
In light of the latest neutrino oscillation data, we examine whether the leptonic flavor mixing matrix can take on an exact form of tri-bimaximal (TBM), golden-ratio (GR) or bimaximal (BM) mixing pattern at a superhigh-energy scale, where such a mixing pattern could be realized by a flavor symmetry, and become compatible with experimental data at the low-energy scale. Within the framework of the Minimal Supersymmetric Standard Model (MSSM), the only hope for realizing such a possibility is to count on the corrections from the renomalization-group (RG) running. In this work we focus on these radiative corrections, and fully explore the allowed parameter space for each of these mixing patterns. We find that when the upper bound on the sum of neutrino masses $Sigma^{}_ u equiv m^{}_1 + m^{}_2 + m^{}_3 < 0.23~text{eV}$ at the $95%$ confidence level from Planck 2015 is taken into account, none of these mixing patterns can be identified as the leptonic mixing matrix below the seesaw threshold. If this cosmological upper bound on the sum of neutrino masses were relaxed, the TBM and GR mixing patterns would still be compatible with the latest neutrino oscillation data at the $3sigma$ level, but not at the $1sigma$ level. Even in this case, no such a possibility exists for the BM mixing.
Inspired by the recent T2K indication of a relatively large theta_{13}, we provide a systematic study of some general modifications to three mostly discussed neutrino mixing patterns, i.e., tri-bimaximal, bimaximal and democratic mixing matrices. The correlation between theta_{13} and two large mixing angles are provided according to each modifications. The phenomenological predictions of theta_{12} and theta_{23} are also discussed. After the exclusion of several minimal modifications, we still have reasonable predictions of three mixing angles in 3 Sigma level for other scenarios.
We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule s = r cos delta + 2/3 a (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and delta is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects.
In this work we analyze the corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining large reactor mixing angle $theta_{13}$ and checking the consistency with other neutrino mixing angles. The corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrix of the form $R_{ij}cdot U cdot R_{kl}$ where $R_{ij}$ is rotation in ij sector and U is any one of these special matrices. We showed the rotations $R_{13}cdot U cdot R_{23}$, $R_{12}cdot U cdot R_{13}$ for BM and $R_{13}cdot U cdot R_{13}$ for TBM perturbative case successfully fit all neutrino mixing angles within $1sigma$ range. The perturbed PMNS matrix $R_{12}cdot U cdot R_{13}$ for DC, TBM and $R_{23}cdot U cdot R_{23}$ for TBM case is successful in producing mixing angles at 2$sigma$ level. The other rotation schemes are either excluded or successful in producing mixing angles at $3sigma$ level.
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