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Register a new userCorrections to Tribimaximal Mixing from Nondegenerate Phases
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We propose a seesaw scenario that possible corrections to the tribimaximal pattern of lepton mixing are due to the small phase splitting of the right-handed neutrino mass matrix. we show that the small deviations can be expressed analytically in terms of two splitting parameters($delta_1$ and $delta_2$) in the leading order. The solar mixing angle $theta_{12}$ favors a relatively smaller value compared to zero order value ($35.3^circ$), and the Dirac type CP phase $delta$ chooses a nearly maximal one. The two Majorana type CP phases $rho$ and $sigma$ turn out to be a nearly linear dependence. Also a normal hierarchy neutrino mass spectrum is favored due to the stability of perturbation calculations.
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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.
In the context of A_4 symmetry, neutrino tribimaximal mixing is achieved through the breaking of A_4 to Z_3 (Z_2) in the charged-lepton (neutrino) sector respectively. The implied vacuum misalignment of the (1,1,1) and (1,0,0) directions in A_4 space is a difficult technical problem, and cannot be treated without many auxiliary fields and symmetries (and perhaps extra dimensions). It is pointed out here that an alternative scenario exists with A_4 alone and no redundant fields, if neutrino masses are scotogenic, i.e. radiatively induced by dark scalar doublets as recently proposed.
General lowest order perturbations to hermitian squared mass matrices of leptons are considered away from the tribimaximal (TBM) limit in which a weak flavor basis with mass diagonal charged leptons is chosen. The three measurable TBM deviants are expressed linearly in terms of perturbation induced dimensionless coefficients appearing in the charged lepton and neutrino flavor eigenstates. With unnatural cancellations assumed to be absent and the charged lepton perturbation contributions to their flavor eigenstates argued to be small, we analytically derive the following result. Within lowest order perturbations, a deviation from maximal atmospheric neutrino mixing and the amount of CP violation in neutrino oscillations cannot both be large (i.e. $12$-$17 % $), posing the challenge of verification to forthcoming experiments at the intensity frontier.
We scrutinize corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining recent global fit neutrino mixing data. These corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrices of the forms big($R_{ij}^lcdot U,~Ucdot R_{ij}^r,~U cdot R_{ij}^r cdot R_{kl}^r,~R_{ij}^l cdot R_{kl}^l cdot U$big ) where $R_{ij}^{l, r}$ is rotation in ij sector and U is any one of these special matrices. We showed that for perturbative schemes dictated by single rotation, only big($ R_{12}^lcdot U_{BM},~R_{13}^lcdot U_{BM},~U_{TBM}cdot R_{13}^r$ big ) can fit the mixing data at $3sigma$ level. However for $R_{ij}^lcdot R_{kl}^lcdot U$ type rotations, only big ($R_{23}^lcdot R_{13}^l cdot U_{DC} $big ) is successful to fit all neutrino mixing angles within $1sigma$ range. For $Ucdot R_{ij}^rcdot R_{kl}^r$ perturbative scheme, only big($U_{BM} cdot R_{12}^rcdot R_{13}^r$,~$U_{DC} cdot R_{12}^rcdot R_{23}^r$,~$U_{TBM} cdot R_{12}^rcdot R_{13}^r$big ) are consistent at $1sigma$ level. The remaining double rotation cases are either excluded at 3$sigma$ level or successful in producing mixing angles only at $2sigma-3sigma$ level. We also updated our previous analysis on PMNS matrices of the form big($R_{ij}cdot U cdot R_{kl}$big ) with recent mixing data. We showed that the results modifies substantially with fitting accuracy level decreases for all of the permitted cases except big($R_{12}cdot U_{BM}cdot R_{13}$, $R_{23}cdot U_{TBM}cdot R_{13}$ and $R_{13}cdot U_{TBM} cdot R_{13}$big ) in this rotation scheme.
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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