Comparing trimaximal mixing and its variants with deviations from tri-bimaximal mixing

Abstract

We analyze in detail the predictions of "trimaximal" neutrino mixing, which is defined by a mixing matrix with identical second column elements. This column is therefore identical to the second column in the case of tri-bimaximal mixing. We also generalize trimaximal mixing by assuming that the other rows and columns of the mixing matrix individually can have the same forms as for tri-bimaximal mixing. The phenomenology of these alternative scenarios and their mixing angle and CP phase correlations are studied. We emphasize how trimaximal mixing scenarios can be distinguished experimentally from broken tri-bimaximal mixing.

Generalised CP and Δ(6n 2) family symmetry in semi-direct models of leptons

“…It is the so-called TM 2 mixing [70]. There are three independent arrangements up to the exchange of the second and the third row,…”

Littlest Seesaw model from S 4 × U(1)

“…The starting point for our approach here is the observation that eq. (1.2) leads to trimaximal TM 1 mixing [32][33][34][35][36][37][38], in which the first column of the tri-bimaximal mixing matrix [39] is preserved. The inspiration for our approach comes from the semi-direct model of trimaximal TM 1 mixing that was developed in [40] in which, denoting the three generators of S 4 as S, U, T , the model preserves a 1 In general, neutrino mass models based on discrete family symmetry may be classified into three types [31]: direct, semi-direct and indirect, depending on the residual symmetry preserved in the neutrino and charged lepton sectors.…”

“…it is the first column of the TB mixing matrix, corresponding to m 1 = 0. We conclude that the neutrino mass matrix leads to so-called TM 1 mixing [32][33][34][35][36][37][38], in which the first column of the mixing matrix is fixed to be that of the TB mixing matrix, but the other two columns are not uniquely determined, Since the neutrino mass matrix yields TM 1 mixing as discussed above, it can be block diagonalised by the TB mixing matrix, It only remains to put m ν block into diagonal form, with real positive masses, which can be done exactly analytically of course, since this is just effectively a two by two complex symmetric matrix which may be diagonalised with a rotation angle θ ν 23 . This procedure leads to the following exact analytic results for neutrino masses and lepton mixing parameters [30].…”

Trimaximal mixing with a texture zero

“…In this context, it has been observed that the first or the second column of TBM mixing matrix can still accommodate the recent neutrino oscillation data [4]. When the second column of TBM mixing matrix remains intact while the other columns deviate from TBM values, we denote that mixing matrix as TM 2 [5]. Similarly, if the first column of TBM remains intact and other columns deviate from TBM, we denote it by TM 1 [5].…”

“…When the second column of TBM mixing matrix remains intact while the other columns deviate from TBM values, we denote that mixing matrix as TM 2 [5]. Similarly, if the first column of TBM remains intact and other columns deviate from TBM, we denote it by TM 1 [5]. When either of these columns of TBM remain intact in the lepton mixing matrix, we can parametrize the mixing matrix in terms of one mixing angle and one CP violating Dirac phase along with two Majorana phases [4,5].…”