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Register a new userDiagonal reflection symmetries, universal four-zero texture, and trimaximal mixing with predicted $theta_{13}$
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Masaki J. S. Yang
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In this paper, we impose a magic symmetry on the neutrino mass matrix $M_{ u}$ with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the MNS matrix has trimaximal mixing inevitably. Since the lepton sector has only six free parameters, physical observables of leptons are all determined from the charged leptons masses $m_{ei}$, the neutrino mass differences $Delta m_{i1}$, and the mixing angle $theta_{23}$. As new predictions, we obtain $sin theta_{12} = 0.584$ and $sin theta_{13} = 0.149$. The latter one is almost equal to the latest best fit.
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In this paper, we consider a set of new symmetries in the SM, {it diagonal reflection} symmetries $R , m_{u, u}^{*} , R = m_{u, u}, ~ m_{d,e}^{*} = m_{d,e}$ with $R =$ diag $(-1,1,1)$. These generalized $CP$ symmetries predict the Majorana phases to be $alpha_{2,3} /2 sim 0$ or $pi /2$. A realization of reflection symmetries suggests a broken chiral $U(1)_{rm PQ}$ symmetry and a flavored axion. The axion scale is suggested to be $langle theta_{u,d} rangle sim Lambda_{rm GUT} , sqrt{m_{u,d} , m_{c,s}} / v sim 10^{12} , $[GeV]. By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well. This scheme predicts the normal hierarchy, the Dirac phase $delta_{CP} simeq 203^{circ},$ and $|m_{1}| simeq 2.5$ or $6.2 , $[meV]. In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix $Y_{ u}$ completely determine the structure of right-handed neutrino mass $M_{R}$. An $u- u$ unification predicts mass eigenvalues to be $ (M_{R1} , , M_{R2} , , M_{R3}) = (O (10^{5}) , , O (10^{9}) , , O (10^{14})) , $[GeV].
The recent T2K, MINOS and Double Chooz oscillation data hint a relatively large $theta_{13}$, which can be accommodated by some general modification of the Tribimaximal/Bimaximal/Democratic mixing matrices. Using such matrices we analyze several Majorana mass matrices with texture one-zero and show whether they satisfy normal or inverted mass hierarchy and phenomenologically viable or not.
In this paper, we consider the diagonal reflection symmetries and three-zero texture in the SM. The three-zero texture has two less assumptions ($(M_{u})_{11} , (M_{ u})_{11} eq 0$) than the universal four-zero texture for mass matrices $(M_{f})_{11} = (M_{f})_{13,31} = 0$ for $f = u,d, u, e$. The texture and symmetries reproduce the CKM and MNS matrices with accuracies of $O(10^{-4})$ and $O(10^{-3})$. By assuming a $d$-$e$ unified relation ($M_{d} sim M_{e}$), this system predicts the normal hierarchy, the Dirac phase $delta_{CP} simeq 202^{circ},$ the Majorana phases $alpha_{12} = 11.3^{circ}, alpha_{13} = 6.90^{circ}$ up to $pi$, and the lightest neutrino mass $m_{1} simeq 2.97,-,4.72,$[meV]. The effective mass of the double beta decay $|m_{ee}|$ is found to be $1.24 sim 1.77 ,$[meV].
In this letter, we consider exact $mu-tau$ reflection symmetries for quarks and leptons. Fermion mass matrices are assumed to be four-zero textures for charged fermions $f = u,d,e$ and a symmetric matrix for neutrinos $ u_{L}$. By a bi-maximal transformation, all the mass matrices lead to $mu-tau$ reflection symmetric forms, which seperately satisfy $T_{u} , m_{u, u}^{*} , T_{u} = m_{u, u}$ and $T_{d} , m_{d,e}^{*} , T_{d} = m_{d,e}$. Reconciliation between the $mu-tau$ reflection symmetries and observed $sin theta_{13}$ predicts $delta_{CP} simeq 203^{circ}$. Moreover, imposition of universal texture $(m_{f})_{11} = 0$ for $f=u,d, u,e$ predicts the normal hierarchy with the lightest neutrino mass $|m_{1}| = 6.26$ or $2.54$ meV.
Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render an $U_{PMNS}$ lepton mixing matrix consistent with data. In particular we are interested in finding the textures with the maximum number of zeros. We explore the cases of real matrices with three and four zeros and find that only ten matrices with three zeros provide solutions in agreement with data. We present the successful Yukawa textures including the relative sizes of their non-zero entries as well as some new and interesting relations among the entries of these textures in terms of the charged lepton masses. We also show that these relations can be obtained directly from a parametrization of the charged lepton mixing matrix $U_l$.
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