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Register a new userInterplay between $mu$-$tau$ reflection symmetry, four-zero texture and universal texture
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Authors
Masaki J. S. Yang
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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.
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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].
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.
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].
Nonstandard interactions (NSIs), possible subleading effects originating from new physics beyond the Standard Model, may affect the propagation of neutrinos and eventually contribute to measurements of neutrino oscillations. Besides this, $ mu-tau $ reflection symmetry, naturally predicted by non-Abelian discrete flavor symmetries, has been very successful in explaining the observed leptonic mixing patterns. In this work, we study the combined effect of both. We present an $S_4$ flavor model with $mu-tau$ reflection symmetry realized in both neutrino masses and NSIs. Under this formalism, we perform a detailed study for the upcoming neutrino experiments DUNE and T2HK. Our simulation results show that under the $mu-tau $ reflection symmetry, NSI parameters are further constrained and the mass ordering sensitivity is less affected by the presence of NSIs.
We analyze the different parametrizations of a general four-zero texture mass matrices for quarks and leptons, that are able to reproduce the CKM and PMNS mixing matrices. This study is done through a Chi-Square analysis. In quark sector, only four solutions are found to be compatible with CKM mixing matrix. In leptonic sector, using the last experimental results about the mixing angles in the neutrino sector, our Chi-Square analysis shows a preferred value for m_nu_3 to be around 0.05 eV independently of the parametrization of the four-zero texture mass matrices chosen for the charged leptons and neutrinos.
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