Neutrino Yukawa Matrix Research Articles

Yukawa Matrix for the Neutrino and Lepton Flavour Violation

We estimate the magnitude of Lepton Flavour Violation (LFV) from the phase of the neutrino Yukawa matrix. In the minimal supersymmetric standard model with right-handed neutrinos, the LFV processes l_i \to l_j \gamma can appear through the slepton mixing, which comes from the renormalization group effect on the right-handed neutrino Yukawa interaction between the Grand Unified Theory scale and the heavy right-handed neutrino mass scale. Two types of phases exist in the neutrino Yukawa matrix. One is the Majorana phase, which can change the magnitude of the LFV branching ratios by a few factor. The other phases relate for the size of the Yukawa hierarchy and its phase effect can change the LFV branching ratios by several orders of magnitude.

Phase contribution to LFV

We analyze the phase effect of the neutrino Yukawa matrix in the context of the Minimal Supersymmetric Standard Model with right-handed neutrinos. Its effect can change the Lepton Flavor Violation branching ratios by a few order of magnitude.

Leptogenesis and bi-unitary parametrization of neutrino Yukawa matrix

We analyze the neutrino Yukawa matrix by considering three constraints: the out-of-equilibrium condition of lepton number violating process responsible for leptogenesis, the upper bound of branching ratio of lepton flavor violating decay, and the prediction of large mixing angles using the see-saw mechanism. In a certain parametrization with bi-unitary transformation, it is shown that the structure which satisfies the constraints can be characterized by only seven types of Yukawa matrices. The constraint of the branching ratio of LFV turns out as a redundant one after applying other two constraints. We propose that this parametrization can be the framework in which the CP asymmetry of lepton number violating process can be predicted in terms of observable neutrino parameters at low energy, if necessary, under assumptions following from a theory with additional symmetries. There is an appealing model of neutrino Yukawa matrix considering the CP asymmetry for leptogenesis and the theoretical motivation to reduce the number of free parameters.

Muon anomalous magnetic moment and τ→μγ in a realistic string-inspired model of neutrino masses

We discuss the lepton sector of a realistic string-inspired model based on the Pati-Salam $SU(4)\times SU(2)_L \times SU(2)_R$ gauge group supplemented by a U(1) family symmetry. The model involves third family Yukawa unification, predicts large $\tan \beta\sim 50$, and describes all fermion masses and mixing angles, including approximate bi-maximal mixing in the neutrino sector. Atmospheric neutrino mixing is achieved via a large 23 entry in the neutrino Yukawa matrix which can have important phenomenological effects. We find that the recent BNL result on the muon ($g-2$) can be easily accommodated in a large portion of the SUSY parameter space of this model. Over this region of parameter space the model predicts a CP-even Higgs mass near 115 GeV, and a rate for $\tau\to \mu\gamma$ which is close to its current experimental limit.

Determining see-saw parameters from weak scale measurements?

The see-saw mechanism is a very attractive explanation for small neutrino masses, parametrized at the GUT scale by the right-handed Majorana mass matrix, ${\cal M}$, and the neutrino Yukawa matrix, ${\bf Y_\nu}$. We show that in a SUSY model with universal soft terms, ${\cal M}$ and ${\bf Y_\nu}$ can be calculated from the light neutrino masses, the MNS matrix, and ${\bf Y^{\dagger}_\nu} {\bf Y_\nu}$, which enters into the left-handed slepton radiative corrections. This suggests that in principle the GUT-scale inputs of the seesaw could be reconstructed from the neutrino and sneutrino mass matrices. We briefly discuss why this is impractical, but advocate the neutrino and sneutrino mass matrices as an alternative bottom-up parametrization of the seesaw.

Neutrino Mixing in the Seesaw Model

We study the neutrino mixing matrix (the MNS matrix) in the seesaw model. By assuming a large mass hierarchy for the heavy right-handed Majorana mass, we show that, in the diagonal Majorana base, the MNS matrix is determined by a unitary matrix, $S$, which transforms the neutrino Yukawa matrix, $y_{\nu}$, into a triangular form, $y_{\triangle}$. The mixing matrix of light leptons is $V_{KM} S^{\prime *}$, where $V_{KM} \equiv {V_{Le}}^{\dagger} V_{L \nu}$ %$V_{Le}$ and $V_{L\nu}$ diagonalize %the Yukawa matrices of charged leptons, %$y_e y_e^{\dagger}$, and neutrinos, $y_{\nu} y_{\nu}^{\dagger}$, %respectively, and $S^{\prime *} \equiv {V_{L\nu}}^{\dagger} S^*$. Large mixing may occur without fine tuning of the matrix elements of $y_{\triangle}$ even if the usual KM-like matrix $V_{KM}$ is given by $V_{KM} =1$. This large mixing naturally may satisfy the experimental lower bound of the mixing implied by the atmospheric neutrino oscillation.

Neutrino Mixing in the Seesaw Model

We study the neutrino mixing matrix (the MNS matrix) in the seesaw model. By assuming a large mass hierarchy for the heavy right-handed Majorana mass, we show that, in the diagonal Majorana base, the MNS matrix is determined by a unitary matrix, S, which transforms the neutrino Yukawa matrix, yν , into a triangular form, y� . The mixing matrix of light leptons is VKMS �∗ , where VKM ≡ VLe † VLν and S �∗ ≡ VLν † S ∗ . Large mixing may � .      

Quark and lepton flavor mixings in the SU(5) grand unification theory

We explain the imbalance of the flavor mixing angles between the quark and the lepton sectors in the context of the SU(5) GUT with the see-saw mechanism. The quark masses and the CKM matrix elements are obtained by using, respectively, the Fritzsch and Branco-Silva-Marcos form for the up- and down-quark Yukawa matrices ( y uand y d) and the GUT scale. The charge-lepton Yukawa matrix ( y e) is the transpose of y d, modified by the Georgi-Jarlskog factor. We show that the neutrino masses and mixing angles suggested by the recent solar and atmospheric neutrinos are then obtained from a simple texture of the neutrino Yukawa matrix ( y ν ) and a diagonal right-handed Majorana mass matrix at the GUT scale.