Neutrino Yukawa textures within type-I see-saw

The arbitrariness of Yukawa couplings can be reduced by the imposition of some flavor symmetries and/or by the realization of texture zeros. We review neutrino Yukawa textures with zeros within the framework of the type-I seesaw with three heavy right chiral neutrinos and in the basis where the latter and the charged leptons are mass diagonal. An assumed non-vanishing mass of every ultralight neutrino and the observed non-decoupling of any neutrino generation allow a maximum of four zeros in the Yukawa coupling matrix $Y_\nu$ in family space. There are seventy two such textures. We show that the requirement of an exact $\mu\tau$ symmetry, coupled with the observational constraints, reduces these seventy two allowed textures to only four corresponding to just two different forms of the light neutrino mass matrix $M_{\nu A}/M_{\nu B}$, resulting in an inverted/normal mass ordering. The effect of each of these on measurable quantities can be described, apart from an overall factor of the neutrino mass scale, in terms of two real parameters and a phase angle all of which are within very constrained ranges. The masses and Majorana phases of ultralight neutrinos are predicted within definite ranges with $3\sigma$ laboratory and cosmological observational inputs. The rate for $0\nu\beta\beta$ decay, though generally below the reach of planned experiments, could approach it in some parameteric regions. Within the same framework, we also study Yukawa textures with a fewer number of zeros, but with exact $\mu\tau$ symmetry. We further formulate the detailed scheme of the explicit breaking of $\mu\tau$ symmetry in terms of three small parameters for allowed four zero textures. The observed sizable mixing between the first and third generations of neutrinos is shown to follow for a suitable choice of these symmetry breaking parameters.Comment: invited review article, to appear in a special issue on neutrinos in the journal Advances in High Energy Physics (AHEP

Constraining {\it CP} violation in a softly broken A4A_4 symmetric Model

To understand the mass spectra of charged lepton and neutrino $A_4$ symmetry has been proposed in addition with the Standard $SU(2)_L\times U(1)_Y$ model. We break $A_4$ symmetry softly and the deviation from the tri-bimaximal mixing arises due to Zee mechanism. In the present work, we express two mixing angles $\theta_{13}$ and $\theta_{23}$ in terms of a single model parameter and experimental observables, such as, mixing angle $\theta_{12}$, mass squared differences $\Delta m^2_{21}$ and $\Delta m^2_{32}$. Using the experimental values of $\theta_{23}$, $\theta_{12}$, $\Delta m^2_{21}$ and $\Delta m^2_{32}$ we restrict the model parameter and we predict $\theta_{13}$. This model gives rise to $\theta_{13}\simeq 11^\circ$ if we allow $1\sigma$ deviation of $\theta_{23}$ and $2^\circ$ deviation of $\theta_{12}$ from their best fit values. Utilizing all those constraints, we explore the extent of CP violation parameter $J_{\rm CP}$ in the present model and found a value of $J_{\rm CP}\approx 2.65\times 10^{-3}$ (for $1\sigma$ deviation of $\theta_{23}$ and $2^\circ$ deviation of $\theta_{12}$) consistent with the other neutrino experimental results. We have studied the mass pattern of neutrino and neutrinoless double beta decay $(\beta\beta_{0\nu})$ parameter $|(M_\nu)_{ee}|$ in this model.Comment: 16 pages, 6 eps figures,revised materials and figures, version to appear in Phys.Rev.

Analysis of a model with a common source of CP violation

We work in a model where all CP violating phenomena have a common source. CP is spontaneously broken at a large scale $V$ through the phase of a complex singlet scalar. An additional $SU(2)_L$ singlet vector-like down-type quark relates this high scale CP violation to low energy. We quantitatively analyze this model in the quark sector. We obtain the numerical values of the parameters of the Lagrangian in the quark sector for a specific ansatz of the $4\times4$ down-type quark mass matrix where the weak phase is generated minimally. $Z \bar b b$ vertex will modify in presence of the extra vector-like down-type quark. From the experimental lower bound of the partial decay width $Z\to \bar b b$ we find out the lower bound of the additional down-type quark mass. Tree level flavor changing neutral current appears in this model due to the presence of the extra vector-like down-type quark. We give the range of values of the mass splitting $\Delta m_{B_q}$ in $B^0_q-{\bar B}^0_q$ system using SM box, $Z$ mediating tree level and $Z$ mediating one loop diagrams together for both $q=d, s$. We find out the analytical expression for $\Gamma_{12}^q$ in this model from standard box, $Z$ and Higgs mediated penguin diagrams for $B^0_q-{\bar B}^0_q$ system, $q=d,s$. From this we numerically evaluate the decay width difference $|\Delta\Gamma_{B_q}/\Gamma_{B_q}|$. We also find out the numerical values of the CP asymmetry parameters $a_J$ and $a_\pi$ for the decays $B^0_d\to J/\psi K_s$ and $B^0_d\to \pi^+ \pi^-$ respectively. We get the lower bound of the scale $V$ through the upper bound of the strong CP phase.Comment: 20 pages, no figures New materials and references have been added. Text has been modified. To be appear in J.Phys.