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.

Statistical Physics Analysis of Maximum a Posteriori Estimation for Multi-channel Hidden Markov Models

The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that correspond to different characteristics of the MAP-estimated sequence. The solution to the MAP estimation problem has different operational regimes separated by first order phase transitions. The transition points for $L$-channel system with identical noise levels, are uniquely determined by $L$ being odd or even, irrespective of the actual number of channels. We demonstrate that for lower noise intensities, the number of solutions is uniquely determined for odd $L$, whereas for even $L$ there are exponentially many solutions. We also develop a semi analytical approach to calculate the estimation error without resorting to brute force simulations. Finally, we examine the tradeoff between a system with single low-noise channel and one with multiple noisy channels.Comment: The paper has been submitted to Journal of Statistical Physics with submission number JOSS-S-12-0039

Lived religion in a plural society: a resource or liability

Recently there is a renewed academic interest in religion bringing it back on the global political agenda. Religion in the post modern global order is fast emerging as a new organizing principle in the face of multi-polarity, trans-nationality and sweeping pluralisation of peoples. Contrary to the secularist self believe, the modern has failed to take over the tradition including religion. Rather a logical opposite seems to be happening, questioning the very presumptions of the modernity project. The present paper is a narrative on this creative tension in the religious modern and post modern. The paper is crafted into four sections. First section seeks to pin down the genesis of “religious” in the search for social order and consciousness beyond the material world. Second section deals with the unfolding of enlightenment project and its manifest consequence with the birth of secularism master theory. Third section delves deep into the immediate Indian religious lived experiences under foreign rule up to the sweeping spell of globalisation. Fourth and last part of the essay makes a case for universality of a multicultural world and religious secularism