arXiv subjects

N. Nimai Singh

Publications and source records attributed to N. Nimai Singh.

At least 37 records · Page 2Linked to original sources

arXiv2013

Leptonic mixing matrix in terms of Cabibbo angle

We phenomenologically build a neutrino mass matrix obeying $μ-τ$ symmetry with only two parameters, Cabibbo angle $(λ)$ and a flavour twister parameter $(η)$. For vanishing $η$, the model assumes TBM mixing. When $η=λ$, the model generates a solar mixing angle and solar mass squared difference that coincide with the experimental best-fits. It motivates us to propose a mixing matrix in the neutrino sector with $ sinθ_{12}<\frac{1}{\sqrt{3}}$, $θ_{13}=0$ and $θ_{23}=π/4$. The corrections in $θ_{13}$ and $θ_{23}$ are conducted following the breaking of $μ-τ$ symmetry, by choosing a proper unitary diagonalizing charged lepton matrix, and this ensures that $θ_{23}$ lies within the first octant. The Cabibbo angle $(λ=\sinθ_{c})$ plays the role of a guiding parameter in both neutrino as well as leptonic sector. The effect of the Dirac CP violating phase $δ_{cp}$ is also studied when it enters either through the charged lepton diagonalizing matrix or through neutrino mixing matrix.

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arXiv2012

Bi-Large neutrino mixing with charged lepton correction

The usual Bi-Maximal (BM) neutrino mixing faces an inherent problem in lowering the solar mixing angle below $\tan^{2}θ_{12}=0.50$ when charged lepton correction is taken. This minimum $θ_{12}$ is achievable only if CP violation is absent. We start with a new model which incorporates a new idea of mixing developed recently, called Bi-Large (BL) mixing, similar to BM mixing execpt that the former chooses rather $θ_{13}$ as Cabibbo angle $(θ_c)$ than zero. We apply this mixing in the neutrino sector, followed by a charged lepton correction with the CKM type matrix $U_{l}$. This model marks a prediction on $θ_{23}$ to lie within the first octant. The CP violating phase $δ_{CP}$ dictates the prediction of all the three mixing angles. A proper choice of $δ_{CP}$ leads to the predictions of all the three mixing angles including $θ_{12}$, to align very precisely with the experimental bestfits. This close agreement thus hoists Bi-Large mixing as an important and promising mixing scheme, in contrast to BM or TBM mixing as a first approximation. A formal derivation of BL mixing from discrete symmetry will be an important investigation in neutrino physics.

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arXiv2012

Dependence of $\tan^2 θ_{12}$ on Dirac CP phase $δ$ in tri-bimaximal neutrino mixing under charged lepton correction

We consider charged lepton correction to Tri-bimaximal(TBM) neutrino mixing, defined by the relation $U_{PMNS}=U^{\dagger}_l U_{TB}$ and find possible form of $U_l$ which can impart non-zero value of $\sin θ_{13}$ as well as $\tan^2 θ_{23}<1$, consistent with latest global analysis data. We adopt a new parametrization, other than the standard PDG parametrization, to introduce Dirac CP violating phase $δ$ in the PMNS matrix which is discussed by Fritzsch. Under such charged lepton correction pattern we note that $\tan^2 θ_{12}$ becomes dependent on the CP phase $δ$ from where constraints on $δ$ phase can be obtained after employing experimental range of mixing angles. To compute the values of mixing angles we assume the charged lepton correction to be of Cabibbo-Kobayashi-Maskawa(CKM) like. Since all the mixing matrices involved in the calculation, are derived from three dimensional rotation matrices they satisfy unitarity condition.

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arXiv2012

Expansion of $U_{PMNS}$ and Neutrino mass matrix $M_ν$ in terms of $sinθ_{13}$ for Inverted Hierarchical case

The recent observational data supports the deviation from Tri-bimaximal (TBM) mixings. Different neutrino mass models suggest the interdependency among the observational parameters involving the mixing angles. On phenomenological ground we try to construct the PMNS matrix $U_{PMNS}$ with certain analytic structure satisfying the unitary condition, in terms of a single observational parameter $sinθ_{13}$. We hypothesise the three neutrino masses $m_{i}$ as functions of $sinθ_{13}$ and then construct the neutrino mass matrix $M_ν$. We assume the convergence of the model to TBM mixing when $θ_{13}$ is taken zero. This mass matrix so far obtained can be employed for various applications including the estimation of matter-antimatter asymmetry of the Universe.

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arXiv2012

Charged lepton contributions to bimaximal and tri-bimaximal mixings for generating $\sinθ_{13}\neq 0$ and $\tan^2θ_{23}<1$

Bimaximal (BM) and tri-bimaximal (TB) mixings of neutrinos are two special cases of lepton mixing matrix, which predict the reactor angle $θ_{13}=0$ and the atmospheric angle $\tan^2θ_{23}=1$. Recent precision measurements and global analysis of oscillation parameters, have confirmed a non-vanishing value of $θ_{13}$ as well as deviations of $θ_{12}$ and $θ_{23}$ from their maximal values predicted by BM or TB mixing. In this work we mainly concentrate on $θ_{13}$ and $θ_{23}$ to assign $\sinθ_{13}\neq 0$ and $\tan^2θ_{23}<1$ with the help of charged lepton corrections defined by $U_{PMNS}=U^{\dagger}_lU_ν$. We first consider $U_ν$ to be given separately by BM and TB mixing matrices and then find the possible forms of $U_l}$ such that the elements of PMNS matrix, finally yield $\sinθ_{13}\neq 0$ and $\tan^2θ_{23}<1$. To compute the values of mixing angles we assume the charged lepton correction to be of CKM-like. All the mixing matrices considered here satisfy the unitarity condition to leading order of expansion parameters. We also analyze both the mixing schemes in presence of Dirac CP phase and find expressions for the rephasing invariant quantity $J_{CP}$ which have been discussed in recent literature.

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arXiv2012

A new method of parametrisation of neutrino mass matrix through breaking of $μ-τ$ symmetry: Normal hierarchy

In the first part of the present work the $μ-τ$ symmetry of the neutrino mass matrix is perturbed at its minimal level in order to produce deviation from Tri-bimaximal mixing (TBM), which includes nonzero value of reactor angle $θ_{13}$ and maximal condition of $\tan^{2}θ_{23}=1$. The parametrisation of neutrino mass matrix which describes Normal hierarchy (NH), has been addressed with minimum number of independent parameters, out of which two parameters $η$ and $α$ take care of $θ_{12}$ and $θ_{13}$ respectively without any interference with mass eigenvalues. In the second part the deviation from maximal condition $\tan^{2}θ_{23}=1$, along with the nonzero value of $θ_{13}$, has been implemented with the introduction of a perturbing matrix which breaks the $μ-τ$ symmetric mass matrix. The model is found to be flexible enough to adjust itself with the changing precise experimental results. The method is also applicable for inverted hierarchy and quasi-degenerate cases.

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arXiv2012

Validity of quasi-degenerate neutrino mass models and their predictions on baryogenesis

Quasi-degenerate neutrino mass models (QDN) which can explain the current data on neutrino masses and mixings,are studied. In the first part, we study the effect of CP-phases on QDN mass matrix obeying $μ-τ$ symmetry in normal hierarchical (QD-NH) and inverted hierarchical (QD-IH) patterns.The numerical predictions are consistent with observed data on solar mixing angle, absolute neutrino mass parameter consistent with neutrinoless double beta decay mass parameter and sum of three absolute neutrino masses from cosmological bound.The neutrino mass matrix is parameterized using only two unknown parameters. The second part deals with the estimation of observed baryon asymmetry of the universe. The prediction is nearly consistent with observation with flavoured thermal leptogenesis scenario. QD-NH model appears to be more favourable than those of QD-IH models.The present analysis shows that the three absolute neutrino masses may exhibit quasi-degenerate pattern in nature. They are far from discrimination at the moment.

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arXiv2012

Quasi-Degenerate Neutrino Masses with Normal and Inverted Hierarchy

The effects of CP-phases on the three absolute quasi-degenerate Majorana neutrino (QDN) masses are stud-ied with neutrino mass matrices obeying μ - τ symmetry for normal as well as inverted hierarchical mass patterns. We have made further investigations on 1) the prediction of solar mixing angle which lies below tri-bimaximal mixing value in consistent with neutrino oscillation observational data, 2) the prediction on absolute neutrino mass parameter (mee) in 0νββ decay, and 3) cosmological bound on the sum of the three absolute neutrino masses. The numerical analysis is carried out through the parameterization of neu- trino mass matrices using only two unknown parameters (ε, η) within μ - τ symmetry. The results show the validity of QDN mass models in both normal and inverted hierarchical patterns. These models are far from discrimination and hence not yet ruled out. The results presented in this article are new and have subtle ef- fects in the discrimination of neutrino mass models.

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arXiv2009

Flavour leptogenesis with tribimaximal mixings and beyond

We compute and compare the baryon asymmetry of the universe in thermal leptogenesis scenario with and without flavour effects for different neutrino mass models namely degenerate, inverted hierarchical and normal hierarchical models, with tribimaximal mixings and beyond. Considering three possible diagonal forms of Dirac neutrino mass matrices $m_{LR}$, the right-handed Majorana mass matrices $M_{RR}$ are constructed from the light neutrino mass matrices $m_{LL}$ through the inverse seesaw formula. The normal hierarchical model is found to give the best predictions of the baryon asymmetry for both cases. This analysis serves as an additional information in the discrimination of the presently available neutrino mass models. Moreover, the flavour effects is found to give enhancement of the baryon asymmetry in thermal leptogenesis.

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arXiv2009

Degenerate neutrino mass models revisited

A parametrisation of the degenerate neutrino mass matrix obeying $μ-τ$ symmetry, is introduced for detailed numerical analysis. As a continuation of our earlier work on normal and inverted hierarchical models, the present parametrisation for degenerate models has the ability to lower the solar mixing angle below the tri-bimaximal value $\tan^{2}θ_{12}=0.5$, while maintaining the condition of maximal atmospheric mixing angle and zero reactor angle. The combined data on the mass-squared differences derived from various oscillation experiments, and also from the bounds on absolute neutrino masses in $0νββ$ decay and cosmology, gives certain constraints on the validity of the degenerate models.

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arXiv2008

Normal versus inverted hierarchical models within $μ-τ$ symmetry

We make a theoretical attempt to compare the predictions from normal and inverted hierarchical models, within the framework of $μ-τ$ symmetry. We consider three major theoretical issues in a self consistent ways, viz., predictions on neutrino mass and mixing parameters, stability under RG analysis in MSSM, and baryogenesis through leptogenesis. We further extend our earlier works on parametrisation of neutrino mass matrices using only two parameters, in addition to an overall mass scale $m_0$, and the ratio of these two parameters fixes the value of solar mixing angle. Such parametrisation though phenomenological gives a firm handle on the analysis of the mass matrices and predicts lower values of solar mixing angle in the range $\tan^2θ_{12}=0.50-0.35$.We check the stability of the model under radiative corrections in MSSM for large $\tanβ\sim 58-60$ region and observe that the evolution of $\bigtriangleup m^2_{21}$ with energy scale, is highly dependent on the input high scale value of solar mixing angle. Solar angle predicted by tri-bimaximal mixings and also values lower than this, do not lead to stability of the model. Similarly, the evolution of the atmospheric mixing angle with energy scale at large $\tanβ$ values, shows sharp decrease for the case with non-zero value of m_3. We apply these mass matrices to estimate the baryon asymmetry of the universe in a self consistent way and find that normal hierarchical model leads to the best result. Considering all these three pieces of theoretical investigations, we may conclude that normal hierarchical model is more favourable in nature.

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arXiv2008

Thermal and non-thermal leptogenesis in different neutrino mass models with tribimaximal mixings

In the present work we study both thermal and non-thermal leptogenesis in all neutrino mass models describing the presently available neutrino mass patterns. We consider the Majorana CP violating phases coming from right-handed Majorana mass matrices to estimate the baryon asymmetry of the universe, for different neutrino mass models namely degenerate, inverted hierarchical and normal hierarchical models, with tribimaximal mixings. Considering two possible diagonal forms of Dirac neutrino mass matrix as either charged lepton or up-quark mass matrix, the right-handed Majorana mass matrices are constructed from the light neutrino mass matrix through the inverse seesaw formula. Only the normal hierarchical model leads to the best predictions for baryon asymmetry of the universe, consistent with observations in both thermal and non-thermal leptogenesis scenario. The analysis though phenomenological may serve as an additional information in the discrimination among the presently available neutrino mass models.

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arXiv2006

Type-II seesaw mass models and baryon asymmetry

We compute and also compare the contributions of canonical and noncanonical mass terms towards baryon asymmetry by considering type-II seesaw mass models of neutrinos: Degenerare(3 varieties), Normal hierarchical and Inverted hierarchical(2 varieties). We have shown that for particular choices of parameter '$γ$'(the so-called discriminator) for different neutrino mass models, the baryon asymmetry is largely dominated by canonical term. Within such type-II seesaw scenario, we find normal hierarchical mass model as the most favourable choice of nature.

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arXiv2006

Lowering solar mixing angle in inverted hierarchy without charged lepton corrections

In the present work, the inverted hierarchical neutrino mass model which is characterised by opposite CP parity in the first two mass eigenvalues $(m_1,-m_2,m_3)$, is studied in order to lower the predicted value of solar mixing angle $\tan^2θ_{12}$, from the tri-bimaximal mixing (TBM), without sacrificing the conditions of maximal atmospheric mixing angle and zero reactor angle. The present attempt is different from the earlier approach where the correction from the charged lepton mass matrix is included in the leptonic mixing matrix to lower the prediction on solar mixing angle. The lowering of the solar mixing angle without charged lepton correction, can be obtained through the variation of the input value of a flavour twister term present in the texture of neutrino mass matrix having a 2-3 symmetry. The present analysis agrees with the latest experimental bounds on neutrino mass parameters and also represents an important result on the survival of the inverted hierarchical neutrino mass models having opposite CP parity in the first two eigenvalues.

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arXiv2006

Estimations of baryon asymmetry for different neutrino mass models

We present a comparison of the numerical prediction on baryon asymmetry of the Universe in different neutrino mass models. We start with a very brief review on the main formalism of baryogenesis via leptogenesis through decay of heavy right-handed Majorana neutrinos, and then calculate the baryon asymmetry of the universe for known six neutrino mass models viz., three quasi-degenerate, two inverted and one normal hierarchical models, which are derived from canonical seesaw formula. The corresponding mass matrices for the right-handed Majorana neutrino as well as the Dirac neutrino, which are fixed at the seesaw stage for generating correct light neutrino mass matrices, are again employed in the calculation of baryogenesis. This procedure removes possible ambiguity on the choices of Dirac neutrino and right-handed Majorana mass matrices, and fixes input parameters at the seesaw stage. We find that the ranges of predictions from both normal hierarchical model and degenerate model (DegT1A) are almost consistent with the observed baryon asymmetry of the universe. Combining the present result with other predictions such as light neutrino masses and mixing angles, and stability under radiative corrections in MSSM, the normal hierarchical model appears to be the most favourable choice of nature.

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arXiv2006

Deviation from tri-bimaximal mixings in two types of inverted hierarchical neutrino mass models

An attempt is made to explore the possibility for deviations of solar mixing angle ($θ_{12}$) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle ($θ_{23}=π/4$) and zero reactor angle ($θ_{13}=0$). We find that the above conjecture can be automatically realised in the inverted hierarchical neutrino mass model having 2-3 symmetry, in the basis where charged lepton mass matrix is diagonal. For the observed ranges of $\bigtriangleup m^2_{21}$ and $\bigtriangleup m^2_{23]$, we calculate the predictions on $\tan^2θ_{12}=0.5, 0.45, 0.35$ for different input values of the parameters in the neutrino mass matrix. We also observe a possible crossing over from one type of inverted hierarchical model having same CP parity (Type-IHA) to other type having opposite CP parity (Type-IHB). Such neutrino mass matrices can be obtained from the canonical seesaw formula using diagonal form of Dirac neutrino mass matrix and non-diagonal texture of right-handed Majorana mass matrix, and may have important implications in model building using discrete as well as non-abelian symmetry groups.

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arXiv2004

Radiative generation of $\bigtriangleup m^2_{21}$ and $θ_{13}$ in two-fold degenerate neutrino models

We study the implications on an important result on radiative corrections (JM conjecture) which states that the solar mass scale $\bigtriangleup m^2_{21}$ corresponding to the large mixing angle (LMA) MSW solution of the solar neutrino problem, can be generated through radiative corrections in the minimal supersymmetric standard model (MSSM) if two of the neutrino masses having opposite CP parity, are assumed to be degenerate and have non-zero value of $U_{e3}$ at high energy scale. We show that the above conjecture can be derived when we take the static solution of mixing angles from the general solution of RGEs. If we consider the simultaneous running of the three neutrino mass eigenvalues and mixing angles, the above two-fold degenerate case $m_i=(m, -m, m')$ with $m'\neq 0$ and $U_{e3}=0$, can also generate through radiative corrections, the non-zero values of $\bigtriangleup m^2_{21}$ and $U_{e3}$ at low scale, which are consistent with the LMA MSW solution. Such generalisation of JM conjecture may have important implications for model buildings from general gauge symmetry.

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arXiv2004

Numerical consistency check between two approaches to radiative corrections for neutrino masses and mixings

We briefly outline the two popular approaches on radiative corrections to neutrino masses and mixing angles, and then carry out a detailed numerical analysis for a consistency check between them in MSSM. We find that the two approaches are nearly consistent with a small discrepancy of a factor of 13 percent in mass eigenvalues at low energy scale, but the predictions on mixing angles are almost consistent. We check the stability of the three types of neutrino models, i.e., hierarchical, inverted hierarchical and degenerate models, under radiative corrections, using both approaches, and find consistent conclusions. The neutrino mass models which are found to be stable under radiative corrections in MSSM are the normal hierarchical model and the inverted hierarchical model with opposite CP parity. We also carry out numerical analysis on some important conjectures related to radiative corrections in MSSM, viz., radiative magnification of solar and atmospheric mixings in case of nearly degenerate model having same CP parity (MPR conjecture) and radiative generation of solar mass scale in exactly two-fold degenerate model with opposite CP parity and non-zero reactor angle (JM conjecture). We observe certain exceptions to these conjectures. Finally the effect of scale-dependent vacuum expectation value in neutrino mass renormalisation is discussed.

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