# Mrinal Kumar Das - Gauhati University

## Contact Details

NameMrinal Kumar Das |
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AffiliationGauhati University |
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CityGuwahati |
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CountryIndia |
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## Pubs By Year |
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## Pub CategoriesHigh Energy Physics - Phenomenology (12) Mathematics - Commutative Algebra (2) Computer Science - Learning (1) Statistics - Methodology (1) Computer Science - Cryptography and Security (1) Mathematics - K-Theory and Homology (1) Cosmology and Nongalactic Astrophysics (1) Statistics - Machine Learning (1) |

## Publications Authored By Mrinal Kumar Das

We study an inverse seesaw model of neutrino mass within the framework of $S_4$ flavour symmetry from the requirement of generating non-zero reactor mixing angle $\theta_{13}$ along with correct dark matter relic abundance. The leading order $S_4$ model gives rise to tri-bimaximal type leptonic mixing resulting in $\theta_{13}=0$. Non-zero $\theta_{13}$ is generated at one loop level by extending the model with additional scalar and fermion fields which take part in the loop correction. Read More

Let $R$ be a regular domain of dimension $d\geq 2$ which is essentially of finite type over an infinite perfect field $k$. We compare the Euler class group $E^d(R)$ with the van der Kallen group $Um_{d+1}(R)/E_{d+1}(R)$. In the case $2R=R$, we define a map from $E^d(R)$ to $Um_{d+1}(R)/E_{d+1}(R)$ and study it in intricate details. Read More

Users of a personalised recommendation system face a dilemma: recommendations can be improved by learning from data, but only if the other users are willing to share their private information. Good personalised predictions are vitally important in precision medicine, but genomic information on which the predictions are based is also particularly sensitive, as it directly identifies the patients and hence cannot easily be anonymised. Differential privacy has emerged as a potentially promising solution: privacy is considered sufficient if presence of individual patients cannot be distinguished. Read More

We present a TeV scale seesaw mechanism for exploring the dark matter and neutrino phenomenology in the light of recent neutrino and cosmology data. A different realization of the Inverse seesaw(ISS) mechanism with $A_{4}$ flavor symmetry is being implemented as a leading contribution to the light neutrino mass matrix which usually gives rise to vanishing reactor mixing angle $\theta_{13}$. Using a non-diagonal form of Dirac neutrino mass matrix and $3\sigma$ values of mass square differences we parameterize the neutrino mass matrix in terms of Dirac Yukawa coupling "$y$". Read More

We study all possible texture zeros in the Majorana neutrino mass matrix which are allowed from neutrino oscillation as well as cosmology data when the charged lepton mass matrix is assumed to take the diagonal form. In case of one-zero texture, we write down the Majorana phases which are assumed to be equal and the lightest neutrino mass as a function of the Dirac CP phase. In case of two-zero texture, we numerically evaluate all the three CP phases and lightest neutrino mass by solving four real constraint equations. Read More

We study a very specific type of neutrino mass and mixing structure based on the idea of Strong Scaling Ansatz (SSA) where the ratios of neutrino mass matrix elements belonging to two different columns are equal. There are three such possibilities, all of which are disfavored by the latest neutrino oscillation data. We focus on the specific scenario which predicts vanishing reactor mixing angle $\theta_{13}$ and inverted hierarchy with vanishing lightest neutrino mass. Read More

We study the possibility of generating non-zero reactor mixing angle $\theta_{13}$ by perturbing the $\mu-\tau$ symmetric neutrino mass matrix. The leading order $\mu-\tau$ symmetric neutrino mass matrix originates from type I seesaw mechanism whereas the perturbations to $\mu-\tau$ symmetry originate from type II seesaw term. We consider four different realizations of $\mu-\tau$ symmetry: Bimaximal Mixing(BM), Tri-bimaximal Mixing (TBM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM) all giving rise to $\theta_{13} = 0, \theta_{23} = \frac{\pi}{4}$ but different non-zero values of solar mixing angle $\theta_{12}$. Read More

In this paper, we prove the moving lemma, addition and subtraction principles, in a more general setup than the available ones. We apply these results to explore a question of Nori on homotopy of sections of projective modules. As another application, we investigate the Segre class of ideals, extending the existing results. Read More

We study the renormalization group effects on neutrino masses and mixing in Minimal Supersymmetric Standard Model (MSSM) by considering a $\mu-\tau$ symmetric mass matrix at high energy scale giving rise to Tri-Bi-Maximal (TBM) type mixing. We outline a flavor symmetry model based on $A_4$ symmetry giving rise to the desired neutrino mass matrix at high energy scale. We take the three neutrino mass eigenvalues at high energy scale as input parameters and compute the neutrino parameters at low energy by taking into account of renormalization group effects. Read More

The baryon to photon ratio in the present Universe is very accurately measured to be $(6.065 \pm 0.090) \times 10^{-10}$. Read More

We study the survivability of neutrino mass models with normal as well as inverted hierarchical mass patterns in the presence of both type I and type II seesaw contributions to neutrino mass within the framework of generic left-right symmetric models. At leading order, the Dirac neutrino mass matrix is assumed to be diagonal with either charged lepton (CL) type or up quark (UQ) type structure which gets corrected by non-leading effects giving rise to deviations from tri-bi-maximal (TBM) mixing and hence non-zero value of $\theta_{13}$. Using the standard form of neutrino mass matrix which incorporates such non-leading effects, we parametrize the neutrino mass matrix incorporating both oscillation as well as cosmology data. Read More

We present an analysis of normal and inverted hierarchical neutrino mass models within the framework of tri-bi-maximal (TBM) mixing. Considering the neutrinos to be quasi-degenerate (QDN), we study two different neutrino mass models with mass eigenvalues $(m_1, -m_2, m_3)$ and $(m_1, m_2, m_3)$ for both normal hierarchical (NH) and inverted hierarchical (IH) cases. Parameterizing the neutrino mass matrix using best fit oscillation and cosmology data for a QDN scenario, we find the right-handed Majorana mass matrix using type I seesaw formula for two types of Dirac neutrino mass matrices: charged lepton (CL) type and up quark (UQ) type. Read More

**Affiliations:**

^{1}ICTP, Trieste, Italy, and Gauhati Univ,

^{2}Gauhati Univ

**Category:**High Energy Physics - Phenomenology

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. Read More

**Affiliations:**

^{1}Gauhati Univ.,

^{2}Cotton college,

^{3}ICTP, Trieste, Italy and Gauhati Univ.

**Category:**High Energy Physics - Phenomenology

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. Read More

**Affiliations:**

^{1}The Abdus Salam ICTP, Trieste, Italy,

^{2}Cotton College,

^{3}Gauhati University

**Category:**High Energy Physics - Phenomenology

In this paper we propose a kind of natural selection which can discriminate the three possible neutrino mass models, namely the degenerate, inverted hierarchical and normal hierarchical models, using the framework of Type II seesaw formula. We arrive at a conclusion that the inverted hierarchical model appears to be most favourable whereas the normal hierarchical model follows next to it. The degenerate model is found to be most unfavourable. Read More