Evaluation of the Majorana Phases of a General Majorana Neutrino Mass Matrix: Testability of hierarchical Flavour Models

We evaluate the Majorana phases for a general $3\times3$ complex symmetric neutrino mass matrix on the basis of Mohapatra-Rodejohann's phase convention using the three rephasing invariant quantities $I_{12}$, $I_{13}$ and $I_{23}$ proposed by Sarkar and Singh. We find them interesting as they allow us to evaluate each Majorana phase in a model independent way even if one eigenvalue is zero. Utilizing the solution of a general complex symmetric mass matrix for eigenvalues and mixing angles we determine the Majorana phases for both the hierarchies, normal and inverted, taking into account the constraints from neutrino oscillation global fit data as well as bound on the sum of the three light neutrino masses ($\Sigma_im_i$) and the neutrinoless double beta decay ($\beta\beta_{0\nu}$) parameter $|m_{11}|$. This methodology of finding the Majorana phases is applied thereafter in some predictive models for both the hierarchical cases (normal and inverted) to evaluate the corresponding Majorana phases and it is shown that all the sub cases presented in inverted hierarchy section can be realized in a model with texture zeros and scaling ansatz within the framework of inverse seesaw although one of the sub case following the normal hierarchy is yet to be established. Except the case of quasi degenerate neutrinos, the methodology obtained in this work is able to evaluate the corresponding Majorana phases, given any model of neutrino masses.Comment: 27 pages, 16 figures, 4 tables, to appear in NP

Neutrino Mass, Coupling Unification, Verifiable Proton Decay, Vacuum Stability and WIMP Dark Matter in SU(5)

Nonsupersymmetric minimal SU(5) with Higgs representations ${24}_H$ and $5_H$ and standard fermions in ${\bar 5}_F\oplus {10}_F$ is well known for its failure in unification of gauge couplings and lack of predicting neutrino masses. Like standard model, it is also affected by the instability of the Higgs scalar potential. We note that extending the Higgs sector by ${75}_H$ and ${15}_H$ not only leads to the popular type-II seesaw ansatz for neutrino masses with a lower bound on the triplet mass $M_{\Delta} > 2\times 10^9$ GeV, but also achieves precision unification of gauge couplings without proliferation of non-standard light Higgs scalars or fermions near the TeV scale. Consistent with recent LUX-2016 lower bound, the model easily accommodates a singlet scalar WIMP dark matter near the TeV scale which resolves the vacuum stability issue even after inclusion of heavy triplet threshold effect. We estimate proton lifetime predictions for $p\to e^+\pi^0$ including uncertainties due to input parameters and threshold effects due to superheavy Higgs scalars and superheavy $X^{\pm 4/3},Y^{\pm 1/3}$ gauge bosons. The predicted lifetime is noted to be verifiable at Super Kamiokande and Hyper Kamiokande experiments.Comment: 36 pages, 9 figures (Accepted for publication in Advances in High Energy Physics

Scaling ansatz with texture zeros in linear seesaw

We investigate scaling ansatz with texture zeros within the framework of linear seesaw mechanism. In this variant of seesaw mechanism a simplified expression of effective neutrino mass matrix $m_\nu$ containing two Dirac type matrices ($m_D$ and $m_{DS}$) and one Majorana type matrix ($m_{RS}$) is obtained by virtue of neglecting the global $U(1)_L$ symmetry breaking term in the mass term of the Lagrangian. Along with the charged lepton mass matrix, the matrix $m_{RS}$ too, is chosen in a diagonal basis whereas a scaling relation is incorporated in $m_D$ and $m_{DS}$ with different scale factors. Our goal in this work is to achieve a completely phenomenologically acceptable $m_\nu$ generated by combinations of $m_D$ and $m_{DS}$ containing least number of independent parameters or maximum number of zeros. At the end of the numerical analysis it is found that number of zeros in any of the constituent Dirac type matrices ($m_D$ and $m_{DS}$) of $m_\nu$ cannot be greater than six in order to meet the phenomenological requirements. The hierarchy obtained here is normal and also the values of the two parameters sum mass ($\sum m_i$) and $|m_{\nu_{ee}}|$ are below the present experimental lower limit.Comment: 18 pages, 10 tables, 1 figure, Accepted for publication in Physics Letters

A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios

We present a systematic study on minimally perturbed neutrino mass matrices which at the leading order give rise to Tri-BiMaximal (TBM) mixing due to a residual $\mathbb{Z}_2\times \mathbb{Z}_2^{\mu\tau}$ Klein symmetry in the neutrino mass term of the low energy effective seesaw Lagrangian. Considering only the breaking of $\mathbb{Z}_2^{\mu\tau}$ with two relevant breaking parameters ($\epsilon_{4,6}^\prime$), after a comprehensive numerical analysis, we show that the phenomenologically viable case in this scenario is a special case of TM1 mixing. For this class of models, from the phenomenological perspective, one always needs large breaking (more than $45\%$) in one of the breaking parameters. However, to be consistent the maximal mixing of $\theta_{23}$, while more than $35\%$ breaking is needed in the other, a range $49.4^\circ-53^\circ$ and $38^\circ-40^\circ$ could be probed allowing breaking up to $25\%$ in the same parameter. Thus though this model cannot distinguish the octant of $\theta_{23}$, non-maximal mixing is preferred from the viewpoint of small breaking. The model is also interesting from leptogenesis perspective. Unlike the standard $N_1$-leptogenesis scenario, here all the RH neutrinos contribute to lepton asymmetry due to the small mass splitting controlled by the $\mathbb{Z}_2^{\mu\tau}$ breaking parameters. Inclusion of flavour coupling effects (In general, which have been partially included in all the leptogenesis studies in perturbed TBM framework) makes our analysis and results pertaining to a successful leptogenesis more accurate than any other studies in existing literature. Finally, in the context of recent discovery of the ultra high energy (UHE) neutrino events at IceCube, assuming UHE neutrinos originate from purely astrophysical sources, we obtain prediction on the neutrino flux ratios at neutrino telescopes.Comment: 48 pages, 9 figures, 2 tables, substantially revised (accepted for publication in JCAP

Reviewing the prospect of fermion triplets as dark matter and source of baryon asymmetry in non-standard cosmology

Indirect searches of Dark Matter (DM), in conjugation with `missing track searches' at the collider seem to confine SU(2)$_L$ fermion triplet DM (FTDM) mass within a narrow range around 1 TeV. The canonical picture of the pure FTDM is in tension since it is under-abundant for the said mass range. Several preceding studies have reported that an extra species ($\phi$), redshifts faster than the radiation ($\sim a^{-(4+n)}$ where $n>0$), leads to a faster expanding early Universe by dominating in the energy density with an enhanced Hubble parameter. This has the potential to revive the under-abundant FTDM ($\mathbb{Z}_2$ odd, lightest generation) by causing freeze-out earlier without modifying the interaction strength between DM and thermal bath. On the other hand, although the CP asymmetry produced due to the decay of $\mathbb{Z}_2$ even heavier generations of the triplet remains unaffected, its evolution is greatly affected by the non-standard cosmology. It has been observed through numerical estimations that the minimum mass of the triplet, required to produce sufficient baryon asymmetry of the Universe (BAU), can be lowered up to two orders (compared to the standard cosmology) in this fast expansion scenario. The non-standard parameters $n$ and $T_r$ (a reference temperature below which radiation dominance prevails), which simultaneously control DM abundance as well as the frozen value of BAU, are tightly constrained from the observed experimental values. We have found that $n$ is strictly bounded within the interval $0.4\lesssim n \lesssim 1.8$ where the upper bound is imposed by the BAU constraint whereas the lower bound arises to satisfy the correct DM abundance. It has been noticed that the restriction on $T_r$ is not so stringent as it can vary from sub-GeV to a few tens of GeV.Comment: 40 pages, 10 figures, 1 table, minor changes, version published in JCA

FACTORS INFLUENCING DELAYED RELEASE FOLLOWED BY RAPID PULSE RELEASE OF DRUGS FROM COMPRESSION COATED TABLETS FOR COLON TARGETING

Objective: This work was undertaken to develop colon targeted tablets that can minimize premature release of ibuprofen (IBP) and metronidazole (MNZ) in a lag period of 7h during which the tablets are likely to remain in the upper gastro-intestinal tract, and produce rapid pulse release within 1-5 h after the lag period when the tablets could be located in the colon with or without intervention of colonic microflora.Methods: Core tablets of ibuprofen and metronidazole containing different amounts of tri-sodium citrate (TSC) as osmogen were compression coated with locust bean gum (LBG) and carboxymethyl LBG (CMLBG). In vitro drug release studies were performed in a dynamic pH shift condition with or without rat cecal matters. The release of the drugs were also monitored at different hydrodynamic conditions.Results: In vitro release studies revealed that increase in the amount of TSC, decrease in coat-weight and change in hydrodynamic conditions influenced the drug release considerably. While LBG coated tablets under the stated conditions failed to provide complete release of the drugs in 12 h, CMLBG coated tablets produced complete release rapidly in the post lag period minimizing the release in the initial 7 h. Presence of rat cecal matter in dissolution medium further accentuated the release of the drugs from CMLBG compression coated tablets in the post lag period.Conclusion: The study revealed that tablets containing appropriate amount of osmogen in the core and compression coated with suitable amount of CMLBG may be suitable for colon targeting of drugs even in the absence of colonic microflora