• Mrinal Kumar Das

      Articles written in Pramana – Journal of Physics

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

      Mrinal Kumar Das Mahadev Patgiri N Nimai Singh

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      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 discrepancy factor of 4.2% with running vacuum expectation value (VEV) (13% for scale-independent VEV) 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 the MSSM, viz., radiative magnification of solar and atmospheric mixings in the 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 Ue3 (JM conjecture). We observe certain exceptions to these conjectures. We find a new result that both solar mass scale and Ue3 can be generated through radiative corrections at low energy scale. Finally the effect of scaledependent vacuum expectation value in neutrino mass renormalisation is discussed

    • Discriminating neutrino mass models using type-II see-saw formula

      N Nimai Singh Mahadev Patgiri Mrinal Kumar Das

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      An attempt has been made to discriminate theoretically the three possible patterns of neutrino mass models,viz., degenerate, inverted hierarchical and normal hierachical models, within the framework of Type-II see-saw formula. From detailed numerical analysis we are able to arrive at a conclusion that the inverted hierarchical model with the same CP phase (referred to as Type [IIA]), appears to be most favourable to survive in nature (and hence most stable), with the normal hierarchical model (Type [III]) and inverted hierarchical model with opposite CP phase (Type [IIB]), follow next. The degenerate models (Types [IA,IB,IC]) are found to be most unstable. The neutrino mass matrices which are obtained using the usual canonical see-saw formula (Type I), and which also give almost good predictions of neutrino masses and mixings consistent with the latest neutrino oscillation data, are re-examined in the presence of the left-handed Higgs triplet within the framework of non-canonical see-saw formula (Type II). We then estimate a parameter (the so-called discriminator) which may represent the minimum degree of suppression of the extra term arising from the presence of left-handed Higgs triplet, so as to restore the good predictions on neutrino masses and mixings already acquired in Type-I see-saw model. The neutrino mass model is said to be favourable and hence stable when its canonical see-saw term dominates over the non-canonical (perturbative) term, and this condition is used here as a criterion for discriminating neutrino mass models.

    • Regge-like initial input and evolution of non-singlet structure functions from DGLAP equation up to next-next-to-leading order at low 𝑥 and low $Q^{2}$

      Nayan Mani Nath Mrinal Kumar Das Jayanta Kumar Sarma

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      This is an attempt to study how the features of Regge theory, along with QCD predictions, lead towards the understanding of unpolarized non-singlet structure functions $F_{2}^{\text{NS}}$ $(x, Q^{2})$ and 𝑥 𝐹3 $(x, Q^{2})$ at low 𝑥 and low $Q^{2}$ . Combining the features of perturbative quantum chromodynamics (pQCD) and Regge theory, an ansatz for $F_{2}^{\text{NS}}$ $(x, Q^{2})$ and 𝑥 𝐹3 $(x, Q^{2})$ structure functions at small 𝑥 was obtained, which when used as the initial input to Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equation, gives the $Q^{2}$ evolution of the non-singlet structure functions. The non-singlet structure functions, evolved in accordance with DGLAP evolution equations up to next-next-to-leading order are studied phenomenologically in comparison with the available experimental and parametrization results taken from NMC, CCFR, NuTeV, CORUS, CDHSW, NNPDF and MSTW Collaborations and a very good agreement is observed in this regard.

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