Updated values of running quark and lepton masses at GUT (Grand unified theories) scales are important for fermion mass model building, and to calculate neutrino masses, in GUTs . We present their values at GUT scales, in SM, MSSM and 2HDM theories, using the latest values of running quark and lepton masses.

We present a modelling and analysis of the COVID-19 outbreak in India with an emphasis on the socio-economic composition, based on the progress of the pandemic (during its first phase-from March to August 2020) in 11 federal states where the outbreak is the largest in terms of the total number of infectives. Our model is based on the susceptible-exposedinfectives-removed (SEIR) model, including an asymptomatic transmission rate, time-dependent incubation period and time-dependent transmission rate. We carry out the analysis with the available disease data up to the end of August 2020, with a projection of 42 days into the months of September and October 2020, based on the past data. Overall, we have presented a projection up to 351 days (till February 2021) for India and we have found that our model is able to predict correctly the first phase of the pandemic in India with correct projections of the peak of the pandemic as well as daily new infections. We also find the existence of a critical day, signifying a sudden shift in the transmission pattern of the disease, with interesting relation of the behaviour of the pandemic with demographic and socio-economic parameters. Towards the end, we have modelled the available data with the help of logistic equations and compare this with our model. The results of this work can be used as a future guide to follow in case of similar pandemics in developing countries.

We study the tensor structure function b 1 (x, Q 2 ) in deep inelastic scattering (DIS) of an electron from a polarized deuteron target. We model the electron-nucleon cross section at the starting point for Q 2 evolution by vector-meson-dominance (VMD). Shadowing due to the double-scattering of vector mesons, along with the presence of a d-state admixture in ground state deuteron wave function gives rise to a non-vanishing contribution to b 1 (x, Q 2 ).We find a large enhancement at low-x in qualitative agreement with other recent estimates of double-scattering contributions to b 1 (x, Q 2 ). If the model is valid, it should apply within the range of present fixed target experiments.

We have explored the possibility of resolving the θ 23 octant degeneracy present in the newly planned Long-Baseline Neutrino Experiment (LBNE) by combining reactor experiments. Reactor experiments have already measured the third mixing angle θ 13 very precisely and this precise measurement of θ 13 in turn helps in determining the octant of θ 23 . We have examined the octant sensitivity with and without data from reactors. Octant sensitivity increases if reactors are added. The comparative study of octant sensitivities of 10 kt and 35 kt liquid argon far detector(FD), with and without the near detector(ND), reveals that the sensitivity increases with an increase in detector mass. Also, the presence of the ND improves the sensitivity. The effect of adding prior on octant determination is also studied in this work.

In this work, we have explored the possibilities of improving CP violation discovery potential of newly planned Long-Baseline Neutrino Experiment (LBNE), U.S.A., by combining with data from reactors. The third mixing angle $\theta_{13}$ is now very precisely measured and this precise measurenent of $\theta_{13}$ helps in measurement of CP violation. Here, CP violation is studied with and without data from reactors. Impact of placing a ND is also studied. It is found that CPV discovery potential of LBNE with ND increases when combined with data from reactors. With a far detector of 35 kt, it is possible to obtain 5$\sigma$ sensitivity of CPV when run for 5 years in $\nu$ and 5 years in $\bar{\nu}$ mode. When hierarchy is assumed to be normal hierarchy, CPV sensitivity is maximum. CPV discovery is possible by combining 5 years neutino data from LBNE with 3 years anti-neutrino from reactors. This study reveals that CPV can also be discovered at 5$\sigma$ cl in IH mode when appearance measurement of LBNE is combined with reactors