We list operators of the superpotential of the effective MSSM that emerge from the NMSGUT up to sextic degree. We give illustrative expressions for the coefficients in terms of NMSGUT parameters. We also estimate the impact of GUT scale threshold corrections on these effective operators in view of the demonstration that $B$ violation via quartic superpotential terms can be suppressed to acceptable levels after including such corrections in the NMSGUT. We find a novel $B$, $B − L$ violating quintic operator that leads to the decay mode $n → e^{−}K^{+}$. We also remark that the threshold corrections to the Type-I seesaw mechanism make the deviation of right-handed neutrino masses from the GUT scale more natural while Type-II seesaw neutrino masses, which earlier tended to utterly negligible receive threshold enhancement. Our results are of relevance for analysing $B − L$ violating operator-based, sphaleron-safe, baryogenesis.

The phenomenological study of neutral heavy gauge boson $(Z'_{B−L})$ of the minimal $B−L$ extension was done in the context of the LHC, on the dimuon production channel. The study begins with the LEP-II constraints on $Z'$ searches, and the dimuon events are simulated at the parton level at CM energies of 7 TeV and 8 TeV and studied with an integrated luminosity of 1.21 $\rm{fb}^{−1}$ and 20.5 $\rm{fb}^{−1}$ respectively. Later, the ATLAS detector-specific cuts unique to the muon pairs are imposed followed by the signal selection cuts on the invariant mass of the dimuon which restrict the events that are to be passed for signal-background analysis, that are finally compared with the ATLAS data, and accounted for no experimental detection of $Z'_{B−L}$ boson. It has been simulated further at 14 TeV CM energy with an integrated luminosity of 300 $\rm{fb}^{−1}$ to predict a possible discovery of this $B − L$ neutral-heavy gauge boson with a mass corresponding to 1.5 TeV and a $Z'$ coupling strength of 0.2 based on the signal-background analysis.

The ‘hierarchy problem’ plagues the Standard Model of particle physics. The source of this problem is our inability to answer the following question: Why is the Higgs mass so much below the GUT or Planck scale? A brief description about how ‘supersymmetry’ and ‘composite Higgs’ address this problem is given here.

The searches for supersymmetry at the Large Hadron Collider (LHC) have so far yielded only null results and have considerably tightened the bounds on the sparticle masses. This has generated some skepticism in the literature regarding the ‘naturalness of SUSY’ which qualitatively requires some sparticles to be relatively light. Re-examining some of the bounds from LHC searches, it is argued with specific examples that the above skepticism is a red herring because (i) a quantitative and universally accepted definition of ‘naturalness’ is not available and (ii) even if some conventional definitions of naturalness is accepted at their face values, the alleged tension with the apparently stringent LHC bounds wither away once the strong assumptions, by no means compelling, underlying such bounds are relaxed.

We consider the s-channel resonance to fit the 2 TeV ATLAS diboson excess.We address the production mechanism of the resonance, its decay and coupling measurement. In order to explain only the hadronic channel excess, we consider the scenario where resonance decays to two new beyond Standard Model (BSM) particles (in the mass range of W/Z boson) and also explore the possibility of three-particle BSM final state mimicking diboson excess. Techniques suggested in this work are generic and could be used for heavy BSM resonance searches.

We outline some of the popular mass restricting variables for the semi-invisible productions at the Large Hadron Collider. In this context, heavy resonating mass, if produced through antler decay topology may already be detectable. New mass variables constructed by applying this mass constraint proved to have an array of interesting properties, including a new kink solution at the true masses of the produced particles. This enables one to measure the mass of the invisible particle and the parent particle simultaneously. This variable in turn can also be applied in reconstructing such events with the momenta of invisible particles. This feature is further demonstrated with the Higgs boson decaying into a pair of third-generation tau-lepton ($\tau$) and thus exploring direct Higgs coupling with the leptonic sector. Dominant discovery signatures rely upon the hadronic decay of tau which is associated with a pair of invisible neutrinos. Exploiting the already measured Higgs mass bound, present technique is capable of providing unique event reconstruction. Moreover, a significant efficiency enhancement is demonstrated in comparison with the existing methods.

In the next-to-minimal supersymmetric Standard Model (NMSSM), a pure singlet-like light pseudoscalar $(A_1)$ can dominantly decay to diphoton mode. In the chargino–neutralino associated production, followed by decays of heavier neutralinos to the lighter ones along with $A_1$ leads to a final-state $\gamma\gamma + l + /slashed{E}_{T}$. In this talk, the enhancement mechanism of diphoton mode of $A_1$ and its detection possibility in the final-state $(\gamma\gamma + l + /slashed{E}_{T})$ at the LHC run-2 are briefly summarized.

A review of the class of models that go under the name bulk Randall–Sundrum models is presented here. The issue of localization of quantum fields in the five-dimensional bulk and the profiles of the zero modes andthe Kaluza–Klein excitations are discussed. The zero modes of these bulk fields are, in general, partially composite. The degree of compositeness of the different fields is discussed and this provides the basis for realizing a Standard Model in the bulk, albeit partially composite. The viability of this model and its extensions when confronted with electroweak precision measurements is also discussed. Two such extensions are: (1) models with a bulk custodial symmetry and (2) models with a deformed metric. The signatures of these models that we expect at collider experiments are discussed and also the search for the Kaluza–Klein excitation of the gluon as the most important of these signatures.

Left–right symmetric gauge theory presents a minimal paradigm to accommodate massive neutrinos with all the known conserved symmetries duly gauged. The work presented here is based on the argument that the see-saw mechanism does not force the new right-handed symmetry scale to be very high, and as such some of the species from the spectrum of the new gauge and Higgs bosons can have masses within a few orders of magnitude of the TeV scale. The scale of the left–right parity breaking in turn can be sequestered from the Planck scale by supersymmetry. We have studied several formulations of such just beyond Standard Model (JBSM) theories for their consistency with cosmology. Specifically, the need to eliminate phenomenologically undesirable domainwalls gives many useful clues. The possibility that the exact left–right symmetry breaks in conjunction with supersymmetry has been explored in the context of gauge mediation, placing restrictions on the available parameter space. Finally, we have also studied a left–right symmetric model in the context of metastable supersymmetric vacua and obtained constraints on the mass scale of right-handed symmetry. In all the cases studied, the mass scale of the right-handed neutrino $M_R$ remains bounded from above, and in some of the cases the scale $10^9$ GeV favourable for supersymmetric thermal leptogenesis is disallowed. On the other hand, PeV scale remains a viable option, and the results warrant a more detailed study of such models for their observability in collider and astroparticle experiments.

Studies on neutrino–nucleon $(\nu{N})$ cross-sections have regained interest due to increasing importance of precision measurements, as they are needed as an ingredient in all neutrino experiments. In this work, we use the QCD-inspired double asymptotic limit fit of electron–proton structure function $F^{ep}_{2}$ to low-x HERA data, to calculate $\nu{N}$ cross-section for charged current (CC) and neutral current (NC) neutrino interactions in ultrahigh energy (UHE) neutrino energy $(E_\nu)$ regime $(10^{9} GeV \leq E_{\nu} \leq 10^{12} GeV)$. The form $F^{ep}_{2} \sim x^{−\lambda(Q^{2})}$, used in our analysis, can be conjectured like a dynamic pomeron (DP)-type behaviour. We also find an analytic form of the total cross-sections, $\sigma^{\nu N}_{CC}$ and $\sigma^{\nu N}_{NC}$ , which appear to be of Reggeon exchange type.We also do a comparative analysis of our results with those available in literature. Future measurements will support/confront our predictions.

The four-body non-resonant rare $B \to \bar{K}\pi\ell\ell$ decay is important both as a background to the benchmark resonant mode $B \to \bar{K}^{\ast}\ell\ell$ and as sensitive probe for new physics beyond the Standard Model (SM). We show that in the SM the branching ratio of $B \to \bar{K}\pi\ell\ell$ is of the order few $10^{−8}$, which is only an order of magnitude smaller than the $B \to \bar{K}^{\ast}\ell\ell$ decay. Nevertheless, the non-resonant mode is the dominant background to $B \to \bar{K}^{\ast}\ell\ell$ compared to other low mass scalars. We study the angular distributions of the non-resonant mode and show that the decay offers new combinations of short-distance couplings that are absent in the resonant decay. We explore interesting phenomenology in the interference of the resonant and non-resonant modes and discuss methods to extract the relative strong phase. The new physics sensitivity in the light of interference is also discussed.

Neutrino oscillations have been firmly established in the past few decades due to a vast variety of experiments and five of the oscillation parameters (three angles and two mass-squared differences) have been measured to varying degrees of precision. Here the focus is on an important parameter entering the oscillation framework – the leptonic CP-violating phase $\delta$, about which we know very little. We study the consequences of additional CP-conserving and CP-violating parameters in the presence of non-standard neutrino interactions (NSI) on CP-violation studies at the upcoming long baseline experiment, Deep Underground Neutrino Experiment (DUNE) and compare the capabilities of DUNE with other experiments.

C S Lam has suggested that the PMNS matrix (or at least some of its elements) can be predicted by embedding the residual symmetry of the leptonic mass terms into a bigger symmetry. We analyse the possibility that the residual symmetries consist of involution generators only and explore how Lam’s idea can be implemented.

Using the residual symmetry approach, we propose a complex extension of the scaling ansatz on the neutrino Majorana mass matrix $M\nu$ which allows a nonzero mass for each of the three light neutrinos as well as a nonvanishing $\theta_{13}$. Leptonic Dirac CP violation must be maximal while atmospheric neutrino mixing need not be exactly maximal. Each of the two Majorana phases, to be probed by the search for $0\nu\beta\beta$ decay, has to be zero or $\pi$ and a normal neutrino mass hierarchy is allowed.

The rare decay $B \to K^{\ast}\ell^{+}\ell^{−}$ is a very significant mode to search for physics beyond the Standard Model (SM). The mode provides a very rich spectrum of observables obtained from the angular distribution ofits decay products. The recent LHCb measured values of these observables are used to conclude an evidence of right-handed currents at the kinematic endpoint of this decay mode. As the conclusion is drawn at the maximum dilepton invariant mass square $(q^2)$ kinematic endpoint, it relies only on heavy quark symmetries where it is valid without significant corrections.

We show that a renormalizable theory based on gauge group $SO(10)$ and Higgs system $10\oplus210\oplus126\oplus\bar{126}$ with no scale supergravity can lead to a Starobinsky kind of potential for inflation. Successful inflation is possible in cases where the potential during inflation corresponds to $SU(3)_\rm{C}×SU(2)_\rm{L}×SU(2)_\rm{R}×U(1)_\rm{B−L}, SU(5)×U(1)$ and flipped $SU(5) × U(1)$ symmetries with suitable choice of superpotential parameters. The reheating in such a scenario can occur via non-perturbative decay of inflaton, i.e. through ‘preheating’. After the end of reheating, when Universe cools down, the finite-temperature potential can have a minimum which corresponds to MSSM.

We propose a hidden sector fermion dark matter model which follows a dark $SU(2)_H$ symmetry. Fermions in the dark sector also carry a global $U(1)_H$ charge while the gauge bosons and dark scalar do not have any global $U(1)_H$ charge. The lightest fermion in dark sector can serve as a potential dark matter candidate. We investigate whether the proposed dark matter candidate can explain indirect detection results from galactic centre.

We discuss physics of exotic high baryon density QCD phases which are believed to exist in the core of a neutron star. This can provide a laboratory for exploring exotic physics such as axion emission, KK graviton production etc.Much of the physics of these high-density phases is model-dependent and not very well understood, especially the densities expected to occur inside neutron stars. We follow a different approach and use primarily universal aspects of the physics of different high-density phases and associated phase transitions. We study effectsof density fluctuations during transitions with and without topological defect production and study the effect on pulsar timings due to changing moment of inertia of the star. We also discuss gravitational wave production due to rapidly changing quadrupole moment of the star due to these fluctuations.