QUANTUM HALL SKYRMIONS IN THE FRAMEWORK OF O(4) NONLINEAR SIGMA MODEL
A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these skyrmions.

title: STOCHASTIC QUANTIZATION AND THE BERRY PHASE
abstract: We study here the Berry phase from the point of view of stochastic quantization. The relativistic generalization of Nelson’s stochastic quantization procedure can be achieved when the Brownian motion process is taken into account in the internal space (apart from that in the external space). This effectively considers the particle as one that is stochastically extended, and nonrelativistic quantum mechanics is obtained in the sharp point limit. This can be formulated in terms of a gauge-field-theoretical extension of the particle. This inherent gauge field gives rise to the holonomy in a Hermitian line bundle, which appears as an extra phase factor in the adiabatic limit for a parameter-dependent Hamiltonian, and determines a unique connection. When the Hamiltonian is degenerate, the holonomy is defined in a complex vector bundle. In the case of a fermion, this Berry connection is found to be related to the Wess-Zumino term and can be considered to be of topological origin.

title: EQUIVALENCE OF STOCHASTIC, KLAUDER AND GEOMETRIC QUANTIZATION
abstract: The relativistic generalization of stochastic quantization helps us to introduce a stochastic-phase-space formulation when a relativistic quantum particle appears as a stochastically extended one. The nonrelativistic quantum mechanics is obtained in the sharp point limit. This also helps us to introduce a gauge-theoretical extension of a relativistic quantum particle when for a fermion the group structure of the gauge field is SU(2). The sharp point limit is obtained when we have a minimal contribution of the residual gauge field retained in the limiting procedure. This is shown to be equivalent to the geometrical approach to the phase-space quantization introduced by Klauder if it is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher-dimensional configuration space when quantization corresponds to freezing the particle to its first Landau level. The geometric quantization then appears as a natural consequence of these two formalisms, since the Hermitian line bundle introduced there finds a physical meaning in terms of the inherent gauge field in stochastic-phase-space formulation or in the interaction with the magnetic field in Klauder quantization.

title: Geometrical aspects of magnetic monopoles
abstract: The possible topological structures of elementary particles have been investigated to explore the possibility of the existence of magnetic monopoles. It is pointed out that when an elementary charged particle is depicted as an extended body such that the orientation of the internal space (“internal helicity”) defines the fermion number, the global conservation of this does not allow the existence of a magnetic monopole. Again it is argued that when anisotropy is introduced in the microlocal space-time depicting the internal space of hadrons, this gives rise to the internal symmetry algebra and no non-Abelian gauge fields and Higgs scalars are necessary to have a grand unified scheme of interactions. This avoids theSU2 and GUT monopoles. Besides, in this formalism, baryon number corresponds to the orientation or internal helicity of the composite system and the global conservation of this quantum number is found to be a consequence of Lorentz invariance. This forbids the existence of any sort of cosmological monopole in this Lorentz invariant Universe.

title: Stochastic field theory at finite temperature, supersymmetry, and witten index
abstract: Finite temperature supersymmetry is studied here from the point of view of stochastic field theory and the formalism of thermofield dynamics. It is shown that the Witten index can take only the values 1 and ½ in this formalism. It is pointed out that when at a critical temperature T c , below which supersymmetry is spontaneously broken, the zero energy mode is given by a thermal doublet of opposite statistics when the index is 1. However, when the index is ½, the zero energy mode is given by a thermal doublet of the same fermionic statistics.

title: Random fields, ising model and bosson-fermion phase transition
abstract: SummaryIt is here shown that when the stochastic quantization procedure is introduced to a massive Thirring fermion where the latter is described as a bound state of massless oscillators interacting through a gradient term in a linear chain, we find that a boson-fermion phase transition occurs at a critical temperatureT =Tc, and atT >Tc supersymmetry is restored. In this scheme supersymmetry is broken by the generation of mass which arises due to the presence of the gradient term.

title: Higgs signatures in inverse seesaw model at the LHC
abstract: A bstractIn the inverse seesaw mechanism where the spontaneously broken B-L symmetry induces tiny B-L violating Majorana masses for right-handed neutrinos, non-standard Higgs signatures can arise due to a possible Higgs doublet and singlet mixing and/or Higgs boson decays to a left- and right-handed neutrino. This leads to a remarkable feature of hadronically quiet di-lepton final states which can exhibit, in particular, lepton flavour violating signatures coming from flavour-dependent neutrino Yukawa couplings. In this process, one lepton coming from the right-handed decay could be soft enough can be missed by the trigger level cuts of CMS and ATLAS for the di-lepton plus missing energy signature. The prospects of such a signature are investigated for 8 TeV and 14 TeV center of mass energy of the LHC, taking the maximum value of the allowed neutrino Yukawa coupling and the right-handed neutrino mass of 100 GeV. A PYTHIA level simulation shows that the integrated luminosity of 10-20/fb and 1.6/fb for 8 TeV is required to observe the inclusive leptonic and lepton flavour violating signatures, respectively. For 14 TeV, the reach is more and a larger parameter space of the inverse seesaw model can be probed.

title: Production of two higgses at the Large Hadron Collider in CP-violating MSSM
abstract: A bstractProduction of two Higgs bosons is studied in a CP violating supersymmetric scenario at the Large Hadron Collider with Ecm = 14 TeV. There exists a region where a very light Higgs ≲ 50 GeV could not be probed by LEP experiment. This leads to so called ’LEP hole’ region. Recently LHC found a Higgs boson around ~ 125 GeV, which severely constrains the possibility of having lighter Higgs bosons, which cannot be detected, i.e., buried Higgs, in this model. We investigate the possibility of buried Higgs bosons along with the direct and indirect bounds coming from LEP, LHC and other experiments. In particular we take into account the constraints from EDM and from B-observables. We analyse first the case where a Higgs boson mass is around 125 GeV and the other two Higgs masses are below 100 GeV and not observed so far. In the second case the lightest Higgs boson mass is around 125 GeV and the other two are decoupled. We analyse the production of two Higgses and their decay modes leading to various final states for these benchmark points. We perform a collider simulation with PYTHIA and Fastjet where we consider all the major backgrounds. Among the final states we have analysed, we find that 2b + 2τ is promising and the signal significance is 5σ at an integrated luminosity ≲ 10 fb−1. For some benchmark points it is also possible to observe the light Higgs mass peak. We also explore the leptonic final state which could be instrumental in the precision measurement of a very light Higgs.

title: Unusual Higgs boson signal in R-parity violating nonminimal supersymmetric models at the LHC
abstract: We predict an unconventional background free signal of the Higgs boson in $R$-parity violating nonminimal supersymmetric models at the Large Hadron Collider (LHC). The signal comprises dilepton plus four hadronic jets and two large displaced vertices. The displaced leptons and jets are coming from the decay of the lightest supersymmetric particle (LSP), which is predominantly a gauge-singlet neutrino. A pair of such LSPs can couple to a Higgs boson, created via gluon fusion. We have analyzed two cases - one corresponding to the tree-level Higgs boson mass and another with the one-loop corrected mass of the Higgs boson. A reliable Higgs mass reconstruction using this signal can lead to discovery at the LHC with center-of-mass energy $\sqrt{s}=14~\rm{TeV}$ and 5 fb$^{-1}$ of integrated luminosity $(\mathcal{L})$. Even at $\sqrt{s}=7~\rm{TeV}$ and $\mathcal{L}$ = 5 fb$^{-1}$, a reasonable number of events are expected. Besides, mass reconstruction of a gauge-singlet LSP can provide an estimate of the seesaw scale.

title: Associated Higgs production in CP-violating supersymmetry: Probing the 'open hole' at the large hadron collider
abstract: A benchmark CP-violating supersymmetric scenario (known in the literature as 'CPX-scenario') is studied in the context of the Large Hadron Collider (LHC). It is shown that the LHC, with low to moderate accumulated luminosity, will be able to probe the existing 'hole' in the m{sub h{sub 1}}-tan{beta} plane, which cannot be ruled out by the Large Electron Positron Collider data. This can be done through associated production of Higgs bosons with top quark and top squark pairs leading to the signal dilepton+ {<=}5 jets (including 3b-jets)+missing p{sub T}. Efficient discrimination of such a CP-violating supersymmetric scenario from other contending ones is also possible at the LHC with a moderate volume of data.

title: Signature of void probability scaling in high energy hadronic interactions
abstract: The rapidity gap probability in the p-AgBr interactions at 2.00 GeV/c and π-AgBr interactions at 200 and 350 GeV/c have been studied in detail. The data indicate scaling behaviour of the void probability in the central rapidity domain, which hints the validity of the linked-pair approximation for the N-particle cumulant correlation function.