Noncommutative Geometry, Quantum Hall Effect and Berry Phase
Taking resort to Haldane's spherical geometry we can visualize fractional quantum Hall effect on the noncommutative manifold $M_4 \times Z_N$ with $N>2$ and odd. The discrete space leads to the deformation of symplectic structure of the continuous manifold such that the symplectic area is given by $\triangle p.\triangle q=2\pi m \hbar$ with $m$ an odd integer which is related to the Berry phase and the filling factor is given by $\frac{1}{m}$. We here argue that this is equivalent to the noncommutative field theory as prescribed by Susskind and Polychronakos which is characterized by area preserving diffeomorphism. The filling factor $\frac{1}{m}$ is determined from the change in chiral anomaly and hence the Berry phase as envisaged by the star product.

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: 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: QUANTUM HALL SKYRMIONS IN THE FRAMEWORK OF O(4) NONLINEAR SIGMA MODEL
abstract: 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: 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: EXTENDED CONFORMAL GROUP, SUPERSYMMETRY, AND GEOMETRICAL PROPERTIES OF HADRONS
abstract: We have studied the interrelation among conformal symmetry, internal symmetry and super-symmetry and have shown that extended conformal group which includes, apart from conformal transformation, space, time and conformal reflection can give rise to internal symmetry algebra as well as supersymmetry algebra. To achieve this result, we have dealt with conformal spinors which are taken to be the constituents of the hadrons and these split into two Cartan semispinors or Dirac spinors in the Minkowski space, giving rise to the particle and antiparticle configurations. Supersymmetry is broken here just by the mass term and as such no massless hadron can exist in nature. The internal symmetry arises from the discrete symmetry of reflection. The most significant feature of this formalism is that the symmetry structure helps us to explain the meson-baryon mass difference in an elegant way and the role of fictitious superpartners is completely avoided. Again, any baryon number nonconserving process like proton decay is found to be forbidden by the Lorentz invariance. Finally, it is noted that though the discrete symmetry of reflection is taken to be the origin of the internal symmetry, topological nontrivial structures like strings do not appear here and this also avoids the possibility of the nonconservation of global charge.

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: Probing non-universal gaugino masses via Higgs boson production under SUSY cascades at the LHC: a detailed study
abstract: Cascade decays of Supersymmetric (SUSY) particles are likely to be prolific sources of Higgs bosons at the Large Hadron Collider (LHC). In this work, we explore, with the help of detailed simulation, the role of non-universal gaugino masses in the production of the Higgs bosons under SUSY cascades. The analysis is carried out by choosing an appropriate set of benchmark points with non-universal gaugino masses in the relevant SUSY parameter space and then contrasting the resulting observations with the corresponding cases having universal relationship among the same. It is shown that even of data at an early phase of the LHC-run with 10 fb−1 one would be able to see, under favourable situations, the imprint of non-universal gaugino masses by reconstructing various Higgs boson resonances and comparing their rates. With increased accumulated luminosities, the indications would naturally become distinct over a larger region of the parameter space.

title: Evidence of multifractality and constant specific heat in hadronic collisions at high energies

title: Higgs production in CP-violating supersymmetric cascade decays: probing the ‘open hole’ at the Large Hadron Collider
abstract: A benchmark CP-violating supersymmetric scenario (known as ‘CPX-scenario’ in the literature) 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_{{h_1}}} $-tan β plane, which cannot be ruled out by the LEP data. We explore the parameter space with cascade decay of third generation squarks and gluino with CP-violating decay branching fractions. We propose a multi-channel analysis to probe this parameter space some of which are background free at an integrated luminosity of 5-10 fb−1. Specially, multi-lepton final states (3l, 4l and like sign di-lepton) are almost background free and have 5σ reach for the corresponding signals with very early data of LHC for both 14 TeV and 7 TeV center of mass energy.

title: Search for Higgs bosons of the universal extra dimensions at the large Hadron collider
abstract: The Higgs sector of the Universal Extra Dimensions (UED) has a rather involved setup. With one extra space dimension, the main ingredients to the construct are the higher Kaluza-Klein (KK) excitations of the Standard Model Higgs boson and the fifth components of the gauge fields which on compactification appear as scalar degrees of freedom and can mix with the former thus leading to physical KK-Higgs states of the scenario. In this work, we explore in detail the phenomenology of such a Higgs sector of the UED with the Large Hadron Collider (LHC) in focus. We work out relevant decay branching fractions involving the KK-Higgs excitations. Possible production modes of the KK-Higgs bosons are then discussed with an emphasis on their associated production with the third generation KK-quarks and that under the cascade decays of strongly interacting UED excitations which turn out to be the only phenomenologically significant modes. It is pointed out that the collider searches of such Higgs bosons face generic hardship due to soft end-products which result from severe degeneracies in the masses of the involved excitations in the minimal version of the UED (MUED). Generic implications of either observing some or all of the KK-Higgs bosons at the LHC are discussed.