Some remarks on nonlocal field theory and space-time quantization
From the point of view that the charge and mass of an electron is of dynamical origin and quantization of charge in units ofe is related to the space-time quantization as developed in an earlier paper, we here show that it is possible to consider that the internal space within the elementary domain of the quantized space-time world is not governed by Lorentz invariance. This helps us to develop a consistent theory of nonlocal fields for extended particles where the infinite mass degeneracy is avoided. Moreover, this ensures the convergence of nonlocal field theories and suggests that massless particles like photons and neutrinos, though they may be taken to be of extended structure, will appear only as point particles in the physical world. In this picture, Lorentz invariance appears to be a consequence of the distribution of matter and energy in the Universe, and this may be taken to be another interpretation of Mach's principle.

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

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: Displaced Higgs production in type III seesaw
abstract: We point out that the type III seesaw mechanism introducing fermion triplets predicts peculiar Higgs boson signatures of displaced vertices with two b jets and one or two charged particles which can be cleanly identified. In a supersymmetric theory, the scalar partner of the fermion triplet contains a neutral dark matter candidate which is almost degenerate with its charged components. A Higgs boson can be produced together with such a dark matter triplet in the cascade decay chain of a strongly produced squark or gluino. When the next lightest supersymmetric particle (NLSP) is bino/wino-like, there appears a Higgs boson associated with two charged tracks of a charged lepton and a heavy charged scalar at a displacement larger than about 1 mm. The corresponding production cross-section is about 0.5 fb for the squark/gluino mass of 1 TeV. In the case of the stau NLSP, it decays mainly to a Higgs boson and a heavy charged scalar whose decay length is larger than 0.1 mm for the stau NLSP mixing with the left-handed stau smaller than 0.3. As this process can have a large cascade production ∼2 pb for the squark/gluino mass ∼1 TeV, one may be able to probe it at the early stage of the LHC experiment.

title: Signatures of gaugino mass non-universality in cascade Higgs production at the LHC
abstract: Supersymmetric cascades, involving charginos and neutralinos at various stages, contribute in a significant way to Higgs production at the LHC. We explore the nature of such cascades, completely relaxing the universality of the gaugino masses. It is found that the deviation from the scenario with universal gaugino masses would be reflected in the relative production rates for the lightest neutral Higgs and the charged Higgses.

title: Working group report: Physics at the Large Hadron Collider
abstract: This is a summary of the activities of the Physics at the LHC working group in the XIth Workshop on High Energy Physics Phenomenology (WHEPP-XI) held at the Physical Research Laboratory, Ahmedabad, India in January 2010. We discuss the activities of each sub-working group on physics issues at colliders such as Tevatron and Large Hadron Collider (LHC). The main issues discussed involve (1) results on W mass measurement and associated QCD uncertainties, (2) an attempt to understand the asymmetry measured at Tevatron in the top quark production, and (3) phenomenology of warped space dimension model.