Stochastic field theory, holomorphic quantum mechanics, and supersymmetry
Holomorphic quantum mechanics are studied from the point of view of stochastic quantization in Minkowski space which involves the introduction of two stochastic fields, one in the external space and the other in the internal space. The equilibrium condition is given by Z2 symmetry between the external and internal fields. In the nonequilibrium case, N=2 Wess–Zumino quantum fields are arrived at giving rise to supersymmetry. This helps to define the supercharge operator Q when the Hamiltonian is given by H=Q2 and an index theorem is derived for an interacting case when the superpotential is given by V(φ)=λφn, φ being complex with n>2. It is found that the vacuum is degenerate and is in conformity with the result obtained by Jaffe, Lesniewski, and Lewenstein  in the two‐dimensional N=2 Wess–Zumino quantum field model.

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: 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: 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: 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.

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: 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: Probing Higgs bosons via the type III seesaw mechanism at the LHC
abstract: We show that the type III seesaw mechanism opens up a promising possibility of searching the Higgs boson in the $b \bar b$ channel through the Higgs production associated with a charged lepton coming from the decay of the triplet seesaw particle. In particular we look for the $2b$ signals with trileptons or same-sign dileptons to construct the Higgs and the triplet fermion mass and calculate the reach with the integrated luminosity of 10 fb$^{-1}$ at the 14 TeV LHC.