International Journal of Modern Physics A

The investigation of the dynamics responsible for electroweak symmetry breaking is one of the prime tasks of experiments at present and future colliders. Experiments at the Tevatron Collider and at the CERN Large Hadron Collider (LHC) must be able to discover a Standard Model Higgs boson over the full mass range as well as Higgs bosons in extended models. In this review, the discovery potential for the Standard Model Higgs boson and for Higgs bosons in the Minimal Supersymmetric extension is summarized. Emphasis is put on those studies which have been performed recently within the experimental collaborations using a realistic simulation of the detector performance. This includes a discussion of the search for Higgs bosons using the vector boson fusion mode at the LHC, a discussion of the measurement of Higgs boson parameters as well as a detailed review of the MSSM sector for different benchmark scenarios. The Tevatron part of the review also contains a discussion of first physics results from data taken in the ongoing Run II.

We show that the renormalization group flows of the massless superstring modes in the presence of fluctuating D-branes satisfy the equations of fluid dynamics. In particular, we show that the D-brane's U(1) field is related to the velocity function in the Navier–Stokes equation while the dilaton plays the role of the passive scalar advected by the turbulent liquid. This leads us to suggest a possible isomorphism between the off-shell superstring theory in the presence of fluctuating D-branes and the fluid mechanical degrees of freedom.

In the Left–Right Symmetric Model, and mass differences are considered, taking the effect of the triplet Higgs, W_R and Z′ bosons in the effective Hamiltonian in Vacuum Insertion Method and in Heavy Quark Effective Theory. It is observed that the masses M_R, M_H, and M_Z′ are well within the experimental search in the forthcoming accelerators.

A massive superparticle action based on the generalised line element in N = 1 global superspace is quantised canonically. A previous method of quantising this action, based on a Fock space analysis, showed that states existed in three supersymmetric multiplets, each of a different mass. The quantisation procedure presented uses the single first class constraint as an operator condition on a general N = 1 superwavefunction. The constraint produces coupled equations of motion for the component wavefunctions. Transformations of the component wavefunctions are derived that decouple the equations of motion and partition the resulting wavefunctions into three separate supermultiplets. Unlike previous quantisations of superparticle actions in N = 1 global superspace, the spinor wavefunctions satisfy the Dirac equation and the vector wavefunctions satisfy the Proca equation.

The off-shell closure of the commutators of the supersymmetry transformations, that include mass parameters, are derived by the introduction of auxiliary wavefunctions.

To avoid the ghosts arising in a previous Fock space quantisation an alternative conjugation is used in the definition of the current, based on a Krein space approach.

Energy resonance in scattering is usually investigated either directly in the complex energy plane (E-plane) or indirectly in the complex angular momentum plane (ℓ-plane). Another formulation complementing these two approaches was introduced recently. It is an indirect algebraic method that studies resonances in a complex charge plane (Z-plane). This latter approach will be generalized to provide a unified algebraic treatment of resonances in the complex E-, ℓ-, and Z-planes. The complex scaling (rotation) method will be used in the development of this approach. The resolvent operators (Green's functions) are formally defined in these three spaces. Bound states spectrum and resonance energies in the E-plane are mapped onto a discrete set of poles of the respective resolvent operator on the real line of the ℓ- and Z-planes. These poles move along trajectories as the energy is varied. A finite L² basis is used in the numerical implementation of this approach. Stability of poles and trajectories against variation in all computational parameters is demonstrated. Resonance energies for a given potential are calculated and compared with those obtained by other studies.

We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also shown that nonassociative algebras naturally appear in this formalism, which are briefly discussed.

Afterwards, a general connection which includes a two-form field is settled-down, solving the problem of setting a gauge theory for the Kalb–Ramond field for generical groups.

Topological Chern–Simons theories can also be defined in four dimensions, and this approach clarifies their relation to the so-called B ∧ F theories. We also revise some standard aspects of Kalb–Ramond theories in view of these new perspectives.

Since this gauge connection is built upon a pair of fields consisting of a one-form and a two-form, one may define Yang–Mills theories as usually and, remarkably, also minimal coupling with bosonic matter, where the Kalb–Ramond field appears naturally as mediator; so, a new associated conserved charge can be defined. For the Abelian case, we explicitly construct the minimal interaction between B-field and matter following a "gauge principle" and find a novel conserved tensor current. This is our most significative result from the physical viewpoint.

This framework is also generalized in such a way that any p-rank tensor may be formulated as a gauge field.

A self-consistent, nonperturbative approximation scheme is proposed which is potentially applicable to arbitrary interacting quantum systems. For the case of self-interaction, the scheme consists in approximating the original interaction H_I(ϕ) by a suitable "potential" V(ϕ) which satisfies the following two basic requirements, (i) exact solvability (ES): the "effective" Hamiltonian H₀ generated by V(ϕ) is exactly solvable i.e., the spectrum of states |n〉 and the eigenvalues E_n are known and (ii) equality of quantum averages (EQA): 〈n|H_I(ϕ)|n〉 = 〈n|V(ϕ)|n〉 for arbitrary n. The leading order (LO) results for |n〉 and E_n are thus readily obtained and are found to be accurate to within a few percent of the "exact" results. These LO-results are systematically improvable by the construction of an improved perturbation theory (IPT) with the choice of H₀ as the unperturbed Hamiltonian and the modified interaction, λH′(ϕ)≡λ(H_I(ϕ) - V(ϕ)), as the perturbation where λ is the coupling strength. The condition of convergence of the IPT for arbitrary λ is satisfied due to the EQA requirement which ensures that 〈n|λH′(ϕ)|n〉 = 0for arbitrary λ and n. This is in contrast to the divergence (which occurs even for infinitesimal λ!) in the naive perturbation theory where the original interaction λH_I(ϕ) is chosen as the perturbation. We apply the method to the different cases of the anharmonic and the double well potentials, e.g. quartic-, sextic- and octic-anharmonic oscillators and quartic-, sextic-double well oscillators. Uniformly accurate results for the energy levels over the full allowed range of λ and n are obtained. The results compare well with the exact results predicted by supersymmetry for the case of the sextic anharmonic potential and the double well partner potential. Further improvement in the accuracy of the results by the use of IPT, is demonstrated. We also discuss the vacuum structure and stability of the resulting theory in the above approximation scheme.