122945882
On Dirac's methods for constrained systems and gauge-fixing conditions with explicit time dependence
Abstract It is shown that Dirac's methods for constrained hamiltonian systems require careful application if gauge-fixing conditions with explicit time dependence are used. It is non-trivial, in general, to find both an appropriate set of variables for the physical phase space and a hamiltonian furnishing the correct time evolution of these quantities. This problem is solved for a certain class of gauge-fixing conditions. As well as offering the possibility of new applications the solution provides a more systematic understanding of some well-known cases, among which are the light-cone and temporal gauges for relativistic particles and strings.
121797186
Complex Toda theories and twisted reality conditions
The Toda equations (based on a finite-dimensional or affine Lie algebra of superalgebra) are discussed as integrable non-linear differential equations for a set of complex scalar fields. We show that such complex Toda fields can either be restricted to take real values the standard way or else they can be subjected to a “twisted” reality condition associated to any Z2 symmetry of the Cartan matrix of Dynkin diagram of the underlying algebra. Different reality conditions give rise to different lagrangian field theories. In the conformal case, however, these theories have the same central charge, while in the affine case they have the same mass spectrum. The construction of N = 2 superconformal theories based on the superalgebras A(n, n−1) is clarified, and a new class of conformal field theories with positive kinetic energy based on the superalgebras C(n) is presented. The ideas developed are also relevant to understanding soliton solutions in affine Toda theories with imaginary coupling constant.
15287410
Dynkin diagrams and integrable models based on Lie superalgebras
Abstract An analysis is given of the structure of a general two-dimensional Toda field theory involving bosons and fetmions which is defined in terms of a set of simple roots for a Lie superalgebra. It is shown that a simple root system for a superalgebra has two natural bosonic root systems associated with it which can be found very simply using Dynkin diagrams; the construction is closely related to the question of how to recover the signs of the entries of a Cartan matrix for a superalgebra from its Dynkin diagram. The significance for Toda theories is that the bosonic root systems correspond to the purely bosonic sector of the integrable model, knowledge of which can determine the bosonic part of the extended conformal symmetry in the theory, or its classical mass spectrum, as appropriate. These results are applied to some special kinds of models and their implications are investigated for features such as supersymmetry, positive kinetic energy and generalized reality conditions for the Toda fields. As a result, some new families of integrable theories with positive kinetic energy are constructed, some containing a mixture of massless and massive degrees of freedom, others being purely massive and supersymmetric, involving a number of coupled sine/ sinh-Gordon theories.
18118661
Integrable theories that are asymptotically CFT
Abstract A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories — in fact SU(2) WZW models at level k . In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed “asymptotically CFI”. These theories have previously been conjectured to be quantum integrable; this is confirmed by postulating a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-function and allows for an evaluation of the mass gap (the ratio of the physical mass to the Λ-parameter) to leading order in 1 k .
16517190
Exact scattering in the SU(n) supersymmetric principal chiral model
Abstract The complete spectrum of states in the supersymmetric principal chiral model based on SU(n) is conjectured, and an exact factorizable S-matrix is proposed to describe scattering amongst these states. The SU(n)L × SU(n)R symmetry of the Lagrangian is manifest in the S-matrix construction. The supersymmetries, on the other hand, are incorporated in the guise of spin - 1 2 charges acting on a set of RSOS kinks associated with su(n) at level n. To test the proposed S-matrix, calculations of the change in the ground-state energy in the presence of a coupling to a background charge are carried out. The results derived from the Lagrangian using perturbation theory and from the S-matrix using the TBA are found to be in complete agreement for a variety of background charges which pick out, in turn, the highest weight states in each of the fundamental representations of SU(n). In particular, these methods rule out the possibility of additional CDD factors in the S-matrix. Comparison of the expressions found for the free-energy also yields an exact result for the mass gap in these models: m Λ MS = ( n π ) sin ( π n ) .
123140877
Supersymmetric Toda field theories
We analyse a class of integrable two-dimensional field theories with N =1 and N = 2 supersymmetry via the Lax, or zero-curvature, construction based on a Lie superalgebra. Some of the theories exhibit extended superconformal symmetries, generalizing the bosonic W-algebras. We also investigate the possible integrable deformations of these models and find that in some cases supersymmetry is broken and in other cases it is preserved.
118632441
Possibility of early Higgs boson discovery in nonminimal Higgs sectors
Particle physics models with more than one Higgs boson occur in many frameworks for physics beyond the standard model, including supersymmetry, technicolor, composite Higgs, and ''little Higgs'' models. If the Higgs sector contains couplings stronger than electroweak gauge couplings, there will be heavy Higgs particles that decay to lighter Higgs particles plus heavy particles such as W, Z, and t. This motivates searches for final states involving multiple W, Z, t, and bb pairs. A two Higgs doublet model with custodial symmetry is a useful simplified model to describe many of these signals. The model can be parameterized by the physical Higgs masses and the mixing angles {alpha} and {beta}, so discovery or exclusion in this parameter space has a straightforward physical interpretation. We illustrate this with a detailed analysis of the process gg{yields}A followed by A{yields}hZ and h{yields}WW. For m{sub A}{approx_equal}330 GeV, m{sub h}{approx_equal}200 GeV we can get a 4.5{sigma} signal with 1 fb{sup -1} of integrated luminosity at the Large Hadron Collider.
119238429
Sensitivity of an Upgraded LHC to R-Parity Violating Signatures of the MSSM
We present a sensitivity study for the pair-production of supersymmetric particles which decay through R-parity violating channels. As the scope of possible RPV signatures is very broad, the reach of several selected signatures spanning a representative variety of possible final states is considered. Preference in representation is given to spectra motivated by naturalness, i.e. light higgsinos, stops and gluinos. The sensitivity studies are presented for proton-proton collisions at 14 TeV with an integrated luminosity of 300 and 3000 fb^-1, as well as at 33 TeV with an integrated luminosity of 3000 fb^-1.
119264520
LHC coverage of RPV MSSM with light stops
A bstractWe examine the sensitivity of recent LHC searches to signatures of supersymmetry with R-parity violation (RPV). Motivated by naturalness of the Higgs potential, which would favor light third-generation squarks, and the stringent LHC bounds on spectra in which the gluino or first and second generation squarks are light, we focus on scenarios dominated by the pair production of light stops. We consider the various possible direct and cascade decays of the stop that involve the trilinear RPV operators. We find that in many cases, the existing searches exclude stops in the natural mass range and beyond. However, typically there is little or no sensitivity to cases dominated by UDD operators or LQD operators involving taus. We propose several ideas for searches which could address the existing gaps in experimental coverage of these signals.
119096508
A swarm of Bs
A bstractNew physics signals containing five or more b-tagged jets, but without T or leptons, could realistically be sitting within the current 8 TeV LHC data set without receiving meaningful constraints from any of the existing LHC searches at either ATLAS or CMS. This work provides several examples of simple, motivated models that yield final states containing many b-jets. To study the potential for uncovering new physics in these high b-jet multiplicity channels, this paper focuses on a natural supersymmetry scenario where each of the pair-produced stops decays to an on-shell chargino, which subsequently decays via an MFV-motivated, R-parity violating coupling. This gives rise to an eight-jet final state containing six b-quarks. Although no public measurements exist, estimates indicate that the standard model backgrounds in high b-jet multiplicity channels should be very small. To circumvent the background uncertainty, an asymmetric method is presented that utilizes two different techniques to conservatively exclude or to discover new physics in high b-jet multiplicity final states.
119234460
LHC searches examined via the RPV MSSM
We confront the ATLAS and CMS new physics searches with simplified models from R-parity violating (RPV) supersymmetry that contain naturally light stops and higgsinos. We emphasize the important role played by searches for exotic heavy quarks and leptoquarks and discuss how these searches could be modified to better address RPV scenarios. We also argue that it would be useful to design searches for new physics based on the ttbar cross section measurements, to enhance searches for taus + jets + MET with regions with b tagging and reduced MET requirements, and to expand the search program for all-jet final states, especially in the presence of multiple b-jets.