Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the 77-n' sector and the U-A(1) anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard SU(3) framework for the octet case and combining the use of the SU(3) framework and the large-Nc expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of U(3) quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.

First time measurements of polarization observables for the charged cascade hyperon in photoproduction

The parity violating weak decay of hyperons offers a valuable means of measuring their polarization, providing insight into the production of strange quarks and the matter they compose. Jefferson Lab's CLAS collaboration has utilized this property of hyperons, publishing the most precise polarization measurements for the Λ and Σ in both photoproduction and electroproduction to date. In contrast, cascades, which contain two strange quarks, can only be produced through indirect processes and as a result, exhibit low cross sections thus remaining experimentally elusive.^ At present, there are two aspects in cascade physics where progress has been minimal: characterizing their production mechanism, which lacks theoretical and experimental developments, and observation of the numerous excited cascade resonances that are required to exist by flavor SU(3) F symmetry. However, CLAS data were collected in 2008 with a luminosity of 68 pb−1 using a circularly polarized photon beam with energies up to 5.45 GeV, incident on a liquid hydrogen target. This dataset is, at present, the world's largest for meson photoproduction in its energy range and provides a unique opportunity to study cascade physics with polarization measurements.^ The current analysis explores hyperon production through the γ p → K+K +Ξ− reaction by providing the first ever determination of spin observables P, Cx and Cz for the cascade. Three of our primary goals are to test the only cascade photoproduction model in existence, examine the underlying processes that give rise to hyperon polarization, and to stimulate future theoretical developments while providing constraints for their parameters. Our research is part of a broader program to understand the production of strange quarks and hadrons with strangeness. The remainder of this document discusses the motivation behind such research, the method of data collection, details of their analysis, and the significance of our results.^

Searching for doubly charged Higgs bosons at the LHC in a 3-3-1 model

Using a peculiar version of the SU(3)(L) circle times U(1)(N) electroweak model, we investigate the production of doubly charged Higgs boson at the Large Hadron Collider. Our results include branching ratio calculations for the doubly charged Higgs and for one of the neutral scalar bosons of the model. (c) 2006 Elsevier B.V. All rights reserved.

Probing doubly charged Higgs bosons in e(+)e(-) colliders at the ILC and the CLIC in a 3-3-1 model

The SU(3)(L) circle times U(1)(N) electroweak model predicts new Higgs bosons beyond the one of the standard model. In this work we investigate the signature and production of doubly charged Higgs bosons in the e(+)e(-) International Linear Collider and in the CERN Linear Collider. We compute the branching ratios for the doubly charged gauge bosons of the model.

Exotic superfluid states of ultra-cold Fermi gases

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant Gf reverse similar, equals 1038 GN (GN being the Newtonian constant) and a cosmological term λf ƒ;μν (ƒ;μν is strong gravity metric and λf not, vert, similar 1028 cm− is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature not, vert, similar10−14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length not, vert, similar2 × 10−14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-Image particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.

The 27-plet contributions to the CP-conserving K -> pi l(+)l(-) decays

We revisit the rare kaon decays K -> pi l(+)l(-) which are of special interest due to the recent measurements of the charged kaon decay spectra. We compute the contribution of the 27-plet to the decay amplitudes in one loop SU(3) chiral perturbation theory. We estimate the resulting impact to be similar to 10% to the branching ratios of the charged kaon decays, and also noticeably influence the shape of the spectra. With current values of the constants G(8) associated with the octet and G(27) associated with the 27-plet, the contribution of the latter pushes the spectrum in the correct direction, towards the charged lepton spectra. We also discuss the impact for neutral decay rates and spectra.

Thermodynamics of higher spin black holes in 3D

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) x SL(3, R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W-3 X W-3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS(3) backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W-3((2)) x W-3((2)) symmetry deformed by a spin-3/2 current. This allows to identify the precise map between UV and HI thermodynamic variables. We find that the high temperature regime is dominated by a black hole branch whose thermodynamics can only be consistently inferred with reference to this W-3((2)) x W-3((2)) CFT.

Black holes in higher spin supergravity

We study black hole solutions in Chern-Simons higher spin supergravity based on the superalgebra sl(3 vertical bar 2). These black hole solutions have a U(1) gauge field and a spin 2 hair in addition to the spin 3 hair. These additional fields correspond to the R-symmetry charges of the supergroup sl(3 vertical bar 2). Using the relation between the bulk field equations and the Ward identities of a CFT with N = 2 super-W-3 symmetry, we identify the bulk charges and chemical potentials with those of the boundary CFT. From these identifications we see that a suitable set of variables to study this black hole is in terms of the charges present in three decoupled bosonic sub-algebras of the N = 2 super-W-3 algebra. The entropy and the partition function of these R-charged black holes are then evaluated in terms of the charges of the bulk theory as well as in terms of its chemical potentials. We then compute the partition function in the dual CFT and find exact agreement with the bulk partition function.

Dirac spectra, summation formulae, and the spectral action

Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

I. Current commutators in quantum electrodynamics. II. Electromagnetic mass differences of the pseudoscalar meson and baryon octets

This thesis is in two parts. In the first section, the operator structure of the singular terms in the equal-time commutator of space and time components of the electromagnetic current is investigated in perturbation theory by establishing a connection with Feynman diagrams. It is made very plausible that the singular term is a c number. Some remarks are made about the same problem in the electrodynamics of a spinless particle.

In the second part, an SU(3) symmetric multi-channel calculation of the electromagnetic mass differences in the pseudoscalar meson and baryon octets is carried out with an attempt to include some of the physics of the crossed (pair annihilation) channel along the lines of the recent work by Ball and Zachariasen. The importance of the tensor meson Regge trajectories is emphasized. The agreement with experiment is poor for the isospin one mass differences, but excellent for those with isospin two.

Relativistic quark models and the current algebra

In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.

We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).

In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m³. However, it may be possible to solve the factorized SU(2) problem with this model.

The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.

Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.

Spin precession induced by an effective magnetic field in a two-dimensional electron gas

We theoretically study the spatial behaviors of the spin precession in a two-dimensional electron system with spin-orbit interaction. Through analysis of interaction between the spin and the effective magnetic field in the system, we obtain the general conditions to generate a persistent spin helix and predict a persistent spin helix pattern in [001]-grown quantum wells. Particularly, we demonstrate that the phase of spin can be locked to propagate in a quantum well with SU(2) symmetry.

A DOUBLE-QUANTUM-WELL IN A DRIVING LASER FIELD

The dynamic effect of electrons in a double quantum well under the influence of a monochromatic driving laser field is investigated. Closed-form solutions for the quasienergy and Floquet states are obtained with the help of SU(2) symmetry. For the case of weak interlevel coupling, explicit expressions of the quasienergy are presented by the use of perturbation theory, from which it is found that as long as the photon energy is not close to the tunnel splitting, the electron will be confined in an initially occupied eigenstate of the undriven system during the whole evolution process. Otherwise, it will transit between the lowest two levels in an oscillatory behavior.