Collective Perspective on Advances in Dyson-Schwinger Equation QCD

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dispersive analysis of KL mu 3 and KLe3 scalar and vector form factors using KTeV data

Using the published KTeV samples of K(L) -> pi(+/-)e(-/+)nu and K(L) -> pi(+/-)mu(-/+)nu decays, we perform a reanalysis of the scalar and vector form factors based on the dispersive parametrization. We obtain phase-space integrals I(K)(e) = 0.15446 +/- 0.00025 and I(K)(mu) = 0.10219 +/- 0.00025. For the scalar form factor parametrization, the only free parameter is the normalized form factor value at the Callan-Treiman point (C); our best-fit results in InC = 0.1915 +/- 0.0122. We also study the sensitivity of C to different parametrizations of the vector form factor. The results for the phase-space integrals and C are then used to make tests of the standard model. Finally, we compare our results with lattice QCD calculations of F(K)/F(pi) and f(+)(0).

Light-Front model of transition form-factors in heavy meson decay

Electroweak transition form factors of heavy meson decays are important ingredients in the extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements from experimental data. In this work, within a. light-front framework, we calculate electroweak transition form factor for the semileptonic decay of D mesons into a pion or a kaon. The model results underestimate in both cases the new data of CLEO for the larger momentum transfers accessible in the experiment. We discuss possible reasons for that in order to improve the model.

A Combined Study of the Pion's Static Properties and form Factors

We study consistently the pion's static observables and the elastic and γ* γ → π0 transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π0 form factor at large q2, yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data. © 2013 Springer-Verlag Wien.

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Delta transition form factors at large momentum transfer squared Q(2). The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.

Electromagnetic hadron form factors and higher Fock components

Investigation of the spacelike and timelike electromagnetic form factors of hadrons, within a relativistic microscopical model characterized by a small set of hypothesis, could shed light on the components of hadron states beyond the valence one. Our relativistic approach has been successfully applied first to the pion and then the extension to the nucleon has been undertaken. The pion case is shortly reviewed as an illustrative example for introducing the main ingredients of our approach, and preliminary results for the nucleon in the spacelike range -10 (GeV/c)(2) <= q(2) <= 0 are evaluated.

Timelike and spacelike hadron form factors, Fock state components and light-front dynamics

A unified description of spacelike and timelike hadron form factors within a light-front model was successfully applied to the pion. The model is extended to the nucleon to study the role of qq pair production and of nonvalence components in the nucleon form factors. Preliminary results in the spacelike range 0 <= Q(2) <= 10 (GeV/c)(2) are presented.

Weak electron scattering for the 3He-3H transition and the weak nuclear form factors

We calculate the differential cross section for weak electron scattering reaction, e + 3He-' 3H + ve, for energies from 100 MeV to 6 GeV as a function of outgoing nucleus angle from 0 to n/2 radians. We find that the differential cross section at low [q2] increases with electron energy from 0.1 GeV to 6.0 GeV, such that the peak value at 6.0 GeV is approximately 3.2 x 10-40 cm 2 / ster, a factor of 10 larger than the peak value at 0.1 GeV. We also find that the width of the peak falls very rapidly with increasing electron energy. At high [q2] we find that the differential cross section falls by approximately three orders of magnitude making experimental observation at this time unlikely. The contributions of the individual form factors are obtained for electron energies of 0.5GeV and 2.0 GeV. It is found that at low [q2] the form factors, FA(q2) and Fv(q2), make contributions of similar size to the differential cross section and might be simultaneously determined , but for the case of FM(q2) we find that the contribution is too small to determine. It is also found that at large [q2] values, the contribution of FM(q2) is substantially enhanced , but that the cross section is probably too small to enable a direct determination of FM(q2).

Time-like and space-like pion form factors within front-form dynamics

An approach for a unified description of the pion electromagnetic form factor in the space- and time-like regions, within a constituent quark model on the light front is briefly illustrated. Three main ingredients enter our approach: i) the on-shell quark-hadron vertex functions in the valence sector, ii) the dressed photon vertex where a photon decays in a quark-antiquark pair, and iii) the emission and absorption amplitudes of a pion by a quark. © 2005 American Institute of Physics.

Measurement of the elastic electron-proton cross section and separation of the electric and magnetic form factor in the Q 2 range from 0.004 to 1 (GeV/c) 2

The electromagnetic form factors of the proton are fundamental quantities sensitive to the distribution of charge and magnetization inside the proton. Precise knowledge of the form factors, in particular of the charge and magnetization radii provide strong tests for theory in the non-perturbative regime of QCD. However, the existing data at Q^2 below 1 (GeV/c)^2 are not precise enough for a hard test of theoretical predictions.rnrnFor a more precise determination of the form factors, within this work more than 1400 cross sections of the reaction H(e,e′)p were measured at the Mainz Microtron MAMI using the 3-spectrometer-facility of the A1-collaboration. The data were taken in three periods in the years 2006 and 2007 using beam energies of 180, 315, 450, 585, 720 and 855 MeV. They cover the Q^2 region from 0.004 to 1 (GeV/c)^2 with counting rate uncertainties below 0.2% for most of the data points. The relative luminosity of the measurements was determined using one of the spectrometers as a luminosity monitor. The overlapping acceptances of the measurements maximize the internal redundancy of the data and allow, together with several additions to the standard experimental setup, for tight control of systematic uncertainties.rnTo account for the radiative processes, an event generator was developed and implemented in the simulation package of the analysis software which works without peaking approximation by explicitly calculating the Bethe-Heitler and Born Feynman diagrams for each event.rnTo separate the form factors and to determine the radii, the data were analyzed by fitting a wide selection of form factor models directly to the measured cross sections. These fits also determined the absolute normalization of the different data subsets. The validity of this method was tested with extensive simulations. The results were compared to an extraction via the standard Rosenbluth technique.rnrnThe dip structure in G_E that was seen in the analysis of the previous world data shows up in a modified form. When compared to the standard-dipole form factor as a smooth curve, the extracted G_E exhibits a strong change of the slope around 0.1 (GeV/c)^2, and in the magnetic form factor a dip around 0.2 (GeV/c)^2 is found. This may be taken as indications for a pion cloud. For higher Q^2, the fits yield larger values for G_M than previous measurements, in agreement with form factor ratios from recent precise polarized measurements in the Q2 region up to 0.6 (GeV/c)^2.rnrnThe charge and magnetic rms radii are determined as rn⟨r_e⟩=0.879 ± 0.005(stat.) ± 0.004(syst.) ± 0.002(model) ± 0.004(group) fm,rn⟨r_m⟩=0.777 ± 0.013(stat.) ± 0.009(syst.) ± 0.005(model) ± 0.002(group) fm.rnThis charge radius is significantly larger than theoretical predictions and than the radius of the standard dipole. However, it is in agreement with earlier results measured at the Mainz linear accelerator and with determinations from Hydrogen Lamb shift measurements. The extracted magnetic radius is smaller than previous determinations and than the standard-dipole value.

Parity violating asymmetry in the electron deuteron quasielastic scattering, strange vector and axial vector form factors and beam normal spin asymmetries

In dieser Arbeit wurde die paritätsverletzende Asymmetrie in derrnquasielastischen Elektron-Deuteron-Streuung bei Q^2=0.23 (GeV/c)^2 mitrneinem longitudinal polarisierten Elektronstrahl bei einer Energie von 315rnMeV bestimmt. Die Messung erfolgte unter Rückwärtswinkeln. Der Detektor überdeckte einen polaren Streuwinkelbereichrnzwischen 140 und 150 deg. Das Target bestand aus flüssigemrnDeuterium in einer Targetzelle mit einer Länge von 23.4 cm. Dierngemessene paritätsverletzende Asymmetrie beträgt A_{PV}^d = (-20.11 pm 0.87_{stat} pm 1.03_{syst}), wobei der erste Fehler den statistischenrnFehlereitrag und der zweite den systematischen Fehlerbeitrag beschreibt. Ausrnder Kombination dieser Messung mit Messungen der paritätsverletzendenrnAsymmetrie in der elastischen Elektron-Proton-Streuung bei gleichem Q^2rnsowohl bei Vorwärts- als auch bei Rückwärtsmessungen können diernVektor-Strange-Formfaktoren sowie der effektive isovektorielle und isoskalarernVektorstrom des Protons, der die elektroschwachen radiativen Anapolkorrekturenrnenthält, bestimmt werden. Diese Arbeit umfasst ausserdem die Bestimmungrnder Asymmetrien bei einem transversal polarisierten Elektronstrahl sowohl beirneinem Proton- als auch einem Deuterontarget unter Rückwärtswinkeln beirnImpulsüberträgen von Q^2=0.10 (GeV/c)^2, Q^2=0.23 (GeV/c)^2rnund Q^2=0.35 (GeV/c)^2. Die im Experiment beobachteten Asymmetrien werdenrnmit theoretischen Berechnungen verglichen, welche den Imaginärteil der Zweiphoton-Austauschamplitude beinhalten.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Exact form factors for the Josephson tunneling current and relative particle number fluctuations in a model of two coupled Bose-Einstein condensates

Form factors are derived for a model describing the coherent Josephson tunneling between two coupled Bose-Einstein condensates. This is achieved by studying the exact solution of the model within the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.

Equivalent representation form of oscillators with elastic and damping nonlinear terms

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others