Showing papers on "Vertex function published in 1997"

Pion and Rho Structure Functions from Lattice QCD

Abstract: We calculate the lower moments of the deep-inelastic structure functions of the $\ensuremath{\pi}$ and the $\ensuremath{\rho}$ meson on the lattice. Of particular interest to us are the spin-dependent structure functions of the $\ensuremath{\rho}$. The calculations are done with Wilson fermions and for three values of the quark mass, so that we can perform an extrapolation to the chiral limit.

Longitudinal and Transverse Ward–Takahashi Identities, Anomaly and Schwinger–Dyson Equation

Abstract: Based on the path integral formalism, we rederive and extend the transverse Ward–Takahashi identities (which were first derived by Yasushi Takahashi) for the vector and the axial vector currents and simultaneously discuss the possible quantum anomaly for them. Subsequently, we propose a new scheme for writing down and solving the Schwinger–Dyson equation in which the transverse Ward–Takahashi identity together with the usual (longitudinal) Ward–Takahashi identity are applied to specify the fermion–boson vertex function. Within this framework, we give an example of exactly soluble truncated Schwinger–Dyson equation for the fermion propagator in an Abelian gauge theory in arbitrary dimension when the bare fermion mass is zero. It is especially shown that in two dimensions, it becomes the exact and closed Schwinger–Dyson equation which can be exactly solved.

Progress on perfect lattice actions for QCD

Abstract: We describe a number of aspects in our attempt to construct an approximately perfect lattice action for QCD. Free quarks are made optimally local on the whole renormalized trajectory and their couplings are then truncated by imposing 3-periodicity. The spectra of these short ranged fermions are excellent approximations to continuum spectra. The same is true for free gluons. We evaluate the corresponding perfect quark-gluon vertex function, identifying in particular the “perfect clover term”. First simulations for heavy quarks show that the mass is strongly renormalized, but again the renormalized theory agrees very well with continuum physics. Furthermore we describe the multigrid formulation for the non-perturbative perfect action and we present the concept of an exactly (quantum) perfect topological charge on the lattice.

A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge

Abstract: A truncation scheme for the Dyson-Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov-Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to vanish for small spacelike momenta whereas the ghost propagator is found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling alpha_c of approx. 9.5. The gluon propagator is shown to have no Lehmann representation. The results for the propagators obtained here compare favorably with recent lattice calculations.

Deep-inelastic structure functions in a covariant spectator model

Abstract: Deep-inelastic structure functions are studied within a covariant scalar diquark spectator model of the nucleon. Treating the target as a two-body bound state of a quark and a scalar diquark, the Bethe-Salpeter equation (BSE) for the bound state vertex function is solved in the ladder approximation. The valence quark distribution is discussed in terms of the solutions of the BSE. {copyright} {ital 1997} {ital The American Physical Society}

Improved local-field corrections to the G 0 W approximation in jellium: Importance of consistency relations

Abstract: We study the effects of local vertex corrections to the self-energy of the electron gas. We find that a vertex derived from time-dependent density-functional theory can give accurate self-energies, provided, however, a proper decay at large momentum transfer (large q) is built into the vertex function. (The local-density approximation for the vertex fails badly.) Total energies are calculated from the Galitskii-Migdal formula, and it is shown that a proper large-q behavior results in a close consistency between the chemical potentials derived from these energies and those obtained directly from the self-energy. We show that this internal consistency depends critically on including the same vertex correction in both the self-energy and the screening function. In addition the total energies become almost as accurate as those from elaborate Monte Carlo calculations. This as well as previous works show that self-energy corrections are important for properly describing electron propagation at energies around and above the plasmon energy. For easy use in calculations of photoemission and x-ray extended fine structure spectra, we parametrize our calculated self-energies in terms of a simple analytical expression. (Less)

The Perfect Quark-Gluon Vertex Function

Abstract: We evaluate a perfect quark-gluon vertex function for QCD in coordinate space and truncate it to a short range. We present preliminary results for the charmonium spectrum using this quasi-perfect action.

Normalization of the covariant three-body bound state vertex function

Abstract: The normalization condition for the relativistic three nucleon Bethe-Salpeter and Gross bound state vertex functions is derived, for the first time, directly from the three body wave equations. It is also shown that the relativistic normalization condition for the two body Gross bound state vertex function is identical to the requirement that the bound state charge be conserved, proving that charge is automatically conserved by this equation.

Generalized forward scattering amplitudes in QCD at high temperature

Abstract: We extend to a general class of covariant gauges an approach which relates the thermal Green functions to forward scattering amplitudes of thermal particles. A brief discussion of the nontransversality of the thermal gluon polarization tensor is given in this context. This method is then applied to the calculation of the ln(T) contributions associated with general configurations of two- and three-point gluon functions. The results are Lorentz covariant and have the same structure as the ultraviolet divergent contributions which occur at zero temperature. {copyright} {ital 1997} {ital The American Physical Society}

Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

Abstract: We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.

Vector Meson Dominance and $g_{\rho\pi\pi}$ at Finite Temperature from QCD Sum Rules

Abstract: A Finite Energy QCD sum rule at non-zero temperature is used to determine the $q^2$- and the T-dependence of the $\rho \pi \pi$ vertex function in the space-like region. A comparison with an independent QCD determination of the electromagnetic pion form factor $F_{\pi}$ at $T eq 0$ indicates that Vector Meson Dominance holds to a very good approximation at finite temperature. At the same time, analytical evidence for deconfinement is obtained from the result that $g_{\rho \pi \pi}(q^{2},T)$ vanishes at the critical temperature $T_c$, independently of $q^{2}$. Also, by extrapolating the $\rho \pi \pi$ form factor to $q^2 = 0$, it is found that the pion radius increases with increasing $T$, and it diverges at $T=T_c$.

Exact renormalization group analysis in Hamiltonian theory: I. QED Hamiltonian on the light front

Abstract: The infinitesimal unitary transformation, introduced recently by F.Wegner, to bring the Hamiltonian to diagonal (or band diagonal) form, is applied to the Hamiltonian theory as an exact renormalization scheme. We consider QED on the light front to illustrate the method. The low-energy generated interaction, induced in the renormalized Hamiltonian to the order \alpha, is shown to be negative to insure together with instantaneous term and perturbative photon exchange the bound states for positronium. It is possible to perform the complete complete elimination of the ee\gamma-vertex in the instant form frame; this gives rise to the cutoff independent e\bar{e}-interaction governed by generated and instantaneous terms. The well known result for the singlet-triplet splitting $7/6 \alpha^2 Ryd$ is recovered in the nonrelativistic limit as long as $\la << m$. We examine the mass and wave function renormalization. The ultraviolet divergencies, associated with a large transverse momentum, are regularized by the regulator arising from the unitary transformation. The severe infrared divergencies are removed if all diagrams to the second order, arising from flow equations method and normal-ordering Hamiltonian, are taken into account. The electron (photon) mass in the renormalized Hamiltonian vary with UV cutoff in accordance with 1-loop renormalization group equations.This indicates to an intimete connection between Wilson's renormalization and the flow equation method. The advantages of the method in comparison with the naive renormalisation group approach are discussed.

High temperature ln(T) contributions in thermal field theory

Abstract: We calculate, to one-loop order, the ln(T) contributions of three-point functions in the {phi}{sup 3} and Yang-Mills theory at high temperature. We find that these terms are Lorentz invariant and have the same structure as the ultraviolet divergent contributions which occur at zero temperature. A simple argument, valid for all N-point Green functions, is given for this behavior. {copyright} {ital 1997} {ital The American Physical Society}

Naturalness and ultraviolet structure of gauge theories with massive fermions

Abstract: According to the principle of naturalness a small, with respect to the cutoff, mass parameter entering a quantum field system is natural only when it is compatible with some symmetry in the limit where it vanishes. In this paper, advantage is taken of the liberty afforded by the renormalization procedure in order to harmonize the cutoff with the physical mass in a non-Abelian gauge field theory with spin-1/2 matter fields. The ultraviolet structure of the theory, from such a vantage point, is explored at the level of the full fermionic propagator, as well as the vertex function, using the world line approach. An interplay between this ultraviolet structure and the infrared behavior of the {ital same} system, but from the customary viewpoint {open_quotes}cutoff much greater than mass,{close_quotes} is pointed out. Direct implications for open fermionic lines in the world line path integral casting of field theories are also made. {copyright} {ital 1997} {ital The American Physical Society}

Instanton induced effective vertex in the Seiberg-Witten theory with matter

Abstract: The instanton-induced effective vertex is derived for N=2 supersymmetric QCD (SQCD) with arbitrary mass matter hypermultiplets for the case of SU(2). The leading term of the low energy effective lagrangian obtained from this vertex agrees with one-instanton effective term of the Seiberg-Witten result.

Three-Quark Bethe-Salpeter Vertex Function Under Pairwise Gluon-Exchange-Like Interaction : Application to n-p Mass Difference

Abstract: A qqq BSE formalism based on an input 4-fermion Lagrangian of 'current' u, d quarks interacting pairwise via a gluon-exchange-like propagator in its nonperturbative regime, is employed for the construction of a relativistic qqq-wave function under the Covariant Instantaneity Ansatz (CIA). The chiral invariance of the input Lagrangian is automatically ensured by the vector character of the gluonic propagator, while the 'constituent' masses are the low momentum limits of the dynamical mass function m(p) generated by the standard mechanism of DB χ S in the solution of the Schwinger Dyson Equation (SDE). The CIA gives an exact reduction of the BSE to a 3D form which is appropriate for baryon spectroscopy, while the reconstructed 4D form identifies the hadron quark vertex function as the key ingredient for evaluating transition amplitudes via quark-loop integrals. In this paper the second stage of this 'two-tier' BSE formalism is extended from the 4D qq-meson to the 4D qqq-baryon vertex reconstruction through a reversal of steps offered by the CIA structure. As a first application of this 4D qqq wave function, we evaluate the quark loop integrals for the neutron (n) - proton (p) mass difference which receives contributions from two sources : i) the strong SU(2) effect arising from the u-d mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference works out at 1.28 MeV (vs. 1.29 expt), with two free parameters C 0 , ω 0 characterizing the infrared structure of the gluonic, which have been precalibrated from a common fit to qq and qqq spectra as well as several other observable quark loop integrals. A formal derivation, based on Green's function techniques for 3 spinless quarks, of the CIA structure of the 4D qqq-baryon vertex function as employed in the text, is given for completeness in Appendix B.

Model Vertices Beyond the GW Approximation

Abstract: We study the effects of local vertex corrections to the self energy of the electron gas. We find that a vertex derived from time-dependent density-functional theory can give accurate self energies without including the explicit time dependence of the exchange-correlation potential provided, however, that a proper decay at large momentum transfer (large q) is built into the vertex function. (The local-density approximation for the vertex fails badly.) Total energies are calculated from the Galitskii-Migdal formula and it is shown that a proper large-q behavior, results in a close consistency between the chemical potentials derived from these energies and those obtained directly from the self energy. We show that this internal consistency depends critically on including the same vertex correction in both the self-energy and the screening function. In addition the total energies become almost as accurate as those from elaborate quantum Monte-Carlo (QMC) calculations. We also study the accuracy and utility of the functional for the total energy proposed by Luttinger and Ward and a generalization by Almbladh, von Barth, and van Leeuwen. For the electron gas, even the simplest and readily evaluated approximations to these functionals yield total energies of similar quality as those of QMC calculations. The functionals depend on the one-electron Green's function and the screened Coulomb interaction and already rather crude approximations to these quantities produce accurate energies thus demonstrating the insensitivity of the functionals to their arguments. Different ways of incorporating vertex corrections beyond the $GW$ level are studied in simple, exactly soluble polaron-like models. We study models of a structureless core electron coupled to valence electrons and a local polaron model by Cini, Hewson and Newns. Our model results indicate that the first vertex correction alone will in general not suffice to improve the spectrum away from the quasi-particle peak. By including a subsequence of Mahan's fractal vertex series, however, we obtain results with correct physical properties which agree better with exact model results. (Less)

QED symmetries in real-time thermal field theory

Abstract: We study the discrete and gauge symmetries of quantum electrodynamics at finite temperature within the real-time formalism. The gauge invariance of the complete generating functional leads to the finite temperature Ward identities. These Ward identities relate the eight vertex functions to the elements of the self-energy matrix. Combining the relations obtained from the Z{sub 2} and the gauge symmetries of the theory we find that only one out of eight longitudinal vertex functions is independent. As a consequence of the Ward identities, it is shown that some elements of the vertex function are singular when the photon momentum goes to zero. {copyright} {ital 1997} {ital The American Physical Society}

Chiral symmetry breaking in the presence of a confining interaction

Abstract: We study chiral symmetry breaking, making use of a generalized Nambu{endash}Jona-Lasinio (NJL) model that includes a description of confinement. The Schwinger-Dyson and Bethe-Salpeter equations are solved for our model of the self-energy of a quark. We show that our analysis is consistent with the Goldstone theorem. That is, the pion has zero mass, if the current quark masses are zero. We use a confining interaction with a (Dirac) matrix structure that leads to simple equations for the self-energy and for a vertex function that serves to sum a ladder of confining interactions. We consider spacelike values of q{sup 2}, and carry out our analysis in a Euclidean momentum space. For timelike q{sup 2}, we use calculational procedures that we have developed in our earlier work in order to exhibit properties of the confining vertex. For the spacelike values of q{sup 2} considered here, we see that the effects due to the introduction of our model of confinement are small. (However, such effects are very important for timelike q{sup 2}. Their consideration is essential, if we wish to study mesons, such as the rho and omega, in our model.) {copyright} {ital 1997} {ital The American Physical Society}

A new contribution to the flavour-changing lepton-photon vertex

Abstract: We show that the correct perturbation theory for mixed fermion states leads to nonvanishing contributions of the dimension-four vertex operators for flavour-changing transitions. Their contributions to the amplitude are of the same order of magnitude as the dimension-five vertex operators. Considerations are valid irrespective of the electroweak model.

ωNN vertex function and the γπππ anomaly

Abstract: We show that the empirical ωNN form factor (cut-off 1400–C1500 MeV) can be understood as arising from a combination of a quark model form factor (typical cut-off 700–C800 MeV) and an anomalous form factor ∼ q2 arising from the 3π-intermediate state. The anomaly contributes to the Dirac form factor F1(q2) with F1(0) = 0, Open image in new window (and sizable), and to the Pauli form factor F2(q2) with F2(0) ≠ 0. The resulting tensor coupling F2(0) is sensitive to the cut-off of the pion momenta in the two-loop integrals and turns out to be small for values around 1 GeV. The quark model ωNN tensor coupling F2(0) vanishes for point-like quarks. The anomaly, however, contributes a non-vanishing tensor coupling which can be seen to effectively enhance the vector coupling in NN models which do not include a tensor coupling.

Gauge Invariance and Factorisation in Exclusive Meson Production

Abstract: The structure of the nonperturbative vector meson vertex function complicates the proof of the factorisation theorem for the reaction $\gamma^*p\to Vp$. It leads to additional contributions but, in a simple model for the vertex function, gauge invariance ensures that they cancel and factorisation is preserved.