Showing papers on "Vertex function published in 1992"

Order from disorder in a kagomé antiferromagnet.

Abstract: A Heisenberg antiferromagnet on a kagom\'e lattice is highly degenerate in the classical limit. I show that quantum fluctuations lift the degeneracy and yeild the low-energy branch of spin-wave excitations with a velocity which is a factor ${\mathit{S}}^{\mathrm{\ensuremath{-}}1/3}$ smaller than for conventional spin waves. The relevance of these results to the experiments on the stacked kagom\'e antiferromagnet ${\mathrm{SrCr}}_{8\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{4+\mathit{x}}$${\mathrm{O}}_{19}$ is discussed.

Gauge-invariant self-energies and vertex parts of the standard model in the pinch technique framework.

Abstract: The pinch technique (PT) is applied to obtain one-loop gauge-invariant self-energies, vertex and box diagrams in the electroweak sector of the standard model. Describing the interaction of vector bosons with fermions in terms of current correlation functions, we propose to directly identify the pinch parts with the contributions of equal-time commutators in the relevant Ward identities. We argue that this procedure isolates the parts of vertex and box diagrams that are independent of strong interaction dynamics. The formalism promptly leads us to very simple gauge-invariant transverse self-energies, as well as vertex and box diagrams relevant to four-fermion processes mediated by charged and neutral currents. They automatically possess very desirable theoretical properties. We then apply the PT to {ital e}{sup +}{ital e{minus}} {r arrow}{ital W}{sup +}{ital W{minus}} and explicitly demonstrate that the propagatorlike pinch parts are absorbed in the same self-energies encountered in the four-fermion case. The PT self-energies and vertex corrections are compared with those obtained in other formulations. A number of applications are discussed, including the possibility of a gauge-invariant on-shell definition of the vector-boson mass.

Photon polarization tensor and gauge dependence in three-dimensional quantum electrodynamics.

Abstract: We calculate the three-dimensional QED (${\mathrm{QED}}_{3}$) photon polarization tensor using dressed fermion propagators and a fermion-photon vertex that satisfies the Ward-Takahashi identity. Irrespective of the structural details of the transverse part of the fermion-photon vertex the photon remains massless; i.e., there is no photon mass generation in the manner of the Schwinger mechanism. Our calculation suggests that ${\mathrm{QED}}_{3}$ is confining when the polarization tensor is calculated using a dressed fermion propagator and fermion-photon vertex. The gauge parameter dependence of the fermion propagator, fermionphoton vertex, and photon polarization tensor is discussed in connection with the Landau-Khalatnikov gauge transformation laws.

CPN-1 models in the 1/N expansion.

Abstract: Two-dimensional CP{sup {ital N}{minus}1} models are analyzed by means of the 1/{ital N} expansion, performed up to the first nonleading order. The expectation values of gauge- and renormalization-group-invariant quantities are computed in a regulated continuum version of the theory: renormalizability and absence of infrared divergences are explicitly verified. Special attention is devoted to open and closed loops of gauge fields and to their correlations. No single-particle mass for the elementary'' gauge-dependent fields can be consistently defined. The observable mass parameter is related to the lowest-energy bound state and shows a nonanalytic dependence on 1/{ital N}. The qualitative picture of the CP{sup {ital N}{minus}1} models resulting from the large-{ital N} approximation is quantitatively confirmed in the 1/{ital N} expansion.

A Hadron-Quark Vertex Function:. Interconnection Between 3d and 4d Wave Functions

Abstract: The interrelation between the 4D and 3D forms of the Bethe–Salpeter equation (BSE) with a kernel which depends on the relative four-momenta, orthogonal to Pμ is exploited to obtain a hadron–quark vertex function of the Lorentz-invariant form . The denominator function is universal and controls the 3D BSE, which provides the mass spectra with the eigenfunctions . The vertex function, directly related to the 4D wave function Ψ which satisfies a corresponding BSE, defines a natural off-shell extension over the whole of four-momentum space, and provides the basis for the evaluation of transition amplitudes via appropriate quark-loop digrams. The key role of the quantity in this formalism is clarified in relation to earlier approaches, in which the applications of this quantity had mostly been limited to the mass shell (q · P = 0). Two applications (fP values for and Fπ for π0 → γγ) are sketched as illustrations of this formalism, and attention is drawn to the problem of complex amplitudes for bigger quark loops with more hadrons, together with the role of the function in overcoming this problem.

Measurement of the π 0 electromagnetic transition form factor

Abstract: We present the result of a measurement of the {pi}{sup 0} electromagnetic transition form factor in the timelike region of momentum transfer. From a data sample of 54000 {pi}{sup 0}{r arrow}{ital e}{sup +}{ital e{minus}}{gamma} decays, observed in the SINDRUM I magnetic spectrometer at the Paul Scherrer Institute (Switzerland), we measure a value of the form factor slope {ital a}=0.025{plus minus}0.014 (stat){plus minus}0.026 (syst). This value is consistent with both the results of the recent measurement by CELLO (DESY) in the spacelike region, and with the vector-meson-dominance prediction of {ital a}{approx}0.03.

Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex

Abstract: The conformal symmetry of the QCD Lagrangian for massless quarks is broken both by renormalization effects and the gauge fixing procedure. Renormalized primitive divergent amplitudes have the property that their form away from the overall coincident point singularity is fully determined by the bare Lagrangian, and scale dependence is restricted to $\delta$-functions at the singularity. If gauge fixing could be ignored, one would expect these amplitudes to be conformal invariant for non-coincident points. We find that the one-loop three-gluon vertex function $\Gamma_{\mu u\rho}(x,y,z)$ is conformal invariant in this sense, if calculated in the background field formalism using the Feynman gauge for internal gluons. It is not yet clear why the expected breaking due to gauge fixing is absent. The conformal property implies that the gluon, ghost and quark loop contributions to $\Gamma_{\mu u\rho}$ are each purely numerical combinations of two universal conformal tensors $D_{\mu u\rho}(x,y,z)$ and $C_{\mu u\rho}(x,y,z)$ whose explicit form is given in the text. Only $D_{\mu u\rho}$ has an ultraviolet divergence, although $C_{\mu u\rho}$ requires a careful definition to resolve the expected ambiguity of a formally linearly divergent quantity. Regularization is straightforward and leads to a renormalized vertex function which satisfies the required Ward identity, and from which the beta-function is easily obtained. Exact conformal invariance is broken in higher-loop orders, but we outline a speculative scenario in which the perturbative structure of the vertex function is determined from a conformal invariant primitive core by interplay of the renormalization group equation and Ward identities.

Approaching low-energy QCD with a gauged, nonlocal, constituent-quark model

Abstract: We study the minimal constituent-quark model with momentum-dependent quark mass in the presence of SU(3){times}SU(3) external gauge fields {ital V}{sub {mu}}({ital x}), {ital A}{sub {mu}}({ital x}), {ital S}({ital x}), and {ital P}({ital x}). The model generates vertex functions, for any number of external fields and pseudo Goldstone bosons coupling to quarks, saturating the Ward-Takahashi identities of QCD. Parameters in the {ital O}({ital p}{sup 4}) chiral Lagrangian are expressed in terms of the quark mass function {Sigma}({ital p}) and are surprisingly consistent with low-energy QCD. By use of the auxiliary-field method we discuss the relation of the model to the improved ladder approximation in QCD.

Magnetic interactions in the metallic phase of the copper oxides: A Fermi-liquid description

Abstract: One of the central issues in the field of high-temperature superconductivity is whether the normal state can be described by Fermi-liquid theory Recent photoemission experiments along with a growing body of Fermi-liquid-based theoretical work have provided some support for this viewpoint However, one major concern in ascertaining the validity of a Fermi-liquid approach is whether the magnetic interactions in the metallic cuprates are sufficiently strong so as to undermine the usual Fermi-liquid description In this paper we address this question by examining the nature of the magnetic interactions in the metallic state These interactions, which are dominantly between the Cu spins, arise via the intermediating oxygenlike states Since the oxygen character changes as the hole doping is increased, it is expected that the Cu-Cu interactions are doping sensitive and evolve away from their value in the insulating limit We deduce these interactions within a physical picture in which the Cu {ital d} electrons are nearly localized and the oxygen bandwidth assumes a finite value While our qualitative results are general, we use a 1/{ital N} expansion as a convenient theoretical tool In the extended Hubbard Hamiltonian the exchange terms are evaluated at order (1/{ital N}{sup 2}) Both superexchange ({ital J}{submore » {ital S}}) and Ruderman-Kittel-Kasuya-Yosida interactions ({ital J}{sub {ital R}}) emerge on a similar footing With increasing carrier concentration, {ital J}{sub {ital S}} decreases rapidly, while {ital J}{sub {ital R}} abruptly increases from zero We find that, because of the reduction in the strength of the superexchange, there is an enhanced stability of the Fermi-liquid phase The dynamical susceptibility is also calculated within this scheme and the consequences for NMR and neutron experiments are discussed elsewhere« less

Vertex corrections to vacuum polarization in hadronic field theories.

Abstract: Vacuum polarization is studied in a model with neutral vector mesons and Dirac baryons. The lowest-order polarization is known to produce a ghost pole when it is summed to all orders in the vector meson propagator. It is also known that the infrared structure of the meson-baryon (NN\ensuremath{\omega}) vertex in this model produces a proper vertex function that is strongly damped at large spacelike momentum transfer; this is analogous to the result first derived by Sudakov in quantum electrodynamics. When the model vertex function is approximated by its on-shell form and combined with the lowest-order polarization, the vacuum contributions are significantly reduced. The resulting random-phase approximation meson propagator has no ghost pole and is finite at large spacelike momenta. Implications and perspectives of this result and necessary extensions of this calculation are also discussed.

Recovery of gauge invariance in strong-coupling qed

Abstract: Under a novel ansatz for the vertex function, the Schwinger- Dyson equation for the fermion propagator in the cutoff QED is solved in the arbitrary gauge, taking account of the vacuum polarization in the photon propagator. For any ultraviolet cutoff Λ, there exists a bifurcation point ec(Λ) of the bare coupling constant above which the trivial fermion-mass function for massless QED bifurcates to another, nontrivial massive solution. With a proper choice of the transverse vertex function and the longitudinal vertex that respects the Ward-Takahashi identity, the critical point ec(∞) and the critical scaling behavior in the vicinity of the critical point are shown to be gauge-independent. In the arbitrary gauge, it is shown that the quenched, planar QED obeys Miransky’s scaling of the essential-singularity type and that the unquenched QED exhibits the mean-field critical behavior with classical critical exponents.

Raman scattering from antiferromagnetic spin fluctuations

Abstract: A microscopic theory for the scattering of light from spin fluctuation pair modes in the two-dimensional Hubbard model is presented. Two-spin fluctuation processes with opposite momenta near the antiferromagnetic wave vectorQ=(π, π) are shown to contribute in particular to the low energy part of the Raman cross section. We explicitly investigate the influence of the Raman vertex function that describes the coupling of the Raman vertex function that describes the coupling of the light to the electrons and distinguishes between the different scattering geometries. In addition we explore the dependence on the correlation strength and on the temperature.

Strong Coupling Unquenched QED. II: Numerical Study

Abstract: Dynamical chiral-symmetry-breaking in massless QED with N fermion species is studied through the numerical solution of the coupled Schwinger-Dyson (SD) equation. We·have taken into account the fermion loop effect (at the I-loop level) in the SD equation for the photon propagator through the vacuum polarization function JI(k 2 ), with and without the standard approximation: JI((p_q)2) ","JI(max (p2, q2)). We have found that the scaling law is unchanged by this approximation and that, irrespective of the fermion flavor N, the dynamical fermion mass and chiral order parameter obey the same mean-field type scaling, while the quenched planar QED without the vacuum polarization (N =0 limit) obeys the Miransky scaling with the essential singularity. l ) we studied analytically the Schwinger-Dyson (SD) equation in massless QED with N fermion species. In this paper we confirm the analytical results by solving the SD equation numerically. The SD equation is the simultaneous integral equation among the fermion propagator S(p), the photon propagator Dpv(k) and the vertex function rp(p, q; k). The SD equation for the fermion propagator S(p) = [jfA(p2)- B(p2)]-l is decomposed into a pair of coupled integral equations for A and B, each of which is a non-linear integral equation containing multiple-integrals. In the previous analytical treatment,I) we avoided several difficulties appearing in solving the SD equation for the fermion propagator as follows. (1) Multiple-integral: The presence of the nontrivial vacuum polarization leads to the integral equation containing the double integral. This can be avoided by replacing the kernel by the separated (degenerate) form K(P, q)=K(p2)8(p2_q2)+K(q2)8(q2_p2) as a conse­ quence of the LAK l ) approximation a la Landau-Abrikosov-Khalatnikov for the vacuum polarization function: (1·1) Then we can carry out the angular integral exactly in the same manner as in the quenched planar case and the SD equation reduces to the integral equation containing the single integral only. (2) Simultaneousness: This has been evaded by taking the Landau gauge. In the Landau gauge A(p2) == 1 follows under the LAK approximation, and the SD equation for the fermion propagator reduces to the single integral equation for B(p2), as shown in the quenched planar approximation. 2 ) (3) Non-linearity: In order to study the scaling behavior in the neighborhood of the.critical point, we do not have to deal with the non-linear equation and it is sufficient to solve the linearized equation, as guaranteed by the bifurcation theory.3)

Delta 33-isobar contribution to the soft nucleon-nucleon potentials. II. pi rho -exchange potentials.

Abstract: Two-pion-exchange (TPE) nucleon-nucleon potentials are derived for one or two {Delta} isobars in the intermediate states. Strong dynamical pair suppression is assumed. At the {ital NN}{pi} and the {ital N}{Delta}{pi} vertices Gaussian form factors are incorporated into the relativistic two-body framework by using a dispersion representation for the one-pion-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators, taking into account the mass difference between the nucleon and the {Delta} isobar. Analytic expressions for the TPE potentials are obtained, which contain at most one-dimensional integrals. The TPE potentials are first calculated up to orders ({ital f}{sub {ital N}{ital N}{pi}} f{sub {ital N}{Delta}{pi}}){sup 2} and {ital f}{sub {ital N}{Delta}{pi}}{sup 4}. These come from the adiabatic contributions of all planar and crossed three-dimensional momentum-space TPE diagrams. We also give the contributions of the OPE iteration, which can be subtracted or not, depending on whether one performs a coupled-channel calculation for, e.g., the {ital NN}, {ital N}{Delta} system, or a single {ital NN}-channel calculation. Next, we calculate the ({ital m}{sub {pi}}/{ital M}) corrections. These are due to the 1/{ital M} terms in the pion-nucleon vertices, and the 1/{ital M} terms in the nonadiabatic expansion of the nucleon energies inmore » the intermediate states.« less

Two interacting magnetic impurities in a metal: Renormalization-group treatment of a simple model.

Abstract: The single-impurity Kondo problem can be mapped onto a resonant level of spinless fermions with an attractive interaction between the localized and extended states. We consider two such impurities at sites {bold R}{sub 1} and {bold R}{sub 2} interacting with each other via a hopping matrix element {ital t} and an interaction {ital G} between the localized fermions. The interactions {ital t} and {ital G} resemble the Ruderman-Kittel-Kasuya-Yosida interaction between the impurities. The physics of the model is most conveniently discussed in terms of even- and odd-parity states with respect to the point 1/2({bold R}{sub 1}+{bold R}{sub 2}). We obtain the {ital k}-space renormalization-group equations for the model, which are integrated and discussed in terms of Ward cancellations. Finally, approximate expressions for the static and dynamical susceptibilities for the response to a homogeneous and staggered field are obtained. No dramatic anomalies are found, probably as a consequence of the broken spin-rotational invariance of the model.

Exact symmetries and the role of the pion cloud in deep-inelastic electron-nucleon scattering.

Abstract: A careful analysis of exact symmetries, such as the charge conjugation symmetry and the electromagnetic and baryon current conservation, shows that exactly two nontrivial Feynman diagrams contribute to deep-inelastic inclusive pion electroproduction from the nucleon to {ital O}({ital g}{sub {pi}{ital N}{ital N}}{sup 2}). The same analysis reveals certain relationships between the two graphs. The two graphs are expressed as convolutions of the pion ({ital g}{sub {pi}}({ital y})) and the nucleon ({ital g}{sub {ital N}}({ital y})) smearing functions and their respective deep-inelastic structure functions. The nucleon smearing functions are evaluated in three models of the nucleon off-shell dependence of the {pi}{ital NN} vertex function and they turn out to have remarkably similar shapes. It is shown that this universality of {ital g}{sub {ital N}}({ital y}) persists in a wide class of models. Such universal {ital g}{sub {ital N}}({ital y}) peaks at {ital y}{sub 0}=1{minus}{ital m}{sub {pi}}/{ital M}{sub {ital N}}=0.85 and allows a simple parton model interpretation. Furthermore, the normalized smearing functions approximately satisfy the Berger-Coester-Wiringa-Thomas ansatz {ital g}{sub {pi}}({ital y})={ital g}{sub {ital N}}(1{minus}{ital y}) for two of the three models examined. Strong constraints on the nucleon off-shell dependence of the {pi}{ital NN} vertex function ({ital g}{sub {pi}{ital N}{ital N}}({ital p}{sub {italmore » N}}{sup 2})) are obtained using the observed Gottfried sum rule violation as empirical input.« less

Recovery of gauge invariance in strong-coupling QED

Abstract: In this paper, under a novel ansatz for the vertex function, the Schwinger-Dyson equation for the fermion propagator in the cutoff QED is solved in the arbitrary gauge, taking account of the vacuum polarization in the photon propagator. For any ultraviolet cutoff [Lambda] there exists a bifurcation point e[sub c]([Lambda]) of the bare coupling constant above which the trivial fermion-mass function for massless QED bifurcates to another, nontrivial massive solution. With a proper choice of the transverse vertex function and the longitudinal vertex that respects the Ward-Takahashi identity, the critical point e[sub c]([infinity]) and the critical scaling behavior in the vicinity of the critical point are shown to be gauge-independent. In the arbitrary gauge, it is shown that the quenched, planar QED obeys Miransky's scaling of the essential-singularity type and the unquenched QED exhibits the mean-field critical behavior with classical critical exponents.

The next step in leptonic decays of eta and kl bound states

Abstract: A systematic discussion of the probability of eta and KL bound-state decays— and (l=e, μ)—within a three-dimensional reduction to the two-body quantum field theory is presented. The bound-state vertex function depends on the relative momentum of constituent-like particles. A structure-transition form factor is defined by a confinement-type quark-antiquark wave function. The phenomenology of this kind of decays is analyzed.

Shifted vertex operator algebras and G‐elliptic systems

Abstract: Shifted vertex operator algebras and superalgebras are defined, both in bosonic and in fermionic pictures. Their isomorphism (Boson–Fermion correspondence) is shown. Partition functions of bosonic shifted vertex operator algebras are realized analytically and are interpreted as string path integrals over elliptic curves. Their modular properties follow, and elliptic systems are constructed based on fermionic shifted vertex operator algebras.

Off-shell effects in quasielastic electron nucleus scattering

Abstract: Using the Ward-Takahashi identity, on-shell condition, bound Dirac equation and off-shell expansion, a reduced version of half off-shell virtual photon nucleon vertex has been suggested. The vertex are decomposed into several different order terms: the on-shell terms, first and second off-shell terms. The off-shell behaviour of the form factors is discussed in the one meson loop model. Using the reduced vertex and parametrized off-shell form factors the quasielastic response functions are calculated for several nuclei at ¦q¦–kf and for56Fe at large ¦q¦ up to 1.14 GeV/c and at −q2=0.9 (GeV/c)2. The Coulomb sums are evaluated and a comparison of the theoretical prediction with data is given. The off-shell electron nucleon cross section is calculated and compared with the “cc1” off-shell extrapolation.

Decay μ-->eγ and the anomalous magnetic moment of the muon in models with heavy neutral leptons and anomalous gauge couplings

Abstract: We present the results of the influence of massive Dirac or Majorana neutrinos on the anomalous magnetic moment of the muon and the decay {mu}{r arrow}{ital e}{gamma}. In our calculations we include the general Lorentz- and {ital CP}-invariant three-vertex function of the anomalous {gamma}{ital WW} coupling. We find that the influence of the massive neutrinos on the anomalous magnetic moment of the muon is negligible whereas it is large on the decay {mu}{r arrow}{ital e}{gamma}. The {lambda}{sub {gamma}} and {Delta}{kappa}{sub {gamma}} terms of the anomalous {gamma}{ital WW} coupling lead to a further enhancement. We also show that a more careful treatment of the Kobayashi-Maskawa matrix in the lepton sector can suppress the results by a further factor of 10.

Pairing due to the exchange of magnetic fluctuations in cuprate superconductors.

Abstract: The possibility for a superconducting instability due to the exchange of magnetic fluctuations is studied by means of low-density expansion. It is shown that if the magnetic fluctuations are centered at ({pi},{pi}), they uniquely favor {ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2} superconductivity close to the magnetic instability no matter at which doping concentration this instability occurs. However, if the magnetic fluctuations are centered around the incommensurate ({pi}(1{minus}{delta}),{pi}) point in the Brillouin zone, they tend to suppress any type of superconductivity.