Sum Rule Technique Research Articles

K 0-K −0 and B 0-B −0 mixing matrix elements from vertex QCD sum rules

The results of the calculation of the mixing matrix elements for neutral pseudoscalar K- and B-mesons within vertex QCD sum rules technique are briefly presented.

Collective excitations of3He clusters

Collective excitations of3He clusters are studied by treating the cluster as a quantum liquid drop. We have used the Random-Phase Approximation sum rules technique within a Density Functional Formalism. Results forL=2 to 10 surface modes and theL=0 volume mode are presented.

Applications of QCD sum rules at finite temperature

QCD sum-rule techniques are applied to the spectra of $\ensuremath{\rho}$ and $\frac{J}{\ensuremath{\psi}}$ mesons at finite temperature to investigate the relative importance of quark and gluon condensates and perturbative thermal effects in determining bound-state parameters. Of particular interest are the consequences of nonperturbative physics persisting above the deconfinement phase transition, which is implied by nonzero gluon condensates found in lattice calculations. For the $\ensuremath{\rho}$ meson, the quark thermal bath induces only a smooth variation in the hadronic parameters as the temperature is increased; the quark condensate and its temperature dependence are the most important factors. For the $\frac{J}{\ensuremath{\psi}}$ meson, perturbative thermal effects overwhelm the gluon condensate contribution at a temperature around 100 MeV, so that high-temperature charmonium physics is consistent with that expected in a weakly interacting quark-gluon plasma. Corrections to other plasma properties from nonperturbative physics are discussed.

Nucleon distribution amplitude and diquark clustering.

We explore the possibility of diquark clustering as a source of the asymmetry in the quark distribution amplitudes found by the QCD sum-rule technique. We consider a simple light-cone wave-function model for the nucleon and find that a two-quark correlation in the spin-zero state provides a significantly better account of the Chernyak-Zhitnitsky asymmetry than does a previous symmetric quark model with uncorrelated quarks.

Asymmetry in inclusive polarized electron scattering from polarized nuclei: Sum rule approach.

The asymmetry of the inelastic cross section for the scattering of polarized electrons from polarized targets is investigated in the quasielastic region by using sum rule techniques. The sum rule method provides for the deuteron and $^{3}\mathrm{He}$ an elegant and direct way to extract the dependence of the asymmetry on the neutron electric form factor. The nuclear structure ingredients entering the expressions for the asymmetry are the nonspherical components of the ground state wave functions and the structure functions. The sum rule predictions for the asymmetry have been compared with the results of microscopic calculations for the deuteron and $^{3}\mathrm{He}$. Application of the method to heavier nuclei shows that the asymmetry is particularly sensitive to core polarization effects.

The QCD sum rules and nuclear matter

An attempt is made to obtain the main properties of nuclear matter by the QCD sum rule technique. The matter is shown to have an equilibrium bound state with density which depends sharply on the value of the πN σ-term. The characteristics of nuclear matter are presented as a power series in ρ 1 3 including the terms of order ρ 8 3 . At σ ≈ 60 MeV the parameters of nuclear matter are close to those obtained in nuclear physics models. Estimates for the swelling of the nucleon in the matter are made.

Radiative muon capture and the value of gP in nuclei

Radiative muon capture by nuclei is analyzed by means of sum rule techniques, providing a total photon yield calculated with RPA precision. The measured yields relative to the ordinary muon capture rate are well reproduced for the nuclei 12C, 16O and 40Ca using a value of the pseudoscalar weak coupling constant g P enhanced by only 25% with respect to its canonical value. Therefore, the large renormalization of g P claimed up to now must be reconsidered.

QCD sum rule analysis of spin-orbit splitting in baryons

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to J P = 1 2 − nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N 1 2 − (1535) . The QCD sum rules coupling to the low-lying Δ 1 2 + , Λ 1 2 − , and Λ 3 2 − , are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ 1 2 + sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ 1 2 + (1550) resonance.

Strong coupling expansions in pure lattice gauge theory mixed actions: Carles Ayala and Marià Baig. Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to JP = 12− nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N12−(1535). The QCD sum rules coupling to the low-lying Δ12+, Λ12−, and Λ32−, are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ12+ sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ12+(1550) resonance.

Stepwise enhancement of bound dipoles in strongly coupled plasma: C. Deutsch. L.P.G.P., Bât. 212, Université Paris XI, 91405 Orsay, France and Department of Applied Physics, Stanford University, Stanford, California 94305; G. Naouri. L.P.G.P., Bât. 212, Université Paris XI, 91405 Orsay, France

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to JP = 12− nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N12−(1535). The QCD sum rules coupling to the low-lying Δ12+, Λ12−, and Λ32−, are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ12+ sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ12+(1550) resonance.

Multipole vibrations of small alkali-metal spheres in a semiclassical description.

We use the jellium model and a semiclassical version of the energy-density variational method to investigate static properties of spherical metal clusters and obtain excellent agreement with the (averaged) microscopical results. Exploiting random-phase-approximation (RPA) sum-rule techniques, we calculate the eigenmode spectrum for collective multipole vibrations of the electrons, including coupling between surface and volume plasmons. In the classical limit the old Mie result is recovered for the surface plasmons of all multipolarities. From the sum rules, we estimate the static dipole polarizabilities and the position and width of the electric dipole resonance. We find that the RPA estimate of the width is in qualitative agreement with recent experiments on small Na clusters.

Some relations for radiative-pion-capture and muon-capture rates.

Using sum rules techniques to calculate the radiative-pion-capture rate ${\ensuremath{\Lambda}}_{\ensuremath{\gamma}}^{\ensuremath{\pi}}(\mathrm{nl})$ and the muon-capture rate ${\ensuremath{\Lambda}}_{\ensuremath{\mu}}$, two results are obtained. First, the ratio ${\ensuremath{\Lambda}}_{\ensuremath{\gamma}}^{\ensuremath{\pi}}(\mathrm{nl})$ over the experimental absorption width ${\ensuremath{\Gamma}}_{\mathrm{nl}}^{\ensuremath{\pi}}$ is independent of the $\mathrm{nl}$ atomic level from which the pion is captured in each nucleus. Second, we explain the empirical observation that the radiative branching ratio scaled with the width ${\ensuremath{\Gamma}}_{1s}^{\ensuremath{\pi}}$ is nearly equal to ${\ensuremath{\Lambda}}_{\ensuremath{\mu}}$ multiplied by 2.33\ifmmode\times\else\texttimes\fi{}${10}^{12}$. This constant is basically determined by coupling constants and masses.

Total Gamow-Teller strength and effect of configuration mixing and proton-neutron correlation in the even-even sd-shell nuclei.

We have calculated the total Gamow-Teller strength S/sub +- / in the even-even sd-shell nuclei making use of the sum rule technique. The ground state wave function is obtained from the shell model calculation in the full (sd)/sup n/ space. It is shown that the proton-neutron correlation effect causes a considerable amount of reduction of the total Gamow-Teller strength. It is also shown that the reduction of the isospin component in S..sqrt.. induced by the configuration mixing becomes more significant with increasing isospin

Light-meson distribution amplitude: Simple relativistic model.

With the basic concepts of the constituent-quark model formulated in the light-cone Fock approach we present a relativistic model of the pion and $\ensuremath{\rho}$-meson valence-quark structure. We point out that a nonstatic relativistic spin wave function and small transverse size of the valence configuration are essential to reproduce the basic features of the Chernyak-Zhitnitsky amplitudes for the $\ensuremath{\pi}$ and $\ensuremath{\rho}$ as they are obtained from QCD sum-rule techniques.

Measurement of local thickness by electron energy-loss spectroscopy

We review various methods which can be used to derive the thickness of an electron-microscope specimen from its transmission energy-loss spectrum. We have applied a sum-rule technique to various kinds of specimen, using a variety of electron-optical conditions, and estimate its accuracy to be typically ±10% (or±2nm if larger) over the thickness range 10–150 nm. This method requires no knowledge of the physical or chemical properties of the specimen other than its refractive index (∞ for metal). It involves only a low radiation dose, allowing good lateral resolution (<10 nm) to be achieved even by selected-area techniques.

Nuclear Shapes Studied by Coulomb Excitation

Publisher Summary This chapter discusses nuclear shapes studied by Coulomb excitation. Nuclear E2 properties are a direct and an unambiguous measure of the collective shape parameters for quadrupole collectivity. Coulomb excitation selectively excites collective states with cross sections that are a direct measure of the E2 matrix elements. Advances in the field of Coulomb excitation make it feasible to measure essentially all the E2 matrix elements for low-lying nuclear levels. The completeness and extent of this E2 information add a new dimension to the study of quadrupole collectivity in nuclei. In particular, now it is practical to use a model-independent method for extracting the collective shape parameters directly from this large body of E2 data. Coulomb excitation can now be used to address open questions such as those regarding the limits of the validity of macroscopic collective models, the role of symmetries in collective motion, and the role of shape transitions and shape coexistence in nuclear structure. It is possible to exploit the model-independent sum rule method to project the significant quadrupole collective shape degrees of freedom directly from the data. The power of the sum rule technique is that it allows a wealth of data to be transformed into a form that clearly shows the extent to which the data are correlated because of collectivity.

Static polarizability and dipolar surface plasmon of small metal particles. II. Including the lattice structure

AbstractThe frequency of the dipolar surface of small particles is calculated using the sum rule techniques due to Lushnikov et al. The effect of surface diffuseness of electron density is included. The screening of the electrons is described within the Thomas‐Fermi approximation. The lattice structure and the lattice relaxation through the introduction of pseudopotentials are taken into account. The ground state charge density is obtained from a variational estimate of the total energy of the clusters based on the local density functional formalism. The surface plasmon frequency is red‐shifted from its classical value.

Experimental predictions of lattice and perturbative quantum chromodynamics.

We discuss several experimental consequences of a lattice-gauge-theory calculation of the first two moments of the $\ensuremath{\pi}$ and $\ensuremath{\rho}$ distribution amplitudes. The second moments for both mesons are considerably larger than the values obtained from QCD sum-rule techniques. We show the qualitative difference that this makes in the predicted distribution amplitude, and demonstrate the consequences for the pion form factor and the $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ cross section.

Can spin-flip quadrupole resonances be observed?

Shell model calculations ofJ=2+,S=0 andS=1 states indicate that the spin flip quadrupole strength is much more fragmented than itsS=0 analog, at least in light nuclei. A sum rule technique is then used to study the coexistence betweenS=0 andS=1 states; it illustrates why theS=0 strength is fairly immune to changes in the noncentral part of the nuclear interaction. In16O, someE2 spin flip strength is predicted to lie in the 40 MeV region where it could be located by inelastic electron and pion scattering experiments.

The SVZ plasmon

The sum rule technique of Shifman, Vainshtein and Zakharov is applied to a non-relativistic many-body system, the homogeneous, degenerate electron gas. The operator product expansion for the nonrelativistic correlation function is derived and shown to be equivalent in lowest order to a moment expansion. The nonperturbative terms in this expansion characterize the interacting ground state (“vacuum”) of the system. For the electron gas they can be related to the correlation energy which is very well known. Following as close as possible the SVZ procedure the mass of the plasmon (i.e. the dispersion coefficient of the collective plasma excitation) is calculated and compared with results from conventional many-body theories.