Calculation of the kaon B parameter using strictly local sum rules

The kaon B-parameter is computed in the framework of strictly local QCD sum rules for a threepoint function involving pseudoscalar currents. As an application of these sum rules we derive a low energy formula for the B-parameter. We show that strictly local QCD sum rules yield more reliable results than other QCD sum rules, since they need less phenomenological information and do not suffer from stability problems. Our result for the B-parameter isB=0.74±0.17.     

Study of systematic errors of bound-state parameters in SVZ sum rules

We study systematic errors of the ground-state parameters obtained from Shifman—Vainshtein—Zakharov sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of sum rules and compare the obtained results with the known exact values. We show that, in the situation when the continuum contribution to the polarization operator is not known and is modeled by an effective continuum, the method of sum rules does not allow one to control the systematic uncertainties of the extracted ground-state parameters. The text was submitted by the authors in English.     

Spectral function sum rules in quantum chromodynamics: (I). Charged currents sector

The Weinberg sum rules of the algebra of currents are reconsidered in the light of quantum chromodynamics (QCD). We derive new finite-energy sum rules which replace the old Weinberg sum rules. The new sum rules are convergent and the rate of convergence is explicitly calculated in perturbative QCD at the first non-trivial order. Phenomenological applications of these sum rules in the charged current sector are also discussed.     

QCD sum rules and electromagnetic polarizabilities of a nucleon

We investigate the electromagnetic polarizabilities of a nucleon using the method of QCD sum rules. The diagrams in the operator product expansion are taken into account up to dimension 6. We find that the polarizabilities of a nucleon can be expressed by means of three new kinds of susceptibilities of quark condensates which represent the response under weak external electromagnetic fields. Estimating the susceptibilities with the QCD sum rules itself based on the formalism by Balitsky et al., we see that good agreement is obtained for the neutron electric polarizability.     

How crossing affects the analytic relationship between low energy ππ amplitudes and their asymptotic behaviour

Different physical assumptions about the asymptotic behaviour of ππ amplitudes are realised in the different number of substractions involved in fixed t dispersion relations for the various amplitudes and their inverses. The fact that each new dispersion relation must be consistent with s - t crossing leads to a number of conditions relating low energy ππ amplitudes to their high energy behaviour. These are discussed in detail. Such relationships supplement finite energy sum rules with which they are compared. The dispersive sum rules, crossing conditions, and finite energy sum rules we discuss are applied to recent phenomenological solutions to Roy's equations and shown not to narrow the presently accepted range of threshold parameters. These results are in marked contrast to the conclusions of other recent studies. To complete the study of finite energy sum rules we consider the behaviour of the isospin zero t-channel amplitude and estimate the asymptotic ππ total cross-section. We present evidence to suggest that the pomeron is late-developing in meson-meson scattering.     

Charmonium spectra at finite temperature from QCD sum rules with the maximum entropy method

Charmonia spectral functions at finite temperature are studied using QCD sum rules in combination with the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. As a result, it is found that while J/ψ and η(c) manifest themselves as significant peaks in the spectral function below the deconfinement temperature T(c), they quickly dissolve into the continuum and almost completely disappear at temperatures between 1.0T(c) and 1.1T(c).     

Particle-hole asymmetry in doped mott insulators: implications for tunneling and photoemission spectroscopies

We use exact sum rules for the one-particle spectral function to quantify the idea that it is more difficult to add an electron than to extract one in a system with strong local repulsion. Our results explain the striking asymmetry in the tunneling spectra of underdoped cuprates which increases with underdoping. We also propose a novel method, based on ratios of sum rules, to estimate local density variations in inhomogeneous materials. Using a variational approach, we show that the origin of the particle-hole asymmetry lies in the incoherent spectral weight.     

Parity Projected QCD Sum Rule of the Nucleon with MEM

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. We derive the parity projected nucleon sum rules with all known first order α _s corrections to the Wilson coefficients of the operator product expansion (OPE). As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. This phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.     

A Comparative Study of fB within QCD Sum Rules with Two Typical Correlators up to Next-to-Leading Order

The B-meson decay constant f_B is an important component for studying the B-meson decays, which can be studied through QCD sum rules. We make a detailed discussion on f_B from two sum rules up to next-to-leading order, i.e. sum rules I and II, which are derived from the conventional correlator and the correlator with chiral currents respectively. It is found that these two sum rules are consistent with each other. The sum rules II involves less non-perturbative condensates as that of sum rules I, and in principle, it can be more accurate if we know the dimension-four gluon condensate well. It is found that f_B decreases with the increment of m_B, and to compare with the Belle experimental data on f_B, both sum rules I and II prefer smaller pole b-quarkmass, m_b=4.68±0.07 GeV. By varying all the input parameters within their reasonable regions and by adding all the uncertainties in quadrature, we obtain f_B=172^{+23}_{-25} MeV for sum rules I and f_B=214_{-34}^{+26} MeV for sum rules II.     

Bound-state perturbation method via SVZ sum rules in quantum mechanics

The perturbation method for bound states within the framework of the Shifman-Vainshtein-Zakharov sum rule method is studied on simple systems (linear harmonic oscillator, hydrogen atom) in external electric fields. It is pointed out that for stronger fields reasonable results for the ground-state energy can only be achieved when sum rules are written for the correction to the Euclidean Green function caused by the external field. Moreover, if the system is bound by a singular (Coulomb) potential, one needs to sum higher perturbative corrections to the Green function and to find a realistic approximation of the continuum contribution to the sum rules. The results are of relevance e.g. for calculations of nucleon magnetic moments and toponium properties via SVZ sum rules in QCD.     

On QCD sum rules of the Laplace transform type and light quark masses

We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in QCD. Two specific examples corresponding to the ?-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwyler's formula for the current algebra quark masses is also given.     

Sum rules from boundary dispersion relations

Sum rules for inelastic reactions are derived from boundary dispersion relations. If sufficient data or a model is available for the amplitude in the direct channel, then these sum rules provide a means of studying the dynamics in the cross channel. The convergence of these sum rules is investigated, assuming they can be saturated with narrow-width resonances, and rough estimates of the coupling constants of cross-channel exchanges for the photoproduction of pseudoscalar mesons are obtained.     

Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension condensates containing at least one pair. We extract the direct single-instanton contribution to the sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel. Received: 15 September 1997 / Revised version: 15 November 1997 / Published online: 26 February 1998     

Equal time commutators of spatial components of axial charges and corresponding sum rules

We derive a set of sum rules by saturating the equal-time commutator of integrated space components of axial currents between nucleon states at rest. The relation of these sum rules to the SU(6) results is discussed.     

Exact sum rules for inhomogeneous systems containing a zero mode

We show that the formulas for the sum rules for the eigenvalues of inhomogeneous systems that we have obtained in two recent papers are incomplete when the system contains a zero mode. We prove that there are finite contributions of the zero mode to the sum rules and we explicitly calculate the expressions for the sum rules of order one and two. The previous results for systems that do not contain a zero mode are unaffected.     

Optical sum rules that relate to the potential energy of strongly correlated systems

A class of sum rules for inelastic light scattering is developed. We show that the first moment of the nonresonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the sum rules provides information about the electronic excitations in different regions of the Brillouin zone. We determine the sum rule for the Falicov-Kimball model, which possesses a metal-insulator transition, and compare our results to the light scattering experiments in SmB(6).     

Dispersion relation approach to the anomalous magnetic moment in gauge theories

The reason why the dispersion relations for the anomalous magnetic moment are not valid in gauge theories is explained. New sum rules are derived based on unitary bounds of scattering amplitudes. In gauge theories these sum rules give the correct values for the anomalous magnetic moment, while, in the case of conventional renormalizable theories which contain no massive vector bosons, they are identical with the usual dispersion relations for the anomalous magnetic moment.     

Sum rules for baryonic vertex functions and the proton wave function in QCD

We consider light-cone sum rules for vertex functions involving baryon-meson couplings. These sum rules relate the non-pertubative, and experimentally known, coupling constants to the moments of the wave function of the proton state. Our results for these moments are consistent with those obtained from QCD sum rules for two-point functions.     

QCD sum rules and pion wave functions

We consider light cone sum rules for a vertex function involving a pion state. These incorporate radiative corrections, continuum effects and power corrections; the latter depend on the non-asymptotic form of a higher twist component of the pion wave function. We derive restrictions on this component from sum rules for two-point functions and propose a model wave function for it. Finally we analyse our vertex sum rules in the light of this information and find results for the lowest twist component in good agreement with those already obtained from two-point function sum rules with derivative currents.     

What neutronos will tell about gauge theories

Neutrino and antineutrino scattering experiments will help determine which, if any, unified gauge theory of weak interactions and electromagnetism is correct. We derive two sum rules for scattering from targets with roughly equal numbers of protons and neutrons, and show how they may be tested most easily by experiment.