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.     

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.     

What QCD sum rules tell about the rho meson — A new answer to an old question

First, a historical overview is presented concerning the use of QCD sum rules to learn about the p-meson properties at finite nuclear densities. Second, it is shown that the combination of the sum rule technique with the large-N _c expansion provides new insight. Especially it is possible to determine from the in-medium sum rules a vacuum(!) quantity which is an important ingredient for hadronic in-medium calculations of the p-meson spectral function. This quantity is the coupling strength of the p-nucleon system to the baryonic resonance N^*(1520).     

Models with rising cross sections and the inverse amplitude sum rules

Models for pion-nucleon scattering with rising cross sections are analyzed using dispersive sum rules which are valid for the inverse of the scattering amplitude. The validity of these sum rules is intimately connected with the positivity of Im T(s, t = 0). A numerical analysis shows that some of the models have difficulties when analytically continued into the complex energy plane.     

Sum rules in QCD for g ηΛΛ and g πΛΣ

New relations between the Borel QCD sum rules for the strong couplings of the Σ⁰ and Λ hyperons are derived. It is shown that, using the sum rules for g _MΣΣ, M = π ⁰, η, as a starting point, one can readily obtain the corresponding sum rules for the coupling constants g _ηΛΛ and g _πΛΣ ⁰. The values of these constants are calculated in a specific parameter region.     

A class of modified sum rules in QCD

We consider a class of modifications to the exponential QCD sum rules, replacing the energy variableq ² by (q ²) ^k withk positive integer. As a result of this modification, (i) the relative role of the condensates on the theoretical side is changed, (ii) the integral on the phenomenological side acquires a rapidly decreasing weight function and (iii) the way of approaching infinity in theq ² complex plane splits intok rays. We explicitly discuss the modified sum rules withk=1,k=2 andk=3 for the ρ meson and conclude that, unlike to thek=1 case, thek=2 andk=3 sum rules do not yield a satisfactory scheme for the prediction of the resonance parameters unless many higher condensates are known. We show that, for practical applications with the present knowledge of condensates, the standard exponential QCD sum rules are the most suitable ones out of the class considered.     

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.     

Infrared renormalons and the relations between the Gross-Llewellyn Smith and the Bjorken polarized and unpolarized sum rules

It is demonstrated that the infrared renormalon calculus indicates that the QCD theoretical expressions for the Gross-Llewellyn Smith sum rule and for the Bjorken polarized and unpolarized ones contain an identical negative twist-4 1/Q² correction. This observation is supported by the consideration of the results of calculations of the corresponding twist-4 matrix elements. Together with the indication of the similarity of the perturbative QCD contributions to these three sum rules, this observation leads to simple new theoretical relations between the Gross-Llewellyn Smith and Bjorken polarized and unpolarized sum rules in the energy region Q² ≥ 1 GeV². The validity of this relation is checked using concrete experimental data for the Gross-Llewellyn Smith and Bjorken polarized sum rules.     

Contribution of higher gluon condensates to light-quark vacuum polarization

A method of classifying quark operators in QCD sum rules is suggested. The expansion coefficients of all thed≦8 bilinear quark condensates in gluon condensates are calculated. The coefficient functions at the gluon operators withd≦8 in the polarization operator ∏(q ²) of the light-quark vector current are obtained. A comparison is performed with the calculations in the covariantly constant fields and self-dual fields. The results obtained can be used in the sum rules for the ρ, ω and ? families.     

QCD determination of theA 1-ρ-π system through vertex light-cone sum rules

We analyze the ρ-A ₁-π system within the context of vertex light-cone sum rules, which are believed to be rigorously satisfied in QCD. It is pointed out that these sum rules provide very strong constraints on the hadronic spectrum and with additional assumptions lead to new predictions, which go significantly beyond those obtained from current algebra in the past. In particular, we report some new results about the ρ-A ₁-π couplings and the various transition form factors in τ-semi-leptonic decays.     

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by 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. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T _c , while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T _c or higher for S-wave and about 2.0 T _c for P-wave states.     

Exchange ofA 1 andZ 1 (J PC=2−−) mesons in charged pion photoproduction

Finite energy sum rules are evaluated for the amplitudes corresponding to the exchange of theA ₁ and its exchange degenerate partner, theZ ₁ (J ^PC=2^??), in charged pion photoproduction. Both sum rules are roughly compatible with theoretical estimates of these exchanges, and a definiteA ₁ signal found.     

Chiral-limit theorems and corrections to PCAC in a model for the scalar Kℓ3 divergence form factor

Three sum rules on vertex functions are derived by applying a model on two-particle Kπ channels. SU(3) × SU(3) breaking is introduced by corrections to the PCAC forms of the axial currents. Taking the m_π → 0 limit the sum rules reduce to the Callan-Treiman theorem, a recent theorem by Dashen, Li, Pagels and Weinstein (DLPW) and a third relation. We encounter non-analytic correction terms in the two first sum rules. In the DLPW theorem we find, contrary to a previous suggestion, non-negligible ε and ε²ln ε terms which are due to the large K-mass. These terms are responsible for a curvature of the scalar K_?3 form factor, however negative values of the slope at the origin require also substantial SU(2) × SU(2) violations. The numerical results taking into account physical masses compare favourably with K_?3 decay and also with s-wave Kπ scattring data.     

QCD sum rules for the coupling constants <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">KYN</Emphasis></Subscript> and <Emphasis Type="Italic">g</Emphasis><Subscript>KYΞ</Subscript>

New relations between Borel QCD sum rules for the strong couplings of baryons to kaons are derived. It is shown that, on the basis of the sum rules for the coupling constants g _πΣΣ and g _πΣΛ, the corresponding sum rules can be directly obtained for the coupling constants g _KYN and g _KYΞ, Y = Σ,Λ. The values of these coupling constants are calculated in the fiducial interval 1.0 ≤ M ² ≤ 1.4 GeV² at t = ?1.     

Non-vanishing of the bare triple-Pomeron coupling from s-channel unitarity

In the crossing symmetric Reggeon calculus based on the $\text{1}\text{N}$ expansion, s-channel unitarity sum rules are written down explicitly to each order in $\text{1}\text{N}$. Some of the lowest order sum rules are shown to imply a non-vanishing bare triple-Pomeron coupling at t = 0, irrespectively of the bare Pomeron intercept.     

Comprehensive sum rules for s-wave amplitudes of nonleptonic hyperon decays

Sum rules for the S-wave amplitudes of the nonleptonic hyperon decays are discussed. A new sum rule √12(Λ₀⁰ + Ξ₀⁰) = (∑_?^? ? ∑₊⁺) is proposed as one of the comprehensive sum rules in the SU(4) symmetry theory.     

Sum rule approach to the nuclear response in the isovector spin channel

We study the global features of the response of infinite nuclear matter in the spin-isospin channel through the energy-weighted sum rules S₁ and S_?1. In particular we compare the outcome of the ring approximation with the exact RPA evaluation of the sum rules. We also investigate the influence of the collective character of the response, induced by the particle-hole force for longitudinal and transverse spin couplings. We show that S₁ is insensitive to the collectivity of the response, as long as the Δ-degree of freedom is ignored. The inverse energy-weighted sum rule on the other hand, which is linked to the paramagnetic susceptibility, always reflects the hardening or softening of the nuclear response, due to the repulsive or attractive character of the p-h force. This quantity is well suited to the comparison with the experiments, which we perform for ¹²C and ⁵⁶Fe.     

Use and misuse of QCD sum rules,factorization and related topics

The purpose of this paper is twofold. First, we are prompted by some recent publications to reply to the criticism of the QCD sum-rules approach contained therein. Hopefully, some of the discussion is of wider interest. In particular, we point out that the multi-gluon operators unlike the multi-quark ones, relevant to the sum rules, do not factorize at large N_c. This implies that the masterfield, even if it is found, will be of no immediate help in evaluating the quarkonium spectrum. Second, we derive new sum rules for light quarks which are sensitive to the mean intensity of the gluon field in the vacuum (the so-called gluon condensate, or 〈vac|G²|vac〉). New sum rules confirm the standard value of 〈vac|G²|vac〉. Some casual remarks on the π⁰ transitions into two virtual photons, π⁰ → γ^*γ^*, are also presented. Finally, we enumerate (in sect. 7) basic points of the sum-rule approach and discuss, im brief, the unsolved problems.