What can we learn from sum rules for vertex functions in QCD?

We demonstrate that the light-cone sum rules for vertex functions based on the operator product expansion and QCD perturbation theory lead to interesting relationships between various non-perturbative parameters associated with hadronic bound states (e.g. vertex couplings and decay constants). We also show that such sum rules provide a valuable means of estimating the matrix elements of the higher spin operators in the meson wave function.     

Form factors of γ * ρ → π and γ * γ → π 0 transitions and light-cone sum rules

The method of light-cone QCD sum rules is applied to the calculation of the form factors of and transitions. We consider the dispersion relation for the amplitude in the variable . At large virtualities and , this amplitude is calculated in terms of light-cone wave functions of the pion. As a next step, the light-cone sum rule for the form factor is derived. This sum rule, together with the quark-hadron duality, provides an estimate of the hadronic spectral density in the dispersion relation. Finally, the form factor is obtained taking the limit in this relation. Our predictions are valid at and have a correct asymptotic behaviour at large . Received: 16 January 1998 / Revised version: 14 May 1998 / Published online: 26 August 1998     

QCD sum rules in exclusive kinematics and pion wave function

We suggest a modification of the QCD sum rules for three-point correlation functions that relates hadron expectation values of an operator of interest to properties of the QCD vacuum in alternating external fields. A new sum rule is obtained for the nucleon magnetic moments. Relations are found between the couplings g_πNN , g_ρωπ and the value of the pion wave function at the point with equal momentum carried by the quark and the antiquark. Our results seem to exclude the possibility of having a pronounced dip in the pion wave function in the middle point, as has been assumed on the evidence of a large value of the second moment.     

Conformal invariance and pion wave functions of nonleading twist

The restrictions are studied for the general structure of pion wave functions of twist 3 and twist 4 imposed by the conformal symmetry and the equations of motion. A systematic expansion of wave functions in the conformal spin is built and the first order corrections to asymptotic formulae are calculated by the QCD sum rule method. In particular, we have found a multiplicatively renormalizable contribution into the two-particle wave function of twist 4 which cannot be expanded in a finite set of Gegenbauer polynonials.     

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.     

What QCD sum rules tell about the rho meson

Using a simple parametrization of Breit-Wigner type for the hadronic side of the QCD sum rule for ϱ mesons in vacuum as well as in a nuclear medium we explore the range of values for the mass and the width of the ϱ meson, which are compatible with the operator product expansion.     

Improved calculations of quark distributions in hadrons: the case of the pion

The earlier introduced method of calculation of quark distributions in hadrons, based on QCD sum rules, is improved. The imaginary part of the virtual photon forward scattering amplitude on some hadronic current is considered in the case, when initial and final virtualities of the current , and are different, . The operator product expansion (OPE) in , is performed. The sum rule for quark distribution is obtained using double dispersion representation of the amplitude on one side in terms of calculated in QCD OPE and on the other side in terms of physical states contributions. Double Borel transformation in , is applied to the sum rule, killing background non-diagonal transition terms which deteriorated the accuracy in previous calculations. The case of the valence quark distribution in the pion is considered, which was impossible to treat by the previous method. OPE up to dimension 6 operators is performed and leading order perturbative corrections are accounted. Valence u-quark distribution in was found at intermediate x, , and normalization point . These results may be used as input for evolution equations. Received: 14 July 1999 / Published online: 6 March 2000     

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H¨older-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters(the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α_s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.     

SYNTHESIS OF PERTURBATIVE AND NONPERTURBATIVE QUANTUM CHROMODYNAMICS

Hadronic structure in QCD has been analyzed by using the Fock state wavefunctions of hadrons defined by quantizing quantum chromodynaraics at equal time of the light-cone. They provide a unified approach to QCD phenomenology. We have presented a convenient method for operator product expansion in the external background fields and have obtained the distributior: amplitude moments values from QCD sum rule by introdution the condensate effect of quarks and gluons. These results are in agreement with the present data.     

Gaussian sum rules in quantum chromodynamics and local duality

A new type of hadronic sum rules are studied in QCD. They correspond to the Gauss-Weierstrass transform of hadronic spectral functions. There is an interesting analogy between these sum rules and the theory of the heat equation which provides a useful framework for formulating quantitatively the notion of local duality. In particular, finite energy sum rules are shown to follow within this framework from the principle of conservation of total heat. Explicit calculations of these sum rules in QCD - from both perturbative and non-perturbative contributions à la Shifman, Vainshtein and Zakharov [1] - have been made in a rather general way which should cover all the practical cases involving light quark systems. A particular case of the -spectral function and its duality to QCD is discussed in detail as an illustration of this new approach.     

The second moments of quark and gluon distribution functions in nucleon

The second moments of quark and gluon distribution functions in proton are calculated on the basis of the QCD sum rule approach. The results obtained are in a good agreement with the experimental data.     

Best values for the CP-odd meson–nucleon couplings from supersymmetry

In the supersymmetric models, the dominant sources of the hadronic flavor-diagonal CP violation at low energy are the theta term and the chromoelectric dipole moments of quarks. Using QCD sum rules, we estimate the preferred range and the best values for the CP-odd meson–nucleon coupling constants induced by these operators. When the theta term is removed by the axion mechanism, the size of the most important isospin triplet pion–nucleon coupling is estimated to be , where chromoelectric dipole moments are given in units of 10⁻²⁶ cm.     

Measurement of the quark and gluon fragmentation functions in Z^0 hadronic decays

The transverse, longitudinal and asymmetric components of the fragmentation function are measured from the inclusive charged particles produced in collisions at LEP. As in deep inelastic scattering, these data are important for tests of QCD. The transverse and longitudinal components of the total hadronic cross section are evaluated from the measured fragmentation functions. They are found to be and respectively. The strong coupling constant is calculated from in next-to-leading order of perturbative QCD, giving Including non-perturbative power corrections leads to The measured transverse and longitudinal components of the fragmentation function are used to estimate the mean charged multiplicity, The fragmentation functions and multiplicities in and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated. Received: 12 September 1997 / Published online: 19 October 1998     

Non-leptonic <Emphasis Type="Italic">B</Emphasis> decays into a charmed tensor meson

In the framework of factorization and the heavy quark effective theory, modes are analyzed. We adopt the result from the QCD sum rule calculation for the hadronic matrix elements at leading order of and . The QCD sum rule results are well compatible with the current data, with the prediction for the branching ratios and for . We give constraints on the interception and the slope parameter of the leading Isgur-Wise function from the experimental bounds. It is argued that the observation of non-zero directly measures the non-factorizable effects. Received: 18 July 2002 / Revised version: 21 October 2002 / Published online: 14 March 2003 RID="a" ID="a" e-mail: jplee@phya.yonsei.ac.kr     

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).     

QCD Sum Rules and J/ψ Suppression in Hot Hadronic Matter and Quark-Gluon Plasma

A consistent treatment based on the QCD sum rules at finite temperature has been established to calculate the J/ψ suppression in hot hadronic matter (HM) and quarkgluon plasma (QGP) respectively. We have found that the J/ψ suppression occurs in both hadronic matter and quark-gluon plasma, but a J/ψ mass shift of about 0.49 GeV exists in QGP background only. The results obtained by QCD sum rules and by potential model are compared.     

The QCD sum rule for the delta (1232) in the instanton medium

The QCD sum rule for the Δ (1232) is considered in the instanton medium. It is found that the instanton effect improves the chirally odd sum rule significantly. This indicates that the operator product expansion does not converge rapidly in the delta state. The chirally even sum rule of Δ suggests that the “standard” value of the higher dimensional condensate m₀ is much smaller than that derived from the instanton model.     

Restrictions on exact current correlation functions and reliability of sum-rule results

Criteria of reliability are studied for results obtained within the sum-rule approach in QCD and in some toy models. The criterion of validity of the approximation for current correlation functions based on operator-product expansion within Borel sum rules, suggested previously in the literature, is critically reexamined. A new criterion of validity of a perturbative approximation that makes use of the Källen-Lehmann representation and finite-energy sum rules is proposed. The stability of criteria against small variations in expansion coefficients is investigated in an exactly solvable model and in QCD.