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.     

Exploring light-cone sum rules for pion and kaon form factors

We analyze the higher-twist effects and the SU(3)-flavor symmetry breaking in the correlation functions used to calculate form factors of pseudoscalar mesons in the QCD light-cone sum rule approach. It is shown that the Ward identities for these correlation functions yield relations between twist-4 two- and three-particle distribution amplitudes. In addition to the relations already obtained from the QCD equations of motions, we have found a new one. With the help of these relations, the twist-4 contribution to the light-cone sum rule for the pion electromagnetic form factor is reduced to a very simple form. Simultaneously, we correct a sign error in an earlier calculation. The updated light-cone sum rule prediction for the pion form factor at intermediate momentum transfers is compared with the recent Jefferson Lab data. Furthermore, from the correlation functions with strange-quark currents the kaon electromagnetic form factor and the weak transition form factors are predicted with accuracy. Received: 30 June 2002 / Published online: 7 October 2002 RID="a"     

QCD sum rules for pion wave function revisited

We analyze new QCD sum rules for the pion wave function (WF) ?_π (x), obtained recently in [1] in the non-local vacuum condensates method for non-diagonal correlators, and suggest a new approach for extracting WF of the π-meson and the mass and WF of the first resonance. As a result, we obtain approximately the same form of the pion WF by two different methods and for two different ansatzes of non-local quark condensates. We predict the mass of the π′-resonance and obtain the form of its WF.     

x-space sum rules and the pion wave function in QCD

From two-point correlators of (derivative) axial currents we construct sum rules in Euclidean configuraton space for the moments of the pion wave-function. Analysis of these sum rules gives a value of the second moment \(\left\langle {\xi ^2 } \right\rangle \) compatible with those obtained from conventional sum rules but in disagreement with that obtained in a recent lattice calculation.     

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.     

Vertex QCD sum rules,quark model and pion wave function

It is shown that the predictions of the QCD sum rules (SR) and the quark model for the low energy pion wave function can be reconciled within the so-called vertex SR in exclusive kinematics. In contrast to the standard procedure, non-singular terms asx→0 in correlation functions are summed up by means of the conformal symmetry arguments. The soft contribution into the pion form factor is argued to dominate at least up toQ ²～4–6 GeV²     

Moments of the heavy-quark parton distribution function from QCD sum rules

The moments of the heavy-quark parton distribution functions in a heavy pseudoscalar meson are calculated from QCD sum rules. Expanding these sum rules in the inverse heavy-quark mass we obtain the heavy-mass limits of the moments. Comparison with the finite-mass results reveals that while the heavy-mass expansion works reasonably well for the b quark, one has to take into account terms of higher order than (1/m _c )² for the c quark. This result can provide a quantitative assessment of c- and b-quark fragmentation models based on the heavy-quark mass limit. The text was submitted by the authors in English.     

Symmetry energy from QCD sum rules

We review the symmetry energy in the context of AdS/CFT correspondence. After constructing D -brane configurations corresponding to dense system in boundary theory, we calculate the symmetry energy by solving DBI action of D branes in confining and deconfining phase. We conclude that the density dependence of the symmetry energy has scaling law, whose power depends only on the dimensionality of the branes and space-time.     

Revisiting hidden-charm pentaquarks from QCD sum rules

We revisit hidden-charm pentaquark states P_c(4380) and P_c(4450) using the method of QCD sum rules by requiring the pole contribution to be greater than or equal to 30% in order to better that the one-pole parametrization is valid. We find two mixing currents, and our results suggest that P_c(4380) and P_c(4450) can be identified as hiddencharm pentaquark states having J~P= 3/2~-and 5/2~+, respectively. However, there still exist other possible spin-parity assignments, such as J~P = 3/2~+ and J~P = 5/2~-, which must be clarified in further theoretical and experimental studies.     

Nucleon charge radius from QCD sum rules

The proton and neutron electric radii are calculated within QCD using the sum rules method for processes with small momentum transfers. The agreement with experimental values is good for the proton radius and somewhat poorer for the neutron one due to the numerical smallness.     

Nucleon distribution amplitudes from lattice QCD

We calculate low moments of the leading-twist and next-to-leading-twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MS[over ] scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature.     

Evaluation of the Skyrme parameter from QCD sum rules

The dimensionless parameter of the Skyrme lagrangian is evaluated by two methods. In one a combination of sum rules for the nucleon and the pion is used, in the other only baryonic sum rules. e = 5−8 and e = 5−7 is found, respectively, in agreement with the phenomenological value e = 5.45. To leading order in the operator-product expansion the analytical expression of e does not depend on the chiral-symmetry-breaking parameters.     

Electromagnetic form factors of the nucleon from perturbative QCD and QCD sum rules

Perturbative quantum chromodynamics (QCD) and QCD sum rules are combined to calculate nucleon wave functions in the light-cone framework. The use of these wave functions leads to predictions for the Dirac form factors of the proton and neutron which are in remarkable agreement with experiment.     

QCD sum rules versus experiment

We show the compatibility of Shifman, Vainshtein and Zakharov (SVZ) sum rules with the sum rules involving the electro-magnetic mass difference of pions and the axial form factor in radiative π^± decay. In spite of good agreement between them, QCD sum rules are unable to explain clearly the experimental data of τ-decay in the axial channel.