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.     

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.     

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.     

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     

Twist-3 distribution amplitudes of the pion and kaon from the QCD sum rules

Twist-3 distribution amplitudes of the pion and kaon are studied in this paper. We calculate the first several moments for the twist-3 distribution amplitudes ( and ) of the pion and kaon by applying the QCD sum rules. Our results show that (i) the first three moments of and the first two moments of and of the pion and kaon can be obtained with 30 uncertainty; (ii) the fourth moment of the and the second moment of the can be obtained when the uncertainty are relaxed to 35 ; (iii) the fourth moment of the can be obtained only when the uncertainty are relaxed to 40 ; (iv) we have and after including the -corrections to the perturbative part. These moments will be helpful for constructing the twist-3 wave functions of the pion and kaon.Received: 6 January 2005, Revised: 29 March 2005, Published online: 22 June 2005PACS: 13.20.He, 11.55.Hx     

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.     

QCD sum rules: charmonium

The dimensiond=4 gluon condensateφ ₁ is determined from an analysis of charmonium, taking model dependent estimates ofd=6.8 condensates into account. ForS-waves, there is a compatibility region, where both these and model dependent higher state corrections to ground state dominance are small, enablingφ ₁ to be determined from a fit to the data. ForP-waves the estimated higher dimension contributions are large in the region of ground state dominance, and noφ ₁ determination is possible. Theφ ₁ value obtained from the fit to theS-wave ratios is 3 5 times bigger than that obtained by RRY using the plateau method. The methods are compared for the vector current. We show that the higher state correction used by RRY does not fit the data; and that the plateau method is much more sensitive to thed=6.8 condensates than the ratio used here. When reasonable estimates of both these and the higher state corrections are taken into account, there is compatibility between the two methods.     

Electromagnetic pion radius and dispersion sum rules

A general set of dispersion sum rules is considered for the pion form factor G(t) in the mixed-modulus phase representation. The connection between the distribution of the G(t) complex zeros and the sizes of dispersion integrals along the cut is stated. Under the assumption that G(t) ～ t^α at large t the following restriction on the asymptotic behaviour of G(t) is obtained: |G(t)| ? at^?2 (a>0). Using present experimental data we evaluate the electromagnetic mean squared radius, r_π = 0.71 ± 0.30 fm.     

QCD sum rules at finite temperature

Finite energy and Laplace transform QCD sum rules atT0 are analyzed, and predictions for vacuum condensates are compared with the low temperature expansion of the energy density and pressure. Results show a serious disagreement which indicates a breakdown of the FESR programme already at dimension four, and which invalidates Laplace transform sum rules, at least in their straightforward extension to finite temperature.     

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.     

QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.We wish to thank Dr. Lech Mankiewicz for very helpful discussions. This work was supported by DFG (G. Hess program).     

Current correlation functions,QCD sum rules and vector mesons in baryonic matter

Based on an effective Lagrangian which combines chiral SU(3) dynamics with vector meson dominance, we have developed a model for the forward vector meson-nucleon scattering amplitudes. We use this as an input to calculate the low energy part of the current-current correlation function in nuclear matter. Its spectrum enters directly in the “left-hand side” of QCD sum rules. For the isovector channel we find a significant enhancement of the in-medium spectral density below the ϱ resonane while the ρ meson mass itself changes only slightly. The situation is different in the isoscalar channel, where the mass and peak position of the ω meson move downward while its width increases less drastically than in the ρ meson case. For the φ meson we find almost no mass shift; the width of the peak broadens moderately. We observe a remarkable degree of consistency with the operator product expansion of QCD sum rules in all three channels. We point out, however, that these results cannot simply be interpreted, as commonly done, in terms of a universal rescaling of vector meson masses in matter.