QCD sum rule for nucleon in nuclear matter

We consider the two-point function of nucleon current in nuclear matter and write a QCD sum rule to analyse the residue of the nucleon pole as a function of nuclear density. The nucleon self-energy needed for the sum rule is taken as input from calculations using phenomenological N N potential. Our result shows a decrease in the residue with increasing nuclear density, as is known to be the case with similar quantities.     

Sum rules and the pion form factor in QCD

We propose a new approach to the investigation of the pion electromagnetic form factor in QCD based on the systematic use of the QCD sum rule technique. The theoretical curve obtained for F_π(Q²) is in good agreement with existing experimental data.     

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.     

The Fubini-Furlan-Rossetti sum rule revisited

The Fubini-Furlan-Rossetti sum rule for pion photoproduction on the nucleon is evaluated by dispersion relations at constant t, and the corrections to the sum rule due to the finite pion mass are calculated. Near threshold these corrections turn out to be large due to pion-loop effects, whereas the sum rule value is closely approached if the dispersion integrals are evaluated for sub-threshold kinematics. This extension to the unphysical region provides a unique framework to determine the low-energy constants of chiral perturbation theory by global properties of the excitation spectrum.     

Electronuclear sum rules. Improved realization and statement. Experiment and theory for4He

The experimental (e, e′) data in the region of highω, necessary for a reliable check of sum rules, are either unavailable or dominated by pion degrees of freedom. To calculate the corresponding sums over (e, e′) spectra, a reliable extrapolation of spectra to this region is proposed. It is based on a quasi-y-scaling type behavior of the spectra. It is shown that the sum rule version corresponding to the summation of the spectra at constantE ₀ andθ, being simplest from the experimental viewpoint, can be made accurate enough if an experimental spectrum is used to estimate the parameters involved in it. It is found that for⁴He nucleus, one of the existing groups of the experimental spectra is in a good agreement with the model-independent sum rule which corresponds to the single-particle approximation for the interaction of a nucleus with an electromagnetic field, while the second group of spectra leads to a considerable deviation from the sum rule.     

The decay π → eνγ: PCAC quark model

We reexamine the PCAC sum rule for radiative pion decay, allowing for a singular short-distance behaviour of the axial divergence. It is shown that the sum rule of Das, Mathur and Okubo follows from a weak form of PCAC even if the axial divergence is allowed to have dimension three, appropriate for free (or asymptotically free) quarks. We find no quark mass corrections.     

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"     

The Fubini-Furlan-Rosetti sum rule and related aspects in light of covariant baryon chiral perturbation theory<Superscript>⋆</Superscript>

We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading-order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E₀₊.     

Spin asymmetry and Gerasimov-Drell-Hearn sum rule for the deuteron

An explicit evaluation of the spin asymmetry of the deuteron and the associated Gerasimov-Drell-Hearn sum rule is presented which includes photodisintegration, and single and double pion and eta production as well. Photodisintegration is treated with a realistic retarded potential and a corresponding meson exchange current. For single pion and eta production the elementary operator from MAID is employed, whereas for double pion production, an effective Lagrangian approach is used. A large cancellation between the disintegration and the meson production channels yields for the explicit GDH integral a value of 27.31 microb to be compared to the sum rule value 0.65 microb.     

The Adler-Weisberger sum rule

Starting from a weak form of the axial current algebra and usingFubini's covariant dispersion method we give a fairly rigorous derivation of the Adler-Weisberger sum rule. Special attention is given to the necessary continuation in the “pion mass”. Combining the sum rule with the forwardπ ^± p dispersion relation we obtain a sum rule containing essentially low energy data. A numerical evaluation is given for two sets of existing s-waveπN scattering lengths. The one reproducesAdler's andWeisberger's results, the other improves the agreement with experiment giving r_A=1.20.     

Gottfried sum rule and the shape ofF 2 ⌍ -F 2 ⌍

The recent experimental determination of the Gottfried sum rule of deep inelastic scattering provides strong evidence that SU(2) flavor symmetry is broken by the sea quark distributions of the nucleon. Two mechanisms have been suggested to explain the data: Pauli blocking and non-perturbative contributions to the sea arising from the pion cloud surrounding the nucleon. We investigate the effects of these two mechanisms on several standard parametrizations of the quark distribution functions and find that each mechanism has different effects on the shapes of these distribution functions. The best agreement between the experimental data and the modified quark distributions occurs when both mechanisms are taken into account using a softπNN form factor and a small Pauli correction.     

Isovector kaon form factor in the dispersion theory and S-wave π K-scattering lengths

A one-dimensional integral representation for isovector kaon form factor is constructed within the dispersion theory in terms of the pion form factor and the backwardπK-scattering amplitude. The normalization condition for isovector kaon form factor at zero momentum transfer gives a sum rule for theπK-scattering amplitude, with the use of which difference between thes-waveπK-scattering lengths in triplet and singlet isospin states is estimated to bea ₀ ^3/2 - a ₀ ^1/2 ≈μ ^{? 1} whereμ is the pion mass. In agreement with the vector-meson-dominance model, deviations of the isovector kaon form factor from half of the pion form factor are found to be small.     

OPE and sum rules for correlators of pseudoscalar and axial currents

We study the operator product expansion (OPE) and quark-hadron duality for two-and three-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit, these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the two-point correlators, we show the sum rule for 〈PP〉 to be sensitive to the excited light pseudoscalar. For the three-point correlators, we derive the Ward identities which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behavior of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the 〈PV P〉 and 〈AV P〉 correlators. The local-duality sum rule for 〈AV A〉 is shown to lead to the pion form factor with the required properties for all values of the momentum transfer. The text was submitted by the authors in English. On leave from Institute of Nuclear Physics, Moscow State University, Moscow, Russia.     

The contribution of pion absorption with two-nucleon emission to the pion-nucleus optical potential

Four terms in the pion-nucleus optical potential which arise from pion absorption with two nucleon emission are calculated using a model in which the nucleon is treated as a bound state of a pion and a nucleon. The contribution of these terms to the reaction cross section of carbon is considered. Two of the terms give rise to a negative reaction cross section, but it is shown that the sum of the four is positive definite. We find that the absorption reaction cross sections are very sensitive to the off-shell behavior of the free pion-nucleon T-matrix.     

The subtraction constant in π± electroproduction

A method is proposed for dealing with the subtraction constant required in fixed-t dispersion relations for π^± electroproduction. The method requires a knowledge of the t-channel cut contribution (evaluated at the subtraction points s₀), which can be determined at k² = 0 using a gauge invariance sum rule. Estimates by this and other methods show that it is small (compared with the pion pole contribution) for ?t ? 1 GeV², and in particular it is irrelevant to determinations of the pion form factor using high-energy forward π⁺ data.     

Valence-Quark-Mixing Contribution to Gottfried Sum Rule

We have discussed the effect of valence quark mixing in DIS process.This effect,together with the pion cloud effect,dominates the violation of Gottfried sum rule.     

Revisiting the vector and axial-vector vacuum susceptibilities

We re-investigate the vector and axial-vector vacuum susceptibilities by taking advantage of the vector and axial-vector Ward–Takahashi identities. We show analytically that, in the chiral limit, the vector vacuum susceptibility is zero and the axial-vector vacuum susceptibility equals three fourths of the square of the pion decay constant. Besides, our analysis reproduces the Weinberg sum rule.     

On the Laplace transform of the Weinberg type sum rules and on the properties of pseudoscalar mesons

We reanalyse the Weinberg type sum rules in the light of the Laplace transform sum rule and including the leading non-perturbative effects. We then estimate the light quark invariant masses \(\hat m_s /\hat m_d ,\hat m_u \hat m_d \) ; the pion decay amplitudef _π and theA ₁ coupling and mass. Using other type of sum rules, we derive bounds on the pseudoscalar decay amplitudesf _p (P≡π, K, D, F) as well as on the gluon component of theU(1) _A meson mass. Our main results are summarized in Sect. 4.     

Nucleon spin with and without hyperon data: a new tool for analysis

We present a simple explanation of the underlying physics in the use of hyperon decay data to obtain information about proton spin structure. We also present an alternative input using nucleon magnetic moment data and show that the results from the two approaches are nearly identical. The role of symmetry breaking is clarified while pointing out that simple models explaining the violation of the Gottfried sum rule via pion emission tend to lose the good SU(3) predictions from Cabibbo theory for hyperon decays.     

A causal approximation scheme for the commutator of the axial vector-currents

An approximation scheme which fulfils the causality condition is used to compute the matrix elements of the commutator of two axial-vector currents between one proton state. The commutator sum rule is supposed to be saturated by taking into account the nucleon, theN ^*(3/2, 3/2) resonance, and the partially disconnected pion-proton intermediate states. For the axial current form factors pion pole formulas are assumed. It is shown that only the subtraction constants are relevant for the equal time limit of the commutator and so the equivalence with similar earlier methods is proven.