Nucleon Sum Rule Research Articles

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 αs cor- rections 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 sup- presses 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.

Application of the Maximum Entropy Method to QCD sum rules

A new method of analyzing QCD sum rules employing the Maximum Entropy Method, is introduced and is applied successfully to the rho meson, the nucleon and the charmonium at finite temperature. This method enables us to directly obtain the spectral function from the sum rules, without having to introduce any model assumption about its functional form. In the nucleon sum rule, we show that the Gaussian sum rule successfully reproduces the ground state. Dependences on the interpolating field operator are discussed. Finite temperature effects for the charmonium sum rule are incorporated by changes of various gluonic condensates, extracted from lattice QCD. As a result, we find that both J/ψ and ηc dissolve into the continuum already at temperatures around 1.0 ∼ 1.2 Tc.

QCD Sum Rules for Skeptics

A new Monte-Carlo based uncertainty analysis is introduced to quantitatively determine the predictive ability of QCD sum rules. A comprehensive analysis of ground stateρ-meson and nucleon spectral properties is performed. Many of the findings contradict the conventional wisdom of both practitioners and skeptics alike. Associations between the phenomenological fit parameters are particularly interesting as they reveal how the sum rules resolve the spectral properties. The use of derivative sum rules for the determination ofρ-meson spectral properties is shown to be a very unfavorable approach. Most prior nucleon sum rule analyses are based on a sum rule which is found to be invalid; the results are suspect, and should be reevaluated. The “Ioffe formula,” argued by many to qualitatively encapsulate a description of the nucleon mass in terms of the chiral symmetry breaking order parameter ⦠qq⦔ is misleading at best. QCD sum rules are found to be self-consistent without contributions from direct instantons. This implies that instanton effects are adequately accounted for in the nonperturbative vacuum condensates. This in-depth examination of QCD sum rule self consistency paints a favorable picture for further quantitative refinements of the QCD sum rule approach.

Isospin breaking and instantons in QCD nucleon sum rules

We study isospin breaking instanton corrections to the operator product expansion of the nucleon correlation functions. After a comparison with quark model calculations based on the 't Hooft interaction, we examine the role of instantons in the corresponding QCD sum rules. Instanton contributions are found to be absent in the chirally even sum rule, but significant in the chirally-odd one. They improve the consistency of both sum rules and favor a value of the isovector quark condensate close to the chiral estimate.

Determination of the pion-nucleon coupling constant from QCD sum rules

We evaluate the πN coupling constant using a QCD sum rule based on the pion-to-vacuum matrix element of the correlator of two interpolating nucleon fields. The part of the correlator with Dirac structure kγ 5 is used, keeping all terms up to dimension 5 in the OPE and including continuum contributions on the phenomenological side. The ratio of this sum rule to the nucleon sum rule involving condensates of odd dimension yields stable resultswith values of g πn in the range 12±5. The sources of uncertainty are discussed.

Spectral asymmetries in nucleon sum rules at finite density.

Apparent inconsistencies between different formulations of nucleon sum rules at finite density are resolved through a proper accounting of asymmetries in the spectral functions between positive- and negative-energy states.

Direct instantons in QCD nucleon sum rules.

We study the role of direct (i.e., small-scale) instantons in QCD correlation functions for the nucleon. They generate sizable nonperturbative corrections to the conventional operator product expansion, which improve the quality of both QCD nucleon sum rules and cure the long-standing stability problem, in particular, of the chirally odd sum rule.

On contribution of instantons to nucleon sum rules

The contribution of instantons to nucleon QCD sum rules is obtained. It is shown that this contribution does provide stabilization of the sum rules and leads to formation of a nucleon as a bound state of quarks in the instanton field.

Effect of short-range correlation on the nucleon sum rule

The nucleon sum rule is calculated for inelastic electron scattering from nuclear matter in the non-relativistic limit. The effect of short-range correlation (SRC) is presented by using LOCV calculations and the Reid soft-core potential. It is found that the non-relativistic version of Bjorken scaling sets in at a momentum transfer of about 1.1 GeV/c and SRC improves the Coulomb sum rule.