Direct instantons in QCD nucleon sum rules

Abstract

We study the role of direct (i.e. small-scale) instantons in QCD correlation functions for the nucleon. They generate sizeable, 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.12.38. Lg, 14.20.Dh Typeset using REVT E X 1 QCD sum rules, introduced by Shifman, Vainshtein and Zakharov (SVZ) [1], provide a systematic, nonperturbative framework for the calculation of hadron properties. They have been intensely studied and applied over the last decade and produced the most exhaustive model-independent analysis of hadron properties to date.The sum-rule approach is based on the comparison of two "dual" descriptions for correlation functions of hadronic currents, in terms of quarks and gluons on the left-hand side (LHS) and in terms of hadrons on the right-hand side (RHS). The RHS uses a simple parametrization of the spectral function in terms of the hadron parameters, such as mass, overlap with the source current and continuum threshold. The QCD calculation on the LHS employs a non-perturbative operator-product expansion (OPE). Long-distance bulk properties of the physical vacuum are efficiently parametrized in terms of the vacuum expectation values of composite quark-gluon operators ("condensates"), which are independent of the hadron considered. The short-distance physics is contained in the perturbatively calculated Wilson coefficients. The inverse renormalization scale of the operators, µ −1 , serves as the dividing line separating long and short distances.Both sides of the sum rules are then Borel-transformed, and the hadron parameters are determined by fitting the two sides in the fiducial region, i.e. in the range of Borel mass values in which both descriptions of the correlator are expected to be adequate. The quality of this fit is the only intrinsic criterion for the accuracy and reliability of the sum rules. If it is met sufficiently well, the resulting hadron parameters will be approximately independent of the Borel mass in the fiducial region. The nucleon sum rules, however, do not show such a stability plateau, despite many improvements over the last decade [2]. It seems that some relevant physics in the fiducial region (around 1 GeV) is missing in the OPE. In this letter we suggest that small-size instantons [3], termed "direct" by SVZ, provide the dominant part of this physics.Instantons [4] are classical solutions of the euclidean Yang-Mills equation. Due to the infrared complexities of QCD, their quantum properties and vacuum distribution cannot yet be derived from first principles. A consistent picture of their importance and bulk 2 features has been established, however, by extensive phenomenological [5,6], analytical [7] and numerical studies (in the instanton liquid model [6] and on the lattice, e.g. in ref.[8]).They indicate, in particular, that the average instanton size ρ c in the vacuum is considerably smaller th...

The electromagnetic pion form factor and instantons

“…Indications supporting this expectation have been found in an analogous study of the nucleon correlation functions [19]. The applicabilty of the sum rule at small Q 2 would then be mainly limited by the unphysical singularity in the perturbative contribution (13). [6].…”

“…In order to allow for a direct comparison with the instanton analysis of the two-point correlator [5], which takes K = 0.7 GeV, we fix K at the lower limit of the phenomenologically acceptable range, K = 1.0 GeV. The effective mass m * , finally, is determined as in [5,13] from the self-consistency relation [8] for the quark condensate, qq = −2n/m * (ρ).…”

Scalar gluonium and instantons

“…In contrast to previously studied IOPE sum rules for quark-based correlators [14,15], those for the scalar glueball are the first where (i) the instanton contributions do not enter via topological quark zero-modes and (ii) the sum rules reach a satisfactory (though not excellent) level of consistency even without any perturbative and soft contributions, i.e., with the instanton terms alone. The latter result explains why the instanton liquid model yields scalar glueball properties similar to those obtained above [10], and can be traced to both the exceptional strength and the particular shape (mainly the curvature) of the instanton contributions.…”

“…[9]). Analogous contributions were found to be important in several nucleon [14] and pion [15] To leading order in the semiclassical approximation, the instanton contribution to Eq.…”

Calculation of 〈p‖u¯u-d¯d‖p〉 from QCD sum rules and the neutron-proton mass difference

“…Further, in the chiral-even sum rule the single pole term corresponding to transition between proton and the excited states dominated over the double pole term. We would also like to point out that inclusion of instanton contributions improves the chiral-even mass sum rule [31]. In the light of our observations above regarding the relation of our sum rules to the mass sum rules it suggests that such instanton contributions can also be significant in our sum rule Eq.…”