Systematic uncertainties of hadron parameters obtained with QCD sum rules

Abstract

We study the uncertainties of the determination of the ground-state parameters from ShifmanVainshtein-Zakharov (SVZ) sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator Π(µ), which allows one to obtain both the OPE to any order and the spectrum of states. We start with the OPE for Π(µ) and analyze the extraction of the square of the ground-state wave function, R ∝ |Ψ0( r = 0)| 2 , from an SVZ sum rule, setting the mass of the ground state E0 equal to its known value and treating the effective continuum threshold as a fit parameter. We show that in a limited "fiducial" range of the Borel parameter there exists a solution for the effective threshold which precisely reproduces the exact Π(µ) for any value of R within the range 0.7 ≤ R/R0 ≤ 1.15 (R0 is the known exact value). Thus, the value of R extracted from the sum rule is determined to a great extent by the contribution of the hadron continuum. Our main finding is that in the cases where the hadron continuum is not known and is modeled by an effective continuum threshold, the systematic uncertainties of the sum-rule procedure cannot be controlled.

Bound-state parameters from dispersive sum rules for vacuum-to-vacuum correlators

“…Thus, our results reported in [4,5,6,7] mainly contained cautious messages concerning the application of sum rules to hadron properties. However, understanding the problem is the necessary first step in solving the problem.…”

“…[3,4]) which are believed to provide such a systematic error. In QCD this, however, always remains a conjecture -it is impossible to prove that the range provided by the standard sum-rule procedures indeed contains the actual value of the bound-state parameter.…”

“…A simple harmonic-oscillator (HO) potential model [4,5,6,7] possesses the essential features of QCD -confinement and asymptotic freedom [8] -and has the following advantages: (i) the bound-state parameters (masses, wave functions, form factors) are known precisely; (ii) direct analogues of the QCD correlators may be calculated exactly.…”

“…Making use of this model, we have already studied the extraction of ground-state parameters from different types of correlators: namely, the ground-state decay constant from two-point vacuum-to-vacuum correlator [4], the form factor from three-point vacuum-to-vacuum correlator [5], and form factor from vacuum-to-hadron correlator [6]. We have demonstrated that the standard adopted procedures for obtaining the systematic errors do not work properly: for all types of correlators the true known value of the bound-state parameter was shown to lie outside the band obtained according to the standard criteria.…”

Pseudoscalar-Meson Form Factors: A Fresh Look by QCD Sum Rules

“…Even if supported by quantum-mechanical solutions [5], modelling of s eff (Q 2 < ∞) is non-trivial [6]. To sharpen our arguments, we define equivalent effective thresholds: sum rules with such integration limit reproduce experiment or any theoretical result exactly (Fig.…”