Effective continuum threshold in dispersive sum rules

Abstract

We study the accuracy of the bound-state parameters obtained with the method of dispersive sum rules, one of the most popular theoretical approaches in nonperturbative QCD and hadron physics. We make use of a quantum-mechanical potential model since it provides the only possibility to probe the reliability and the accuracy of this method: one obtains the bound-state parameters from sum rules and compares these results with the exact values calculated from the Schrödinger equation. We investigate various possibilities to fix the crucial ingredient of the method of sum rules -the effective continuum threshold -and propose modifications which lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method. Although the rigorous control of systematic uncertainties in the method of sum rules remains unfeasible, the application of the proposed procedures in QCD promises a considerable increase of the actual accuracy of the extracted hadron parameters.

Properties ofDs2*(2573)charmed-strange tensor meson

“…The above analyses have been done based on, so called, the standard procedure in QCD sum rule technique such that the quark-hadron duality assumption as a systematic error has been used and the continuum threshold has been taken independent of Borel mass parameter. However, as also stated in [17], the continuum threshold can depend on M 2 . Hence the standard procedure does not render the realistic errors and, in fact, the actual errors should be large.…”

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.…”

“…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.…”

“…In a recent paper [7] we proposed a new algorithm for extracting the parameters of the ground state. The simple idea of [7] is to relax the standard assumption of a Borel-parameter independent effective continuum threshold, and allow for a Borel-parameter dependent quantity.…”

“…The simple idea of [7] is to relax the standard assumption of a Borel-parameter independent effective continuum threshold, and allow for a Borel-parameter dependent quantity. In [7] we have illustrated the way the procedure works for the extraction of the form factor from three-point vacuum-to-vacuum correlator.…”