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

Abstract

We study the extraction of the ground-state parameters from vacuum-to-vacuum correlators. We work in quantum-mechanical potential model which provides the only possibility to probe the reliability and the actual accuracy of this method: one obtains the bound-state parameters from the correlators by the standard procedures adopted in the method of sum rules and compares these results with the exact values calculated from the Schrödinger equation. We focus on the crucial ingredient of the method of sum rules -the effective continuum threshold -and propose a new algorithm to fix this quantity. In a quantum-mechanical model, our procedure leads to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method and used in all previous applications of dispersive sum rules in QCD. The application of the proposed procedure in QCD promises a considerable increase of the accuracy of the extracted hadron parameters.

Decay Constants of Beauty Mesons from QCD Sum Rules

“…Define and apply an appropriate criterion for fixing the effective continuum threshold s eff (τ). To this end, we employ an earlier developed algorithm [6][7][8][9] that allows for a reliable extraction of the ground-state properties in quantum mechanics and of the charmed-meson decay constants in QCD. We introduce the dual invariant mass M dual and the dual decay constant f dual by defining…”

Heavy-Meson Decay Constants: Isospin Breaking from QCD Sum Rules

“…Some time ago, we embarked on thorough investigations of both the accuracy and precision actually achievable by and the systematic uncertainties inherent to the formalism of QCD sum rules [2][3][4][5][6]. As a consequence of these studies, we proposed a somewhat modified algorithm that provides estimates of intrinsic errors [7][8][9][10][11]. With this improvement at our disposal, we revisited QCD sum-rule extractions of a variety of hadronic observables, particularly of the leptonic decay constants of the heavy-light mesons [12][13][14][15][16], which led us to the conclusion [17][18][19][20][21] that, in the bottom-meson system, the decay constants of the pseudoscalar mesons exceed those of their vector counterparts, as has been confirmed thereafter in lattice QCD [22].…”

“…The derivative of any such decay-constant ratio with respect to x q , that is, its slope, at the origin x q = 0, eff (τ) proves crucial for the accuracy of QCD sum-rule outcomes and our ability to estimate their intrinsic uncertainties [2][3][4][5][6][7][8][9][10][11]. Application of all these procedures to interpolating currents of type J = A, V results in QCD sum rules…”

Effective Continuum Thresholds for Quark-Hadron Duality in Dispersive Sum Rules

“…Our approach [1][2][3][4][5][6][7][8][9][10][11][12][13][14] seeks to quantify the uncertainty induced by such an approximation and to improve the accuracy of all predictions by allowing our threshold to depend on the involved momenta and parameters introduced upon application of Borel transformations. The Borel transformation to a new variable, the Borel parameter (called T or τ hereafter), serves to remove subtraction terms and suppress excitation and continuum contributions.…”

“…However, in order to extract from q)) the elastic form factor F g (q) by exploiting only the knowledge of E g and R g we simultaneously have to pin down the actual behaviour of the effective continuum thresholds. We thus adopt for our thresholds the simple polynomial ansatz [10][11][12] …”