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

Abstract

Abstract. Modifying the standard approaches to nonperturbative QCD based on Borel-transformed dispersive sum rules by allowing the effective continuum thresholds required for the implementation of quark-hadron duality to depend on the Borel parameters and on any relevant momentum promises to entail higher accuracy and reliable error estimates for the extracted predictions of hadron features.Keywords: nonperturbative quantum chromodynamics, dispersive sum rules, quark-hadron duality PACS: 12.38.Lg, 11.10.St, 11.55.Hx, 03.65.Ge INCENTIVE: IMPROVEMENT OF QCD SUM RULES [1-14]Within the method of QCD sum rules, à la Shifman-Vainshtein-Zakharov, the concept of quark-hadron duality is usually implemented by assuming that above specific continuum thresholds the contributions to suitably defined correlators of interpolating currents at the level of the QCD degrees of freedom equal those at the level of the hadronic bound states. 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.Any such idea is best tested first in a situation in which the outcome for all bound-state characteristics one is interested in is known exactly. So let's study a quantum-mechanical model defined by a nonrelativistic Hamiltonian H with a harmonic-oscillator interaction:This model is exactly solvable: ground-state energy, decay constant, and form factor readWe inspect the analogues of a few N-point correlation functions of interpolating currents. The Borelized polarization function or 2-point vacuum-vacuum correlator [1][2][3][4][5]8] reads.