Constraints on QCD sum rules from the Hölder inequalities

Abstract

A new technique based on Hölder's integral inequality is applied to QCD sum rules to provide fundamental constraints on the sum-rule parameters. These constraints must be satisfied if the sum rules are to consistently describe integrated physical cross-sections, but these constraints do not require any experimental data and therefore can be applied to any hadronic spectral function. As an illustration of this technique the Laplace sum rules of the light-quark correlation function for the vector and the axial-vector currents are examined in detail. We find examples of inconsistency between the inequalities and sum-rule parameters used in some previous analyses of the vector and axial-vector channels.