Holder Inequalities and Bounds on the Masses of Light Quarks

Abstract

QCD Laplace sum-rules must satisfy a fundamental (Holder) inequality if they are to consistently represent an integrated hadronic cross-section. After subtraction of the pion-pole, the Laplace sum-rule of pion currents is shown to violate this fundamental inequality unless the up and down quark masses are sufficiently large, placing a lower bound on the 1.0 GeV MS-bar running masses.

latex2e, 8 pages, 2 figures. Error corrected in equation (41)

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• A Sum-Rules Analysis of Next-to-Leading-Order (NLO) QCD Perturbative Contributions to a $J^{PC}=0^{+-}$, $du\bar{d}\bar{u}$ Tetraquark Correlator
• Hoelder Inequalities and QCD Sum-Rule Bounds on the Masses of Light Quarks