Light Quark Masses from QCD Finite Energy Sum Rules

Mes, Alexes K

Light Quark Masses from QCD Finite Energy Sum Rules

Master Thesis

2019

Abstract

Due to quark-gluon confinement in QCD, the quark masses entering the QCD Lagrangian cannot be measured with the same techniques one would use to determine the mass of non-confined particles. They must be determined either numerically from Lattice QCD, or analytically using QCD sum rules. The latter makes use of the complex squared energy plane, and Cauchy’s theorem for the correlator of axial-vector divergences. This procedure relates a QCD expression containing the quark masses, with an hadronic expression in terms of known hadron masses, couplings, and lifetimes/widths. Thus, the quark masses become a function of known hadronic information. In this dissertation, the light quark masses are determined from a QCD finite energy sum rule, using the pseudoscalar correlator to six-loop order in perturbative QCD, with the leading vacuum condensates and higher order quark mass corrections included. The systematic uncertainties stemming from the hadronic resonance sector are reduced, by introducing an integration kernel in the Cauchy integral in the complex squared energy plane. Additionally, the issue of convergence of the perturbative QCD expression for the pseudoscalar correlator is examined. Both the fixed order perturbation theory (FOPT) method and contour improved perturbation theory (CIPT) method are explored. Our results from the latter exhibit good convergence and stability in the window s0 = 3.0 − 5.0 GeV2 for the strange quark and s0 = 1.5 − 4.0 GeV2 for the up and down quarks; where s0 is the radius of the integration contour in the complex s-plane. The results are: ms(2 GeV) = 91.8 ± 9.9 MeV, mu(2 GeV) = 2.6 ± 0.4 MeV, md(2 GeV) = 5.3 ± 0.4 MeV, and the sum mud ≡ (mu + md)/2, is mud(2 GeV) = 3.9 ± 0.3 MeV. They compare favourably to the PDG and FLAG world averages. Further in this dissertation the updated series expansion of the quark mass renormalization group equation (RGE) to five-loop order is derived. The series provides the relation between a light quark mass in the modified minimal subtraction (MS) scheme defined at some given scale, e.g. at the tau-lepton mass scale, and another chosen energy scale, s. This relation explicitly depicts the renormalization scheme dependence of the running quark mass on the scale parameter, s, and is important in accurately determining a light quark mass at a chosen scale. The five-loop QCD β(as) and γ(as) functions are used in this determination.

Keywords

Physics

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