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Up- and down-quark masses from QCD sum rules

2018/09/30 by C. A. Dominguez, A. Mes, K. Schilcher
Physics and Astronomy · #Chiral perturbation theory #Hadron #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #QCD sum rules #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #Sum rule in quantum mechanics #hep-lat #hep-ph

paper · pdf · doi:10.1007/jhep02(2019)057

A Mathematica^(C) file pertaining to numerical evaluations is attached as Ancillary

openalex created_date 2018/09/27 · arxiv created 2018/12/21 · openalex publication_date 2019/02/01 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05

Abstract

A bstract The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: mu(2 GeV)=(2.6± 0.4) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>u</mml:mi> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mspace/> <mml:mi>GeV</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>2.6</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> MeV, md(2 GeV)=(5.3± 0.4) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>d</mml:mi> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mspace/> <mml:mi>GeV</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>5.3</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> MeV, and the sum mud≡ (mu+md)/2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>u</mml:mi> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> <mml:mtext>≡</mml:mtext> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>d</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:math> , is mud(2 GeV)=(3.9± 0.3) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>u</mml:mi> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mspace/> <mml:mi>GeV</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>3.9</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.3</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> MeV.

Citations