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C.A. Dominguez Centre for Theoretical Physics & Astrophysics University of Cape Town Department of Physics, Stellenbosch University South Africa VIII SILAFAE VALPARAISO, CHILE, 6-12/ DEC /2010 DETERMINATION OF THE FUNDAMENTAL PARAMETERS OF QCD

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WHY DO WE NEED THEORETICAL PHYSICISTS TO MEASURE THE QUARK MASSES & THE QUARK- GLUON COUPLING?

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QUANTUM CHROMODYNAMICS

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FUNDAMENTAL PARAMETERS OF QCD STRONG COUPLING s (q 2 ) 1/ ln(-q 2 / 2 ) QUARK MASSES m q (q 2 ) [1/ ln(-q 2 / 2 )] A fractal

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STRONG COUPLING hadrons Z hadrons e + e - hadrons etc.

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hadrons (s)

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CURRENT CORRELATOR (GREEN FUNCTION)

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QUARK-HADRON DUALITY

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R -ratio

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hadrons

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CURRENT VALUES OF S (q 2 ) S (M 2 ) = 0.342 0.012 (Pich, 2010) S (M Z 2 ) = 0.1213 0.0014 S (M Z 2 ) = 0.1231 0.0038 (Bethke, 2010) S (M Z 2 ) = 0.1183 0.0008 (Lattice, 2010)

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CONTENTIOUS ISSUE WORK IN PROGRESS

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QUARK MASSES CPT: Light quark mass ratios Lattice QCD QCD Sum Rules (Operator Product Expansion)

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NEXT TO LEADING ORDER ONLY ONE PARAMETER-FREE RELATION ( J. Gasser & H. Leutwyler 1985)

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NEXT TO LEADING ORDER SCALE & RENORMALIZATION CONSTANT(S) DEPENDENT

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BARYON MASS SPLITTING P. Minkowski & A. Zepeda (1980)

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Q C D SUM RULES Shifman-Vainshtein-Zakharov (1979)

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Q C DQ C D

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HADRONIC

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CONFINEMENT STRONG MODIFICATION TO QUARK & GLUON PROPAGATORS NEAR THE MASS SHELL INCORPORATE CONFINEMENT THROUGH A PARAMETRIZATION OF PROPAGATOR CORRECTIONS IN TERMS OF QUARK & GLUON VACUUM CONDENSATES

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QUARK CONDENSATE

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GLUON CONDENSATE

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Q C D SUM RULES (SVZ)

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QUARK-HADRON DUALITY

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PROBLEM WITH Im (S)| resonance e + e - hadrons Im (s)| V hadrons Im (s)| V & Im (s)| A PSEUDOSCALAR CHANNEL (beyond pole): Not measured & not measurable SYSTEMATIC UNCERTAINTY

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1980s 2007-2008 CAD, Nasrallah, Schilcher (2007) CAD, Nasrallah, Rntsch, Schilcher (2008)

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INTEGRATION KERNEL 5 (s) Analytic function ds (s) 5 (s) = 0

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PURPOSE OF THE INTEGRATION KERNEL ENHANCE / SUPPRESS SPECIFIC CONTRIBUTIONS HADRONIC: resonance region: non-existing experimental data CAUCHYS THEOREM STILL VALID

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HADRONIC SPECTRAL FUNCTION Pseudoscalar meson pole (pion, kaon) OK Resonances: (???) hadrons (J P = 0 - ) NOT FEASIBLE

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PION (KAON) RADIAL EXCITATIONS (1300): M = 1300 100 MeV = 200 600 MeV (1800): M = 1812 14 MeV = 207 13 MeV K (1460) & K (1830) 250 MeV

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SYSTEMATIC UNCERTAINTY MASS & WIDTH OF RESONANCES: NOT ENOUGH TO RECONSTRUCT HADRONIC SPECTRAL FUNCTION !!! HADRONIC BACKGROUND & CONSTRUCTIVE/DESTRUCTIVE INTERFERENCE COMPLETELY UNKNOWN

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BEST MODEL THRESHOLD CONSTRAINT FROM CHPT 3-PION Pagels & Zepeda (1972) CAD (1984), CAD, de Rafael (1987), CAD, Pirovano, Schilcher (1998)

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5 (s) 5 (s) = 1 - a 0 s a 1 s 2 5 (M 1 2 ) = 5 (M 2 2 ) = 0

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Realistic Spectral Function Im s E 2 s0s0

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S 0 DEPENDENCE PHYSICAL QUANTITIES ARE INDEPENDENT OF S 0 IN PRACTICE : S 0 1 3 GeV 2

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ERROR ANALYSIS 5 (Q 2 )| RESONANCE : factor 5 smaller than PQCD

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RESULTS m s (2 GeV) = 102 8 MeV m d (2 GeV) = 5.3 0.4 MeV m u (2 GeV) = 2.9 0.2 MeV (m u + m d )/2 = 4.1 0.2 MeV

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BARYON MASS SPLITTING P. Minkowski & A. Zepeda (1980))

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HEAVY QUARKS CHARM & BOTTOM (+) DATA: e + e - hadrons ( c & b region) (-) (s) 1 + O( s ) + + O[ j (m 2 / s) i ]

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CHARM QUARK MASS m c (3 GeV)| MS-bar KARLSRUHE GROUP: Chetyrkin, Kuhn, Maier, Maierhofer, Marquard, Steinhauser, Sturm CAPE TOWN-MAINZ-VALENCIA: Bodenstein, Bordes, CAD, Penarrocha, Schilcher

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m c (3 GeV)| MS-bar 986 13 MeV Karlsruhe 1008 26 MeV CPT-Mainz-Valencia 986 6 MeV HPQCD (2010)

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