1. 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

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

3. QUANTUM CHROMODYNAMICS

4. FUNDAMENTAL PARAMETERS OF QCD STRONG COUPLING α s (q 2 )  1/ ln(-q 2 / Λ 2 ) QUARK MASSES m q (q 2 )  [1/ ln(-q 2 / Λ 2 )] γ A fractal

5. STRONG COUPLING τ → hadrons Z → hadrons e + e - → hadrons etc.

6.  → hadrons (π’s)

9. CURRENT CORRELATOR (GREEN FUNCTION)

11. QUARK-HADRON DUALITY

14. R  -ratio

16.   hadrons

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

19. CONTENTIOUS ISSUE WORK IN PROGRESS

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

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

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

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

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

26. Q C DQ C D

27. HADRONIC

28. 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

31. QUARK CONDENSATE

34. GLUON CONDENSATE

36. Q C D SUM RULES (SVZ)

37. QUARK-HADRON DUALITY

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

42. 1980’s – 2007-2008 CAD, Nasrallah, Schilcher (2007) CAD, Nasrallah, Röntsch, Schilcher (2008)

43. INTEGRATION KERNEL Δ 5 (s) Analytic function  ds П (s) Δ 5 (s) = 0

45. PURPOSE OF THE INTEGRATION KERNEL ENHANCE / SUPPRESS SPECIFIC CONTRIBUTIONS HADRONIC: resonance region: non-existing experimental data CAUCHY’S THEOREM STILL VALID

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

47. PION (KAON) RADIAL EXCITATIONS π (1300): M = 1300 ± 100 MeV Γ = 200 – 600 MeV π (1800): M = 1812 ± 14 MeV Γ = 207 ± 13 MeV K (1460) & K (1830) Γ ≈ 250 MeV

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

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

50. Δ 5 (s) Δ 5 (s) = 1 - a 0 s – a 1 s 2 Δ 5 (M 1 2 ) = Δ 5 (M 2 2 ) = 0

51. Realistic Spectral Function Im Π s ≡ E 2 s0s0

52. S 0 DEPENDENCE PHYSICAL QUANTITIES ARE INDEPENDENT OF S 0 IN PRACTICE : S 0  1 – 3 GeV 2

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

57. 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

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

61. HEAVY QUARKS CHARM & BOTTOM (+) DATA: e + e - → hadrons ( c & b region) (-) Π (s) ≈ 1 + O(α s ) + … + O[α j (m 2 / s) i ]

63. 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

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