C.A. Dominguez Centre for Theoretical Physics & Astrophysics University of Cape Town Department of...
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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
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
Slide 2
WHY DO WE NEED THEORETICAL PHYSICISTS TO MEASURE THE QUARK
MASSES & THE QUARK- GLUON COUPLING?
Slide 3
QUANTUM CHROMODYNAMICS
Slide 4
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
Slide 5
STRONG COUPLING hadrons Z hadrons e + e - hadrons etc.
Slide 6
hadrons (s)
Slide 7
Slide 8
Slide 9
CURRENT CORRELATOR (GREEN FUNCTION)
Slide 10
Slide 11
QUARK-HADRON DUALITY
Slide 12
Slide 13
Slide 14
R -ratio
Slide 15
Slide 16
hadrons
Slide 17
Slide 18
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)
Slide 19
CONTENTIOUS ISSUE WORK IN PROGRESS
Slide 20
QUARK MASSES CPT: Light quark mass ratios Lattice QCD QCD Sum
Rules (Operator Product Expansion)
Slide 21
Slide 22
NEXT TO LEADING ORDER ONLY ONE PARAMETER-FREE RELATION ( J.
Gasser & H. Leutwyler 1985)
Slide 23
NEXT TO LEADING ORDER SCALE & RENORMALIZATION CONSTANT(S)
DEPENDENT
Slide 24
BARYON MASS SPLITTING P. Minkowski & A. Zepeda (1980)
Slide 25
Q C D SUM RULES Shifman-Vainshtein-Zakharov (1979)
Slide 26
Q C DQ C D
Slide 27
HADRONIC
Slide 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
Slide 29
Slide 30
Slide 31
QUARK CONDENSATE
Slide 32
Slide 33
Slide 34
GLUON CONDENSATE
Slide 35
Slide 36
Q C D SUM RULES (SVZ)
Slide 37
QUARK-HADRON DUALITY
Slide 38
Slide 39
Slide 40
Slide 41
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
INTEGRATION KERNEL 5 (s) Analytic function ds (s) 5 (s) =
0
Slide 44
Slide 45
PURPOSE OF THE INTEGRATION KERNEL ENHANCE / SUPPRESS SPECIFIC
CONTRIBUTIONS HADRONIC: resonance region: non-existing experimental
data CAUCHYS THEOREM STILL VALID
Slide 46
HADRONIC SPECTRAL FUNCTION Pseudoscalar meson pole (pion, kaon)
OK Resonances: (???) hadrons (J P = 0 - ) NOT FEASIBLE
Slide 47
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
Slide 48
SYSTEMATIC UNCERTAINTY MASS & WIDTH OF RESONANCES: NOT
ENOUGH TO RECONSTRUCT HADRONIC SPECTRAL FUNCTION !!! HADRONIC
BACKGROUND & CONSTRUCTIVE/DESTRUCTIVE INTERFERENCE COMPLETELY
UNKNOWN
Slide 49
BEST MODEL THRESHOLD CONSTRAINT FROM CHPT 3-PION Pagels &
Zepeda (1972) CAD (1984), CAD, de Rafael (1987), CAD, Pirovano,
Schilcher (1998)
Slide 50
5 (s) 5 (s) = 1 - a 0 s a 1 s 2 5 (M 1 2 ) = 5 (M 2 2 ) =
0
Slide 51
Realistic Spectral Function Im s E 2 s0s0
Slide 52
S 0 DEPENDENCE PHYSICAL QUANTITIES ARE INDEPENDENT OF S 0 IN
PRACTICE : S 0 1 3 GeV 2