ELECTROMAGNETIC FORM FACTORS IN QUANTUM FIELD THEORIES

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LIGHT QUARK MASSES FROM QCD FESR WITH MINIMAL
HADRONIC RESONANCE BIAS
C.A. Dominguez Centre for Theoretical Physics
Astrophysics University of Cape Town Department
of Physics, Stellenbosch University South
Africa Work done with N. Nasrallah, R.
Röntsch, K. Schilcher
QCD- 2008 Montpellier
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QUARK MASSES

• CPT Light quark mass ratios
• Lattice QCD
• QCD Sum Rules

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Q C D SUM RULESShifman-Vainshtein-Zakharov
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Q C D
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HADRONIC
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Q C D SUM RULES (SVZ)
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Real Spectral Function
Im G
E2
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QUARK-HADRON DUALITY
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HADRONIC SPECTRAL FUNCTION

• Pseudoscalar meson pole (pion, kaon)
• Resonances (???)
• ? ? hadrons (JP 0-)
• ? ? hadrons (JP 1-)

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PION (KAON) RADIAL EXCITATIONS

• p (1300) M 1300 100 MeV
• G 200 600 MeV
• p (1800) M 1812 14 MeV
• G 207 13 MeV
• K (1460) K (1830) G 250 MeV

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?5 (s)

• ?5 (s) 1 - a0 s a1 s2
• ?5 (M12) ?5 (M22) 0

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FOPT as(s0) mq(s0) frozen. RG ? after
integration CIPT as(s0) mq(s0) running.
RG ? before integration
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ERROR ANALYSIS

• ?QCD 365 397 MeV (ALEPH 08)
• as (M2?) 0.344 0.005
  0.007
• ltas G2gt 0.06 GeV4 within a factor 2
• ?5(Q2)6 LOOP ?5(Q2)5 LOOP
• ?5(Q2)RESONANCE factor 5 smaller than PQCD

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RESULTS

• ms (2 GeV) 102 8 MeV
• md (2 GeV) 5.3 0.4 MeV
• mu (2 GeV) 2.9 0.2 MeV
• (mu md)/2 4.1 0.2 MeV

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SUMMARY

• A method to decrease substantially the systematic
  uncertainties from the hadronic resonance sector
• Future improvement from more precise ?QCD
  higher loop order in PQCD

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