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Schwinger-Dyson approach to hadron physics

Schwinger-Dyson approach to hadron physics. Goecke, Fischer & Williams. Q C D. confinement. strong coupling. 1. strong QCD. 0. - 15. 0. 10. r (m). asymptotic freedom. strong QCD. pQCD. Schwinger-Dyson Equations. QED. Bound State Equations. Schwinger-Dyson Equations. P. V.

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Schwinger-Dyson approach to hadron physics

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  1. Schwinger-Dyson approach to hadron physics Goecke, Fischer & Williams

  2. QCD confinement strong coupling 1 strong QCD 0 -15 0 10 r (m) asymptotic freedom strong QCD pQCD

  3. Schwinger-Dyson Equations . . . . QED

  4. Bound State Equations Schwinger-Dyson Equations P V Axial Ward Identity QCD

  5. effective interaction strength fp , mp Maris & Tandy p2 GeV2 10-3 103

  6. quark mass function  SB < qq >0 ~ - (240 MeV)3 chiral m 0 = s > 1 Williams, Fischer, P Maris & Roberts

  7. SDE/BSE – ANL/KSU v MV (GeV) pion/vector mesons CP-PACS q 2 MP (GeV2) q P V

  8. electromagnetic formfactors constant mass quark propagator running mass 103 10-3 p2 (GeV)2 q q q q q qq N*

  9. Pion electromagnetic formfactor Maris, Tandy

  10. Pion electromagnetic formfactor g* p+ n p Further extend Fp(Q2) w/ 12 GeV • Measure F up to 6 (GeV/c)2 to probe onset of pQCD • +/- measurements to test t-channel dominance of L • Q2 = 0.30 (GeV/c)2 close to pion pole to compare to +e elastic

  11. Pion electromagnetic formfactor g* p+ n p Further extend Fp(Q2) w/ 12 GeV • Measure F up to 6 (GeV/c)2 to probe onset of pQCD • +/- measurements to test t-channel dominance of L • Q2 = 0.30 (GeV/c)2 close to pion pole to compare to +e elastic

  12. effective interaction strength Qin, Chang, Liu, Roberts, Wilson p2 GeV2 10-3 103

  13. effective interaction strength constant mass running mass p2 GeV2 10-3 103

  14. Schwinger-Dyson Equations • remove divergences (eg. quadratic div.) • (ii) ensure correct gauge dependence (eg. transversality of boson) . . . . Consistent truncation Gauge Invariance & Multiplicative Renormalizibility QED

  15. Gauge Invariance Fermion propagator m -1 -1 = k p k p q m - -1 -1 wavefunction renormalisation mass function

  16. Gauge Invariance m m q -1 -1 = k p k p k p q m qm 0 1,2,..,8 Ward-Green-Takahashi

  17. Gauge Invariance m m q -1 -1 = k p k p k p q m Ball & Chiu Ward-Green-Takahashi Ball & Chiu

  18. Gauge Invariance m m q -1 -1 = k p k p k p q m Ward-Green-Takahashi Goecke, Fischer & Williams step I

  19. Testing for gauge invariance invariant not invariant little invariant

  20. Fermion propagator gm gm F(p) a = 0.5 F(p) a = 1 - -1 -1 p2/L2 wavefunction renormalisation CP BC CP mass function BC

  21. Fermion propagator gm CP R BC p2/L2 - -1 -1 wavefunction renormalisation mass function

  22. Schwinger-Dyson Equations QED . . . . Gauge Invariance & Multiplicative Renormalizibility Kizilersu & P

  23. Transverse components at O (a) Kizilersu, Reenders & P Davydychev

  24. Transverse vertex Kizilersu & P R. Williams, K, Sizer, P & A.G. Williams

  25. Unquenched Massless renormalised at m2 < L2: a=0.2, z : varying Kizilersu et al

  26. Unquenched Massless renormalised at m2 < L2: a=0.2, z : varying Kizilersu et al

  27. Light by Light gauge invariance is NOT optional

  28. Light by Light gauge invariance is NOT optional

  29. Fermion propagator mass gauge dependent  = cutoff

  30. Gauge Invariance and Multiplicative Renormalizibility -1 -1 - CP vertex mass almostgauge independent

  31. Slavnov-Taylor Identity axial gauges BBZ Schwinger-Dyson Equations QCD

  32. Schwinger-Dyson Equations Slavnov-Taylor Identity QCD covariant gauges

  33. Building bridges SDE/BSE in the continuum

  34. Building bridges SDE/BSE in the continuum connects the lattice to the continuum

  35. Building bridges SDE/BSE in the continuum connects theory to experiment

  36. Extra Slides

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