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Strong Coupling Q C D

Michael Pennington Jefferson Lab. ECT*, Trento September 2014. Strong Coupling Q C D. d. u. u. Michael Pennington Jefferson Lab. ECT*, Trento September 2014. Strong Coupling Q C D. Fritzsch. Gell-Mann. q ( i D - m ) q. =. q. Leutwyler. QCD. q=u,d,s, c,b,t. 1.

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Strong Coupling Q C D

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  1. Michael Pennington Jefferson Lab ECT*, Trento September 2014 Strong Coupling QCD

  2. d u u Michael Pennington Jefferson Lab ECT*, Trento September 2014 Strong Coupling QCD

  3. Fritzsch Gell-Mann q ( i D - m ) q = q Leutwyler QCD q=u,d,s, c,b,t 1 - F F 4 QCD

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

  5. Strong physics problems u d strong coupling pQCD u _ u s

  6. Strong physics problems strong coupling pQCD

  7. Strong physics problems strong coupling pQCD

  8. Schwinger-Dyson Equations -1 -1 -

  9. Fermion propagator -1 -1 - wavefunction renormalisation mass function

  10. Fermion propagator -1 -1 - wavefunction renormalisation mass function Gauge variant quantities: only physical quantities are gauge independent

  11. Schwinger-Dyson Equations Bound State Equations QCD M V

  12. Schwinger-Dyson Equations Bound State Equations QCD M V dressed quark propagator

  13. Schwinger-Dyson Equations Bound State Equations QCD qq scattering kernel M V dressed quark propagator

  14. Schwinger-Dyson Equations Bound State Equations P V fp , mp QCD

  15. SDE/BSE – ANL/KSU v pion/vector mesons q 2 MP (GeV2) q q q P + = G 5 - - q q q q V + = G - - q q MV (GeV)

  16. effective interaction strength Maris & Tandy p2 GeV2 10-3 103

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

  18. electromagnetic formfactors q q q q q qq

  19. Maris-Tandy model q q Can Maris-Tandy (or Qin et al. ) modelling be deduced from the SDE/DSEs? V p s

  20. q q q q q 1 q ( i D - m ) q - F F = q 4 QCD q=u,d,s, c,b,t

  21. Schwinger-Dyson Equations

  22. 2 equations 2 equations 12 equations Schwinger-Dyson Equations QED

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

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

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

  26. Fermion propagator -1 -1 - wavefunction renormalisation mass function how to regularize: d4kdnk

  27. Gauge Invariance & Multiplicative Renormalizibility Kizilersu & P Schwinger-Dyson Equations QED k2, q2 >> p2 k2, p2 >> q2

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

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

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

  31. Consistent Solutions of QCD 1 q ( i D - m ) q - F F = q 4 QCD q=u,d,s, c,b,t

  32. Dmn (q)orthogonal toqm andnm - the axial vector Schwinger-Dyson Equations axial gauges Baker, Ball & Zachariasen QCD

  33. Slavnov-Taylor Identity Dmn (q)orthogonal toqm andnm - the axial vector Schwinger-Dyson Equations axial gauges BBZ QCD

  34. _ Richardson Potential b b heavy quark potential spectrum

  35. b

  36. _ _ b b b b positronium e- bottomonium bottomonium g 1 fm 1 fm b b b b e+ V(r) V(r) r r g  0.1 nm

  37. interquark potential gluon propagator rp ~ 1 Coulomb : OBE r << 1, p >> 1 r >> 1, p << 1

  38. interquark potential Richardson Potential rp ~ 1 Coulomb : OBE r << 1, p >> 1 r >> 1, p << 1

  39. Schwinger-Dyson Equations Dmn (q)orthogonal toqm andnm - the axial vector QCD axial gauges G1(q2, n.q), G2(q2, n.q)

  40. Schwinger-Dyson Equations Dmn (q)orthogonal toqm andnm - the axial vector Baker, Ball & Zachariasen G2(q2, n.q) = 0 G1(q2, n.q) ~ 1/q2 QCD ieDmn ~ 1/q4 axial gauges G1(q2, n.q), G2(q2, n.q)

  41. Schwinger-Dyson Equations Dmn (q)orthogonal toqm andnm - the axial vector QCD axial gauges G1(q2, n.q), G2(q2, n.q) Baker, Ball & Zachariasen G2(q2, n.q) = 0 G1(q2, n.q) ~ 1/q2 ieDmn ~ 1/q4 West showed axial gauge Dmn could NOT be more singular than 1/q2

  42. Schwinger-Dyson Equations Dmn (q) QCD covariant gauges x

  43. Schwinger-Dyson Equations qmqn Gl (q) Dmn (q) = Tmn + x q2 q2 Dmn (q) qmqn - Tmn (q) = gmn q2 Gh(q) D (q) = q2 QCD covariant gauges x

  44. Studies in covariant gauges first just gluons Pagels, Mandelstam, Bar-Gadda Gl (q)

  45. Studies in covariant gauges STI Gl Dmn ~ 1/q4possible first just gluons Pagels, Mandelstam, Bar-Gadda Gl (q)

  46. Schwinger-Dyson Equations Slavnov-Taylor Identity qmqn Gl (q) Dmn (q) = Tmn + x q2 q2 Dmn (q) qmqn - Tmn (q) = gmn q2 Gh(q) D (q) = q2 i Dlm P mn=gln covariant gauges x

  47. Schwinger-Dyson Equations Slavnov-Taylor Identity qmqn Gl (q) Dmn (q) = Tmn + x q2 q2 Dmn (q) qmqn - Tmn (q) = gmn q2 Gh(q) D (q) = q2 Landau gauge x = 0 Brown & P (1988)Gh = 1

  48. Studies in the Landau gauge Gl R(q) q2 (GeV2) Gl (q) Brown & P 1988

  49. Studies in the Landau gauge s = 0.25 s = 0.25 Nf = 2 Nf = 2 Gl R(q) Gl R(q) q2 (GeV2) q2 (GeV2) Gl (q) Brown & P 1988

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