1 / 71

Exploring Strong Coupling QCD Continuum in Valencia - Mass Generation & Confinement Study

Dive deep into strong coupling Quantum Chromodynamics (QCD) continuum theory in Valencia, analyzing mass generation mechanisms, confinement, and more. Explore QCD equations, asymptotic freedom, perturbative and non-perturbative QCD aspects, mass generation from nothing, and gauge invariance.

sanchezf
Download Presentation

Exploring Strong Coupling QCD Continuum in Valencia - Mass Generation & Confinement Study

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Strong Coupling Continuum QCD Valencia

  2. q Strong Coupling Continuum QCD Valencia

  3. Q C D q ( i D - m ) q = q QCD q=u,d,s,c,b 1 - G G 4 1971

  4. confinement strong coupling 0.5 0 -15 0 10 r (m) QCD asymptotic freedom strong QCD pQCD strong QCD

  5. confinement perturbative QCD non-perturbative QCD

  6. Masses from Nothing perturbative mass m0

  7. Schwinger-Dyson Equations

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

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

  10. Fermion mass generation -1 -1 -

  11. Fermion mass generation -1 -1 - -1 -1 - + . . . + + quenched rainbow

  12. Fermion mass generation -1 -1 -  = cutoff quenched rainbow

  13. Fermion mass generation -1 -1 - quenched rainbow Landau gauge:  = 0 quenched rainbow

  14. Fermion mass generation -1 -1 - M(p) = 0 m0 = 0 quenched rainbow Landau gauge:  = 0 quenched rainbow

  15. Fermion mass generation -1 -1 - M(p) = 0 m0 = 0 quenched rainbow Landau gauge:  = 0 quenched rainbow

  16. Fermion mass generation -1 -1 - quenched rainbow Landau gauge:  = 0 quenched rainbow

  17. Fermion mass generation -1 -1 - m /  m/ quenched rainbow Landau gauge:  = 0 quenched rainbow

  18. BUT in other gauges

  19. gauge dependent BUT in other gauges mass  = cutoff

  20. Ward – Green –Takahashi m q m -1 -1 = k p k p k p q m

  21. mass  = cutoff almost gauge independent Gauge Invariance and Multiplicative Renormalizibility CP vertex

  22. Schwinger-Dyson Equations Ward-Green-Takahashi: q -1 -1 q k p k p Gauge Invariance & Multiplicative Renormalizibility QED

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

  24. ghosts Studies in covariant gauges ghost functions = 1 QCD

  25. ghosts ghost functions = 1 Studies in covariant gauges QCD forget ghosts

  26. STI Studies in covariant gauges first just gluons Pagels, Mandelstam, Bar-Gadda

  27. Studies in Landau gauge Brown & P 1988

  28. s = 0.25 Nf = 2 Studies in Landau gauge Brown & P 1988

  29. SB QCD running coupling (Q2) > 1 for Q2 < Q022 Williams, Fischer, P

  30. SB chiral m 0 = QCD running coupling (Q2) > 1 for Q2 < Q022 Williams, Fischer, P

  31. QCD vacuum < qq >0 ~ - (240 MeV)3 chiral m 0 =  SB + 1 Maris & Roberts

  32. Mass < qq >0 ~ - (240 MeV)3 Mass generation 300 MeV Batley et al 0 Ke4 results 10-17 10-14 r (m) DIRAC experiment

  33. a 0 V  m mq Lattice QCD model QCD

  34. a 0 V  Lattice QCD

  35. a 0 V  Lattice QCD

  36. a 0 V  Lattice QCD

  37. Lattice and SDE results Bowman et al Roberts et al

  38. q Hadrons & quark confinement q

  39. q q Hadrons & quark confinement q Q Wilson area law

  40. interquark potential gluon propagator M + + …

  41. interquark potential gluon propagator M + + …

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

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

  44. Charmonium Binding energy [meV] Ionisation energy 0 3 D 3 S 3 S 3 1 3 3 D 1 2 0 1 2 3 D 3 -1000 1 2 P 3 2 P 3 D 3 2 1 2 S 3 2 2 S 1 1 2 P 1 3 ~ 600 meV 0 1 2 P 3 0 10-4 eV -3000 -5000 1 S 3 8·10-4 eV 1 S 1 1 0 -7000 0.1 nm + - e e positronium of QCD • Charmonium • Positronium Mass [MeV] 4100 y ¢¢¢ (4040) P (~ 3940) 3 2 3900 D 3 (~ 3800) P (~ 3880) 3 3 1 P (~ 3800) D 3 1 y ¢¢ (3770) 0 2 D 3 D 3 2 1 Threshold ¢ y (3686) 3700 h ¢ (3590) c c (3556) 2 h (3525) c c (3510) 1 3500 c (3415) 0 3300 y (3097) 3100 C 1 fm h (2980) C c 2900

  45. Tübingen studies in covariant gauges QCD von Smekal, Alkofer et al

  46. Deep Infrared 0.02 20 2 0.2 distance (fm) Tübingen, Graz, Darmstadt Ghost Fischer Gluon

  47. Deep Infrared 0.02 20 2 0.2 distance (fm) Tübingen, Graz, Darmstadt Ghost Fischer Gluon

  48. Confinement potential QCD von Smekal, Alkofer et al

  49. rp ~ 1 (p) 0, p 0 interquark potential Richardson Potential how does confinement happen?

  50. Alkofer, Fischer, Llanes-Estrada & Schwenzer + + + …

More Related