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QCD – from the vacuum to high temperature

QCD – from the vacuum to high temperature. an analytical approach. Analytical description of phase transition. Needs model that can account simultaneously for the correct degrees of freedom below and above the transition temperature.

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QCD – from the vacuum to high temperature

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  1. QCD – from the vacuum to high temperature an analytical approach

  2. Analytical description of phase transition • Needs model that can account simultaneously for the correct degrees of freedom below and above the transition temperature. • Partial aspects can be described by more limited models, e.g. chiral properties at small momenta.

  3. Higgs picture of QCD “spontaneous breaking of color “ in the QCD – vacuum octet condensate for Nf = 3 ( u,d,s ) C.Wetterich, Phys.Rev.D64,036003(2001),hep-ph/0008150

  4. Many pictures … … of the QCD vacuum have been proposed monopoles, instantons, vortices, spaghetti vacuum … in principle, no contradiction – there may be more than one valid picture most proposals say essentially nothing about the low mass excitations in real QCD, i.e mesons and baryons different for Higgs picture !

  5. Electroweak phase diagram

  6. Masses of excitations (d=3) small MH large MH O.Philipsen,M.Teper,H.Wittig ‘97

  7. Continuity

  8. Higgs phase and confinement can be equivalent – then simply two different descriptions (pictures) of the same physical situation Is this realized for QCD ? Necessary condition : spectrum of excitations with the same quantum numbers in both pictures - known for QCD : mesons + baryons -

  9. Spontaneous breaking of color • Condensate of colored scalar field • Equivalence of Higgs and confinement description in real (Nf=3) QCD vacuum • Gauge symmetries not spontaneously broken in formal sense ( only for fixed gauge ) Similar situation as in electroweak theory • No “fundamental” scalars • Symmetry breaking by quark-antiquark-condensate

  10. Analogy between weak and strong interactions

  11. Quark –antiquark condensate

  12. Octet condensate < octet > ≠ 0 : • “Spontaneous breaking of color” • Higgs mechanism • Massive Gluons – all masses equal • Eight octets have vev • Infrared regulator for QCD

  13. Electric charge < octet > ≠ 0 : • Spontaneous breaking of electromagnetic U(1) symmetry (some components of octet carry electric charge – similar to Higgs mechanism for hypercharge in electroweak theory) • Combined U(1) symmetry survives (cf. Q=I3 + ½ Y in e.w. standard model)

  14. Electric charge of “quarks”

  15. Flavor symmetry for equal quark masses : octet preserves global SU(3)-symmetry “diagonal in color and flavor” “color-flavor-locking” (cf. Alford,Rajagopal,Wilczek ; Schaefer,Wilczek) All particles fall into representations of the “eightfold way” quarks : 8 + 1 , gluons : 8

  16. Related earlier ideas: K.Bardakci,M.Halpern; I.Bars ’72 R.Mohapatra,J.Pati,A.Salam ’76 A.De Rujula,R.Giles,R.Jaffe ‘78 T.Banks,E.Rabinovici ’79 E.Fradkin,S.Shenker ’79 G. t’Hooft ’80 S.Dimopoulos,S.Raby,L.Susskind ’80 T.Matsumoto ’80 B.Iijima,R.Jaffe ’81 M.Yasue ’90 M.Alford,K.Rajagopal,F.Wilczek ’99 T.Schaefer,F.Wilczek ‘99

  17. Color-flavor-locking Chiral symmetry breaking : SU(3)L x SU(3)R SU(3)V Color symmetry breaking : SU(3)c x SU(3)V SU(3)diagonal Quarks :3 x 3 8 + 1 Gluons :8 x 1 8 Similar to high density QCD : Alford,Rajagopal,Wilczek ; Schaefer,Wilczek _ color~ flavor

  18. Octet condensate Color symmetry breaking : SU(3)c x SU(3)V SU(3)diagonal 8 x 8 1 + … < χ > : color~ flavor

  19. Quarks and gluons carry the observed quantum numbers of isospin and strangenessof the baryon and vector meson octets !They are integer charged!

  20. Duality

  21. Quantum numbers match ! Of course , there are many more excitations (resonances ). Strong interactions bound states

  22. Higgs description seems possible - is it simple ?

  23. Effectivelow energy model for QCD • Composite scalars ( quark-antiquark- bound states ) • Gauge invariance • Approximation: renormalizable interactions for QCD with scalars • Comparison with observation?

  24. Low energy effective action γ=φ+χ

  25. Simplicity This simple effective action will yield the masses and couplings of the baryons, pseudoscalars and vector mesons, ( including electromagnetic couplings by covariant derivatives ) ! ( five parameters , to be later determined by QCD )

  26. New scalar interactions • Gauge covariant kinetic term • Effective potential • Yukawa coupling to quarks

  27. Calculability • Remember : no fundamental scalars • Effective couplings should be calculable from QCD – i.e. gauge coupling or confinement scale

  28. Effective octet potential simple instanton computation χ0 = 150 MeV U Mρ= 850 MeV χ Chiral anomaly !

  29. Masses of physical particles determine three phenomenological parameters

  30. 5 undetermined parameters predictions Phenomenological parameters

  31. Chiral perturbation theory + all predictions of chiral perturbation theory + determination of parameters

  32. First conclusions • Spontaneous color symmetry breaking plausible in QCD • QCD - computation of effective vector mass needed • Simple effective action can account for mass spectrum of light baryons and mesons as well as their couplings • Gluon - Meson duality • Quark - Baryon duality

  33. Nonlinear formulation • Use of nonlinear fields makes physical content of the effective action more transparent. • Similar to nonlinear fields for pions • Selection of nonlinear fields follows symmetry content of the theory

  34. Gauge invariance • Higgs picture is a guide for ideas and a way to compute gauge invariant quantities at the end • Intuition can be misleading for certain questions • Effective action, U( φ,χ ) : gauge invariant • Nonlinear fields : gauge singlets Only assumptions : A) minimum of U preserves global SU(3) B) minimum not for χ=0 ( for appropriate gauge and normalization of χ )

  35. Nonlinear fields : π,K,η, η’

  36. Nonlinear fields : diquark cloud • The product W•v transforms as an antidiquark • B=-2/3 • v : color triplet

  37. How quarks get dressed as baryons

  38. Gauge bosons/vector mesons

  39. All fields except v are gauge singlets

  40. Effective action in terms of physical fields

  41. Effective action in terms of physical fields linear fields nonlinear fields Insert expressions for ψ,A,χ,φ

  42. Nonlinear local symmetry Has been investigated since long ago in the context of chiral theories, describes ρ - bosons Here : • Not postulated • Consequence of local color symmetry + “SSB” • Gauge bosons = gluons = ρ - bosons Predictions correct !

  43. Reparameterization symmetry Decomposition into nonlinear fields is not unique. E.g. N can be multiplied by unitary transformation from left, and W from right. local U(3) reparameterization symmetry infinitesimal transformation

  44. Baryons

  45. Pion nucleon coupling Two more successful predictions F,D are not fixed by chiral symmetry !

  46. Kinetic term for pseudoscalar mesons as in chiral perturbation theory meson decay constant Pseudoscalar mesons

  47. Vector mesons

  48. Electromagnetic interactions include by covariant derivative

  49. ρ - couplings

  50. ρ - couplings experiment : prediction : Vector dominance is realized by Higgs picture of QCD

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