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Cosmological constant

baryons. Universe. QCD Spectral Functions and Dileptons. T. Hatsuda (RIKEN). bare quark. quark. quark. 5. 27. hadron. 68. 3. Cosmological constant. “Higgs” condensate. Englert-Brout, Higgs (1964). Einstein (1917). “Chiral” condensate. Nambu (1960). 3.

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Cosmological constant

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  1. baryons Universe QCD Spectral Functions and Dileptons T. Hatsuda (RIKEN) bare quark quark quark 5 27 hadron 68 3 Cosmological constant “Higgs” condensate Englert-Brout, Higgs (1964) Einstein (1917) “Chiral” condensate Nambu (1960) 3 Condensates ⇔ Elementary excitations

  2. Outline • QCD symmetries • II. Chiral order parameters • III. In-medium hadrons • IV. Summary “QCD Constraints on Vector Mesons at finite T and Density” T.H., http://www-rnc.lbl.gov/DLS/DLS_WWW_Files/DLSWorkshop/dilepton.html (1997) “Hadron Properties in the Nuclear Medium” R. Hayano + T.H., Rev. Mod. Phys. 82 (2010) 2949 “The Phase Diagram of Dense QCD” K. Fukushima + T.H., Rep. Prog. Phys. 74 (2011) 014001

  3. John Wheeler's First Moral Principle from "Spacetime Physics (Taylor – Wheeler, 2nd ed.)” Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle.

  4. Chiral basis : Symmetry realization in QCD vacuum QCD Lagrangian : classical QCD symmetry (m=0) Quantum QCD vacuum (m=0) Axial anomaly : quantum violation of U(1)A Chiral condensate : spontaneous mass generation

  5. Dim.3 chiral condensate in QCD Gell-Mann-Oakes-Renner (GOR) formula (1968) LQCD free Di Vecchia-Veneziano formula (1980) Banks-Casher relation (1980) 0 0

  6. II. Chiral order parameters Axial Charge : Axial rotation : θ = 0 (no SSB) ≠ 0 (SSB) Order parameter : Examples Order parameters : NOT unique !

  7. Spectral evidence of SSB in QCD T.H. LBNL WS (1997) <AA> <VV> σ（６００） <SS> <PP>

  8. <VV> - <AA> fromτ-decays at LEP-1 ALEPH Collaboration, Phys. Rep. 421 (2005) 191 ρV(s)/s [ρV(s)-ρA(s)] /s ρA(s)/s

  9. Energy weighted “chiral” sum rules from QCD (mq=0) Dim.6 chiral condensate Koike, Lee + T.H., Nucl.Phys. B394 (1993) 221 Kapusta and Shuryak, PRD 49 (1994) 4694 Klingl, Kaiser and Weise, NPA 624 (1997) 527

  10. III. In-medium hadrons Energy weighted “vector” sum rules from QCD (mq=0) Dim.4 gluon condensate -ρpQCD(ω)) Dim.6 quark and gluon condensates -ρpQCD(ω))= C4<GG> -ρpQCD(ω))= C6<Chiral inv> +C6’<chiral non-inv> Lattice QCD simulations (with gradient flow method) + Space-time average (by hydro or other models) Dilepton data (after Cocktail subtraction)

  11. T.H. LBNL WS (1997) Slide p.31 c.f. GLS sum rule Adler sum rule Bjorken sum rule

  12. QGP Hadron-Quark Continuity in dense QCD （Nc=3, Nf=3） Quark-Gluon Plasma Hadron phase Baryon superfluid Quark superfluid Chiral symmetry is always broken at finite density

  13. Continuity in the ground state condensates m Continuity in the excited state ? excitation Low m High m p’ (8) & H NGs p(8) & H Vectors V (9) gluons (8) Fermions Baryons (8) Quarks (9) Possible fate of hadrons at high density （Nc=3, Nf=3） Vector Mesons = Gluons ?! Baryons = Quarks ?! Tachibana, Yamamoto + T.H., PRD78 (’08) Schafer & Wilczek, PRL 82 (’99)

  14. Spectral continuity of vector mesons T.H., Tachibana and Yamamoto, PRD78 (2008) Nonet vector mesons (heavy) Octet vector mesons (light) Octet gluons in CFL: mg=1.362Δ Gusynin & Shovkovy, NPA700 (2002) Malekzadeh & Rischke, PRD73 (2006)

  15. Mass formula from Finite Energy Sum Rules At low density: At intermediate density: At high density:

  16. IV. Summary • I. Chiral order parameters • not unique : Dim.3 condensate, Dim.6 condensate, etc • II. In-medium hadrons • ・ chiral restoration can be seen in spectral degeneracy • ・ moment analysis is important for model independence • ・ interesting possibility of hadron-quark crossover • (Vector mesons = Gluons, Baryons = Quarks)

  17. Back up slides

  18. QCD sum rules in the superconducting medium • Vector current： • Current correlation function： • Operator Product Expansion (OPE) up to O(1/Q6) : Chiral condensate Diquark condensate 4-quark condensate

  19. Continuity in the ground state Continuity in the excited state?? condensates m Generalized Gell-Mann-Oakes-Renner relation : ○ excitation Low m High m Yamamoto, Tachibana, Baym + T.H., PR D76 (’07) p’ (8) & H NGs p(8) & H ○ Continuity of vector mesons Vectors V (9) gluons (8) Tachibana, Yamamoto +T.H., PRD78 (2008) Fermions baryons (8) Quarks (9) Possible fate of hadrons at high density （Nc=3, Nf=3） Schafer and Wilczek, PRL 82 (1999) Yamamoto, Tachibana, Baym + T.H., PRL97(’06), PRD76 (’07) Explicit realization of spectral continuity Vector Mesons = Gluons ?! Baryons = Quarks ?!

  20. Continuity in the ground state Continuity in the excited state?? condensates m excitation Low m High m p’ (8) & H NGs p(8) & H Vectors V (9) gluons (8) Fermions baryons (8) Quarks (9) Hadron-quark continuity in dense QCD Schafer and Wilczek, PRL 82 (1999) Hatsuda, Tachibana, Yamamoto & Baym, PRL 97 (2006)

  21. T.H. Slide p.2 (1997)

  22. I. Why SPF is important ? http://www-rnc.lbl.gov/DLS/DLS_WWW_Files/DLSWorkshop/dilepton.html

  23. I. Status of QCD Running masses: mq(Q) Running coupling: αs(Q)=g2/4π FLAG Collaboration update( July 26, 2013) http://itpwiki.unibe.ch/flag/ PDG (2012) http://pdg.lbl.gov/

  24. Hadron masses from Lattice QCD Improved Wilson + Iwasaki gauge action a = 0.09 fm, L=2.9 fm, mπ=135 MeV PACS-CS Coll., Phys. Rev. D 81, 074503 (2010) 3% accuracy ⇒　L~9.6 fm, mπ=135 MeV on K-computerunderway

  25. III. In-medium hadrons In-vacuum  Nambu-Goldstone bosons  Other hadrons Examples: Gell-Mann-Oakes-Renner relation (1968) QCDSR from OPE by SVD (1979) QCDSR from Commutator by Hayata, PRD88 (2013)

  26. In-medium hadrons Complex pole (even for the pion) One-parameter example (T≠0) : * For the pion, f(x) and g(x) can be evaluated for small x. See e.g. Jido, Kunhihiro + T.H., Phys. Lett. B670 (2008) * In general, experimental inputs are really necessary. * Sometimes, spectral function is better to be studied.

  27. Dim.3 Chiral condensate in the medium Finite baryon density (χPT) Finite Temperature (LQCD) Nuclear chiral perturbation Kaiser et al., PRC 77 (2008) Lattice QCD, (2+1)-flavor Borsanyi et al., JHEP 1009 (2010)

  28. Wish list 1 Spectral difference between chiral partners π-σ, ρ-a1, ω-f1, etc Determination of D=6 chiral condensates in the vacuum? Tau-decay in nuclei ? 2 Individual properties of NG and “Higgs” bosons π, K, η (NG), σ (Higgs), η’ (anomaly) Mesic nuclei σ2γ, η2γ, η’2γ 3 Individual properties of vector bosons ρ, ω, and φ Dileptons Precision/systematic studies (dispersion relation, different targets, …)

  29. T.H. Slide p.7 (1997)

  30. III. Exact sum rules in QCD medium T.H. Slide p.20 (1997)

  31. III. In-medium hadrons In-vacuum  Nambu-Goldstone bosons  Other hadrons Examples: Gell-Mann-Oakes-Renner relation (1968) QCDSR from OPE by SVD (1979) QCDSR from Commutator by Hayata, PRD88 (2013)

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