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Implications of vector manifestation in hot and dense medium

YKIS06@YITP. Implications of vector manifestation in hot and dense medium. BLR, PRC 74, 024906 (2006) BLPR, PRL 96, 062303 (2006). Chang-Hwan Lee @. Contents. Part I: Hot Medium : STAR r 0 / p - Ratio Part II: Dense Medium : Kaon Condensation. Part I Hot Medium : STAR r 0 / p - Ratio.

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Implications of vector manifestation in hot and dense medium

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  1. YKIS06@YITP Implications of vector manifestationin hot and dense medium BLR, PRC 74, 024906 (2006) BLPR, PRL 96, 062303 (2006) Chang-Hwan Lee @

  2. Contents Part I: Hot Medium : STAR r0/p- Ratio Part II: Dense Medium : Kaon Condensation

  3. Part I Hot Medium : STAR r0/p- Ratio BLR, PRC 74, 024906 (2006)

  4. M. Rho’s Talk Below Tc: Chiral Symmetry Restoration • Dropping Masses a la Brown/Rho Scaling • Harada/Yamawaki & Harada/Sasaki/Rho Vector Manifestation. Fixed Point of RG approach gives vanishing coupling, vanishing mass towards chiral symmetry restoration point. both mass & decay-width scale !

  5. below TcChiral Symmetry Restoration Vector Manifestation RG fixed point Vanishing coupling M r s RHIC p Tc Q) What happens above Tc ? Hadronization ?

  6. What RHIC found • RHIC data is consistent with ideal hydrodynamics. • Matter formed at RHIC is not weakly interacting quasi-particle gas. • Very strongly coupled regime • sQGP, Quark-Gluon-Liquid

  7. Mesonic bound states above Tc: • Hatsuda & Kunihiro, PRL 55 (1985) 158(para pion & sigma)Asakawa, Hatsuda, & Nakahara, NPA 715 (2003) 863cBrown, Lee, Rho, & Shuryak, NPA 740 (2004) 171Quark-antiquark bound states exists above Tc.

  8. Potential from Bielefeld Lattice Results Assumption: finite value of V1 at r=∞ is absorbed into the renormalized thermal mass of quarks.

  9. Heavy quark potential (renormalized) from Bielefeld lattice mq=1.4 GeV

  10. Mass of Bound States (with heavy quark potential) thermal quark mass Solid lines are just to guide you.

  11. Modification for light quarks in chiral limit color-magnetic effects (cf K-electron) a =velocity of particles (c=1 unit) With chirally restored u, d quarks (helicity eigenstates) 32 degrees of freedom = lattice result 32 above Tc !

  12. Effective degrees of freedom [Karsch et al.] Idea gas limit staggered fermions Effective degrees of freedom is lower by 20% from ideal gas limit (massless limit). 32 istead of 37 (ideal gas limit)

  13. With modified potential (chiral limit)

  14. heavy quark potential chiral limit heavy quark potential chiral limit

  15. Unorthodox phase structure (Hypothesis) 2mq* a1 M r Mesons disappear qq s Ideal Liquid QGP p Tc Tzb • Masses of colorless pion, sigma-like modes above Tc go to zero at T = Tc;+

  16. Lattice Results from Miller: Gluon Condensate Hard glue is responsible for ldeal liquid Soft glue Hard glue

  17. Implications for RHIC Scaling decay width Vector manifestation by Harada & Yamawaki No decay near Tc ! dominant decay is around & below T=120 MeV

  18. Braun-Munzinger, Stachel, Wetterich (2003) • Chemical freezeout temperature is close to Tc. • Equilibration in the chirally broken sector just below Tc. • Puzzle: “r/p” ratio (= 4 x 10-4 ) was lower than STAR experiment roughly by a factor of 2 PRL 92 (2004) 092301

  19. Our point of view Equilibrium of hadronic mode has to be already established above Tc at RHIC ! STAR: Peripheral collisions: Tchemical freeze out = Tc Tc : chemical equilibrium Delayed decay of rho at T=120 MeV

  20. With massless mesonic bound states at Tcthis ratio is governed mainly by degrees of freedom 3 (r0) = 0.16 19 (pi- from s & r, …) [ Brown, Lee, Rho, PRC 74, 024906 (2006) ] 4 x 10-4 with vacuum mass( Braun-Munzinger et al. )

  21. Conclusions in Hot Medium • Our analysis (chiral symmetry restoration + Bielefeld Lattice Result) indicates masslessmesonic bound states at Tc;+. • mass & width (simultaneous scaling):delayed rho decay is consistent with rho/pi ratio in peripheral collisions in STAR. Thanks to Bielefeld Lattice Group (F. Zantow) for providing us their results.

  22. Part II Dense Medium : Kaon Condensation BLPR, PRL 96, 062303 (2006)

  23. Why Strange Quarks in Neutron Stars ? • proton, neutron: u, d quarks • By introducing strange quark, we have one moredegrees of freedom, energy of the system can be reduced! • In what form ? Kaon, Hyperons…… Kaon is the lighest particle with strange quark !

  24. reduce pressure forming denser medium Kaon Condensation p + e- p + K- M e- chemical potential Kaon effective mass density

  25. “Neutron/Strange/Quark” Star

  26. deep discrete bound states:with binding energy ~ 100 MeV Strong in-medium KN interactions. Precursor to kaon condensation. Kaonic Nuclei - Mini Strange Star Very strong K--p attraction Yamazaki, Akaishi, Dote, et al. Barnea & Friedman, n-t/0611020

  27. Q) What is the critical density for kaon condensation ? • Conventional approach (bottom-up):from zero density to higher density • New approach (top-down):from VM fixed point to lower density

  28. Problems in bottom-up approach • Problem in K-p Scattering amplitude:experiment : - 0.67 + i 0.63 fm (repulsive) chiral symmetry : + ( attractive ! ) • Problem of L(1405)pole position of L(1405) => only 30 MeV below KN threshold Perturbation breaks down in bottom-up approach !

  29. Far below L(1405) pole, L(1405) is irrelevant ! One has to start below L(1405) pole !

  30. Essense of KN scattering & kaon condensation puzzle Near w=MK/2, L(1405) is irrelevant !

  31. New Top-down approach Q) Is there a proper way to treat kaon condensation which doesn’t have problems with the irrelevant terms, e.g., L(1405), etc, from the beginning ? Kaon Condensation `a la HY Vector Manifestation => All irrelevant terms are out in the analysis from the beginning!

  32. Kaon condensation from fixed point Lots of problems due to irrelevant terms mK me ? Vector Manifestation density nc chiral symmetry restoration

  33. Weinberg-Tomozawa term: • most relevant from the point of view of RGE `a la VM. • w, r exchange between kaon & nucleon. |VN(w)| = 171 MeV at n0 is well below experimental 270 MeV BR scaling is needed !

  34. Deeply bound pionic atoms [Suzuki et al.] fixed point of VM a*=1 (Harada et al.) Enhancement at fixed point due to BR & VM

  35. Kaon potential at critical density without BR & VM 10% p, nc=3.1 n0 Kaon potential at fixed point ( 4n0) with BR + VM Enough attraction to bring kaon effective mass to zero at VM fixed point ! BR scaling & HM-VM At fixed point, kaon effective mass goes to zero !

  36. All the arguments against kaon condensation (which is based on bottom-up approach) is irrelevant at densities near VM fixed point ! mK Kaon-condensed system Bottom-up Vector Manifestation me Top-down nc After kaon condensation, the system will follow the line guided by fixed-point analysis

  37. Kaon condensation from fixed point mK me ? Chiral symmetry restoration rc density Only EOS which gives rc < rcSB is acceptable !

  38. Conclusion • Vector manifestation can explain the STAR r0/p- ratio by simple counting on degrees of freedom • Vector manifestation indicates that the critical density for kaon condensation is lower than the chiral symmetry restoration density. Thank you !

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