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Kaon Condensation through Vector Manifestation and Its Astrophysical Implicatios

APCTP@2006.06.23. Kaon Condensation through Vector Manifestation and Its Astrophysical Implicatios. Chang-Hwan Lee @. Contents. Motivation: Vector Manifestation Part I: Kaon Condensation through Vector Manifestation

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Kaon Condensation through Vector Manifestation and Its Astrophysical Implicatios

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  1. APCTP@2006.06.23 Kaon Condensation through Vector Manifestation and Its Astrophysical Implicatios Chang-Hwan Lee @

  2. Contents Motivation: Vector Manifestation Part I: Kaon Condensation through Vector Manifestation - Introduction to Kaonic Physics - Kaon Condensation `a la Vector Manifestation Part II: Astrophysical Implications Issues are not settled down yet, so this talk is biased.

  3. Motivation Vector Manifestation M.Harada/K.Yamawaki/C.SasakiM.Rho/Youngman Kim Slides taken from Harada’s lectures

  4. Theoretical description of dropping r mass ? ☆ Vector Manifestation M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001) near chiral restoration point longitudinal r= Chiral partner of p Dropping r mass ・・・ necessary for the VM. ☆ Brown-Rho scaling implies dropping rmass ⇔ chiral symmetry restoration

  5. matching integrate out ~ 1 GeV Bare theory bare parameters Quantum effects Quantum theory physical quantities ☆ Wilsonian matching between EFT and QCD high energy QCD quarks and gluons (perturbative treatment) Both (perturbative) QCD and EFT are applicable Λ EFT for hadrons low energy

  6. ☆ Wilsonian matching at T → Tc - e • current correlators in the OPE ☆ Can we satisfy GV → GA in the HLS ?

  7. ☆ Yes ! ◎VM Conditionsin hot matterfor T → Tc ☆ Can we satisfy GV → GA for T → Tc in the HLS ? ◎ current correlators in the bare HLS

  8. mρ→ 0・・・ signal of the chiral symmetry restoration ! G.E.Brown and M.Rho, PRL 66, 2720 (1991) ☆ Is mr(T) → 0 related to the chiral symmetry restoration ? ◎ Wilsonian matching near Tc add the quantum and hadronic thermal corrections ◎ Quantum theory

  9. Summary ◎ Hidden Local Symmetry Theory・・・ EFT for r and p Systematic low-energy expansion including dynamical r loop expansion ⇔ derivative expansion ◎ Wilsonian matching between the HLS and QCD Matching of axial-vector and vector current correlators → Determination of the bare parameters + quantum corrections improved by Wilsonian RGEs Physical predictions ・・・ very good agreement ! ◎ Vector Manifestation in hot matter ・・・ mρ → 0 for T → Tc ⇒ mρ→ 0・・・ signal of the chiral symmetry restoration !

  10. Part I Kaon Condensation Dropping Kaon Mass in Dense Medium

  11. Kaons interactions with chiral symmetry Interactions within up & down quarks (in K, p, n) s-quark doesn’t do much because it’s different quark !

  12. Kaon Effective Mass (Chemical Potential) K+ us us K- Mass drops Easier to produce

  13. Kaon Production in Heavy Ion Collision supports Dropping K- mass !

  14. Recent Developments: Kaonic Nuclear Bound States Yamazaki et al.

  15. PLB 597 (2004) 263 Total binding energy : 194 MeV from K-ppn Mass = 3117 MeV, width < 21 MeV

  16. Dote et al. Kaonic Nuclei - Mini Strange Star 3He 3He + K- p n K

  17. 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

  18. Kaon Condensation `a la Vector Manifestation

  19. 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 !

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

  21. “Neutron/Strange/Quark” Star

  22. Astrophysical Implications Neutron Star Neutrinos Reduce Pressure Formation of low mass Black Hole

  23. Maximum Mass of NS Black Holes Neutron Stars

  24. 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

  25. 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 !

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

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

  28. 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!

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

  30. 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 !

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

  32. Fixed point of chiral symmetry restoration NChiralSR = 4 n0 r-mass drops to zero around 4 n0 Brown/Rho [PR 396 (2004) 1]

  33. 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 !

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

  35. 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

  36. By expanding about the fixed point of Harada-Yamawaki Vector Manifestion, we have strong theoretical support on kaon condensation against criticisms which are based on bottom-up approach. Kaon condensation comes in before chiral symmetry restoration (in u-, d-quark sector)

  37. Part II Astrophysical Implications Bethe, Brown, Lee, … ApJ 541 (2000) 918 New Astronomy 6 (2001) 331 ApJ 575 (2002) 996 PASJ 56 (2004) 347 astro-ph/0510379

  38. Smoking Gun for kaon condensation • SN 1987A • Radio Pulsars • Double Neutron Star Binaries • Short-Hard Gamma-ray Bursts Speculations • Isolated Single Neutron Stars • X-ray Binary [Vela X-1] • X-ray QPO source [4U1636-536] • Radio pulsar in J0751+1807 (white dwarf companion)

  39. SN 1987A • Formation of 1.5 Msun NS : theoretically confirmed by neutrino detection. • Progenitor 16 Msun O-star, 1.5 Msun Fe core. • No evidence of NS, yet. (e.g., no Pulsar signal, lower total luminosity by an order of magnitude) • NS went into Small Mass Black Hole (after cooling & accretion) !!

  40. Masses of Radio Pulsars NS-NS NS-WD Large uncertainty due to WD mass determination 1.5

  41. Double Neutron Stars (NS-NS binary) are all consistent with kaon condensation J0737-3039: 1.337 Msun & 1.290 Msun “Most recent observation of binary neutron star is also consistent with the limit suggested by kaon condensation.” [nature, 2003] PSR J1756-2251: 1.4 Msun & 1.2 Msun astro-ph/0411796

  42. How to make NS’s in NS-NS Binaries ? Binary stars Fe core masses of single & binary stars

  43. How to make NS-NS Binaries ? • Both NS’s in binaries are born with < 1.5 Msun. • Hypercritical Accretion: First-born NS should accrete when the progenitor of second NS evolves! • The only way to avoid the accretion is to have supernova explosion nearly at the same time.

  44. Hypercritical Accretion onto First-born NS ? • In the formation of NS in SN1987AHypercritical Accretion ( 108 Eddington Limit) occurred. • Otherwise NS couldn’t be formed at all ! • Thermal Neutrinos are responsible (T>1 MeV) ! Hypercritical Accretion onto Black Holes ? • No surface: Trapped photons ? • BH Binaries: Ultra Luminous X-ray Sources ?

  45. Evolution of binary NS <1% A Life time 10% B 90% He H red giant super giant Original ZAMS(Zero Age Main Sequence) Stars • Probability = 1/M2.5 • Life Time = 1/M2.5 • DM=4%, DTlife=(1 - 1/1.042.5)= 10%, DP=10% (population probability)

  46. H red giant He red giant A NS Life time 90% 10% NS B A H He He B +0.2 Msun +0.7 Msun Case 1 : DT > 10% Hypercritical Accretion: First born NS should accrete 0.9 M⊙ !

  47. H red giant He red giant A NS Life time NS B H common envelope H A He B +0.2 Msun No accretion Case 2 : DT < 10% First born NS should accrete only 0.2 M⊙ !

  48. A NS Life time NS B H common envelope H He A He H B He common envelope Case 3 : DT < 1% No accretion : same mass pulsars !

  49. Companion Masses in NS-?? Binaries BH ?

  50. Population of NS-?? Binary Max NS mass = 1.5 – 1.7 Msun • NS binaries with heavier companion should be more dominant. • But, we see only NS binaries with companion mass < 1.5 Msun. • Heavier ones went into BH. Case 1 Lee, Brown, a-p/0510380

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