Teiji Kunihiro (YITP, Kyoto) A Summary and Concluding Remarks Chiral05 RIKEN Feb , 2005

CS C T   SB QGP QCD critical point meson condensation? ?  0 CFL QCD phase diagram H matter?

What Lattice tells us on the possible CEP

Quark number susceptibility (S.Ejiri) We find a pronounced peak for q/T~ 1. Critical endpoint in the (T,)? Critical endpoint in the (T,  )? Peak position moves left as  increases, corresponds to the shift of Tc()

Color SuperConductivity Nice summary by M. Buballa charge neutralities and beta eq. and Ms>>Mu,d Various interesting complications; dSC (Matsuura);GL approach at T~Tc gapless SC ’ s and its instability; Interplay with chiral condensates (Buballa, Abuki et al) Imaginary Gluon Meissner mass Pressure  Normal QM never realized? A unified approach both for NM and QM(S. Lawley) LOFF?

Abuki, Kitazawa and T.K.(hep-ph/ )

The Physical Picture of the QCD matter above Tc Charmonia survive QCD ph. Tr. (T. Hatsuda) Precursory Soft modes Chiral (T.Hatsuda and T.K. ;1985) CSC (M. Kitazawa et al) and their effects on quark spectra eg. pseudogap (M. Kitazawa et al)

Spectral function ρ(ω) J/ψ(3.1 GeV) 1.J/ψ survives up to 1.6 Tc 2. J/ψ disappears in 1.6 Tc < T < 1.7 Tc Umeda et al, hep-lat/ Datta et al., PRD 69 (’04) Asakawa & Hatsuda, PRL 92 (’04) J/ψ and η c above T c (quenched simulation) Dependent on volume of the Lattice

QCD phase structure BCS-BEC crossover Leggett, Lec. Notes in Phys. (’82) Abuki, Itakura & T.H. Phys. Rev. D (’02) Cond. of Fermionic-Atom Pairs 40 K 40 K : JILA, PRL 92 (2004) 6 Li : Innsbruck, MIT, PRL 92 (2004) M.Kitazawa et al T.Hatsuda-T.K. M.Kitazawa et al Based on Hatsuda ’ s figure

Powerful Theoretical Approach to BCS-BEC crossover Exact Renormalization group (M. Birse) a first attempt; promising higher order corrections beyond MF turned out small. a long line of the to-do list.

Mesons in Nuclei, as probes of Chiral properties General Introduction; S. Hirenzaki, K.Itahashi Deeply bound pionic nuclei; the existence itself interesting and also play a role as a powerful probe of the chiral properties of the nuclear matter! 30% reduction of quark condensate! depends on the estimate of the radii the validity of GOR at finite density seems O.K. in the medium chiral pert. Exp.

Physics Motivation Evaluate the order parameter of Chiral symmetry restoration quantitatively with small ambiguity.

Pion-nucleus Isovector interaction strength Theoretical study to investigate the effect of partial restoration of chiral symmetry on the modification of isovector interaction strength. in vacuum b 1 is changed in nucleus.

Gell-mann-Oakes-Renner relation Tomozawa-Weinberg relation Theoretical Treatment Bringing these relations to finite density medium, we obtain... Meissner et al. Ann. Phys.297(2002)27 Kolomeitsev et al, PRL90(02) input

Pion-nucleus Isovector interaction strength Theoretical treatment 33% reduction of Largest ambiguity comes from the uncertainties in the matter radii of nuclei.

Experiment should be made and is being anallyzed: Spring-8 (Muramatsu) (Metag); CB/TAPS 4 Vecotr Mesons Hatsuda-Lee, Brown-Rho: vacuum change (chiral tr.) leads to a mass shift of the vector mesons. KEK-PS (Yokkaichi): show a mass drop!

The data from Nb target shows (Metag); Charmed mesons in the Theory: QCD sum rules (Hayashigaki) modification of D mesons, relevant for J/Psi suppression from the hadron origin (KEK-PS;Yokkaichi) Cabrera: a theory on Consistency between KEK-PS v.s. LEPS, the latter of which shows a large absorption beyond the theoretical expectation.

What is the Vector Mesons, especially, What is their chiral properties? An answer: Hidden local Symmetry approach (Bando etal) Vector Manifestation occurs at T~Tc? (1/2, 1/2) + ((3.1)+(1,3)) representation Pure (3,1)+(1,3) pi and rho get degenerated?! Yes, according to C. Sasaki, M. Rho through the theory of Harada and Yamawaki. Lattice calculation and hopefully will tell through checking the many interesting predictions, including Theta+ in the Skyrm model (Rho)

+ +  1540  10 MeV  < 25 MeV Gaussian significance 4.6  background T. Nakano et al., Phys.Rev.Lett. 91 (2003) Renaissance of hadron spectroscopy !  

New Experiment and New analysis by LEPS (Nakano) The peak is there! little produced by the rescattering, but Correlated with (1520) Which may tell us the nature of ! Theoretical works: Overview by M. OKa Detailed analysis of the decay width (Hosaka) -  3/2^(+,-)? But a lattice cal. suggests ½ ^- (T.T.Takahashi et al) even in nuclei, i.e., hypernuclei might exist! Can be tested in J-PARC and J-Lab.

NK scattering state vs Pentaquark state( T.T. Takahashi et al)  Small L Large L  (u,d,s)=(100,100,100)MeV (u,d,s)=(100,100,240)MeV (u,d,s)=(240,240,100)MeV(u,d,s)=(240,240,240)MeV M N +M K NK scattering Mass (GeV) 1fm 2.4fm 4fm

Meson: Related to Anomaly; otherwise ; ideal mixing realized Also selective coupling of with N*(1535) chiral dynamics v.s. Chiral doublet (a la DeTar-Kunihiro( ‘ 89) )type? a funny density dependence of the opt. pot. in the latter. Hayano, Nagahiro: Near future experiment in GSI!

; energy-momentum tensor of QCD Quantum effects! () Current divergences and Quantum Anomalies Dilatation Chiral Anomaly Dilatation(scale) Anomaly

Problem # of the generators 2x(8+1)=18 1+8=9 G= H= # of NG-bosons= dim G - dim H = 18 – 9 = 9 (?) Nambu-Goldstone Theorem # of the lightest pseudo-scalar mesons = 8 ! (140)(500)(550)<< (958) Why is so massive ? U A (1) Problem Anomaly Operator Equation! even in the chiral limit!

The Meson N.Grion (CHAOS) S. Schadamand (TAPS) T. Itabashi (RCNP) G. Chanfray (Th)

A condensed matter physics of vacuum (Y. Nambu; 1960)

Gauge invariance Axial gauge (chiral) symm. c.f. Bogoliubov, Anderson

Chiral Transition and the collective modes 0 c.f. Higgs particle in WSH model ; Higgs field Higgs particle

  What is the significance of the  in hadron physics? the softening of the  with increasing T and

T. Hatsuda and T. K., Phys. Rev. Lett. 55 (1985), 158 T dependence of the (`para’) sigma and (`para’) pion masses Large T

The significance of the  meson in low energy hadron physics and QCD 1. The pole in this mass range observed in the pi-pi S-matrix. As a compilation of the pole positions of the  obatined in the modern analyses: Significance of respecting chiral symmetry,unitarity and crossing symmetry to reproduce the phase shifts both in the  (s)- and , (t)-channels with a low mass  pole;(Igi and Hikasa(1999)). 2. Seen in decay processes from heavy particles; E. M. Aitala et al, Phys. Rev. Lett. (86), 770 (2001) 3. Responsible for the intermediate range attraction in the nuclear force. 4. Accounts for  I=1/2 enhancement in K ! 2  compared with K + !    . E.P. Shabalin (1988); T. Morozumi, C.S. Lim and I. Sanda (1990).  -N sigma term MeV (naively » 15 MeV) enhanced by the collectiveness of the  (.T.Hatsuda and T.K.(1990)) ; see the next slide.  6. The  of the chiral order parameter The Higgs particle in the WSG model

K. Igi and K. Hikasa, Phys. Rev. D59, (1999) The phase shifts in the sigma and rho channel in the N/D Method; resp. chiral symm., crossing symm and so on. No  but  in the t-channel and the  in the t-channel Both with the  in the s-

The poles of the S matrix in the complex mass plane for the sigma meson channel: complied in Z. Xiao and H.Z. Zheng (2001) G.Colangero, J. Gasser and Leutwyler (2001)

Issues with the low-mass  meson in QCD In the constituent quark model; the mass in the GeV region. Some mechanism needed to down the mass; (i) Color magnetic interaction between the di- quarks? (Jaffe; 1977: Alford-Jaffe;2000) (ii) The collectiveness of the scalar mode as the ps mode; a superposition of states. Chiral symmetry (NJL) (iii) The - molecule as suggested in scatt.

The Scalar mesons on the Lattice The Scalar Collaboration: S. Muroya,A. Nakamura,C. Nonaka,M. Sekiguchi, H. Wada,T. K. (Phys. Rev. D70, (2004)) ---- A full QCD calculation -----

Simulation parameters Lattice size : 8 3 × 16  = 4.8  = , , CP-PACS well established light meson with large lattice a = 0.197(2) fm,  c = (14) ( CP - PACS, Phys. Rev. D60(1999) ) Number of the Z 2 noise = 1000 Wilson Fermions & Plaquette gauge action Disconnected diagram

Propagator for  meson (2) Where Connected diagram Disconnected diagram - Vacuum contribution

m_m_ The meson masses

 meson propagators Connected Part & Disconnected Parts (  = )

Chiral Transition and the collective modes 0 c.f. Higgs particle in WSG model ; Higgs field Higgs particle

The poles of the S matrix in the complex mass plane for the sigma meson channel: complied in Z. Xiao and H.Z. Zheng (2001) G.Colangero, J. Gasser and Leutwyler (2001) Softening !

T. Hatsuda, H. Shimizu, T.K., Phys. Rev. Lett. 82 (1999), 2840 Spectral function in the  channel

The spectral enhancememnt in the nonlinear ｒ ealization D. Jido, T. Hatsuda and T. K.,Phys. Rev. D63} (2000), (R). In the polar decomposition M=SU, In the heavy S-field limit, fixed ;

The renormalization of the wave function Due to the new vertex: C.f. Importance of the w.f. renormalization in other physics: U. Meissner, J. Oller and A. Wirzba, Ann. Phys. 297 (2002) 27 E. Kolomeitzev, N. Kaiser and W. Weise, P.R.L. 90 (2003) Deeply bound pionic nucleiw.f. renormalization E-dependece of opt. pot. c.f. Freidman and Gal (04)

D. Jido et al (2000) Softening of the in-medium pi-pi cross section In the non-linear realization

Chiral Lagrangian in the Medium Chiral Lagrangian: The pion field: Pion decay constants: In the vacuum: (  = ) Normalization of the  the pion mass:

In the medium: Thorsson-Wirzba Lagrangian (1996)

Then, The normalization of  and The pion mass: The quark condensate: ( ; isoeven scatt. Length )

Gell-Mann-Oakes-Renner relation in the nuclear medium holds up to : (GeV^(-1)) ρ ρ

- Scattering amplitude in the medium: Enhancement of the scattering amplitude in the sigma-meson channel! Owing to the wave-function renormalization as desribed by the pion-decay const. in the medium. A unified picture of the physics of the deeply bound pionic nuclei and the pi-pi scattering in I=J=0 channel of nuclei. (D. JIdo, T. Hatsuda and T.K. ;in preparation) (Jido, Hatsuda, T.K.(2000))

This ratio represents the net effect of nuclear matter on the interacting system. CB: Phys. Rev. Lett. 85, 5539 (2000). CHAOS:Phys. Rev. C60, (1999). P. Camerini et al, Phys. Rev. C64, (2001). (CHAOS coll.) A’=2 !208 CHAOS (1996)

C  ; A-dependence of  A Oset: Full model of the       process, standard nuclear effects discussed, P-wave pionic modes included and the  -meson dynamically generated. Oset and Vicente, PRC60(1999) Muhlich: Model based on Oset’s developed for the       and       reactions, better treatment of FSI of pions with the nucleus, no medium modifications. Muhlich et al., PLB595(2004)216 TAPS CHAOS     I=0     I=1 E~420 MeV  ~ 2/3  0     I~0     I=2 E~420 MeV  ~ 1/3  0

Differential cross sections of the reaction A( ,     )A' J.G. Messchendorp et al, Phys. Rev. Lett. 89 (2002), phase space TAPS experiment: L. Roca et al (2002) without softening

 A   o  o X  A   +/-  o X m(  o  o ) for isoscalar channel only: drops with increasing A consistent with isotropic angular distribution  o  o angular distribution E  = MeV J.G.Messchendorp et al., PRL 89, L. Roca, et a l., PLB 541 (2002) 77, priv. comm. preliminary    S.Schadmand

G.Chanfray concerned with the stability of Nuclear Matter Non-lin.(strong coupl.) v.s. Lin. Representation. Systematic analysis should be made.

(1405) and (deeply bound) Kaonic-nuclei (1405) and (deeply bound) Kaonic-nuclei (1405) another longstanding problem 3 quark or “ pentaquark ” ? or K-N bound state? if so, as M.Soyeur showed, Kaonic-nuclei may open new aspect of manybody problem with strangeness T. Suzuki, Y. Akaishi, T. Yamazaki Experimental and theoretical works are accelerated by  + effect! Discovery and Confirmation of the strange TriBaryons! or nona-quark states (Y. Maezawa)

   KN   Chiral dynamics of two  (1405) states D. Jido, J.A. Oller, E. Oset, A. Ramos & U.-G. Meissner, Nucl. Phys. A 725 (2003) 181 Experimental check ! Consistent to K-atom data ?(Y.Akaishi)

T. Suzuki H. Bhang G. Franklin K. Gomikawa R.S. Hayano T. Hayashi K. Ishikawa S. Ishimoto K. Itahashi M. Iwasaki T. Katayama Y. Kondo Y. Matsuda T. Nakamura S. Okada H. Outa B. Quinn M. Sato M. Shindo H. So P. Strasser T. Sugimoto K. Suzuki S. Suzuki D. Tomono A.M. Vinodkumar E. Widmann T. Yamazaki T. Yoneyama Discovery of S 0 (3115) in 4 He(stopped K -,p)K - pnn Phys. Lett. B597 (2004) 263 Press release on Aug. 24, 

Evidence for K - ppn Oct.16, 2003 M. Iwasaki et al. M. Iwasaki T. Suzuki H. Bhang G. Franklin K. Gomikawa R.S. Hayano T. Hayashi K. Ishikawa S. Ishimoto K. Itahashi T. Katayama Y. Kondo Y. Matsuda T. Nakamura S. Okada H. Outa B. Quinn M. Sato M. Shindo H. So T. Sugimoto P. Strasser K. Suzuki S. Suzuki D. Tomono A.M. Vinodkumar E. Widmann T. Yamazaki T. Yoneyama nucl-ex/ from 4 He(stopped K -,n)

A. Dote et al., Phys. Rev. C70 (2004) NN LS potential effect 3 P 2 pairing N(0s) 2 (0p) K _ N(0s) 3 K _ T=1 T=0 T=1 T=0 T=1 T=0 T=2

Problems Quite larger binding energy than expected by brave Akaishi-Yamazaki! relativistic effects/precursor of Kaon condensation (Y.Akaishi) Consistency with experiment for larger nuclei O16 by T. Kishimoto as well as Kaonic atom (S. Hirenzaki, T. Ishiwatari) Single kaon can take care of only a few nucleons but not, say 15. (Akaishi-Yamazaki) NN ? 940x =3135 (M. Oka, M. Vicent-Vacas) rejected experimentally ?

Energy Spectrum (In-flight K,n) P K = 930 MeV/c bound region [ T.Kishimoto et al., Prog. Theor. Phys. Suppl. 149 (2003) 264 ] [ Fig. taken from the seminar by Dr.Hayakawa ] (In-flight K,p) P K = 976 MeV/c

Worth further study S. Piano (FINUDA) invariant mass analysis of three bodies observed a PP deeply bound system T.Yamazaki Possible Heavy-Ion production (Quark-Gluon Bound (QGB) systems) and conjectures on high density matter with kaon (condensation?) Intriguing to re-analyses strange nuggets with chiral symmetry taken into account; M.Rho, S. Yasui

Concluding Remarks Certainly, the field is rich in physics, promising and involves pleasant experiment- theory people collaboration and discussions. Fun! The continuation of the work shop originated from Chiral02 (YITP) is planned to be held in Europe. Also, there will be a YKIS 2006, entitled `Exotic Hadrons and Hadronic Matter ’, YITP, Kyoto, Oct.30 – Nov.17, 2006 Get together again and again! Thank you!