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Recent Lattice Results relevant for Heavy Ion Collisions

Recent Lattice Results relevant for Heavy Ion Collisions. Kazuyuki Kanaya Institute of Physics, Univ. of Tsukuba kanaya@rccp.tsukuba.ac.jp. QM 2001 Theoretical Conference Summary by Jean-Paul Blaizot

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Recent Lattice Results relevant for Heavy Ion Collisions

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  1. Recent Lattice Resultsrelevant for Heavy Ion Collisions • Kazuyuki Kanaya • Institute of Physics, Univ. of Tsukuba • kanaya@rccp.tsukuba.ac.jp QM2002 Nantes, July 2002 / K. Kanaya

  2. QM 2001 Theoretical Conference Summary by Jean-Paul Blaizot ... to calculate (QGP’s) detailed properties from the first principles of QCD ... Progress in this direction are constant though, and the gap between what can be calculated from QCD and what can be measured, although it is still large, is diminishing. This remains true and the gap is not small yet, but ... QM 2001 New York 1 / 2001 Lattice 2001 Berlin 8 / 2001 Lattice 2002 Cambridge, MA 6 / 2002 QM 2002 Nantes 7 / 2002  Several big developments. QM2002 Nantes, July 2002 / K. Kanaya

  3. Related lattice papers on hep-?? afterQM2001 hep-lat/0103009 A.Cucchieri et al. hep-lat/0103013 R.V.Gavai, S.Gupta hep-lat/0103037 E.Laermann, P.Schmidt hep-lat/0103271 J.B.Kogut, D.Toublan hep-lat/0104001 Z.Fodor, S.D.Katz hep-lat/0104010 J.B.Kogut et al. hep-lat/0104011 J.B.Kogut, D.K.Sinclair hep-lat/0105023 C.Gattringer et al. hep-lat/0105026 J.B.Kogut et al. hep-lat/0106002 Z.Fodor, S.D.Katz hep-lat/0106019 F.Karsch hep-lat/0107002 QCD-TARO: S.Choe et al. hep-lat/0107004 S.Hands et al. hep-lat/0107020 F.Karsch et al. hep-lat/0107022 R.V.Gavai et al. hep-lat/0108016 P.R.Crompton hep-lat/0109017 Frithjof Karsch hep-lat/0109023 R.V.Gavai, et al. hep-lat/0109034 S.Hands hep-lat/0110014 T.Schulze et al. hep-lat/0110015 C.Gattringer et al. hep-lat/0110017 R.Fiore et al. hep-lat/0110019 S.Hands hep-lat/0110022 J.B.Kogut, D.K.Sinclair hep-lat/0110024 K.Langfeld et al. hep-lat/0110030 C.Bernard et al. hep-lat/0110032 R.V.Gavai et al. hep-lat/0110039 Ch.Schmidt et al. hep-lat/0110048 E.Bittner et al. hep-lat/0110054 R.V.Gavai hep-lat/0110067 C.Bernard et al. hep-lat/0110080 S.Ejiri et al. hep-lat/0110089 O.Miyamura, S.Choe hep-lat/0110090 S.Hands et al. hep-lat/0110092 J.Ambjorn et al. hep-lat/0201017 J.B.Kogut, D.K.Sinclair hep-th/0201168 H.Kleinert et al. hep-lat/0202005 S.Gupta hep-lat/0202006 R.V.Gavai, S.Gupta hep-lat/0202024 C.Allton et al. hep-lat/0202026 Keh-Fei Liu hep-lat/0202027 S.V.Molodtsov, G.M.Zinovjev hep-lat/0202028 J.B.Kogut, D.K.Sinclair hep-lat/0203013 C.Gattringer et al. hep-lat/0203015 Rajiv V.Gavai hep-lat/0203024 T.Takaishi hep-lat/0204010 C.R.Allton et al. hep-lat/0204013 O.Miyamura et al. hep-lat/0204029 Z.Fodor, S.D.Katz hep-lat/0205008 M.Caselle et al. hep-lat/0205016 Ph.de Forcrand, O.Philipsen hep-lat/0205019 J.B.Kogut et al. hep-lat/0205030 H.Kr\"oger et al. hep-ph/0206004 E.-M.Ilgenfritz et al. hep-lat/0206020 N.Ishii et al. hep-lat/0206028 B.Alles, E.M.Moroni hep-lat/0206029 B.Lucini et al. hep-ph/0206200 C.R.Allton et al. hep-lat/0110095 CP-PACS: S.Aoki et al. hep-lat/0110102 Z.Fodor, S.D.Katz hep-lat/0110103 F.Zantow et al. hep-lat/0110106 F.Zantow et al. hep-lat/0110109 T.R.Miller, M.C.Ogilvie hep-lat/0110111 P.Petreczky et al. hep-lat/0110122 K.Kajantie et al. hep-lat/0110132 I.Wetzorke et al. hep-lat/0110136 J.Clowser, C.Strouthos hep-lat/0110137 C.Strouthos hep-lat/0110138 S.Kratochvila, P.de Forcrand hep-lat/0110139 A Barresi et al. hep-lat/0110145 G.Aarts et al. hep-lat/0110152 P.Giovannangeli, C.P Korthals Altes hep-lat/0110160 M.Caselle et al. hep-lat/0110177 S.Sakai et al. hep-lat/0110182 C.Gattringer et al. hep-lat/0110204 K.Nomura et al. hep-lat/0110208 F.Karsch et al. hep-lat/0110223 QCD-TARO S.Choe et al. hep-lat/0111013 X.Liao hep-lat/0111052 N.Ishii et al. hep-lat/0111059 F.Karsch et al. hep-lat/0111064 Z.Fodor, S.D.Katz nucl-th/0111082 S.Muroya et al. hep-lat/0112046 I.Montvay et al. T >0 andm=0 [Quench / Nf=2 / Nf=2+1,3 ] m  0 [small m/ large m] Others QM2002 Nantes, July 2002 / K. Kanaya

  4. Finite T, m talks/posters at Lattice2002 • Asakawa • Ishii • Datta • Papa • Saito • Bornyakov • Caselle • Aarts • Kroger • Miller • Christ • Schmidt • Levkova • Heller • Gavai • Wenger • Philipsen • Ejiri • Nonaka • Fodor • Crompton • Walters • Sinclair • Kogut • Goubankova • Svetisky • Barresi • Necco • Y. Nakamura • Bettencourt • Bringoltz • Nemoto • Nomura • Schroeder • Sugar • Takaishi Lattice results at QM2002 T>0 andm=0 [Quench / Nf=2 / Nf=2+1,3] m 0 [small m/ large m] Others • Thursday 18th Parallel (III) “Theory (general)” • Asakawa • DiGiacomo • Friday 19th Parallel (II) “Leptons/Photons” • Karsch • Tuesday 23rd Plenary • Fodor • and Posters (Takaishi, DElia, Muroya, Nakamura). QM2002 Nantes, July 2002 / K. Kanaya

  5. What’s new on the lattice? • Toward the physical point • New NF=2+1 and 3 studies • QCD transition at the physical point • Toward the continuum limit • New simulations at larger Nt • Anisotropic lattices for EOS • Spectral functions byMEM • Philosopher’s stone, or ... ? • T >0, m=0 • m 0 • Summary Constant developments, new methods A (partial) breakthrough! • Small m • Reweighting along TCiImaginary m • Rew.+Taylor expansion iDerivatives at m=0 • Large m • Finite isospiniTwo-color QCDiNJL QM2002 Nantes, July 2002 / K. Kanaya

  6. Issues not covered here: • Application of new lattice fermions to T>0 QCD Overlap fermions (Gavai et al.) HYP fermions (A.Hasenfratz & Knechtli) • Topological structure around TC Gattringer et al., Illgenfritz et al., di Giacomo et al., ... • Large NC QCD Lucini et al., ... • Algorithms Takaishi, Luo, Caron et al., Alles-Moroni,... • Model studies ChPT, Polyakov loop model, Instanton, ... NJL, ... etc. etc. Sorry! QM2002 Nantes, July 2002 / K. Kanaya

  7. ? ? Where is the physical point? 1. T >0, m=0 1.1 Toward the physical point Theoretical expectations from effective models 3d Z(3) Potts 3d O(4) scaling tricritical point 2nd order line: mud (ms*-ms)5/2 near the tricritical point 3d Ising scaling QM2002 Nantes, July 2002 / K. Kanaya

  8. Ns Nt Phys.Pt. Phys.Pt. Phys.Pt. Larger Nt with improved-action needed! Toward the physical point (2) Previous results • NF=2, mostly Nt = 4 (and 6) • Improvement of lattice action  TC and EOS converging • TC(NF=2)  170--175 MeV in the chiral limit, etc. • CP-PACS, PRD63(2001) 034502; Bielefeld, hep-lat/0012023 • Expected O(4) scaling observed only with impr.-Wilson • Iwasaki et al. PRL78(1997)179; CP-PACS, PRD63(2001) 034502. • but not with stand.-KS. • Karsch-Laermann, PRD50(1994)6954; JLQCD, PRD57(1998)3910; MILC, PRD61(2000)054503 •  Nt=4 too small? Lattice artifact due to non-locality? Operator mixing? or ?? • NF=2+1, Nt = 4 • 1st results of EOS with impr.-KS. • Karsch et al, PLB478(2000)447 • Location of the physical point : • stand.-KS, Nt=4  crossover • Columbia, PRL65(1990)2491; JLQCD, NPB(PS)73(1999)459 • stand.-Wilson, Nt=4  1st order • Iwasaki et al., PRD54(1996)7010 QM2002 Nantes, July 2002 / K. Kanaya

  9. Toward the physical point (3) New: Updates of NF=2+1, stand.-KS, Nt=4 • Schmidt (Bielefeld-Swansea)@ Lattice2002 • stand.-gauge & stand.-KS • NF = 2+1: mud=0.03, ms=0.045, 0.06 • 123x4 • Binder cumulant • Christ (Columbia)@ Lattice2002 • stand.-gauge & stand.-KS • NF = 3: m=0.015-0.045 • 83x4, 163x4, 323x4 • Binder cumulant • Critical line determined around the NF=3 critical point. Confirm the previous phase diagram (stand.-KS at Nt=4). Note: (mPS)C(NF=3)~280-290 MeV  ~190 MeV with impr.-KS(p4) [heplat/011039] QM2002 Nantes, July 2002 / K. Kanaya

  10. Nature of the QCD transition at the physical point is still an open problem on the lattice. Toward the physical point (4) New: • Sugar et al. (MILC)@ Lattice2002 • impr.-gauge(1-loop Symanzik)& impr.-KS(Asqtad)  Improvements in dispersions, flavor sym., and scaling at T=0 [PRD64 (2001) 054506] • NF = 2+1 [ms=msphys, mud/ms=.6, .4, .2], NF = 3 [mq/ msphys =1, .6, .4] • 123x6, 163x8 • Crossover at all simulation points. • A crude extrapolation mud0 suggests TC > 170MeV if it exists. • Simulation at smaller mud needed to clarify the nature of the transition at the physical point. QM2002 Nantes, July 2002 / K. Kanaya

  11. Toward the physical point (5) Current HMC algorithm exact only for NF=2n Wilson-type and NF=4n KS-type quarks. Approximate “R-algorithms” have been employed for odd #f of lavors and also NF=2 KS-type quarks. New: • Exact odd #flavor algorithms for Wilson-type • Takaishi-deForcrand, J.Mod.Phys.C13 (2002) 343; JLQCD, PR D65 (2002) 094508 • Exact NF=2 algorithms for staggered-type Horvath et al. @ Lattice98; Ishikawa (JLQCD) @ Lattice2002 • Feasible on present computers. Time is ripe to start large-scale 2+1 flavor simulations with improved-quarks at Nt ≥ 6 to resolve the long-standing problem of the physical point. QM2002 Nantes, July 2002 / K. Kanaya

  12. 1.2 Toward the continuum limit • Lattice results must be extrapolated to a  0. • Finite temperature simulations: Nt  large. • Large Nt expensive • Thermodynamic limit: Ns >> Nt (Ns/Nt ≥4 to be safe). • Computer time ~ (Ns 3 ∙ Nt )5/4 • Major full QCD studies have been limited to Nt = 4-6 where we sometimes encounter non-negligible lattice artifacts. • Two spellsto overcome the problem: • Improvement • Anisotropic Lattice QM2002 Nantes, July 2002 / K. Kanaya

  13. Toward the continuum limit (2) • Improvement • Remove lattice artifacts of stand.-Wilson at Nt =4. • Universal TC, etc. Insufficient for EOS at Nt =4. Energy density (NF=2) CP-PACS, PRD64 (2001) 074510 • impr.-gauge & impr.-Wilson • 163x4, 163x6 Nt =4 Large scaling violation: 40% decrease by Nt =46.  Nt =4 far from the cont. lim. Nt =6 Nt = 6 EOS close to the continuum limit? Nt = 6 EOS looks universal between impr.-Wilson and stand.-KS. Nt =6 QM2002 Nantes, July 2002 / K. Kanaya

  14. Toward the continuum limit (3) • Sugar et al. (MILC)@ Lattice2002 • impr.-gauge & impr.-KS • NF=3 • 83x4, 123x6, 163x8 No EOS yet. Triplet quark number susceptibility Nt =6 and 8 roughly scaling! Precise continuum extrapolation of with Nt=6, 8, ...? Nt ≥ 8 EOS data needed. Recent studies of quark number susceptibilities and derivatives: • NF=2 stand.-KS: QCD-TARO, PR D65(2002)054501; Gavai et al., ibid.054506 quenched QCD: Gavai-Gupta, PR D65 (2002) 094515 Wroblewski parameter lscs/cu etc. may be less sensitive to lattice artifacts. QM2002 Nantes, July 2002 / K. Kanaya

  15. The first controlled continuum extrapolation of EOS in QCD, but quenched. • Umeda (CP-PACS)@ Lattice2002 • NF=2 full QCD with impr.-gauge & impr.-Wilson(status report). Toward the continuum limit (4) • Anisotropic Lattice An observation: at-errors larger than as-errors in EOS. SU(3) gauge theory in the high-T limit: • Idea: at < as efficiently reduces the lattice artifacts in EOS. • x= as/at = 2 optimum. CP-PACS, PR D64 (2001) 074507 • Test in quenched QCD •  promising: Continuum extrapolation of p/T QM2002 Nantes, July 2002 / K. Kanaya

  16. Maximum Entropy Method • was successful in image reconstruction in astrophys. / criminal researches, etc. • calculate “the most probable” f(w) • by maximizing P[f | DH]: • prob. of f(w)given the data D(t ) and prior knowledge H on f(w). 1.3 Spectral functions byMEM Hadronic spectral function f(w) important in R-ratio, dilepton rate, etc. In Euclidian sp.-time, spectral function is related to correlation function D by a Laplace transformation. Lattice: D(t ) available only at t/at = 0, 1, 2, ... , tmax (tmax< Nt), with errors. f(w)  D(t ) is an ill-posed problem. QM2002 Nantes, July 2002 / K. Kanaya

  17. Spectral functions byMEM (2) Defines what we think “probable”. Shannon-Jaynes entropy ~ “probable” in the statistical sense. Inputs: D, m, a[MEM] Output: f m : default model for f (f = m maximizes S) a : relative weight of S[f  m]against L[f  D] Uniqueness of Max{P[f|DH]}: Asakawa et al., Prog.Part.Nucl.Phys.46 (2001) 459 Dependence on a is (usually) very weak. We can eliminate a by an additional statistical argument. (optimum a, or average over a). Dependence on m is (usually) weak, when MEM works. QM2002 Nantes, July 2002 / K. Kanaya

  18. MEM works when # and quality of data are sufficiently high. • MEM correctly reproduces • ground st. and 1st exited st. energies  peak positions • decay constants  area of peaks • lattice artifacts (doublers etc.) at high wD at small t • decay modes • MEM is easier (no smearings etc.) and gives smaller errors. Spectral functions byMEM (3) • Tests in LQCD • Asakawa et al., Prog.Part.Nucl.Phys.46 (2001) 459 Systematic study of #data and error dependences. • Yamazaki et al. (CP-PACS), PR D65 (2001) 014501 Using the best lattice data in quenched QCD by CP-PACS. • Yamazaki@ Lattice2002 Decay s pp in O(4) f4 theory through spectral functions. QM2002 Nantes, July 2002 / K. Kanaya

  19. Spectral functions byMEM (4) It is nevertheless important to understand the characteristics of the method and estimate systematic errors, in order to see which info. of f(w) are reliably calculated. The role of the input data: D(t) ~ area of f(w) with an exponential cutoff to w < c / t where c = O(1) depending on the precision [~ 2 (7) when the error of D(t) is ~10 (1)%]. f(w) at w > c / tmincannot be determined, when we remove small t to avoid lattice artifacts.  Choice of m(w) affects f(w) at large w. f(w) at very small w (<< 1/tmax) cannot be determined.  False peak of f(w) at w 0 when tmax not large enough.Yamazaki et al. Aarts and Martinez Resco, hep-ph/0203177 D(t) insensitive to f(w) at w << T ~ 1/Nt.  Transport coeff. difficult. The location and area of a peak of f(w) can be determined when precise data around t ~ 1/wpeak are available. The width of a peak of f(w) may be determined when enough # of precise data around t ~ 1/ (wpeak+/-dw) are there. QM2002 Nantes, July 2002 / K. Kanaya

  20. Spectral functions byMEM (5) # of data points: • Asakawa et al. @ Lattice2002, QM2002 • Nt > 30 required in a study at T>0. • Anisotropicx= 4 lattice • Karsch et al., PL B530 (2002) 147, QM2002 • quenched QCD, isotropic 483x12, 643x16 • Low w gap in the Low w decrease of • vector spectral function  differential dilepton rate #Nt and statistics look critical, but the results are qualitatively consistent with Asakawa et al. QM2002 Nantes, July 2002 / K. Kanaya

  21. 2. m 0 Universe QGP RHIC ???? T GSI, JHF ?????? ??????? ??????? color-super? CFL? hadron phase ? m A simulation of this on the lattice is not straight-forward. QM2002 Nantes, July 2002 / K. Kanaya

  22. LQCD at m 0 • Quark determinant not real at m 0: detM = |detM| eiq • Phase (sign) problem: Large cancellations due to phase fluctuations Exponentially large statistics needed to keep an accuracy. Two directions in recent studies: • Small m • Large m QM2002 Nantes, July 2002 / K. Kanaya

  23. 2.1 Small m • Reweighting Falcioni et al.(‘82), Marinari(‘84), Ferrenberg-Swendsen(‘88) • From the distribution of Oi’s measured at “A”, • we can infer the distribution at “B”. • Error of the distribution “A” must be sufficiently small in the range relevant for “B”. In practice, two distributions should have a reasonable overlap. A B A B QM2002 Nantes, July 2002 / K. Kanaya

  24. unimproved-KS at Nt =4 • heavy mud [mPS > 2mp] Crossover, because Real world may be different. Small m(2) Reweighting from m=0 (Glasgow method) failed at T =0. I.M. Barbour et al., ..., (’92-’98) Width ~ e-V due to the phase problem. • Cooperative factors to lead a wider width: • small V • T >0(*) • on the critical/crossover-line(*) (*): New by Fodor-Katz • Fodor-Katz, JHEP 03 (2002) 014; QM2002 • stand.-gauge & stand.-KS • NF=2+1 [mud=0.025, ms=0.2] • (4, 6, 8)3x4 End point: TE = 160+/-3.5 MeV mE = 725+/-35 MeV QM2002 Nantes, July 2002 / K. Kanaya

  25. Small m(3) Reweighting of quark system: detM computationally demanding. F-K calculated it through eigen values. Becomes expensive at large V. • Allton et al.(Bielefeld-Swansea), hep-lat/0204010; Lat02 At small m, Taylor expansion can be used to calculate detM: Trby the noise method: Large V no problem in this part of the calculation. • impr.-gauge & impr.-KS(p4) • NF=2 [mq=0.1, 0.2], NF=3 [mq=0.1] • 163x4 • Method well-applicable to the RHIC region (m/T0.1). • TC, EOS, c Difference between m=0 and RHIC region is ~1% for e or p. QM2002 Nantes, July 2002 / K. Kanaya

  26. Small m(4) • de Forcrant-Philipsen, hep-lat/0205016 See also D’Elia-Lombardo, hep-lat/0205022; Takaishi, QM2002 Pure imaginary m detM is real positive  simulation OK • Analytic continuation limited to small Rem. • |Im m | < pT/ 3 due to Z(3)-periodicity • Fitting observables to low-order polynomials of Im m • stand.-gauge & stand.-KS • NF=2 [m=0.025] • 83x4, 63x4 TC bC = c0+c1(Imm)2 Imm - i Rem Results consistent among various methods. Next: Reduce lattice artifacts. larger V , larger Nt, smaller mud, ...  larger phase fluctuations! QM2002 Nantes, July 2002 / K. Kanaya

  27. 2.2 Large m • Special cases with real detM • Finite isospinKogut et al., S. Gupta, Bielefeld-Swansea detM(-m) = detM(m)*, mu = -md detM(m)detM(-m) = |detM|2 p+-condensation observed. Compatible with predictions from effective ChPT. • Two-color QCDKogut et al.(KS), Hands et al.(KS-adj), Di-quark condensation observed. Agree with effective ChPT. Muroya et al.@ Lattice2002, QM2002 Wilson quark mr decreases with m ?? di-lepton enhancement @ CERES • NJL Hands et al., Miyamura et al.(small m) QM2002 Nantes, July 2002 / K. Kanaya

  28. Summary • T >0, m =0 Constant progress, new methods • Toward the physical point: New simulations  nature of the QCD transition still open • Toward the continuum limit: Nt=6 and 8 scaling,anisotropic lattice promising • MEM: enlarges the predictability of lattice when used carefully. 　 Hard numbers unchanged, but more confident: TC(NF=2 )170-175MeV, e (NF=2)/T4|T/TC=1.5 14, p(NF=2)/T4|T/TC=1.5 3, etc. • m 0 A (partial) breakthrough • 1st sensible results for QCD atm 0 Currently limited to small m, small V, near TC • High-m QCD-like theories  new insights for QCD QM2002 Nantes, July 2002 / K. Kanaya

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