els Addis on to the status on to the status on to the status of QCD Critical Point – what, why, whether, where, and how – t. Pigon, Pigon Kenji Fukushima Yukawa Institute for Theoretical Physics Kyoto University
October 2008 at ATHIC08
INTRODUCTION
ification of the state or state or state
, within the status of the p
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Why ? T
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Whether, Where, How ??? pilled. Allowing the bo ■ Whether:  the QCD critical point exists? ■■ Where:  the QCD critical point lives? ■■ How:  the QCD critical point shows itself ? Which ? office. Allow from officers anyal, sig ■ Whether:  the QCD critical point exists? ■■ Where:  the QCD critical point lives? ■■ How:  the QCD critical point shows itself ? ■ Which is the most relevant question ???
October 2008 at ATHIC08

Affirmative
□  Chiral Effective Models ♦ Nambu-Jona-Lasinio model,  Linear sigma model ♦ Chiral random matrix theory ♦ Strong coupling + Large dimensional expansion □ Lattice QCD Simulations ♦ Reweighting method ♦ Taylor expansion ♦ Canonical ensemble ■ Negative □  Chiral Effective Models ♦ Large vector interaction,  Small 't Hooft interaction □  Lattice QCD Simulations ♦ Taylor expansion on the critical hypersurface
October 2008 at ATHIC08

ed starts to the starts of the starts of the  Affirmative □  Chiral Effective Models ♦ Nambu-Jona-Lasinio model,  Linear sigma model ♦ Chiral random matrix theory ♦ Strong coupling + Large dimensional expansion □ Lattice QCD Simulations ♦ Reweighting method ♦ Taylor expansion ♦ Canonical ensemble ■■ Negative □  Chiral Effective Models ♦ Large vector interaction,  Small 't Hooft interaction □  Lattice QCD Simulations ♦ Taylor expansion on the critical hypersurface
October 2008 at ATHIC08
LATTICE QCD Difficulty in Lattice QCD ed to the constitu ■ Fine Lattice □ Fermion density is saturated at the lattice site density. □ Low temperature requires large N .
■ Large Volume
□ 1-st order transition is smeared in a finite-volume box. □ Canonical ensemble is not equivalent to grand canonical.
■ Sign Problem
□ Finite density breaks the validity of computation. □ Loss of validity confuses with 1-st order transition.
October 2008 at ATHIC08
Difficulty in Lattice QCD ed. Pignet status ans the depart, pignet status ans the dispatial status of ■ Fine Lattice □ Fermion density is saturated at the lattice site density. □ Low temperature requires large N,.      Resource ■ Large Volume □ 1-st order transition is smeared in a finite-volume box. □ Canonical ensemble is not equivalent to grand canonical. Resource
■ Sign Problem
□ Finite density breaks the validity of computation. □ Loss of validity confuses with 1-st order transition. Principle!
October 2008 at ATHIC08
Difficulty in Lattice QCD ed. Pigned starts of the ■ Fine Lattice □ Fermion density is saturated at the lattice site density. □ Low temperature requires large N,.      Resource ■ Large Volume □ 1-st order transition is smeared in a finite-volume box. □ Canonical ensemble is not equivalent to grand canonical. Resource
■ Sign Problem
□ Finite density breaks the validity of computation. □ Loss of validity confuses with 1-st order transition. Principle!
October 2008 at ATHIC08

ing the constrted of the constrt

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■■ Overlap-improving Multi-parameter Reweighting □ 2+1 flavors, staggered, N, =4, physical quark mass 165 □ Idea ■■ Lee-Yang Zero MeV Sign Problem → Boltzmann weight? → 1-st order phase transition?? (S. Eiiri) ■■ Estimate ( T / T c )crit ～0.99 )crit ～2.2　 T c = 164MeV μ (MeV)
October 2008 at ATHIC08

■■ Overlap-improving Multi-parameter Reweighting ⊂ 2+1 flavors, staggered, N =4, physical quark mass 165 □ Idea ■■ Lee-Yang Zero MeV Sign Problem → Boltzmann weight? → 1-st order phase transition?? (S. Eiiri) ■■ Estimate ( T / T c )crit <0.99 j > 2.2      T c = 164 MeV
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μ (MeV) Gavai-Gupta  (0806.2233 [hep-lat]) philoship of starts from to the starts for the starts for the starts

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Schmidt et al. (RBC-Bielefeld)  (0810.0375 [hep-lat]) phistorics. Phistorics from the status of the status ■■ Taylor Expansion up to Sixth Order □ 2+1 flavor, staggered, N, =6, physical pion mass ■■ Radius of Convergence ■■ Estimate (T IT c)crit =?    (μ B I T c)crit>2.7 c.f.  Isentropic trajectories October 2008 at ATHIC08 Liu et al. (Kentucky)  (0711.2692 [hep-lat]) ify of status ans ans a status ans ans a status ans ans a status ans ans ans ans ■■ Canonical Ensemble □ Imaginary μ  →  No sign problem □ Fourier transform of μ 1 → n B ■ No conclusive message so far. □ Difficulty in μ , integration. □ Canonical not equivalent with Grand Canonical.
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Fodor-Katz-Schmidt (hep-lat/0701022) ■ Density of States Method 〈g〉= [ __ d x p ( x ) g ( x ) d x p(x)δ(φ−x) 〈g〉= 〉d Φ〈g〉φρ (Φ) with ρ (Φ)= J _∞ 8 8 | d φ ( g e ' ) ｡ ρ ( φ ) with ρ ( φ ) = |_ d x | p ( x ) | δ ( φ − x ) { g } = Nishimura et al. 4-flavors October 2008 at ATHIC08 No direct relation to CP E]IRl (0804.3227 [hep-lat]) ters of the programme orsers of the stat ■■ Taylor Expansion + Canonical Ensemble + Density of States Method + Gaussian Approx. □ 2-flavor, staggered, N =4, m/T =0.4 ρ(φ)∞ e-α®²  Fourier transform is done analytically □ Idea 〈g〉=∫ dφ〈g e’o〉φρ(Φ) with ρ(Φ)=∫_ d x | p(x)| δ(Φ−x) ■ Estimate ( T I c )crit ~0.76 ( μ B / C )crit ~ 7.5 October 2008 at ATHIC08 de Forcrand-Philipsen  (0808.1096 [hep-lat]) Andress of the constract status only and the constract of constract ■■ Taylor Expansion up to Fourth Order □ 3-flavor, staggered, N, =4, various masses □ Idea ■■ Estimate No Critical Point? October 2008 at ATHIC08 CHIRAL EFFECTIVE MODEL
は、そのようなもののかにもならばないしともないしともないしともない■■ 3D Plots – Order Parameters Quarks cost less energy
■■ Chiral and Quark Number Susceptibility
■ s/n = constant lines
CONCLUSIONS Conclusion – Whether ? – ed signals. Philoses , philoses T October 2008 at ATHIC08
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s the core or special strests ongsters. Angeos speci T
Roger October 2008 at ATHIC08
October 2008 at ATHIC08 To get (draw?) a better net ? ■ Experiment – Energy Scan ■ Lattice QCD □ Confirmation of 1-st at zero (small) T □ Matter of time (money) ■ Model □ PNJL is most promising. □ Ambiguities fixed by Lattice □ Color superconductivity phase boundaries for the indicated phases. The solid circle depicts the critical point. Possible trajectories for systems created in the QGP phase at different accelerator facilities are also shown.
October 2008 at ATHIC08