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Second Berkeley School on Collective Dynamics, May 21-25, 2007 Tetsuo Hatsuda, Univ. Tokyo

PHYSICS is FUN. LATTICE is FUN. [1] Lattice QCD basics [2] Nuclear force on the lattice (  dense QCD) [3] In-medium hadrons on the lattice (  hot QCD) [4] Summary. I. II. Second Berkeley School on Collective Dynamics, May 21-25, 2007 Tetsuo Hatsuda, Univ. Tokyo.

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Second Berkeley School on Collective Dynamics, May 21-25, 2007 Tetsuo Hatsuda, Univ. Tokyo

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  1. PHYSICS is FUN LATTICE is FUN [1] Lattice QCD basics [2] Nuclear force on the lattice ( dense QCD) [3] In-medium hadrons on the lattice ( hot QCD) [4] Summary I II Second Berkeley School on Collective Dynamics, May 21-25, 2007 Tetsuo Hatsuda, Univ. Tokyo

  2. Why lattice ? • well defined QM (finite a and L) • gauge invariant • fully non-perturbative What one can do • hadron mass, coupling, form factor etc • scattering (phase shift, potential etc) • hot plasma What one cannot do (at present) quarks q(n) on the sites • cold plasma • far from equilibrium system gluons Um(n) on the links Lattice QCD Basics

  3. a n+n 1/T n+m+n  link variable L  n+m plaquette n  Wilson gauge action quenched QCD : det F=1 (exploratory studies) full QCD : det F≠1 (precision studies) QCD partition function • Zero temperature : 1/T ~ L • Finite temperature : 1/T << L

  4. L-1 Simulation techniques Fermions: staggered, Wilson, Domain-wall, Overlap different way of handling chiral symmetry a m Improved actions: asqtad, p4, stout, clover … different way of reducing the discretization error Modern algorithms: RHMC, DDHMC … techniques to make the simulations fast and reliable Important limits and theory-guides L-1 0 (thermodynamics limit): finite size scaling a 0 (continuum limit): asymptotic freedom m 0 (chiral limit): chiral pert. theory

  5. Example of improvement: Number of floating-point operations To collect 100 config. on 2LxL3 lattice with DDHMC algorithm: 31 76 5  0.05 HNCDDHMC Del debbio, Giusti, Luscher, Petronzio, Tantalo, hep-lat/0610059 1 year = 3 x 107 sec

  6. To collect 1000 indep. gauge conf. on 243x40, a=0.08 fm lattice (T=0) Clark, hep-lat/0610048.

  7. QCD Cluster @ FNAL PACS-CS @ Tsukuba BlueGene/L @ KEK QCDOC @ RBRC-Columbia ApeNEXT @ Rome

  8. Typical measurement of mass : QQ pair M ∞ M = finite r space space time time Meson mass Heavy quark potential E0 = ground state mass E0 = 2M + V(r)

  9. Linear confining string Charmoniums R 2S+1LJ 0.5 fm 1.0 fm Bali, Phys. Rep. 343 (’01) 1 CP-PACS, Phys. Rev. D65 (’02) 094508 Examples in quenched QCD

  10. string breaking Charmoniums [ V(r) - 2mHL ] a spin ave. 1S energy 1.5fm 0.5fm 1fm Nf= 2, Wilson sea-quarks, 243x40 a= 0.083 fm, L= 2 fm, mp/mr= 0.704 Nf= 2+1, staggered sea-quarks, 163x48, 203x64, 283x96 a = 0.18, 0.12, 0.086 fm, L= 2.8, 2.4, 2.4 fm MILC Coll., PoS (LAT2005) 203 [hep-lat/0510072] SESAM Coll., Phys.Rev.D71 (2005) 114513 Examples in full QCD

  11. Many applications • light hadron spectroscopy • heavy hadron spectroscopy • exotic hadrons • various “charges” • form factors • weak matrix elements • etc One of the latest developments The nuclear force Ishii, Aoki & Hatsuda, hep-lat/0611096 (to appear in Phys. Rev. Lett.)

  12. H. Yukawa, “On the Interaction of Elementary Particles, I”, Proc. Phys. Math. Soc. Japan (1935) Nuclear force H. Bethe, “What holds the Nucleus Together?”, Scientific American (1953) F. Wilczek, “Hard-core revelations”, Nature (2007) Nuclear Force nucleus • Why the nuclear force important now? • How to extract the nuclear force from QCD ?

  13. One-pion exchange by Yukawa (1935) Multi-pions & heavy mesons 2p, 3p, ... r, w, s repulsive core p Repulsive core by Jastrow (1950,1951) Modern Nuclear Force from NN scatt. data

  14. High precision NN potentials Machleidt and Entem, nucl-th/0503025

  15. Nuclear force CAS A remnant Nuclear repulsive core Origin of RC is not known …. But, it is intimately related to １．Nuclear saturation • Maximum mass of neutron stars • Ignition of Type II supernovae

  16. Akmal, Pandharipande & Ravenhall, PRC58 (’98) State-of-the-art nuclear EoS Z=0 E/A (MeV) N=Z ρ(fm-3) ρ0 = 0.16 fm-3 3ρ0 5ρ0 Nuclear Equation of State

  17. Neutron star - WD binary J0751+1807 X-ray binaries Cyg-X2 Vela-X1 PSR1913+16 Neutron star binary EXO0748-676 (X-ray bursts) Mass-Radius relation of neutron star in Akmal-Pandharipande-Ravenhall EoS (ρmax～ 6ρ0)

  18. (ii) NN “wave function”  NN potential Ishii, Aoki & Hatsuda, hep-lat/0611096 • similar in spirit with phenomenological potentials (phase shift data  NN potential) How to extract (bare) NN force in QCD ? (i) Born-Oppenheimer potential r • unrealistic • fundamental difficulty Takahashi, Doi & Suganuma, hep-lat/0601006

  19. Nucleon interpolating field: Equal time BS amplitude: Probability amplitude to find nucleonic three-quark cluster at point x and another nucleonic three-quark cluster at point y x + y cf: for π-πscattering, Lin, Martinelli, Sachradja & Testa, NP B169 (2001) CP-PACS Coll, Phys. Rev. D71 (2005) Equal time BS amplitude f (r)

  20. Ishii, Aoki & Hatsuda, hep-lat/0611096 　　　　　 　　　　　＋paper in preparation LS equation : Non-local potential: Local potential: • asymptotic form of f (r) (= the phase shift) • determined by elastic pole • interpolating operator independent • inelastic contribution: • interpolating operator dependent • exponentially localized in space • magnitude suppressed by Ep/Eth

  21. Typical measurement of mass : QQ pair M ∞ M = finite r space space time time Meson mass Heavy quark potential E0 = ground state mass E0 = 2M + V(r)

  22. x J J y y y space NN potential: time Measurement of f (r)(s-wave) + all possible combinations

  23. a = 0.137 fm L = 4.4 fm mr = 0.84 GeV mN= 1.18 GeV mr = 0.89 GeV mN= 1.34 GeV BlueGene/L @ KEK Simulation details • 324 lattice • Quenched QCD • Plaquette gauge action • Wilson fermion • Periodic (Dirichlet) B.C. • for spatial (temporal) direction as of today

  24. 2s+1LJ BS amplitude f (r) for mp =0.53 GeV Ishii, Aoki & Hatsuda, hep-lat/0611096

  25. 1S0 channel repulsive core 3S1 channel mid-range attraction Yukawa tail 2s+1LJ NN central potential Vc(r) for mp =0.53 GeV Ishii, Aoki & Hatsuda, hep-lat/0611096

  26. 1S0 channel 3S1 channel 2s+1LJ NN central potential Vc(r) for mp =0.53 GeV Ishii, Aoki & Hatsuda, hep-lat/0611096

  27. Pion exchange attraction for 1S0 & 3S1 ghost exchange (quenched artifact) + attraction for 1S0 repulsion for 3S1 Beane & Savage, PLB535 (2002)

  28. Quark mass dependence (preliminary) Ishii, Aoki & Hatsuda, in preparation

  29. NN scattering length: fragile object in NN case Luscher’s formula: Luscher, CMP 105 (1986), NPB 354 (1991) But situation is not that simple as “first Born” tells: Born Remarks 2. Tensor force ? coupled channel 3S1-3D1 3. Different Interpolating operators ? same phase shift but different V(r) at short distances 4.Hyperons ? to be announced in two weeks (INPC2007)

  30. Nuclear chart MCSM Z GFMC AMD LQCD N Nuclear force : bridge between one and many

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