PHYSIK der STARKEN WECHSELWIRKUNG: PHASEN und STRUKTUREN aus QUARKS und GLUONEN

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1 Mainz, 23. November 2004 PHYSIK der STARKEN WECHSELWIRKUNG: PHASEN und STRUKTUREN aus QUARKS und GLUONEN Wolfram Weise TU München Stichworte zur Quanten Chromo Dynamik Struktur und Masse des Nukleons Niederenergie - QCD: Chirale Symmetrie und spontane Symmetriebrechung Kondensatstruktur des Vakuums Materie unter extremen Bedingungen: QCD - Thermodynamik Suche nach dem Quark-Gluon Plasma

2 QCD: PHASES and STRUCTURES TEMPERATURE Tc ~ 0.2 GeV quark gluon phase NUCLEI hadron phase qq 0 1 GeV NEUTRON STARS superconducting phase qq 0 BARYON CHEMICAL POTENTIAL m 1 fm NUCLEON 2 fm QCD VACUUM 3 VALENCE QUARKS + GLUONS + QUARK-ANTIQUARK PAIRS

3 1. Quanten Chromo Dynamik

4 QUANTUM CHROMO DYNAMICS (H. Fritzsch, M. Gell-Mann, H. Leutwyler: Phys. Lett. B47 (1973) 365) L QCD = q(iγ µ D µ m)q 1 4 G µνg µν g s GLUON QUARK MASSES GLUE QUARK QUARKS: q = u d s c b t light heavy m u,d m < m m m s c b t 10 = = = = -2 (almost massless) GeV ( ) MeV ( ) GeV ( ) GeV ( ) GeV

5 Running Coupling in QCD α s (Q) = g2 s(q) 4π = 4π β 0 ln(q 2 /Λ 2 ) Quantum chromodynamics 17 (β 0 = 11 2N f ) Λ 0.2 GeV a s (m) α s (Q) = g2 s(q) 4π 7KH1REHO3UL]HLQ3K\VLFV IRUWKHGLVFRYHU\RIDV\PSWRWLFIUHHGRPLQWKHWKHRU\RIWKHVWURQJ LQWHUDFWLRQ m GeV Q 'DYLG-*URVV +'DYLG3ROLW]HU )UDQN:LOF]HN

6 HIGH - Q ( QCD BASIC CONCEPTS and STRATEGIES > several GeV) SHORT DISTANCE ( < 0.1 fm) Theory of WEAKLY INTERACTING QUARKS and GLUONS (Perturbative QCD) LOW - Q ( << 1 GeV) LONG DISTANCE ( > 1 fm) SPONTANEOUS (CHIRAL) SYMMETRY BREAKING Effective Field Theory of WEAKLY INTERACTING GOLDSTONE BOSONS (Pions) LATTICE QCD Large-scale computer simulations on EUCLIDEAN SPACE-TIME Lattices τ a x

7 LATTICE QCD Gluonic Flux Tube and Confining Potential between Heavy Quarks V(r) = 4 3 α s r + σ r STRING TENSION σ 1 GeV/fm G.S. Bali, Phys. Reports 343 (2001)1

8 2. Quarks und Gluonen im Nukleon

9 DEEP - INELASTIC LEPTON - NUCLEON SCATTERING E W µν F 1,2 (x, Q 2 ) STRUCTURE FUNCTIONS ANTIQUARKS ANTIQUARKS

10 PROTON STRUCTURE FUNCTION F 2 (x,q 2 ) * 2 i x H1 ZEUS BCDMS E665 NMC SLAC 2 Q - dependence : QCD evolution F 2(x,Q ) = const. at fixed x : pointlike partons (quarks) in the nucleon Q 2 (GeV 2 )

11 QCD Analysis, part I Next-to-leading order Evolution Equations (Dokshitzer, Gribov, Lipatov, Altarelli, Parisi) photon quark gluon quark Parton distributions x f(x,q) gluon 1 lnq 2 f(x, Q2 ) = α s (Q 2 ) x antiquark dz z P (z)f(x z, Q2 ) Th. Weigl, Dissertation, TUM 1997 x f(x) g u v quark and gluon distributions of the proton Quarks contribute x s c d u d v only 1/2 of the nucleon s total momentum x

12 QCD Analysis, part II Spin Structure of the Nucleon Deep-inelastic scattering of polarised leptons on polarised nucleons x Du v (x) HERMES SMC x Quark spins x Dd v (x) contribute x less than 1/3 of the nucleon s spin x Dq sea (x) x

13 3. Niederenergie - QCD CHIRALE SYMMETRIE und SPONTANE SYMMETRIEBRECHUNG QCD auf dem GITTER und CHIRALE EFFEKTIVE FELDTHEORIE: die MASSE des NUKLEONS

14 Hierarchy of Quark Masses in QCD u d s c b t Q M heavy light medium heavy GeV Λ QCD CHIRAL SYMMETRY spontaneous symmetry breaking GOLDSTONE BOSONS CONDENSATES qq expansion parameter: Q (with fπ 2 qq ) 4πf π HEAVY QUARKS non-relativistic QCD CONFINEMENT GLUONIC FLUX TUBES expansion parameter: Q M heavy

15 MASS SPLITTINGS of SINGLET and TRIPLET states [ Q q ] 1S0 [ Q q ] 3S1 Spectroscopic patterns: LIGHT versus HEAVY M meson m Q m q [GeV] B B hyperfine splitting D D K K ρ mass gap π J P = 1 J P = 0 b d c d s d u d

16 CHIRAL SYMMETRY QCD WITH (ALMOST) MASSLESS u - and d - QUARKS spin spin momentum left - handed right - handed CHIRAL SU(2) L X SU(2) R SYMMETRY SPONTANEOUS SYMMETRY BREAKING LOW T HIGH T U eff U eff < f > < f > CHIRAL (QUARK) CONDENSATE <qq> = 0 (Nambu Goldstone) <qq> = 0 (Wigner Weyl) GOLDSTONE BOSONS : PIONS (π +, π 0, π )

17 LOW ENERGY QCD - pictorial summary - SPONTANEOUS SYMMETRY BREAKING and MASS SPECTRUM Mesons, Baryons: 1 GeV a 1 r D N HADRONS: quasiparticle excitations of the condensed QCD Vacuum MASS GAP D = 4 p p ~ 1 GeV Goldstone Bosons: Ground State: m p 0 PION <qq> p _ ~ <qq> QCD VACUUM PION DECAY CONSTANT f π = 92.4 MeV ( qq 2 ) fπ THERMODYNAMICS : Change of spectrum as function of TEMPERATURE and BARYON DENSITY

18 short digression: THERMODYNAMICS of the CHIRAL CONDENSATE Spontaneous Chiral Symmetry Breaking and Restoration T - dependence of CHIRAL (QUARK) CONDENSATE from LATTICE QCD G. Boyd et al., Phys. Lett. B349 (1995)170 T c 170 MeV Low-Energy QCD as a Condensed Matter problem see: analogy with Magnetization of a Ferromagnet

19 LOW - ENERGY QCD Physics in the HADRONIC (low T) phase of QCD Z = tr exp CONFINEMENT [ H QCD k B T Spontaneously broken CHIRAL SU(2) x SU(2) SYMMETRY non-trivial VACUUM 0 : CHIRAL (QUARK) CONDENSATE qq 1.8 fm 3 low-mass collective excitations : GOLDSTONE BOSONS (PIONS) ] = n at T < T crit : n e E n/k B T n Eigenstates n are (colour-singlet) HADRONS... interact weakly at low energy / momentum Gell-Mann, Oakes, Renner Relation m 2 πf 2 π = 1 2 (m u + m d ) qq

20 CHIRAL EFFECTIVE FIELD THEORY (Weinberg; Gasser & Leutwyler) LOW-ENERGY QCD: Effective Field Theory of weakly interacting GOLDSTONE BOSONS (PIONS) Interacting systems of PIONS coupled to NUCLEONS: (Weinberg ( 68); modern developments: Ecker et al. ( 94), Bernard, Kaiser, Meissner ( 95) + many others) L eff (U, U,..., N,...); U(x) = exp[iτ a π a (x)/f π ] SU(2) π π π N π N

21 Low-Energy Expansion: CHIRAL PERTURBATION THEORY small parameter : Q 4πf π energy / momentum / pion mass mass gap of order 1 GeV successfully applied to: PION-PION scattering PION-NUCLEON scattering PION photoproduction and COMPTON scattering on the NUCLEON long range NUCLEON-NUCLEON interaction NUCLEAR MATTER and NUCLEI

22 4. MASSE des NUKLEONS GITTER - QCD und CHIRALE EFFEKTIVE FELDTHEORIE

23 NUCLEON MASS in QCD M N = N T 00 N... mostly gluonic in origin TRACE of ENERGY-MOMENTUM TENSOR: M N = N T µ µ N T µ µ = β(g) 2g G µνg µν + m u ūu + m d dd +... glue quark mass term CHIRAL LIMIT (m q 0) : M 0 = N β 2g G2 N SIGMA TERM: M N = M 0 + σ N σ N = N m u ūu + m d dd N empirical value: σ N 50 MeV (Gasser, Leutwyler, Sainio 1991)

24 LATTICE QCD Computer simulations of the NUCLEON MASS on large EUCLIDEAN SPACE-TIME LATTICES τ 1 M N = lim τ τ ln (τ = N τ a) (V = (Na) 3 ) d 3 x 0 N( x, τ) N(0) 0 a x ( N = [qqq] S=1/2 )... in practice with LARGE quark masses: m u,d > 100 MeV ( recall: m 2 π (m u + m d ) ) use CHIRAL EFFECTIVE FIELD THEORY to extrapolate

25 LATTICE QCD and CHIRAL EFFECTIVE FIELD THEORY pion nucleon M N = M 0 + c m 2 π + d m 4 π + 3π ( ) 2 [ ] mπ 2 g2 A m π 1 + m2 π 4πf π 4M0 2 + O(m 6 π) M. Procura, Th. Hemmert, W. W. Phys. Rev. D69 (2004) physical point lattice (CP-PACS, JLQCD, QCDSF) see also: Adelaide group D. Leinweber, A.W. Thomas et al. M GeV (chiral limit) M N 0.94 GeV (physical mass) SIGMA TERM: σ N = (47 ± 3) MeV (empirical: σ N = (45 ± 8) MeV )

26 5. Thermodynamik der QCD CHIRALES (QUARK) KONDENSAT als Funktion von TEMPERATUR und BARYON-DICHTE GOLDSTONE-BOSONEN in MATERIE Ausblicke: QUASI-TEILCHEN, QCD-THERMODYNAMIK auf dem GITTER und SCHWERIONENSTÖSSE bei HOHEN ENERGIEN

27 THERMODYNAMICS of the CHIRAL CONDENSATE qq ρ,t qq 0 = f 2 π dp (T, ρ) dm 2 π T - dependence from LATTICE QCD G. Boyd et al., Phys. Lett. B349 (1995)170 T c 170 MeV [GeV] f π (T, ρ) [MeV] ρ[fm -3 ] ρ leading low - T and low - density behaviour: qq T,ρ qq 0 1 T 2 8f 2 π T[GeV] σ N m 2 π f 2 π NJL MODEL based on CHIRAL SYMMETRY S. Klimt, M. Lutz, W. W. Phys. Lett. B249 (1990) 386 update: M. Thaler, W. W. (2004) ρ +... f 2 π(t, ρ) f 2 π(0)

28 GOLDSTONE BOSONS in MATTER Experiment at GSI (Darmstadt):... and Sn isotopes Fingerprints of CHIRAL SYMMETRY RESTORATION?

29 DEEPLY BOUND STATES of PIONIC ATOMS Experiment (GSI) Calculation: In-medium Chiral Perturbation Theory with energy dependent Pion-Nucleus Potential 1s state E. Kolomeitsev, N. Kaiser, W. W. Phys. Rev. Lett. 90 (2003) Nucl. Phys. A721 (2003) 835 K. Suzuki et al. Phys. Rev. Lett. 92 (2004) f π(ρ 0 ) 0.8 f π

30 QCD: MATTER under EXTREME CONDITIONS GSI - SIS 100/200 Experiments: Ultra-relativistic HEAVY-ION COLLISIONS Theory: EQUATION of STATE / LATTICE QCD HYDRODYNAMICS / TRANSPORT THEORY

31 OUTLOOK: towards the QCD EQUATION of STATE LATTICE QCD: Thermodynamics in comparison with QUASIPARTICLE Approach based on CHIRAL SYMMETRY and CONFINEMENT R. Schneider, W. W. Phys. Rev. C64 (2001) R. Schneider, M. Thaler, W. W. Phys. Rev. C69 (2004) C. Ratti, W. W. Phys. Rev. D70 (2004) Energy and Entropy density, Pressure n q T 3 Μ 0.6 T c Quark number density lattice: G. Boyd et al. Nucl. Phys. B469 (1996) 419 nq T Μ 0.4 T c Μ 0.2 T c lattice: C.R. Allton et al. Phys. Rev. D68 (2003) T T c

32 GeV m Σ m Π T=0 THERMODYNAMICS of TWO-COLOUR QCD LATTICE results vs. QUASIPARTICLE model scalar pion µ = 0 f Π T GeV diquark condensate quark condensate m p /m p (0) m/m p C. Ratti and W. W., Phys. Rev. D 70 (2004) Nambu & Jona-Lasinio model with colour current-current interaction T=0 pion pion decay constant m /m p (0)

33 QCD: PHASES and STRUCTURES TEMPERATURE NUCLEI hadron phase 1 fm 2 fm QCD VACUUM quark gluon phase 1 GeV BARYON CHEMICAL POTENTIAL NUCLEON Thanks to: Jochen EDELMANN Thomas HEMMERT Norbert KAISER Evgeni KOLOMEITSEV Gunther PILLER Massimiliano PROCURA Claudia RATTI Thorsten RENK Roland SCHNEIDER Michael THALER Thomas WEIGL