Selected Challenges in LOW ENERGY QCD and HADRON PHYSICS

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1 Fundamental Challenges of QCD Schladming 6 March 29 Selected Challenges in LOW ENERGY QCD and HADRON PHYSICS Wolfram Weise Is the NAMBU-GOLDSTONE scenario of spontaneous CHIRAL SYMMETRY BREAKING well established? Entanglement of CHIRAL and DECONFINEMENT transitions in QCD? PHASE DIAGRAM at finite BARYON DENSITY, NUCLEAR MATTER, CRITICAL POINT, and all that...

2 Topic I LOW-ENERGY QCD with Light Quarks Meson Sector... a QUANTITATIVE Science!

3 Chiral Symmetry Breaking Scenario - Lattice QCD -.8 (am! ) 2.6 Chiral Perturbation Theory m! "676 MeV.8.6 fit to 5 points (am PS ) 2 fit to 4 points (pion mass) M. Lüscher Proc. Lattice 25 physical point amq.2.4 Ph. Boucaud et al. (ETM Coll.) Phys. Lett. B65 (27) 34.8 quark mass (aµ) Gell-Mann, Oakes, Renner relation works m 2 π = m u + m d qq + O(m 2 q) f 2 π Chiral Perturbation Theory applicable up to pion masses < 5 MeV ~ confirmation of standard spontaneous symmetry breaking with Pion as Nambu-Goldstone Boson and Strong Chiral Condensate

4 Test of Chiral Symmetry Breaking Scenario - Low-Energy Constants on the Lattice - Chiral Perturbation Theory at NLO vs. Lattice QCD: m 2 π = m 2 [ 1 + m2 32π 2 f 2 lnm2 Λ 2 3 ] + O(m 4 ) f π = f [1 m2 16π 2 f 2 lnm2 Λ 2 4 ( m 2 = m ) q f 2 ψψ ] + O(m 4 ) Low-Energy constants: l 3 ln Λ2 3 m 2 π l 4 ln Λ2 4 m 2 π wyler ( 85) ) N f =2 2 8) N f =2+1, SU(2) 8) N f =2+1, SU(3) =2+1, SU(2) f N f =2+1, SU(3) +1, SU(3) PACS-CS(`8) ETM(`7) JLQCD(`8) JLQCD(`8) l l 3 RBC/ UKQCD(`8) l l 4 ETM(`7) ETM(`7) PACS-CS(`8) RBC/UKQCD(`8) JLQCD JLQCD (`8) (`8) Colan ETM JLQC RBC RBC PACS PACS MILC Gasser & Leutwyler(`85) Colangelo et al. (`1)

5 Test of Chiral Symmetry Breaking Scenario - Pion-Pion Scattering Theory: Chiral Symmetry + Roy Equations G. Colangelo et al. Nucl. Phys. B 63 (21) 125 NA48/2 Ke4 (23+24) δ = δ δ1 1 [rad] sππ [GeV] a a 2 Precision measurements of ππ scattering lengths a, a 2 Sensitivity to K ± π + π e ± ν Theory (ChPT) l 3, l 4 EPJ C54 (28) 411 PRELIMINARY NA48/2 Ke4 (prel.) Exp (NA48/2).22 ± ± ± ±.84 (in units of m 1 π ) * NA48/2 E865 E865 Geneva Saclay NA48/2 CGKR NA48/2 CI DIRAC 25 Ke4 Data cusp Data atoms 6pts 5pts from: B. Bloch-Devaux Confinement8 5% th error Preliminary % 7

6 Test of Chiral Symmetry Breaking Scenario K S γγ... one more example of Chiral Perturbation Theory at work: ()*#+, ' "$&% "$% "$!% "./5J./1KLL K S γγ./1k45 new KLOE result: M. Martini et al. (28)!$&%!$%!$!%! #$&% #$% #$!% #!?@IE2! I6 CDEF B(K S γγ) = B(K S γγ) = (2.26 ±.12 ±.6) 1 6 in perfect agreement with ChPT

7 Low-Energy QCD with light quarks is indeed realized as an Effective Field Theory of Nambu-Goldstone Bosons with spontaneously broken Chiral Symmetry SU(N f ) L SU(N f ) R SU(N f ) V Non-Linear Sigma Model plus well organized corrections Chiral Perturbation Theory works as expansion in p/λ χ, m π /Λ χ Λ χ 4π f π 1 GeV N f = 2 : established as a quantitative science in the meson (Nambu-Goldstone boson) sector N f = 3 : also successful with s-quarks, but slower convergence

8 %KK-bar(MC) n spectrum, 1 the spectral informations contained in T) of the).5 correlators, schematically v 1 FT V V.! " #(V ",I=1)$! ALEPH Perturbative QCD (massless) Parton model prediction %% %3%,3%%,6%(MC) the one1.5 contained in V and the one contained in A. &%,'%%,KK (MC) Mass 2 (GeV/c 2 ) 2 y a chiral transformation. Thus, if chiral symmetry fferences of a few MeV. These spectral informations in Fig One observes the ρ-peak in the vector a ρ Mass 2 (GeV/c 2 ) 2! " #(A ",I=1)$! v Perturbative QCD (massless) Parton model prediction a 1 2 %%.8 Note on PARITY %3%,3%%,6%(MC) PARTNERS 1.5 &%,'%%,KK (MC).6 ALEPH %2%,3% %4%,3%2%,5% %KK-bar(MC) %KK-bar(MC) Spontaneous Chiral Symmetry.4 Breaking v 1 -a 1 a 1 is a (dynamical) low-energy,.2 long wavelength phenomenon Current algebra: m 2 a 1 m 2 ρ = 8π 2 fπ Mass 2 (GeV/c 2 ) 2 Traces of ChSB disappear at high energy s >> 4π fπ 1 GeV ρ a 1! " #(V,A,I=1)$! ALEPH Perturbative QCD/Parton model V A %4%, %KK-b Mass 2 (GeV/c 2 ) Mass 2 (GeV/c 2 ) 2

9 Topic II DECONFINEMENT and CHIRAL TRANSITION Dynamical entanglement?

10 LATTICE QCD THERMODYNAMICS: CHIRAL and DECONFINEMENT TRANSITIONS spontaneously broken chiral symmetry ψψ T l,s ψψ T= Tr chiral condensate p4fat3: N τ =4 6 8 T [MeV] crossover transitions no critical temperature in strict sense chiral and deconfinement transitions seem to coincide LΦ ren Lattice QCD (2+1 flavours) almost physical quark masses M. Cheng et al. Bielefeld/BNL-Riken/Columbia Phys. Rev. D77 (28) F. Karsch et al. arxiv: [hep-lat] spontaneously broken Z(3) symmetry Tr Polyakov loop N τ =4 6 8 T [MeV] but: still under dispute (see: Y. Aoki, Z. Fodor, S.D. Katz, K.K. Szabo; Phys. Lett. B643 (26) 46 )

11 Modelling the CHIRAL and DECONFINEMENT Transitions POLYAKOV LOOP dynamics Confinement Synthesis of K. Fukushima (23) C. Ratti, M. Thaler, W.W. (25) PNJL MODEL NAMBU & JONA-LASINIO model Chiral Symmetry Action : S(ψ, ψ, φ) = β=1/t Fermion (quark) effective Hamiltonian Polyakov loop effective potential dτ d 3 x [ ψ τ ψ + H(ψ, ψ, φ) ] V T U(φ, T) VT V identify collective degrees of freedom (order parameters) which drive dynamics and thermodynamics quarks as quasiparticles with dynamically generated masses

12 Sketch of (non-local) PNJL MODEL Action : S(ψ, ψ, φ) = β=1/t dτ V d 3 x [ ψ τ ψ + H(ψ, ψ, φ) ] T V VT U(φ, T) Fermionic Hamiltonian density (NJL) : H = iψ ( α + γ 4 m φ) ψ + V(ψ, ψ ) chiral invariant Non-local fermion interaction Temporal background gauge field Φ = 1 N c Tr [ exp ( i 1/T φ = φ 3 λ 3 + φ 8 λ 8 )] dτ A 4 1 Tr exp(iφ/t) 3 SU(3) Polyakov loop Effective potential : U(Φ) confinement T < T c U(Φ) T > T c deconfinement

13 Polyakov Loop Effective Potential from PURE GLUE Lattice Thermodynamics Minimization of U(Φ(T), T) = p(t) R. Pisarsky (2) K. Fukushima (24) U(Φ, T) = 1 2 a(t) Φ Φ b(t) ln[1 6 Φ Φ + 4(Φ 3 + Φ 3 ) 3(Φ Φ) 2 ] energy density, entropy density, pressure ε T 4 3 s 4 T 3 3 p T TT c lattice results: O. Kaczmarek et al. PLB 543 (22) 41 first order phase transition U U T Polyakov loop effective potential.5 T.75 T 2. T 1. T 1.25 T S. Rößner, C. Ratti, W. W. PRD 75 (27) 347 T c (pure gauge) T 27 MeV

14 GAP EQUATION momentum dependent, dynamical quark mass M(p) = M(p) m + = 4N f N c G d 4 q M(q) C(p q) (2π) 4 q 2 + M 2 (q) M(p) [GeV].4 dynamical quark mass old NJL instanton model non-local PNJL lattice QCD P.O. Bowman et al. (22) consistent with self-energy from Dyson-Schwinger calc. (Landau gauge) iσ(p) = p [GeV] T. Hell, S. Rößner, M. Cristoforetti, W. W. Phys. Rev. D79 (29) 1422 C.D. Roberts, S.M. Schmidt, et al. R. Alkofer et al. + many others

15 Entanglement of CONFINEMENT and SPONTANEOUS CHIRAL SYMMETRY BREAKING... within thermodynamics of PNJL model σ/σ chiral condensate ψψ T Φ ψψ 2nd order T [GeV] Polyakov loop 1st order chiral limit m q = model (2 flavors) m q 3.5 MeV S. Rößner, C. Ratti, W. W.: Phys. Rev. D 75 (27) 347 T. Hell, S. Rößner, M. Cristoforetti, W. W. Phys. Rev. D79 (29) Φ M. Cheng et al. Phys. Rev. D77 (28) chiral condensate ψψ T ψψ Lattice QCD (2+1 flavours) Φ Polyakov loop T/T c

16 LATTICE QCD THERMODYNAMICS: TRANSITION TEMPERATURE(S) Chiral ( ) and Deconfinement ( ) transitions monitored through susceptibilities T [MeV] } N f = 2?? } M. Cheng et al., Phys. Rev. D77 (28) N f = Y. Aoki et al., Phys. Lett. B643 (26) 46 from: F. Karsch arxiv: [hep-lat]

17 Topic III SCENARIOS at FINITE DENSITY Critical Point? (Existence? Location?) Constraints from NUCLEAR MATTER

18 PHASE DIAGRAM and CRITICAL POINT temperature µ [GeV].3.4 quark chemical potential σ/ σ.5. CEP profile of scalar field / chiral order parameter from non-local PNJL model T. Hell, S. Rößner, M. Cristoforetti, W. W. Phys. Rev. D79 (29) T [GeV]

19 PHASE DIAGRAM Issues: Critical Point Diquarks and SuperConducting Phase hadronic phase qq PNJL model with local fermion interactions quark gluon phase N f = 2 diquark phase qq S. Rößner, C. Ratti, W. W.: Phys. Rev. D 75 (27) 347 T MeV quark chemical potential K 1.4 K K 1.2 K K K K.7 K K.656 K K.654 K Μ MeV N f = K.9 K K.8 K K. Fukushima (28); N. Bratovich, T. Hell, S. Rößner, W.W. (29) critical point: role of axial U(1) A breaking (`t Hooft interaction) u u d d K s s Location of critical point depends sensitively on quark masses, axial anomaly, etc.... U(1) A (Yamamoto, Hatsuda, Baym)

20 non-zero CHEMICAL POTENTIAL (contd.) µ µ P. de Forcrand, O. Philipsen m s physical point * QCD critical point m u,d µ = µ m u,d X m u,d crossover m s 1rst m s! Strategies: QCD critical point DISAPPEARED Taylor expansion around µ = µ iµ analytic continuation m u,d X m u,d crossover m s 1rst m s!

21 NUCLEAR THERMODYNAMICS NUCLEAR CHIRAL (PION) DYNAMICS BINDING & SATURATION: Yukawa + Van der Waals + Pauli N π π N V(r) e 2m πr + N N... plus contact terms N, r 6 P(m π r) P [MeV/fm 3 ] nuclear matter: equation of state pressure 3-loop in-medium ChEFT T = 25 MeV 2 T=25MeV T=2MeV T=15MeV T=1MeV T=5MeV ρ [fm -3 ] T = T=MeV Liquid - Gas Transition at Critical Temperature T = 15 MeV c (empirical: T = MeV) c baryon density S. Fritsch, N. Kaiser, W. W. : Nucl. Phys. A 75 (25) 259

22 NUCLEAR MATTER EQUATION of STATE VIRIAL EXPANSION P = ρ T [ 1 + B(T) ρ + C(T) ρ ] *)+),- & ). )"!("!'"!&"!%"!$"!#" Nuclear *@/A Matter %6B)C5?15)DCEFGH-H4E),H )9)!)(('),- & ) :)9)(!;'<&&),- & )1=!( >)9)!(;'#$),- & )12!'?)9)";"%%###!),- & )1=!& 1)9)!";"""#),- B(T) & )12!% 1st virial coefficient 4 35 in-medium chiral effective field theory S. Fiorilla, N. Kaiser, W. W. C(T) Hyperbolic fit Nuclear Matter!!" )$ )(" )($ )'" )'$ /)+12. Virial coefficients have a chiral expansion as well: C [fm 6 ] nd virial coefficient Parameter: C(T) K = 1528±12 MeV fm 6 B(T, m π ), C(T, m π ) T [MeV]

23 CHIRAL CONDENSATE at finite DENSITY T sigma term qq ρ qq = 1 ρ f 2 π baryon chemical potential m q M N m q [ σn m 2 π? ( 1 3 p2 F 1 M 2 N T first ψψ order ψψ µ B in-medium chiral effective field theory ) +... baryon density ρ + m 2 π coexistence N? π π ( )] Eint (p F ) A N (T = ) (free) Fermi gas of nucleons nuclear interactions (dependence on pion mass)

24 CHIRAL CONDENSATE: DENSITY DEPENDENCE In-medium Chiral Effective Field Theory (NLO 3-loop) constrained by realistic nuclear equation of state N. Kaiser, Ph. de Homont, W. W. Phys. Rev. C 77 (28) 2524 Symmetric Nuclear Matter condensate ratio ψψ (ρ) ψψ (ρ = ). chiral limit m π ρ ρ [fmρ [fm 3-3 ] chiral limit m π T = chiral in-medium dynamics m π =.14 GeV leading order leading order (Fermi gas) Substantial change of symmetry breaking scenario between chiral limit m q = and physical quark mass m q 5 MeV Nuclear Physics would be very different in the chiral limit!

25 Selected Challenges in LOW ENERGY QCD and HADRON PHYSICS Is the NAMBU-GOLDSTONE scenario of spontaneous CHIRAL SYMMETRY BREAKING well established? Yes! Entanglement of CHIRAL and DECONFINEMENT crossover transitions in QCD? transition temperatures coincide in PNJL models and on the Lattice (modulo Lattice disputes) PHASE DIAGRAM at low T, finite BARYON DENSITY, NUCLEAR MATTER, CRITICAL POINT, and all that... basically unknown role of axial U(1) anomaly constraints from realistic nuclear EoS

26 Supplementary Materials

27 Results PNJL model vs. Lattice QCD Thermodynamics PRESSURE and ENERGY DENSITY at zero chemical potential p = Ω(T, µ = ) ε = T p(t, µ = ) T p(t, µ = ) (ε 3P )/T MF+π, σ MF interaction measure T/T c (ε-3p)/t 4 T [MeV] Tr asqtad: N τ =6 8 p4: N τ =6 8 hotqcd preliminary T. Hell, S. Rößner, M. Cristoforetti, W. W. Phys. Rev. D79 (29) 1422 lattice data: F. Karsch et al. : arxiv: [hep-lat]

28 Sound Velocity: PNJL and LATTICE QCD PNJL model PNJL S. Rössner, Th. Hell, C. Ratti, W.W. arxiv: [hep-ph] c 2 s = dp dε p ε N f = p/! Lattice C. Bernard et al., Phys. Rev. D 75 (27) T [MeV] N f = F. Karsch, arxiv: [hep-lat] N " =4 6 fit: p/! HRG: p/! c s 2 SB! 1/4 [(GeV/fm 3 ) 1/4 ] PNJL model works Active degrees of freedom around critical temperature Quarks as quasiparticles interacting with Polyakov loop T > T c :

29 Beyond Mean Field: Mesonic Excitations [ P/T 4 contribution of mesonic quark-antiquark modes to pressure 2.5 MF + π, σ (in-medium) 2. MF + π (in-medium) MF quarks [ ] [ mesons (mostly π) T. Hell, S. Rößner, M. Cristoforetti, W. W. Phys. Rev. D79 (29) 1422 p qk p q + pk. Π π,σ (ν m, p ) = 4N f i=,± T n Z T/T c P meson (T ) = M=π,σ d M 2 T m Z d 3 p (2π) 3 ln [1 GΠ M(ν m, p )] d 3 k (2π) 3 C(ωi n + ν m, k + p ) C(ω i n, k ) ωn i (ωi n + ν m) + k( k + p ) ± M(ωn i + ν m, k + p )M(ωM n i, k ) [(ωn i + ν m) 2 + ( k + p ) 2 + M(ωn i + ν m, ] k + p ) [(ω 2 n i )2 + ] +M 2 k 2 + +MM 2i (ωn i, k ) 2 (3.1

30 Non-zero QUARK CHEMICAL POTENTIAL Role of CONFINEMENT (POLYAKOV loop dynamics) suppression of quark propagator in forbidden region 1.8 NJL classic (no confinement) quark number density C. Ratti, M. Thaler, W.W. PRD 73 (26) nqt PNJL (incl. confinement) Μ 12 MeV TT c Lattice data : Allton et al. Phys. Rev. D 68 (23)

31 Non-zero QUARK CHEMICAL POTENTIAL Taylor expansion of pressure: p(t, µ) = T 4 n c n (T) ( µ T) n c 2 c 4 c 6 S. Rößner, C. Ratti, W. W. Phys. Rev. D 75 (27) 347 Lattice: C.R. Allton et al. Phys. Rev. D 71 (25) 5458