INTERFACE of QCD and NUCLEAR PHYSICS

Transcription

1 Confinement8 Mainz 5 September 28 ITERFACE of QCD and UCLEAR PHYSICS Wolfram Weise Low-Energy QCD and CHIRAL SYMMETRY uclear Forces in the context of CHIRAL EFFECTIVE FIELD THEORY uclear Matter Energy Density Functional and Finite uclei Symmetry Breaking Patterns: density dependence of the CHIRAL CODESATE

2 1. Prelude: UCLEAR PHYSICS explores PHASES and STRUCTURES of QCD T [GeV] f = 2 (q = u, d) QCD PHASE DIAGRAM nuclei.2 temperature T c hadron phase qq nuclear matter quark gluon phase nuclear matter critical point 1 GeV? (color) CSC phases qq superconductor? µ B baryon chemical baryon potential chemical potential.15 density [fm 3 ] Scales in nuclear matter momentum scale: Fermi momentum distance: energy per nucleon: (in)compressibility: k F 1.4 fm 1 2m d 1.8 fm 1.3 m 1 E/A 16 MeV K = (26 ± 3) MeV

3 QCD Phases and Symmetry Breaking Pattern QCD Thermodynamics ψψ T ψψ chiral condensate S. Rössner, T. Hell, M. Cristoforetti, W.W. (28) Polyakov loop T/T c Φ.4.2 Lattice QCD (2+1 flavours) M. Cheng et al. Phys. Rev. D77 (28) Quasiparticle Model Chiral Quarks + Polyakov Loop (PJL Model) S. Rössner, C. Ratti, W.W. Phys. Rev. D 75 (27) 347 Spontaneously broken CHIRAL SYMMETRY at low temperature T < T c.2 GeV

4 Spontaneously Broken CHIRAL SYMMETRY AMBU - GOLDSTOE BOSO: PIO ORDER PARAMETER: PIO DECAY COSTAT A a µ() b (p) = iδ ab p µ f µ Axial current f = 92.4 MeV ν SYMMETRY BREAKIG SCALE: Λ χ = 4 f 1 GeV PCAC: m 2 f 2 = m q ψψ + O(m 2 q) Gell-Mann - Oakes - Renner Relation

5 CHIRAL EFFECTIVE FIELD THEORY Gasser & Leutwyler Weinberg Ecker... many others LOW-EERGY QCD: Effective Field Theory of weakly interacting ambu-goldstone Bosons (PIOS) representing QCD at scales Q << 4 f 1 GeV Interacting systems of PIOS (light / fast) and UCLEOS (heavy / slow): L eff = L (U, U) + L (Ψ, U,...) U(x) = exp[iτ a a (x)/f ] Construction of Effective Lagrangian: Symmetries short distance dynamics: contact terms

6 Low-Energy Expansion: CHIRAL PERTURBATIO THEORY small parameter: Q 4f energy / momentum / pion mass 1 GeV successfully applied to: PIO-PIO scattering PIO-UCLEO scattering PIO photoproduction and COMPTO scattering on the UCLEO long range UCLEO-UCLEO interaction UCLEAR MATTER and UCLEI

7 2. uclear Forces - Recent Developments - V III II I Hierarchy of SCALES potential short distance two-pion exchange one-pion exchange two-pion exchange one-pion exchange r [µ 1 ]

8 ucleon-ucleon Interaction M. Taketani, Suppl. Prog. Theor. Phys. (1956) more than 5 years ago... Fig. I. Three Regions of uclear Potential.* Region I. Classi.cal region, r*\.irc-t, (r-t is the pion Comp' ton wave length) where the one-pion-exchange potential domi' nates and the quantitative behavior of the potential has been established. Region II. D.ynamical regi.on,.7{l!r{i.5rc-r, where the two-pion-exchange potential competes with and exceeds the one' pion-exchange potential. The recoil effect is also appreciable in this region. The qualitative behavior, however, has been clarified. Region III. Phenomenologi.cal region, r1.7rc-r, where exist so many complicated effects,.g., the relativistic effect, the isobar effect, the effect of new particles, etc., that at present we may have no means but some phenomenological treatment to fit with experiments. M. Taketani, S. akamura, M. Sasaki Prog. Theor. Phys. 6 (1951) 581 region 1 long distance: one-pion exchange H. Yukawa (1935) region 1I intermediate distance: two-pion exchange H. Miyazawa et al. (1957) region 1I1 short distance: unresolved

9 UCLEAR ITERACTIOS from CHIRAL EFFECTIVE FIELD THEORY Weinberg Bedaque & van Kolck Bernard, Epelbaum, Kaiser, Meissner;... ( ) Q O Λ ( ) Q 2 O Λ 2 ( ) Q 3 O Λ 3 ( ) Q 4 O Λ 4 Systematically organized HIERARCHY

10 Scattering Phase Shifts from CHIRAL EFFECTIVE FIELD THEORY Entem, Machleidt, Phys. Rev. C68 (23) 411 Epelbaum, Glöckle, Meißner, ucl. Phys. A747 (25) 362 LO 2 LO 3 LO uclear Fo om m ChEFT quantitatively accurate at same level of precision as best phenomenological potentials

11 Explicit (123) DEGREES of FREEDOM Large spin-isospin polarizabilty of the ucleon " 3/2 - " 1/2 (µbarn) This wor Ref.[1] HDT SAID UIM example: polarized Compton scattering β = g 2 A f 2 (M M ) 5 fm (MeV) E γ MAMI (21) M M 2 m << 4 f (small scale) Pionic Van der Waals - type intermediate range central potential. Kaiser, S. Gerstendörfer, W. W., PA637 (1998) 395. Kaiser, S. Fritsch, W. W., PA75 (25) 259 C. Ordonez, L. Ray, U. van Kolck, PRL 72 (1994) g2 A V c (r) = 32 2 f 2 J. Fujita, H. Miyazawa; Prog. Theor. Phys. 17 (1957) 36 Pieper, Pandharipande, Wiringa, Carlson, PRC64 (21) 141 β e 2m r r 6 P(m r) strong 3-body interaction

12 Explicit (123) DEGREES of FREEDOM (contd.) Kaiser et al., Ordonez et al. Krebs, Epelbaum, Meißner (27) Important physics of (123) promoted to LO Improved convergence

13 3. CHIRAL DYAMICS and the UCLEAR MAY-BODY PROBLEM Small scales: PIOS (and DELTA isobars) as explicit degrees of freedom I-MEDIUM CHIRAL PERTURBATIO THEORY pion exchange processes in presence of filled Fermi sea short-distance dynamics:. Kaiser, S. Fritsch, W. W. (22-25) k F 2 m M M << 4 f in-medium Loop expansion in ChPT Systematic expansion of EERGY DESITY E(k F ) in powers of Fermi momentum [modulo functions f n (k F /m )], 2nd order TESOR force + nucleon s SPI-ISOSPI polarizability contact interactions In-medium nucleon propagator: i γ p M + iɛ 2(γ p + M )δ(p 2 M 2 )θ(p )θ(k F p )

14 UCLEAR MATTER In-medium ChPT 3-loop (,, ) Input parameter: single contact term basically: analytic calculation Output: E/A [MeV] S. Fritsch,. Kaiser, W. W. ucl. Phys. A 75 (25) 259 empirical 3-body + Pauli [ ] ρ [fm 3 ] Binding & saturation E /A = 16 MeV, ρ =.16 fm 3, K = 29 MeV Realistic (complex, momentum dependent) single-particle potential... satisfying Hugenholtz - van Hove and Luttinger theorems (!) Asymmetry energy A(k F) = 34 MeV Landau parameters Spin-orbit interaction (2nd contact term)

15 UCLEAR THERMODYAMICS UCLEAR CHIRAL (PIO) DYAMICS BIDIG & SATURATIO: Yukawa + Van der Waals + Pauli V(r) e 2m r +... plus contact terms, r 6 P(m 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,. Kaiser, W. W. : ucl. Phys. A 75 (25) 259

16 gure 7.6: The current knowledge of nuclear masses. Preliminary results obtained on-line from the uclei in the Universe Z from QCD via CHIRAL EFFECTIVE FIELD THEORY Proton umber eutron umber to the stable nuclei known masses up to 95 mass measurement s 95 - mass measurement s 2 (on-line identification) unknown masses T > 1s unknown masses T < 1s unknown masses only UCLEAR CHART?

17 UCLEAR MAY-BODY CALCULATIOS... using and interactions from Chiral Effective Field Theory!"#$"%&#'(&))#*"+&),%&-.)/-,"%, , 15 $,67+, 18 $,,9,,! 5 :;!"#$"%&' (%)"'*+),-.)//)12234) systematic improvements with inclusion of 3-body interactions

18 DESITY FUCTIOAL STRATEGIES... constrained by (chiral) symmetry breaking pattern of Low-Energy QCD E[ρ] = E kin + d 3 x [E () (ρ) + E exc (ρ)] + E coul ρ ρ(x) Kohn - Sham equations E exc (ρ) : from in-medium Chiral Perturbation Theory ( Pionic fluctuations ) E () (ρ) : Hartree mean field(s) from contact terms strong SCALAR and VECTOR mean fields leading order I-MEDIUM changes of QCD CODESATES

19 Strategy : deviations (in %) between calculated and measured binding energies per nucleon... Examples (part I) Calculate physics at long and intermediate distances using nuclear chiral effective field theory Fix short distance constants (contact interactions) e.g. in Pb region Predict systematics for all other nuclei... and charge radii P. Finelli et al., ucl. Phys. A77 (26) 1 ch δe/a (%) 16 O 4 Ca 48Ca 72 i 9Zr 116 Sn124Sn 132 Sn 24Pb 28 Pb 214Pb 21 Po P. Finelli et al.: ucl. Phys. A77 (26) 1 δ r 2 1/2 (%) L3 DD-ME1 FKVW_new

20 Examples (part II) 48 charge density of Ca F(q) Exp. values FKVW_new ρ cgh (fm -3 ).8.8 ρ ch (r).6.6 [fm 3 ] ρ cgh (fm -3 ) Ca Exp. Th q (fm -1 ) ρ(fm r [fm] -3 ) P. Finelli,. Kaiser, D. Vretenar, W. W. : ucl. Phys. A735 (24) 449, A77 (26) 1

21 Examples (part III): deviations (in %) between calculated and measured binding energies DEFORMED UCLEI Ground state deformations δe (%) d Sm Gd Dy Er Yb A Hf Os Pt β Exp. data FKVW [25] d Sm Gd P. Finelli et al., ucl. Phys. A77 (26) 1 Systematics through isotopic chains governed by isospin dependent forces from chiral pion dynamics Er Dy Yb A Hf Os Pt TESOR force

22 5. CHIRAL CODESATE at finite DESITY T? T first ψψ order ψψ coexistence? baryon chemical potential µ B baryon density ρ sigma term m q M m q in-medium Chiral Effective Field Theory qq ρ qq = 1 ρ f 2 [ σ m 2 ( 1 3 p2 F 1 M 2 ) m 2 ( )] Eint (p F ) A (T = ) (free) Fermi gas of nucleons nuclear interactions (dependence on pion mass)

23 CHIRAL CODESATE: DESITY DEPEDECE Symmetric uclear Matter Results from: T = In-medium Chiral Effective Field Theory constrained by realistic nuclear equation of state condensate ratio ψψ (ρ) ψψ (ρ = ) chiral limit m ρ chiral limit m chiral in-medium dynamics m =.14 GeV leading order leading order (Fermi gas). Kaiser, Ph. de Homont, W. W. Phys. Rev. C 77 (28) ρ [fmρ [fm 3-3 ] Substantial change of symmetry breaking scenario between chiral limit m q = and physical quark mass m q 5 MeV uclear Physics would be very different in the chiral limit! (smaller quark mass stronger binding)

24 CHIRAL CODESATE: DESITY DEPEDECE eutron Matter ψψ (ρ n ) ψψ (ρ n = ) chiral in-medium dynamics leading order linear T = m =135MeV. Kaiser, W. W. (28) arxix: neutron star territory ρ n [fm -3 ] Qualitative difference between nuclear and neutron matter Important: realistic treatment of two-body and three-body correlations in extrapolations to high-density matter

25 ITERFACE of QCD and UCLEAR PHYSICS Low-Energy QCD Spontaneously broken CHIRAL SYMMETRY uclear Forces from CHIRAL EFFECTIVE FIELD THEORY 3- and 4-body interactions Convergence issues interaction from Lattice QCD? uclear Matter Low-momentum eff. interaction Energy Density Functional... and hypernuclei Convergence issues RG strategies Finite uclei Spin-orbit interactions Symmetry Breaking Patterns density dependence of the CHIRAL CODESATE implications for cold compressed baryonic matter

26 proach to nuclear force POTETIAL from LATTICE QCD. Ishii, S. Aoki, T. Hatsuda: Phys. Rev. Lett. 99 (27) 221; arxiv: Ish φ(r) φ(x,y,z=; 1 S ) x y r time (Euclidean) -1 x[fm] space Reconstruct potential from wave function: r [fm] S 3 S y[fm] V C (r) = E + 2 φ(r) 2µ φ(r) V C (r) [MeV] S 3 S1 m =.53 GeV r [fm] so far: quenched QCD large quark/pion masses ave functions in 1 S and 3 S 1 channels (left), and potentials (right), i.e., central force i effective central Repulsive force in 3 Score 1 channel for κ = The inset of the left figure is a 3D plo ction φ(x,y,z from = ; 1 Lattice S QCD ).... looking forward

27 ITERFACE of QCD and UCLEAR PHYSICS Low-Energy QCD Spontaneously broken CHIRAL SYMMETRY uclear Forces from CHIRAL EFFECTIVE FIELD THEORY 3- and 4-body interactions Convergence issues interaction from Lattice QCD uclear Matter Low-momentum effective interaction Convergence issues RG strategies Energy Density Functional... and hypernuclei Finite uclei Spin-orbit interactions Symmetry Breaking Pattern density dependence of the CHIRAL CODESATE implications for cold compressed baryonic matter