EMMI Workshop “Cold Dense Nuclear Matter: from Short-Range Nuclear Correlations to Neutron Stars” GSI 15 October 2015 CHIRAL DYNAMICS and NUCLEAR MATTER Wolfram Weise ECT * Trento and T echnische U niversität M ünchen Chiral EFT approaches to nuclear many-body systems Beyond mean field: fluctuations and Functional Renormalisation Group Nuclear matter, neutron matter and neutron stars Pion mass in the nuclear medium Thermodynamics of the chiral order parameter Outlook: Chiral SU(3) dynamics and hypernuclear matter 1
PHASES and STRUCTURES of QCD - facts and visions - J. Wambach, ? K. Heckmann, M. Buballa arXiv:1111.5475v2 [hep-ph] ? ? 2
CHIRAL SYMMETRY RESTORATION from Nambu - Goldstone to Wigner - Weyl Realisation of Chiral Symmetry PHASE TRANSITION or smooth CROSSOVER ? . MeV � P ? ? fm 3 CHIRAL PHASE TRANSITION nuclear physics terrain T [ MeV ] Chiral first - order phase transition and critical point ? . . . based on chiral quark models which do not respect nuclear physics constraints Needed: systematic approach to nuclear thermodynamics 3
PIONS , NUCLEONS and NUCLEI in the context of LOW - ENERGY QCD CONFINEMENT of quarks and gluons in hadrons Spontaneously broken CHIRAL SYMMETRY LOW-ENERGY QCD with light (u,d) quarks: Effective Field Theory of (weakly) interacting Nambu - Goldstone Bosons (pions) Chiral EFT represents QCD at energy/momentum scales Q << 4 π f π ∼ 1 GeV Strategies at the interface between QCD and nuclear physics : In-medium Ch iral P erturbation T heory Chiral Nucleon - Meson model based on non - linear sigma model based on linear sigma model (with inclusion of nucleons) non - perturbative expansion of free energy density Renormalization Group approach in powers of Fermi momentum 4
Spontaneously Broken CHIRAL SYMMETRY mesons baryons a 1 ∆ Axial Triplet + 1 + 3 Dipole 2 of f 0 0 + 1 . 0 + ¯ 1 ρ K ∗ NAMBU - [ GeV ] N 2 1 − Dipole GOLDSTONE ρ , ω ω BOSONS : GAP Gap mass π + , π 0 , π − 0 . 5 4 π f π ¯ Goldstone K Boson PION Characteristic Goldstone Goldstone 0 − Boson 0 π Symmetry condensates VACUUM Breaking SCALE : PION DECAY CONSTANT 4 π f π ∼ 1 GeV Axial current µ π f π = 92 . 2 ± 0 . 2 MeV ν 5
UV SCALES and SCHEMES Λ χ = 4 π f π 1 GeV . UV (energy / momentum) Renormalization Group . LINEAR SIGMA MODEL 0 . 5 λ ⌧ Λ χ , m σ IR π , σ N 0 Q NON-LINEAR V low − k SIGMA MODEL DOMAIN Chiral EFT Nuclear Physics π N m π Achim Schwenk’s talk 0 IR 6
and “old” Transverse distributions of quarks in the proton core - plus - cloud structure ? � D � D = � D � � � � � � Deeply Virtual Compton Scattering (expectations for DVCS @ JLab - 12 GeV) M. Guidal, H. Moutarde, M. Vanderhaeghen Rep. Prog. Phys. 76 (2013) 066202 , 3 ρ ( b ) 4 [ fm − 2 ] ρ ( b ) x = 0 . 4 2 → PROTON [ fm − 2 ] Q 2 = 2 . 5 GeV 2 compact core: 3 x B = 0 . 44 valence quarks 1 x B = 0 . 1 x = 0 . 1 b < 0.5 fm 2 0 0.5 1.0 b [ fm ] 1 valence + sea quarks b [ fm ] (core + (pion) cloud) 0 0.5 1.0 2.0 7
NN Interaction Hierarchy of SCALES Chiral Effective III II I V Field Theory NN potential r [ m − 1 π ] 1 2 3 r [ µ − 1 ] & two-pion exchange Lattice QCD π π π one-pion exchange two-pion π exchange N N N N one-pion π exchange S. Aoki, T. Hatsuda, N. Ishii short Prog. Theor. Phys. 123 (2010) 89 distance π N N N N contact terms explicit treatment of two-pion exchange NN Central Potential from Lattice QCD 8
CHIRAL EFFECTIVE FIELD THEORY Realization of Low-Energy QCD based on Non-Linear Sigma Model plus (heavy) baryons Interacting systems of PIONS (light / fast) and NUCLEONS (heavy / slow): L eff = L π ( U, ∂ U ) + L N ( Ψ N , U, ... ) U ( x ) = exp [ i τ a π a ( x ) /f π ] Construction of Effective Lagrangian: Symmetries short distance + . . . + + dynamics: contact terms N N π π π π 9
NUCLEAR INTERACTIONS from CHIRAL EFFECTIVE FIELD THEORY Weinberg Bedaque & van Kolck Bernard, Epelbaum, Kaiser, Meißner; . . . � Q 0 � O Λ 0 � Q 2 � O Λ 2 � Q 3 � O Λ 3 � Q 4 � O Λ 4 Systematically organized HIERARCHY 10
Explicit DEGREES of FREEDOM ∆ ( 1230 ) Large spin - isospin polarizability of the Nucleon ∆ ( 1230 ) in pion-nucleon scattering Dominance of π + p σ tot [ mb ] ∆ g 2 π ( M ∆ − M N ) ∼ 5 fm 3 A β ∆ = f 2 M ∆ − M N ≃ 2 m π << 4 π f π ( small scale ) N p lab [ GeV / c ] Pionic Van der Waals - type intermediate range central potential N. Kaiser, S. Gerstendörfer, W. W. , NPA637 (1998) 395 N. Kaiser, S. Fritsch, W. W. , NPA750 (2005) 259 π V c ( r ) = − 9 g 2 e − 2m π r π A P ( m π r ) β ∆ ∆ 32 π 2 f 2 π r 6 π π N N N N N strong 3 - body J. Fujita, H. Miyazawa (1957) interaction Pieper, Pandharipande, Wiringa, Carlson (2001) 11
Explicit DEGREES of FREEDOM (contd.) ∆ ( 1230 ) Kaiser et al. , Ordonez et al. Krebs, Epelbaum, Meißner (2007) Important physics of ∆ ( 1230 ) promoted to NLO Improved convergence 12
Important : Explicit treatment of two - pion exchange dynamics N , ∆ π 3 - body + + + + forces π N N N N contact terms contact terms Short digression: “Discovery” of two-pion exchange at LHC: elastic pp scattering at √ s = 8 TeV d σ deviation from standard exponential behaviour dt ∝ e bt π 0 . 06 ref = 527 . 1 e − 19 . 39 | t | P P data, statistical uncertainties N b = 1 0 . 05 full systematic uncertainty band N b = 2 V. A. Khoze, A.D. Martin, π 0 . 04 syst. unc. band without normalisation N b = 3 M.G. Ryskin 0 . 03 J. Phys. G 42 (2015) 025003 0 . 02 0 . 01 0 , d σ / d t − ref − 0 . 01 P L. Jenkovszky, A. Lengyel G. Antchev et al. (TOTEM coll.) ref − 0 . 02 Acta Phys. Pol. Nucl. Phys. B 899 (2015) 527 − 0 . 03 B 46 (2015) 863 − 0 . 04 − 0 . 05 0 . 02 0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14 0 . 16 0 . 18 0 . 2 0 [GeV 2 ] | t | 13
Important pieces of the CHIRAL NUCLEON - NUCLEON INTERACTION 200 N π ISOVECTOR ∆ ( 1232 ) 100 TENSOR FORCE [ MeV ] π N N 0 π +2 π V T [MeV] s 1 -100 s 2 V T π nge π -200 N N note: no meson -300 ρ Isovector Tensor Potential r [ fm ] -400 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 0.6 1.5 r [fm] N. Kaiser, S. Gerstendörfer, W.W. : Nucl. Phys. A 637 (1998) 395 CENTRAL ATTRACTION from TWO - PION EXCHANGE N Van der WAALS - like force: π ∆ ( 1232 ) V c ( r ) ∝ − exp[ − 2m π r ] P ( m π r ) π r 6 N N ... at intermediate and long distance note: no boson σ 14
IN - MEDIUM CHIRAL PERTURBATION THEORY Small energy, momentum, m π , k F << 4 π f π ∼ 1 GeV scales : “Medium insertion” in the nucleon propagator: � � i ( γ µ p µ + M N ) N + i ε − 2 π δ ( p 2 − M 2 N ) θ ( p 0 ) θ ( k F − | ⃗ | ~ p | ) p ) p 2 − M 2 Loop expansion of ( I n- M edium) Ch iral P erturbation T heory Expansion of ENERGY DENSITY in E ( k F ) powers of Fermi momentum [modulo functions f n ( k F / m π ) ] Nuclear thermodynamics : compute free energy density (3-loop order) N. Kaiser, S. Fritsch, W. W. (2002-2004) in - medium nucleon propagators incl. Pauli blocking 15
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