Theory of ANTIKAON interactions with NUCLEONS and NUCLEI a state-of-the-art report

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1 67th Annual Meeting of the Physical Society of Japan 25 March 2012 Theory of ANTIKAON interactions with NUCLEONS and NUCLEI a state-of-the-art report Wolfram Weise Low-energy QCD: symmetries and symmetry breaking patterns Strangeness and chiral SU(3) dynamics KN threshold physics and kaonic hydrogen Antikaons in baryonic matter New constraints from neutron stars

2 Hierarchy of QUARK MASSES in QCD light quarks separation of scales 0 u, d s 1 GeV c heavy quarks mass m d 4 6MeV m u /m d m s MeV (µ 2 GeV) m c 1.25 GeV m b 4.2 GeV m t 174 GeV LOW-ENERGY QCD: CHIRAL EFFECTIVE FIELD THEORY m q expansion in and in powers of low momentum Non-Relativistic QCD: HEAVY QUARK EFFECTIVE THEORY expansion in powers of 1/m Q

3 LOW-ENERGY QCD with STRANGE QUARKS: Chiral SU(3) Dynamics... realized as an EFFECTIVE FIELD THEORY with SU(3) octet of pseudoscalar Nambu-Goldstone bosons coupled to the baryon octet... explicit chiral symmetry breaking by non-zero quark masses (at a renormalization scale µ 2 GeV): m q = m u + m d 2 = 3 5 MeV m s 25 m q

4 BASIC ISSUES Strange quarks are intermediate between light and heavy : interplay between spontaneous and explicit chiral symmetry breaking in low-energy QCD Testing ground: high-precision antikaon-nucleon threshold physics strongly attractive low-energy KN interaction Nature and structure of Λ(1405) three-quark valence structure vs. molecular meson-baryon system? (B = 1, S = 1, J P = 1/2 ) Quest for quasi-bound antikaon-nuclear systems? Role of strangeness in dense baryonic matter? new constraints from neutron stars

5 CHIRAL Spontaneously Broken SU(3) L SU(3) R SYMMETRY NAMBU - GOLDSTONE BOSONS: Pseudoscalar SU(3) meson octet {φ a } = {π, K, K,η 8 } ORDER PARAMETERS: 0 A µ a(0) φ b (p) = iδ ab p µ f b DECAY CONSTANTS ( chiral limit: f = 86.2 MeV) axial current π K µ ν f π = 92.4 ± 0.3 MeV f K = ± 0.9 MeV f η = ± 4.6 MeV Gell-Mann Oakes Renner relations m 2 π f 2 π = m u + m d 2 m 2 K f 2 K = m u + m s 2 ū u + dd ū u + ss + higher order corrections

6 CHIRAL SU(3) EFFECTIVE FIELD THEORY Interacting systems of NAMBU-GOLDSTONE BOSONS (pions, kaons) coupled to BARYONS L eff = L mesons (Φ) + L B (Φ, Ψ B ) Leading DERIVATIVE couplings (involving ) µ Φ determined by spontaneously broken CHIRAL SYMMETRY + Φ Φ Φ B Φ Low-Energy Expansion: CHIRAL PERTURBATION THEORY p energy / momentum small parameter : 4π f π 1 GeV works well for low-energy pion-pion and pion-nucleon interactions... but NOT for systems with strangeness S = 1 ( KN, πσ,...) B higher orders with additional low-energy constants

7 _ Low-Energy K N Interactions Chiral Perturbation Theory NOT applicable: Λ(1405) resonance 27 MeV below K - p threshold Σ * (1385) Λπ Σπ Λ * (1405) KN _ KN 1500 Λ ** (1520) s [MeV] orld of antikaon-nucleon scattering th Non-perturbative Coupled Channels approach based on Chiral SU(3) Dynamics N. Kaiser, P. Siegel, W. W. (1995) E. Oset, A. Ramos (1998) Leading s-wave I = 0 meson-baryon interactions (Tomozawa-Weinberg) K N Σ π π Σ K N π Σ K N πσ KN channel coupling

8 CHIRAL SU(3) COUPLED CHANNELS DYNAMICS T ij = K ij + n K in G n T nj Leading s-wave I = 0 meson-baryon interactions (Tomozawa-Weinberg) Note: ENERGY DEPENDENCE characteristic of Nambu-Goldstone Bosons 1 = KN, I = 0 2 = πσ, I = 0 K N π Σ K N K 11 = 3 2f 2 K ( s M N ) K 22 = 2 π Σ f 2 π ( s M Σ ) driving interactions individually strong enough to produce KN bound state πσ resonance strong channel coupling : π K Σ K 12 = N 1 2f π f K 3 2 ( s M Σ + M N 2 )

9 CHIRAL SU(3) COUPLED CHANNELS DYNAMICS T ij = K ij + n K in G n T nj input from chiral SU(3) meson-baryon effective Lagrangian loop functions (dim. regularization) with subtraction constants encoding short distance dynamics coupled channels: K p, K 0 n,π 0 Σ 0,π + Σ,π Σ +,π 0 Λ,ηΛ, ησ 0, K + Ξ, K Ξ 0

10 CHIRAL SU(3) COUPLED CHANNELS DYNAMICS: - NLO hierarchy of driving terms - (a) direct and crossed Born terms input: axial vector constants D and F from hyperon beta decays g A = D + F =1.26 (d) L MB L MB 1 =Tr ( D B leading order (Weinberg-Tomozawa) terms input: physical pion and kaon decay constants (b) 2 ( Bγ µ γ 5 {u µ,b})+ F ) 2 ( Bγ µ γ 5 [u µ,b]) O next-to-leading order (NLO) input: 7 low-energy constants (c) O(p 2 ) 2 =b D Tr ( B{χ+,B} ) + b F Tr ( B[χ+,B] ) + b 0 Tr( BB)Tr(χ + ) + d 1 Tr ( B{u µ, [u µ,b]} ) + d 2 Tr ( B[u µ, [u µ,b]] ) + d 3 Tr( Bu µ )Tr(u µ B)+d 4 Tr( BB)Tr(u µ u µ ),

11 The TWO POLES scenario!"#$%& #(' πσ KN T +,+&#-.'"(% #(' [MeV 1 ] #(% #(% #(" #($ #(" #($ &%# &'# dominantly πσ dominantly KN!"%#!"#$%&#'"(%!""#!"$#!"## &$# &"# )*#$%&#'"(% D. Jido et al., Nucl. Phys. A723 (2003) 205 T. Hyodo, W. W. : Phys. Rev. C 77 (2008) T. Hyodo, D. Jido : Prog. Part. Nucl. Phys. 67 (2012) 55

12 KN Threshold Physics: Kaonic hydrogen precision data EM value!"#$! /0%(1+23"#$%&'(! K p! 31&3'$ NEWS from SIDDHARTA strong interaction shift and width: E = 283 ± 36 (stat)± 6 (syst) ev Γ = 541 ± 89 (stat)± 22 (syst) ev :12/ /968 /98; TW :12/ /456 /768 M. Bazzi et al. (SIDDHARTA collaboration) Phys. Lett. B 704 (2011) /958 /468 /<=>5 SIDDHARTA Theory: leading order (Tomozawa - Weinberg) B. Borasoy, R. Nißler, W. W. Eur. Phys. J. A25 (2005) 79 B. Borasoy, U.-G. Meißner, R. Nißler PRC74 (2006) R. Nißler PhD thesis (2008)

13 Improved constraints on chiral SU(3) dynamics from kaonic hydrogen Yoichi Ikeda a,b,, Tetsuo Hyodo a and Wolfram Weise c a Department of Physics, Tokyo Institute of Technology, Meguro , Japan b RIKEN Nishina Center, 2-1, Hirosawa, Wako, Saitama , Japan c Physik-Department, Technische Universität München, D Garching, Germany Abstract A new improved study of K -proton interactions near threshold is performed using coupledchannels dynamics based on the next-to-leading order chiral SU(3) meson-baryon effective Lagrangian. Accurate constraints are now provided by new high-precision kaonic hydrogen measurements. Together with threshold branching ratios and scattering data, these constraints permit an updated analysis of the complex KN and πσ coupled-channels amplitudes and an improved determination of the K p scattering length, including uncertainty estimates. arxiv: Physics Letters B 706 (2011) 63

14 UPDATED ANALYSIS of K p THRESHOLD PHYSICS Y. Ikeda, T. Hyodo, W.W. Phys. Lett. B 706 (2011) 63 Nucl. Phys. A (2012), in print Chiral SU(3) coupled-channels dynamics Tomozawa-Weinberg + Born terms + NLO kaonic hydrogen shift & width theory (NLO) exp. E (ev) ± 36 ± 6 Γ (ev) ± 89 ± 22 threshold branching ratios (SIDDHARTA) Γ(K p π + Σ ) Γ(K p π Σ + ) Γ(K p π + Σ,π Σ + ) Γ(K p all inelastic channels) Γ(K p π 0 Λ) Γ(K p neutral states) ± ± ± 0.02 scattering length (fm) Re a(k p)= 0.65 ± 0.10 Im a(k p)=0.81 ± 0.15 best fit achieved with χ 2 /d.o.f. 0.9

15 UPDATED ANALYSIS of K p THRESHOLD PHYSICS with SIDDHARTA constraints Y. Ikeda, T. Hyodo, W.W. Phys. Lett. B 706 (2011) 63 Nucl. Phys. A (2012), in print Non-trivial result: best NLO fit prefers physical values of decay constants: f K (MeV) f η (MeV) Tomozawa-Weinberg terms dominant (f π = 92.4 MeV) Born terms significant (a) (b) (c) NLO parameters are non-negligible but small Subtraction constants (encoding unresolved high energy behaviour) are of natural size (d)

16 UPDATED ANALYSIS of K p LOW-ENERGY CROSS SECTIONS 250 σ(k p K p) [mb] 300 σ(k p π + Σ ) [mb] K - p -> - +(mb) Plab(MeV) σ(k p π Σ + ) [mb] Plab(MeV) Plab(MeV) 140 σ(k p π 0 Σ 0 ) [mb] Plab(MeV)

17 K p SCATTERING AMPLITUDE f(k p)= 1 2 [ f KN(I = 0)+f KN(I = 1) ] threshold region and subthreshold extrapolation: Λ(1405) : KN (I = 0) quasibound state embedded in the πσ continuum 1.5 [fm] [fm] Im f(k p K p) Re f(k p K p) Λ(1405) s [MeV] 0 s [MeV] Re a(k p) Im a(k p) complex scattering length (including Coulomb corrections) Re a(k p)= 0.65 ± 0.10 fm Im a(k p)=0.81 ± 0.15 fm Y. Ikeda, T. Hyodo, W.W. : Phys. Lett. B 706 (2011) 63

18 K n SCATTERING AMPLITUDE [fm] real part f(k n)=f KN(I = 1) threshold region and subthreshold extrapolation 1400 WT WTB NLO s [MeV] imaginary part Re f(k n K n) [fm] Im f(k n K n) WT TW WTB TW + Born NLO TW TW + Born NLO complex scattering length s [MeV] Re a(k n)= fm Im a(k n)= fm Y. Ikeda, T. Hyodo, W.W. : Nucl. Phys. A (2012), in print

19 Implications & Comments K p scattering length more accurately determined than K n (SIDDHARTA constraints vs. uncertainties in I = 1 channels) Kaonic deuterium measurements important for providing further constraints on K n interaction B = 2 systems - key issue: KNN YN absorption into non-mesonic hyperon - nucleon final states e.g.: p K n Λ(1405) n π Σ N Λ nucleon potential m π 1 GeV K pn channel K pp channel Repulsive short-distance interaction? Λ (uds) N Lattice QCD Y. Ikeda et al. (HAL QCD collaboration)

20 Kaons and Antikaons in Nuclear Matter In-medium Chiral SU(3) Dynamics with Coupled Channels Kaon spectrum in baryonic matter determined by: ω 2 q 2 m 2 K Π K (ω, q; ρ) =0 Π K = 2ωU K = 4π [ ] Pauli blocking, f K p ρ p + f K n ρ n Fermi motion, 2N correlations V. Koch Phys. Lett. B 337 (1994) 7 M. Lutz Phys. Lett. B 426 (1998) 12 A. Ramos, E. Oset Nucl. Phys. A 671 (2000) 481 M. Lutz, C.L. Korpa, M. Möller Nucl. Phys. A 808 (2008) 124 K - mass K - - width / 100 MeV T. Waas, N. Kaiser, W. W. : Phys. Lett. B 379 (1996) 34 T. Waas, W. W. : Nucl. Phys. A 625 (1997) 287 _ Note: In-medium K width drops when mass falls below πσ threshold

21 Kaon Condensation in Neutron Star Matter first suggested by D. Kaplan, A. Nelson (1985) on the basis of attractive K -N Tomozawa - Weinberg term at high density, energetically favourable to condense K -?? T. Waas, M. Rho, W. W. : Nucl. Phys. A 617 (1997) 449 electron chemical potential including NN correlations in-medium chiral SU(3) dynamics conversion to hyperons via K NN YN?

22 Outlook: new constraints from NEUTRON STARS direct measurement of neutron star mass from increase in travel time near companion J most edge-on binary pulsar known (89.17 ) + massive white dwarf companion (0.5 M sun ) heaviest neutron star with 1.97±0.04 M sun Nature, Oct. 28, 2010

23 log 10 P [dyne / cm 2 ] crust EOS neutronstar star matter matter with (chiral c i uncertainties EFT) log 10 [g / cm 3 ] ρ 0 ρ 1 n [ 0] : Pressure of neutron star matter based on chiral low-momentum interactions for densities ρ < ρ 1 (corresponding 80 eutron densitynew ρ 1,n =1.1ρ constraints 0 ). The band estimates the theoretical uncertainties from many-body forces and from an 1 lete many-body from calculation. EFT At and low densities, condensate the results are compared to a standard crust EOS [16], where the right 60 emonstrates the importance of 3N forces. The extension to higher densities using piecewise polytropes r ph >>R (as explained in t) is illustratedneutron schematicallystar in the left panel. 40 for densities ρ 0 /8 < ρ < ρ 1 = gcm 3 rresponds to a neutron density ρ 1,n =1.1ρ 0 ). We the following symmetry energy parameters and fractions: News from NEUTRON STARS K. Hebeler, J. Lattimer, C. Pethick, A. Schwenk PRL 105 (2010) observables kaon quark matter M (M ) Exotic equations of state ruled out? P [10 33 dyne / cm 2 ] A.W. Steiner, J. Lattimer, E.F. Brown Astroph. J. 722 (2010) 33 NN only, EM NN only, EGM realistic nuclear EoS A. Akmal, V.J. Pandharipande, D.G. Ravenhall Phys. Rev. C 58 (1998) ! tron star matter EOS taking 1.5 < Γ 1,2 < 4.0 and transi- 0 tion densities 6 ρ 12 8 ( )ρ We therefore 16 18extend the pressure of neutron starr matter (km) based on chiral EFT using two general piecewise polytropes, as illustrated in 20 2

24 NEUTRON STAR MATTER Equation of State Low-density (crust) + ChEFT (FKW) Constrained extrapolation (polytropes) Akmal, Pandharipande, Ravenhall (1998) P = const ρ Γ S. Fiorilla, N. Kaiser, W. W. Nucl. Phys. A 880 (2012) 65 nuclear physics constraints astrophysics constraints M(R) B. Röttgers, W. W. (2011) W. W. Prog. Part. Nucl. Phys. (2012), in print Including new neutron star constraints plus Chiral Effective Field Theory at lower density

25 Mass - Radius relation Option I: Conventional hadronic (baryonic + mesonic) degrees of freedom In-medium Chiral Effective Field Theory up to 3 loops (reproducing thermodynamics of normal nuclear matter) S. Fiorilla, N. Kaiser, W. W. : Nucl. Phys. A 880 (2012) PSR J conventional eq. of state 1.0 nucleons + pions (1230) 3 body forces in-medium chiral EFT density profile 0.6 Ρ fm 3 M M NEUTRON STAR MATTER M 2.00 M R km 8 10 R km T. Hell, S. Schultess, W. W. (2012) - (preliminary) 6 8 r km

26 M M NEUTRON STAR MATTER Mass - Radius relation (contd.) Option II: Polyakov - Nambu - Jona-Lasinio (PNJL) model (u-,d- and s-quarks as quasiparticles with dynamically generated constituent masses)... features first order chiral phase transition at low temperatures and moderate baryon chemical potentials... produces too soft equation of state for neutron matter does not work Option III: Conventional hadronic (ChEFT) EoS PSR J matched smoothly at densities ρ! 3 ρ PNJL realistic EoS Gv = 0 ChEFT + PNJL to PNJL EoS including repulsive vector coupling between quarks Gv /G = 0.45 no 1st order phase transition R km soft crossover between hadronic and quark phases T. Hell, S. Schultess, W. W. (2012) - (preliminary)

27 SUMMARY New consistent analysis of KN threshold physics and scattering data based on chiral SU(3) effective Lagrangian at next-to-leading order. New evaluation of K p scattering length: a(k p)= i [fm] (~ 15 % accuracy) deduced: a(k n) i [fm] (less accurate) Need kaonic deuterium to complete KN and set constraints for KNN YN absorption channel. New constraints from two-solar-mass neutron star and window of n-star radii: conventional EoS works best - kaon condensate ruled out (hyperons may contribute if short-range YN interactions sufficiently repulsive).