KbarN and KbarNN INTERACTIONS - Theory Status -

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1 LEANNIS Meeting Frascati, 8/9 April 21 KbarN and KbarNN INTERACTIONS - Theory Status - Wolfram Weise Low-Energy QCD with strange quarks: Chiral SU(3) Dynamics Non-perturbative (coupled-channels) approach to antikaon-nucleon interaction Important constraints: KN threshold physics πσ mass spectra Nature and properties of Λ(145) as KNquasibound state embedded in the KNN quasibound systems? Theory status report and update... next steps? πσ Astrophysical constraints from neutron stars in binaries continuum

2 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

3 _ Low-Energy K N Interactions Chiral Perturbation Theory NOT applicable: Λ(145) just below K - p threshold Σ * (1385) Λπ Σπ Λ * (145) KN _ KN 15 Λ ** (152) s [MeV] th Non-perturbative Coupled Channels approach based on Chiral SU(3) Dynamics N. Kaiser, P. Siegel, W. W. (1995) E. Oset, A. Ramos (1998) orld ofkantikaon-nucleon p scattering amplitude scattering π Σ + mass spectrum Im a(k p) Re a(k p)

4 CHIRAL SU(3) COUPLED CHANNELS DYNAMICS T ij = K ij + n K in G n T nj Leading s-wave I = meson-baryon interactions (Weinberg-Tomozawa) ch. π 1 : ch. 2 : K N Σ K N K 11 = 3 2f 2 ( s M N ) K 22 = 2 f 2 ( s M Σ ) π Σ strong enough to produce KN bound state πσ resonance strong channel coupling : π K Σ N K 12 = 1 3 2f 2 2 ( ) s M N + M Σ 2 Dynamical generation of Λ(145) as quasi-bound KN (I = ) state early history: R.H. Dalitz et al. (1967)

5 The TWO POLES scenario Γ 2-2 Im z [MeV] Singularities of KN amplitude in the complex energy plane starting point: no channel coupling T. Hyodo, W. W., Phys. Rev. C77 (28) z 2 (ORB) Pole 1 KN ) (dominantly z 2 (BNW) z 2 (HNJH) Re z [MeV] z 1 (ORB) z 1 (HNJH) z 1 (BMN) D. Jido et al., Nucl. Phys. A725 (23) 181 z 1 (BNW) z 2 (BMN) thr 144 Im z [MeV] z 2 (!" only) 136 Pole 1I (dominantly ) πσ KN πσ z 1 (KN only) z 2 (2) Re z [MeV] πσ z 2 (4) z 1 (4) bound state resonance z 1 (2) 144 channel coupling at work KN

6 The TWO POLES scenario (contd.) KN and πσ amplitudes: T. Hyodo, W. W. : Phys. Rev. C77 (28) F KN [fm] 4 2 KN(I=) F!" [fm] 1..5.!"(I=) Re F -.5 Im F s 1/2 [MeV] s 1/2 [MeV] Note difference in pole positions and spectra of D. Jido et al., NP A725 (23) 263 KN and πσ Equivalent KN effective interaction should produce quasibound state at 142 MeV (not 145 MeV)

7 I = KN Effective Interaction KN KN T. Hyodo, W. W. : Phys. Rev. C 77 (28) 3524 πσ πσ V eff ( KN KN) V eff ( KN KN) is: complex energy dependent non-local AY phenom. potential chiral SU(3) dynamics ( )* +,-./ F KN [fm]!" # $ % & " '& '%!&" : +@ : +@.+6;8<=>?:!$"!%""!1+,234/!%%" large differences in subthreshold extrapolations Chiral dynamics predicts significantly weaker attraction than AY (local, energy independent) potential in far-subthreshold region

8 Γ (ev) width KN Threshold Physics Precision measurements of kaonic hydrogen: SIDDHARTA (expected) NLO DEAR KEK WT (LO) energy shift E (ev) from DEAR to SIDDHARTA important constraints for Chiral SU(3) Dynamics B. Borasoy et al. Eur. Phys. J. A25 (25) 79 Phys. Rev. C74 (26) 5521 Deser-Trueman formula + corrections (Rusetsky et al.) a(k -p) (DEAR / LNF) -.47 ( ±.1) + i.3 ( ±.17) [fm] scattering length a(k -p) (KEK) -.78 ( ±.18) + i.49 ( ±.37) [fm] (G. Beer et al., Phys. Rev. Lett. 94 (25) 21232) (M. Iwasaki et al., Phys. Rev. Lett. 78 (1997) 367)

9 4 q K p cm s σk p π Σ + (mb GeV2 ) CONSTRAINTS for SUBTHRESHOLD EXTRAPOLATIONS K p π Σ q K p cm s σk p π + Σ (mb GeV2 ) K p π + Σ s (GeV) s (GeV) with without πσ B. Borasoy, R. Nissler, W. W. : Eur. Phys. J. A25 (25) 79 kaonic hydrogen (DEAR) constraints Sensitivity of mass spectrum to K p threshold conditions looking forward to SIDDHARTA data need accurate πσ mass distributions... in order to have sufficient predictive power for subthreshold extrapolations

10 KN Threshold Physics (contd.) Antikaon-nucleon scattering lengths 1.4 Im ai [fm] a a 1 R. Nissler PhD thesis (28).4.2 I = I = Re a i [fm]... still large uncertainties: need accurate K-proton and K-deuteron data

11 Re f(i=) [fm] Chiral SU(3) Coupled Channels Dynamics Relevant amplitudes, subthreshold extrapolations and uncrtainty analysis KN KN πσ πσ KN πσ s B. Borasoy, R. Nissler, W. W. : Eur. Phys. J. A25 (25) 79 [GeV] Im f(i=) [fm] R. Nissler PhD thesis (28) s [GeV]

12 πσ MASS 3 SPECTRA WTB WTB 2 Chiral SU(3) dynamics with uncertainty analysis R. Nissler, PhD thesis 1 (28) 2 full 3 WT full WT π Σ π Σ WT full WTB WTB 1.45 s [GeV] s [GeV] 2 s [GeV] 5.7: Left: π Σ + event distribution for the three different approaches compared old data 1 a from [182] (which have been supplemented by statistical ANKE errors data following [194]). est fits are represented R.J. Hemingway, by Nucl. the Phys. I. Zychor et al. solid lines while the shaded areas indicate the 1σ B253 (1985) ence regions. Right: π 742 Σ Phys. Lett. B66 (28) 167 event distribution as predicted by the chiral unitary 3 achesfull compared to the recent data from [183] which were not included full in the fit; arbitrary units arbitrary units

13 πσ MASS SPECTRA (contd.) ANKE data: p p p K + {Σ π } I. Zychor et al. Phys. Lett. B66 (28) 167 K + (p K ) p(p) Σ K (q) π... in comparison with theory: Chiral SU(3) coupled channels L. Geng, E. Oset Eur. Phys. J A34 (27) 45 p(p) π /ρ (q) Σ N (171) π K + (p K + p(p 1 ) p(p 2 ).1 p(p 1 ) p(p 2 ) d!/dm "# [µb/mev] N * set I N * set II Data M "# [MeV]

14 πσ MASS SPECTRA (contd.) Kaonic (in-flight) production of Λ(145) from deuterium K (k) Λ(145) π (p π ) Σ (p Σ ) $!" #!" KN #!" d (p d ) n (p n ) M!" [MeV] Two- Pole scenario D. Jido, E. Oset, T. Sekihara Eur. Phys. J. A42 (29) 268 exp. data: O. Braun et al. Nucl. Phys. B129 (1977) 1

15 πσ MASS SPECTRA (contd.) Photoproduction of Λ(145) JLAB) (see also LEPS / SPring-8) γ + p π K + + Σ Λ(145) 33% Σ + π 52% p(π )π K + γ. Λ(145) K p 33% 33% Σ π + Σ π 48% 1% 64% (n)π + π pπ (π, γ) $ # d( "! ) ) T $ T $ Re T T $ O T dm I ( ) 1 & ' & ' (1) 2 () 2 () (1)* (2) # $ d( "! ) ) T $ T # Re T T $ O T dm I & ' & ' (1) 2 () 2 () (1)* (2) d( "! ) T $ O& T dm 3 I () 2 (2) ' J. Nacher et al. Phys. Lett. B455 (1999) 55

16 πσ MASS SPECTRA (contd.) Photoproduction of Λ(145) JLAB) K. Moriya, R. Schumacher: HYP-X Conference (29) d#/dm [arbitrary scale] <E $ < <W< "! thresholds "! Invariant Mass [GeV] " +! - "-! + weighted average "! PDG Breit-Wigner Preliminary d#/dm [arbitrary scale] <E $ < <W<2.65 "! thresholds "! Invariant Mass [GeV] " +! - "-! + weighted average "! PDG Breit-Wigner Preliminary Displacements and deviations from naive single pole picture... but splitting of π Σ + vs. π + Σ opposite to expectations Energy dependence?

17 πσ MASS SPECTRA (contd.) d#/dm [arbitrary scale] Photoproduction of Λ(145) JLAB) γ p K + Σ + π 1.99<E $ < <W<2.25 Preliminary "! % p!! "! % n! +! weighted average PDG Breit-Wigner "! Invariant Mass [GeV] K. Moriya, NFQCD Kyoto (21)

18 Prototype Antikaon-Nuclear Few-Body System: K -pp 3-Body (Faddeev) Calculations Variational Calculations Limited predictive power in both approaches (subthreshold / off shell extrapolations, necessary approximations,... )

19 OVERVIEW Binding energies and widths of quasibound { K[NN] T=1 } I=1/2 variational AY phenomenol. potential variational chiral SU(3) dynamics variational coupled channels phenom. input 3-body coupled channels separable potentials variational variational Faddeev [1] [2] [3] [4] [5] B [MeV] 48 2± Γ [MeV] [1] T. Yamazaki, Y. Akaishi: Phys. Lett. B535 (22) 7; Phys. Rev. C76 (27) 4521 [2] A. Doté, T. Hyodo, W. W. : Nucl. Phys. A84 (28) 197; Phys. Rev. C79 (29) 143 [3] S. Wycech, A.M. Green: Phys. Rev. C79 (29) 141 [4] N.V. Shevchenko, A. Gal, J. Mares: Phys. Rev. Lett. 98 (27) 8231; (+ J. Révay) Phys. Rev. C76 (27) 444 [5] Y. Ikeda, T. Sato: Phys. Rev. C76 (27) 3523; Phys. Rev. C79 (29) 3521 note: width includes only KNN πσn, not KNN Y N

20 Results: Variational Calculations A. Doté, T. Hyodo, W. W. : Nucl. Phys. A 84 (28) 197, Phys. Rev. C 79 (29) 143 Input: realistic NN interaction (Argonne v18) KN effective interaction from Chiral SU(3) Dynamics Width [MeV] K pp binding energy and width using a variety of chiral models Total B. E. [MeV] Result: weak binding B(K pp) = 2 ± 3 MeV Γ = 4 7 MeV but: KNN πσn 3-body dynamics incomplete additional increase of width by KNN YN absorption δγ abs 1 MeV see also: T. Sekihara, D. Jido, Y. Kanada-En yo: Phys. Rev. C79 (29) 6221

21 K - pp System: Coupled-Channels Faddeev Approach N.V. Shevchenko, J. Mares, A. Gal, PRL 98 (27) 8231 N.V. Shevchenko, et al., PRC 76 (27) 444 Y. Ikeda, T. Sato, PRC 79 (29) 3521 Separable approximation for (s-wave) two-body potentials K N N K p K p K p πσ NN, ΣN Constrained by measured cross sections and scattering lengths K N N π Y Y. Ikeda, T. Sato, PRC 76 (27) 3523 spectator dynamics is important Results: B 5 7 MeV Γ 9 11 MeV (Shevchenko et al.) B 6 95 MeV Γ 45 8 MeV (Ikeda & Sato) effect of separable approximation on subthreshold behaviour?

22 K - pp System: Coupled-Channels Faddeev Approach (contd.) Importance of full 3-body coupled-channels dynamics Y. Ikeda, T. Sato, PRC 79 (29) 3521 t α,β (W ) = v α,β + γ v α,γ G γn (W )t γ,β (W ) G αn (W ) = 1 W E N ( p N ) (E Mα ( q) + E Bα ( q)) 2 + p 2 N + iɛ... tends to increase binding as compared to variational approaches (with effective single-channel interactions) but: separable approximation and strong cutoff (off-shell) dependence in extrapolations to far-subthreshold region

23 K - pp System: Coupled-Channels Faddeev Approach (contd.) interacting pair Y. Ikeda et al., YITP Kyoto (21) spectator Recent advanced calculation: Importance of full, energy dependent based on KN and πσ interactions chiral SU(3) dynamics Two-pole structure also seen in 3-body amplitude

24 K - pp System: Coupled-Channels Faddeev Approach (contd.) Y. Ikeda et al., YITP Kyoto (21) Search for 3-body resonances on KNN physical sheet Energy dependent interactions two poles in 3-body amplitude I II Λ N KNN Full [MeV] implications for spectral functions? weak binding

25 About DISTO T. Yamazaki et al., arxiv: [nucl-ex] Remaining questions: M(Λπp) = How can a few-body cluster with a lifetime of less than 2 fm/c be quasibound? K + Λ How can one make sure that K - pp is a dominant component of the DISTO signal? Why should the antikaon-less 3-body coupled-channels scenario be suppressed? p. Σ Y π p πσn Λp Σ p, Σ + n Note: similar questions apply to FINUDA and FOPI p π Λp, π + Λn

26 About COSY - TOF p p K + Λp S. Abd El-Samad et al., arxiv:13.63 [nucl-ex] pσ thr. pσ tot thr. tot res fsi res fsi p beam = 2.95 GeV/c p beam = 3.2 GeV/c Mostly N* resonance formation and final state interactions A. Sibirtsev et al., nucl-th/422 Spectral shape changes with energy

27 NEUTRON STARS and the EQUATION OF STATE of DENSE BARYONIC MATTER J. Lattimer, M. Prakash: Astrophys. J. 55 (21) 426 Phys. Reports 442 (27) 19 Mass-Radius Relation Neutron Star Scenarios tron Neutron Star Structure Star Structure Tolman-Oppenheimer-Volkov an-oppenheimer-volkov equations equations equations dp dr dm dr STRANGE QUARK MATTER dp = G (m + 4πpr 3 )(ɛ + p) c 2 = G (m + 4πpr 3 )(ɛ + p) dr r(r c 2 2Gm/c r(r 2 ) 2Gm/c 2 ) dm = 4π ɛ c 2 = r2 4π ɛ dr c 2 r2 maximum mass maximum mass NUCLEAR MATTER

28 New Constraints from NEUTRON STARS in BINARIES... using observables such as apparent surface and flux during cooling phase of bursts technique applied to three neutron stars in binaries 4U EXO U Black Hole Horizon F. Özel, G. Baym, T. Güver arxiv: [astro-ph.he]

29 Implications for EQUATION of STATE pressure Nucleons. + Hyperons A. Akmal et al. PRC 58 (1998) 184. F. Özel, G. Baym, T. Güver arxiv: [astro-ph.he] Kaon Condensate N.K. Glendenning, J. Schaffner-Bielich PRC 6 (1999) 2583 density Nucleons + Hyperons more likely than Kaon Condensate

30 Summary Low-Energy QCD: spontaneous chiral symmetry breaking scenario well established Chiral Effective Field Theory framework for low-energy hadron structure and dynamics including strange quarks Antikaons in interaction: extrapolations to far-subthreshold region still uncertain needed: KNN quasibound system? high-precision KN threshold data much improved πσ mass spectra Answers in sight? SIDDHARTA, J-PARC, AMADEUS, GSI Constraints from astrophysics / neutron stars in binaries: nucleons + hyperons favoured over kaon condensate?