8 September Dear Paul...

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1 EXA 2011 Vienna PK Symposium 8 September 2011 Dear Paul...

2 DEEPLY BOUND STATES of PIONIC ATOMS Experiment (GSI): K. Suzuki et al. Phys. Rev. Lett. 92 (2004) Theory: Energy Dependent Pion-Nucleus Potential based on In-medium Chiral Perturbation Theory E. Kolomeitsev, N. Kaiser, W. W. Phys. Rev. Lett. 90 (2003) Nucl. Phys. A721 (2003) 835 f π(ρ 0 ) 0.8f π 1 σ N 2 m 2 π f 2 π ρ 0 deduced from exp. theory (σ N 50 MeV) Fingerprints of CHIRAL SYMMETRY RESTORATION

3 EXA 2011 Vienna PK Symposium Theory of ANTIKAON - NUCLEON INTERACTION in the age of SIDDHARTA Wolfram Weise 8 September 2011 with Yoichi Ikeda and Tetsuo Hyodo RIKEN & Tokyo Institute of Technology RIKEN - TUM cooperation agreement (initiated by Paul Kienle) Low-energy QCD with strange quarks: Chiral SU(3) Effective Field Theory + Coupled Channels KN threshold physics and kaonic hydrogen New next-to-leading-order (NLO) analysis with constraints from SIDDHARTA measurements New determination of K - - N scattering lengths

4 1. LOW-ENERGY QCD with STRANGE QUARKS and SPONTANEOUSLY BROKEN CHIRAL SYMMETRY... 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

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 axial current π K f π = 92.4 ± 0.3 MeV f K = ± 0.9 MeV f η = ± 4.6 MeV µ ν DECAY CONSTANTS ( chiral limit: f = 86.2MeV) spontaneous symmetry breaking m 2 π f 2 π = m q ψψ + O(m 2 q) explicit symmetry breaking

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] 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 orld of antikaon-nucleon s-wave I = 0 meson-baryon scattering interactions (Weinberg-Tomozawa) K N π Σ strong enough to produce π KN bound state K N π Σ πσ resonance K N Σ Dynamical generation of Λ(1405) as quasi-bound KN (I = 0) state πσ KN channel coupling

8 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

9 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 ),

10 2. KN THRESHOLD and LOW-ENERGY OBSERVABLES Kaonic hydrogen Threshold branching ratios Low-energy scattering data

11 Kaonic hydrogen precision data NEWS from SIDDHARTA M. Bazzi et al. arxiv: [nucl-ex] strong interaction shift and width: E = 283 ± 36 (stat)± 6 (syst) ev Γ = 541 ± 89 (stat)± 22 (syst) ev theory: leading order B. Borasoy, R. Nißler, W. W. Eur. Phys. J. A25 (2005) 79 B. Borasoy, U.-G. Meißner, R. Nißler PRC74 (2006) WT approach R. Nißler PhD thesis (2008) 800 WT χ 2 /d.o 1.4 < Γ (ev) SIDDHARTA 1.6 < 2.33 < 4.0 < 6.0 < 200 DEAR KEK E (ev)

12 UPDATED ANALYSIS of K p THRESHOLD PHYSICS Chiral SU(3) coupled-channels dynamics Weinberg-Tomozawa + Born terms + NLO kaonic hydrogen shift & width theory (NLO) exp. E (ev) Γ (ev) threshold branching ratios Y. Ikeda, T. Hyodo, W.W. (2011) ± 36 ± ± 89 ± 22 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 fit achieved with χ 2 /d.o.f 1.0

13 UPDATED ANALYSIS of K p THRESHOLD PHYSICS with SIDDHARTA constraints Y. Ikeda, T. Hyodo, W.W. (2011) Non-trivial result: best fit prefers physical values of decay constants: f K (MeV) f η (MeV) Weinberg-Tomozawa terms dominant Born terms significant (b) (f π = 92.4 MeV) (a) (c) NLO parameters are non-negligible but small (d)

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

15 UPDATED ANALYSIS of K p LOW-ENERGY CROSS SECTIONS σ(k p K 0 n) [mb] σ(k p π 0 Λ) [mb] Plab(MeV) Plab(MeV) Mass spectrum I= E c.m. (MeV)

16 K p SCATTERING AMPLITUDE threshold region and subthreshold extrapolation [fm] [fm] Im f(k p K p) Re f(k p K p) s [MeV] 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

17 SUMMARY New consistent analysis of KN threshold physics and scattering data based on chiral SU(3) effective Lagrangian at next-to-leading order Substantial improvements through constraints provided by SIDDHARTA kaonic hydrogen measurements New more precise evaluation of scattering lengths (~15 % accuracy) a(k p)= i [fm] a(k n)= i [fm] Near future need kaonic deuterium at SIDDHARTA 2 to complete KN and set constraints for KNN

18 PK... Ha!y Bi"hday!