Meson-baryon interactions and baryon resonances

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1 Meson-baryon interactions and baryon resonances Tetsuo Hyodo Tokyo Institute of Technology supported by Global Center of Excellence Program Nanoscience and Quantum Physics 2011, June 16th 1

Contents Contents Λ(1405) in meson-baryon scattering T. Hyodo, D. Jido, arxiv:1104.4474, submitted to Prog. Part. Nucl. Phys.

2 Contents Contents Λ(1405) in meson-baryon scattering T. Hyodo, D. Jido, arxiv: , submitted to Prog. Part. Nucl. Phys. Chiral SU(3) dynamics Pole structure of Λ(1405) Toward realistic meson-baryon interaction Constraint by accurate KN data Y. Ikeda, T. Hyodo, W. Weise, in preparation Information of πσ channel Y. Ikeda, T. Hyodo, D. Jido, H. Kamano, T. Sato, K. Yazaki, arxiv: [nucl-th], to appear in Prog. Theor. Phys., T. Hyodo, M. Oka, arxiv: [nucl-th] Summary 2

3 Chiral symmetry breaking in hadron physics Chiral symmetry: QCD with massless quarks Consequence of chiral symmetry breaking in hadron physics 3

4 Chiral symmetry breaking in hadron physics Chiral symmetry: QCD with massless quarks Consequence of chiral symmetry breaking in hadron physics - appearance of the Nambu-Goldstone (NG) boson m π 140 MeV - dynamical generation of hadron masses M p 1 GeV 3M q, M q 300 MeV v.s. 3 7 MeV - constraints on the NG-boson--hadron interaction low energy theorems <-- current algebra systematic low energy (m,p/4πfπ) expansion: ChPT 3

Chiral symmetry breaking in hadron physics Chiral symmetry: QCD with massless quarks Consequence of chiral symmetry breaking in hadron physics - appearance of the Nambu-Goldstone (NG) boson m π 140

5 Chiral symmetry breaking in hadron physics Chiral symmetry: QCD with massless quarks Consequence of chiral symmetry breaking in hadron physics - appearance of the Nambu-Goldstone (NG) boson m π 140 MeV - dynamical generation of hadron masses M p 1 GeV 3M q, M q 300 MeV v.s. 3 7 MeV - constraints on the NG-boson--hadron interaction low energy theorems <-- current algebra systematic low energy (m,p/4πfπ) expansion: ChPT Chiral symmetry and its breaking SU(3) R SU(3) L SU(3) V Underlying QCD <==> observed hadron phenomena 3

6 s-wave low energy interaction in ChPT Leading order term for the meson-baryon scattering L WT = 1 4f 2 Tr Biγ µ [Φ µ Φ ( µ Φ)Φ, B] 4

7 s-wave low energy interaction in ChPT Leading order term for the meson-baryon scattering L WT = 1 4f 2 Tr Biγ µ [Φ µ Φ ( µ Φ)Φ, B] s-wave contribution: Weinberg-Tomozawa (WT) term Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) V ij = C ij 4f 2 (ω i + ω j ) 4

8 s-wave low energy interaction in ChPT Leading order term for the meson-baryon scattering L WT = 1 4f 2 Tr Biγ µ [Φ µ Φ ( µ Φ)Φ, B] s-wave contribution: Weinberg-Tomozawa (WT) term Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) V ij = C ij 4f 2 (ω i + ω j ) C ij = 8 8 α [6 C 2 (α)] I α ī, Y ī I i, Y i I, Y 8 8 α I j, Y j I j, Y j I, Y Y = Y ī + Y i = Y j + Y j, I = I ī + I i = I j + I j, - Flavor SU(3) symmetry --> sign and strength 4

9 s-wave low energy interaction in ChPT Leading order term for the meson-baryon scattering L WT = 1 4f 2 Tr Biγ µ [Φ µ Φ ( µ Φ)Φ, B] s-wave contribution: Weinberg-Tomozawa (WT) term Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) V ij = C ij 4f 2 (ω i + ω j ) C ij = 8 8 α [6 C 2 (α)] I α ī, Y ī I i, Y i I, Y 8 8 α I j, Y j I j, Y j I, Y Y = Y ī + Y i = Y j + Y j, I = I ī + I i = I j + I j, - Flavor SU(3) symmetry --> sign and strength - Derivative coupling --> energy dependence 4

10 s-wave low energy interaction in ChPT Leading order term for the meson-baryon scattering L WT = 1 4f 2 Tr Biγ µ [Φ µ Φ ( µ Φ)Φ, B] s-wave contribution: Weinberg-Tomozawa (WT) term Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) V ij = C ij 4f 2 (ω i + ω j ) +... C ij = 8 8 α [6 C 2 (α)] I α ī, Y ī I i, Y i I, Y 8 8 α I j, Y j I j, Y j I, Y Y = Y ī + Y i = Y j + Y j, I = I ī + I i = I j + I j, - Flavor SU(3) symmetry --> sign and strength - Derivative coupling --> energy dependence - Systematic improvement by higher order terms (later) 4

11 s-wave low energy interaction in ChPT Leading order term for the meson-baryon scattering L WT = 1 4f 2 Tr Biγ µ [Φ µ Φ ( µ Φ)Φ, B] s-wave contribution: Weinberg-Tomozawa (WT) term Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) V ij = C ij 4f 2 (ω i + ω j ) +... C ij = 8 8 α [6 C 2 (α)] I α ī, Y ī I i, Y i I, Y 8 8 α I j, Y j I j, Y j I, Y Y = Y ī + Y i = Y j + Y j, I = I ī + I i = I j + I j, - Flavor SU(3) symmetry --> sign and strength - Derivative coupling --> energy dependence - Systematic improvement by higher order terms (later) If the interaction is strong, resummation is mandatory. 4

12 Scattering amplitude and unitarity Unitarity of S-matrix: Optical theorem Im[T 1 (s)] = ρ(s) 2 phase space of two-body state 5

13 Scattering amplitude and unitarity Unitarity of S-matrix: Optical theorem Im[T 1 (s)] = ρ(s) 2 phase space of two-body state General amplitude by dispersion relation T 1 ( s)= i R i s Wi +ã(s 0 )+ s s 0 2π s + ds ρ(s ) (s s)(s s 0 ) Ri, Wi, a: to be determined by chiral interaction 5

14 Scattering amplitude and unitarity Unitarity of S-matrix: Optical theorem Im[T 1 (s)] = ρ(s) 2 phase space of two-body state General amplitude by dispersion relation T 1 ( s)= i R i s Wi +ã(s 0 )+ s s 0 2π s + ds ρ(s ) (s s)(s s 0 ) Ri, Wi, a: to be determined by chiral interaction Identify dispersion integral = loop function G, the rest = V -1 T ( s)= 1 V 1 ( s) G( s; a) Scattering amplitude 5

15 Scattering amplitude and unitarity Unitarity of S-matrix: Optical theorem Im[T 1 (s)] = ρ(s) 2 phase space of two-body state General amplitude by dispersion relation T 1 ( s)= i R i s Wi +ã(s 0 )+ s s 0 2π s + ds ρ(s ) (s s)(s s 0 ) Ri, Wi, a: to be determined by chiral interaction Identify dispersion integral = loop function G, the rest = V -1 T ( s)= 1 V 1 ( s) G( s; a) Scattering amplitude The function V is determined by the matching with ChPT T (1) = V (1), T (2) = V (2), T (3) = V (3) V (1) GV (1),... Amplitude T: consistent with chiral symmetry + unitarity 5

16 Chiral unitary approach Meson-baryon scattering amplitude - Interaction <-- chiral symmetry Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) - Amplitude <-- unitarity in coupled channels R.H. Dalitz, T.C. Wong, G. Rajasekaran, Phys. Rev. 153, 1617 (1967) 6

17 Chiral unitary approach Meson-baryon scattering amplitude - Interaction <-- chiral symmetry Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) - Amplitude <-- unitarity in coupled channels R.H. Dalitz, T.C. Wong, G. Rajasekaran, Phys. Rev. 153, 1617 (1967) T = 1 1 VG V T = + chiral T cutoff N. Kaiser, P. B. Siegel, W. Weise, Nucl. Phys. A594, 325 (1995), E. Oset, A. Ramos, Nucl. Phys. A635, 99 (1998), J. A. Oller, U. G. Meissner, Phys. Lett. B500, 263 (2001), M.F.M. Lutz, E. E. Kolomeitsev, Nucl. Phys. A700, 193 (2002),... many others It successfully reproduces the scattering observables as well as the dynamically generated resonances. 6

18 The Λ(1405) resonance (PDG) mass : ± 4.0 MeV, width : 50 ± 2 MeV decay mode: 100% 7

19 The Λ(1405) resonance (PDG) mass : ± 4.0 MeV, width : 50 ± 2 MeV decay mode: 100% naive quark model : p-wave ~1600 MeV? N. Isgur, G. Karl, PRD18, 4187 (1978) M B Coupled channel multi-scattering R.H. Dalitz, T.C. Wong, G. Rajasekaran, PR153, 1617 (1967) 7

20 The Λ(1405) resonance (PDG) mass : ± 4.0 MeV, width : 50 ± 2 MeV decay mode: 100% naive quark model : p-wave ~1600 MeV? N. Isgur, G. Karl, PRD18, 4187 (1978) M B Coupled channel multi-scattering R.H. Dalitz, T.C. Wong, G. Rajasekaran, PR153, 1617 (1967) KN interaction below threshold T. Hyodo, W. Weise, PRC 77, (2008) KN? KN scatt. --> KN potential, kaonic nuclei A. Dote, T. Hyodo, W. Weise, NPA804, 197 (2008); PRC 79, (2009) πσ Λ(1405) energy 7

21 A simple model (1 parameter) v.s. experimental data Total cross section of K-p scattering Branching ratio K - p " 0 # " + $ % 150 γ Rc Rn! T [mb] exp theo ! T [mb] Plab [MeV/c] K 0 n Plab [MeV/c] " 0 $ T. Hyodo, S.I. Nam, D. Jido, A. Hosaka, PRC68, (2003); PTP 112, 73 (2004) Plab [MeV/c] " % $ mass distribution πσ spectrum 1360 Λ(1405) s [MeV] Good agreement with data above, at, and below KN threshold more quantitatively --> fine tuning, higher order terms,

22 Pole structure in the complex energy plane Resonance state ~ pole of the scattering amplitude D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 723, 205 (2003) T ij ( s) g i g j s MR + iγ R /2!"#$%& #(' +,+&#-.'"(% #(' #(% #(% #(" #($ #(" #($ &'# &%# &"# )*#$%&#'"(%!"%#!""#!"$# &$#!"#$%&#'"(%!"## T. Hyodo, D. Jido, arxiv:

23 Pole structure in the complex energy plane Resonance state ~ pole of the scattering amplitude D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 723, 205 (2003) T ij ( s) g i g j s MR + iγ R /2!"#$%& Λ*2 Two poles for one resonance (bump structure) +,+&#-.'"(% #(' #(% Λ*1 #(' #(% #(" #($ --> Superposition of two states? --> different πσ spectra? #(" #($ &'# &%# &"# )*#$%&#'"(%!"%#!""#!"$# &$#!"#$%&#'"(%!"## T. Hyodo, D. Jido, arxiv:

Pole structure in the complex energy plane Resonance state ~ pole of the scattering amplitude D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys.

24 Pole structure in the complex energy plane Resonance state ~ pole of the scattering amplitude D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 723, 205 (2003) T ij ( s) g i g j s MR + iγ R /2!"#$%& Λ*2 Two poles for one resonance (bump structure) +,+&#-.'"(% #(' #(% Λ*1 #(' #(% #(" #($ --> Superposition of two states? --> different πσ spectra? #(" #($!"%#!"#$%&#'"(% What is the origin of this structure?!""#!"$#!"## &$# &"# &%# &'# )*#$%&#'"(% T. Hyodo, D. Jido, arxiv:

25 Origin of the two-pole structure Leading order chiral interaction for KN-πΣ channel T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) V ij = C ij ω i + ω j 4f 2 C ij = KN πσ at threshold ω i m i, 3.3m π m K V KN 2.5V πσ 10

26 Origin of the two-pole structure Leading order chiral interaction for KN-πΣ channel T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) V ij = C ij ω i + ω j 4f 2 C ij = KN πσ at threshold ω i m i, 3.3m π m K V KN 2.5V πσ 10

27 Origin of the two-pole structure Leading order chiral interaction for KN-πΣ channel T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) V ij = C ij ω i + ω j 4f 2 C ij = KN πσ 3 at threshold ω i m i, V KN 2.5V πσ m π m K Without off-diagonal Im z [MeV] πσ resonance Re z [MeV] KN bound state KN

28 Origin of the two-pole structure Leading order chiral interaction for KN-πΣ channel T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) V ij = C ij ω i + ω j 4f 2 C ij = KN πσ 3 at threshold ω i m i, V KN 2.5V πσ m π m K Without off-diagonal Im z [MeV] πσ resonance Re z [MeV] KN bound state KN

29 KN Origin of the two-pole structure Leading order chiral interaction for KN-πΣ channel T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) V ij = C ij ω i + ω j 4f 2 C ij = πσ 3 at threshold ω i m i, V KN 2.5V πσ m π m K Without off-diagonal Im z [MeV] πσ resonance Re z [MeV] KN bound state z 2 (full) z 1 (full) KN

30 KN Origin of the two-pole structure Leading order chiral interaction for KN-πΣ channel T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) V ij = C ij ω i + ω j 4f 2 C ij = πσ 3 at threshold ω i m i, V KN 2.5V πσ m π m K Without off-diagonal Im z [MeV] W.Weise πσ resonance Re z [MeV] KN bound state z 2 (full) z 1 (full) KN 1440 Very strong attraction in KN (higher energy) --> bound state Strong attraction in πσ (lower energy) --> resonance Model dependence? Effects from higher order terms? 10

31 Toward realistic meson-baryon interaction Experimental constraints for S=-1 MB scattering K-p total cross sections (bubble chamber, large errors) KN threshold observables - threshold branching ratios (old but accurate) - K-p scattering length KN πσ? KN scatt. energy 11

32 Toward realistic meson-baryon interaction Experimental constraints for S=-1 MB scattering K-p total cross sections (bubble chamber, large errors) KN threshold observables - threshold branching ratios (old but accurate) - K-p scattering length KN πσ πσ mass spectra? KN scatt. energy 11

33 Toward realistic meson-baryon interaction Experimental constraints for S=-1 MB scattering K-p total cross sections (bubble chamber, large errors) KN threshold observables - threshold branching ratios (old but accurate) - K-p scattering length KN πσ? KN scatt. energy πσ mass spectra - new data is becoming available (LEPS, CLAS, HADES,...) - normalization, reaction dependence,... <-- to be predicted? 11

34 Toward realistic meson-baryon interaction Experimental constraints for S=-1 MB scattering K-p total cross sections (bubble chamber, large errors) KN threshold observables - threshold branching ratios (old but accurate) - K-p scattering length KN πσ? KN scatt. energy πσ mass spectra - new data is becoming available (LEPS, CLAS, HADES,...) - normalization, reaction dependence,... <-- to be predicted? πσ threshold observables (so far no data) 11

35 Toward realistic meson-baryon interaction Experimental constraints for S=-1 MB scattering K-p total cross sections (bubble chamber, large errors) KN threshold observables - threshold branching ratios (old but accurate) - K-p scattering length <-- SIDDHARTA exp. KN πσ? KN scatt. energy πσ mass spectra - new data is becoming available (LEPS, CLAS, HADES,...) - normalization, reaction dependence,... <-- to be predicted? πσ threshold observables (so far no data) 11

36 Toward realistic meson-baryon interaction Constraints from KN data - K-p total cross sections K p (K p, K 0 n, π 0 Λ, π 0 Σ 0, π + Σ, π Σ + ) 12

37 Toward realistic meson-baryon interaction - Threshold branching ratios R n = Γ(K p π 0 Λ) Γ(K p neutral states) Constraints from KN data - K-p total cross sections K p (K p, K 0 n, π 0 Λ, π 0 Σ 0, π + Σ, π Σ + ) γ = Γ(K p π + Σ ) Γ(K p π Σ + ) R c = =2.36 ± 0.04 Γ(K p π + Σ, π Σ + ) Γ(K p all inelastic channels) =0.664 ± =0.189 ± R.J. Nowak, et al., Nucl. Phys. B139, 61 (1978); D.N. Tovee, et al., ibid, B33, 493 (1971) 12

38 Toward realistic meson-baryon interaction - Threshold branching ratios R c = R n = Γ(K p π 0 Λ) Γ(K p neutral states) Constraints from KN data - K-p total cross sections K p (K p, K 0 n, π 0 Λ, π 0 Σ 0, π + Σ, π Σ + ) γ = Γ(K p π + Σ ) Γ(K p π Σ + ) =2.36 ± 0.04 Γ(K p π + Σ, π Σ + ) Γ(K p all inelastic channels) =0.664 ± =0.189 ± R.J. Nowak, et al., Nucl. Phys. B139, 61 (1978); D.N. Tovee, et al., ibid, B33, 493 (1971) - Shift and width of 1s level of kaonic hydrogen (SIDDHARTA) E = 283 ± 36 ± 6 ev, Bazzi, et al., arxiv: [nucl-ex] Γ = 541 ± 89 ± 22 ev E i 2 Γ = 2α3 µ 2 ca K p[1 2αµ c (ln α 1)a K p] U.-G. Meissner, U. Raha, A. Rusetsky, Eur. Phys. J. C35, 349 (2004) Width [ev] KEK-PS Shift E [ev] SIDDHARTA DEAR <-- scattering length 12

39 Toward realistic meson-baryon interaction Construction of the realistic amplitude Systematic χ2 fitting with SIDDHARTA data Y. Ikeda, T. Hyodo, W. Weise, in preparation Interaction kernel: NLO ChPT B. Borasoy, R. Nissler, W. Weise, Eur. Phys. J. A25, (2005); B. Borasoy, U.G. Meissner, R. Nissler, Phys. Rev. C74, (2006) 13

40 Toward realistic meson-baryon interaction Construction of the realistic amplitude Systematic χ2 fitting with SIDDHARTA data Y. Ikeda, T. Hyodo, W. Weise, in preparation Interaction kernel: NLO ChPT B. Borasoy, R. Nissler, W. Weise, Eur. Phys. J. A25, (2005); B. Borasoy, U.G. Meissner, R. Nissler, Phys. Rev. C74, (2006) 1) WT term O(p) 2) Born terms O(p) 3) NLO terms O(p 2 ) 13

41 Toward realistic meson-baryon interaction Construction of the realistic amplitude Systematic χ2 fitting with SIDDHARTA data Y. Ikeda, T. Hyodo, W. Weise, in preparation Interaction kernel: NLO ChPT B. Borasoy, R. Nissler, W. Weise, Eur. Phys. J. A25, (2005); B. Borasoy, U.G. Meissner, R. Nissler, Phys. Rev. C74, (2006) 1) WT term 2) Born terms O(p) WT model O(p) 3) NLO terms O(p 2 ) 13

42 Toward realistic meson-baryon interaction Construction of the realistic amplitude Systematic χ2 fitting with SIDDHARTA data Y. Ikeda, T. Hyodo, W. Weise, in preparation Interaction kernel: NLO ChPT B. Borasoy, R. Nissler, W. Weise, Eur. Phys. J. A25, (2005); B. Borasoy, U.G. Meissner, R. Nissler, Phys. Rev. C74, (2006) 1) WT term 2) Born terms 3) NLO terms O(p) WT model O(p) WTB model O(p 2 ) 13

43 Toward realistic meson-baryon interaction Construction of the realistic amplitude Systematic χ2 fitting with SIDDHARTA data Y. Ikeda, T. Hyodo, W. Weise, in preparation Interaction kernel: NLO ChPT B. Borasoy, R. Nissler, W. Weise, Eur. Phys. J. A25, (2005); B. Borasoy, U.G. Meissner, R. Nissler, Phys. Rev. C74, (2006) 1) WT term 2) Born terms 3) NLO terms O(p) WT model O(p) WTB model O(p 2 ) NLO model 13

44 Toward realistic meson-baryon interaction Construction of the realistic amplitude Systematic χ2 fitting with SIDDHARTA data Y. Ikeda, T. Hyodo, W. Weise, in preparation Interaction kernel: NLO ChPT B. Borasoy, R. Nissler, W. Weise, Eur. Phys. J. A25, (2005); B. Borasoy, U.G. Meissner, R. Nissler, Phys. Rev. C74, (2006) 1) WT term 2) Born terms 3) NLO terms O(p) WT model O(p) WTB model O(p 2 ) NLO model Parameters: 6 cutoffs (+ 7 low energy constants in NLO) 13

45 Toward realistic meson-baryon interaction Result by NLO model!(mb)!(mb) Observables Theory Experiment E (ev) ± 42 Γ (ev) ± 111 γ ± 0.04 R c ± R n ± a K p (fm) i0.87 Poles of the Λ(1405) (MeV) i26.3, i K - p -> K - p Plab(MeV) NLO1 NLO3!(mb) K - p -> bark 0 n$ Plab(MeV) NLO1 NLO3 PRELIMINARY K - p -> " 0 # Plab(MeV) NLO1 NLO3!(mb) K - p -> " 0 # Plab(MeV) NLO1 NLO3!(mb) arbitrary unit NLO1 NLO3 Good description of data ( χ2/dof ~ 1 ) K - p -> " + # - Plab(MeV) NLO1 NLO3 Mass spectrum I=0!" E c.m. (MeV)!(mb) K - p -> " - # Plab(MeV) NLO1 NLO3 14

46 Toward realistic meson-baryon interaction Summary of results Results from three models WT WTB NLO Width [ev] χ2/dof Shift and width Pole positions PRELIMINARY KEK-PS SIDDHARTA DEAR im Z [MeV] Shift E [ev] Error analysis is now underway Y. Ikeda, T. Hyodo, W. Weise, in preparation re Z [MeV] 15

47 Toward realistic meson-baryon interaction πσ threshold behavior Effect of the πσ threshold data for KN-πΣ amplitude Y. Ikeda, T. Hyodo, D. Jido, H. Kamano, T. Sato, K. Yazaki, arxiv: [nucl-th], to appear in Prog. Theor. Phys. Extrapolations with a given KN(I=0) scattering length --> uncertainty in subthreshold Model A1 A2 B E-dep B E-indep parameter (πσ) d πσ = 1.67 d πσ = 2.85 Λ πσ =1005MeV Λ πσ =1465MeV parameter ( KN) d KN = 1.79 d KN = 2.05 Λ KN =1188MeV Λ KN =1086MeV pole 1 [MeV] i i i i pole 2 [MeV] i (R) 1321 (B) i (R) 1325 (V) a πσ [fm] r e [fm] a KN [fm] (input) i i i i 16

48 Toward realistic meson-baryon interaction πσ threshold behavior Effect of the πσ threshold data for KN-πΣ amplitude Y. Ikeda, T. Hyodo, D. Jido, H. Kamano, T. Sato, K. Yazaki, arxiv: [nucl-th], to appear in Prog. Theor. Phys. Extrapolations with a given KN(I=0) scattering length --> uncertainty in subthreshold Model A1 A2 B E-dep B E-indep parameter (πσ) d πσ = 1.67 d πσ = 2.85 Λ πσ =1005MeV Λ πσ =1465MeV parameter ( KN) d KN = 1.79 d KN = 2.05 Λ KN =1188MeV Λ KN =1086MeV pole 1 [MeV] i i i i pole 2 [MeV] i (R) 1321 (B) i (R) 1325 (V) a πσ [fm] r e [fm] a KN [fm] (input) i i i i subthreshold behavior f [fm] KN f [fm] <-- πσ scattering length, effective range W [MeV] W [MeV]

49 Toward realistic meson-baryon interaction Determination of the πσ scattering length π π scattering length from K --> π π π decay N. Cabibbo, Phys. Rev. Lett. 93, (2004); NA48/2, J.R. Batley, et al., Phys. Lett. B686, 101 (2010) 17

50 Toward realistic meson-baryon interaction Determination of the πσ scattering length π π scattering length from K --> π π π decay N. Cabibbo, Phys. Rev. Lett. 93, (2004); NA48/2, J.R. Batley, et al., Phys. Lett. B686, 101 (2010) Analogy: πσ scattering lengths from Λc --> π π Σ decays T. Hyodo, M. Oka, arxiv: [nucl-th] isospin violation + threshold cusp + amplitude interference d!/dw [arbitrary unit] a -+ mode a = fm (Virtual state) a = fm (Bound state) a = 0.00 fm W [MeV] Expansion of the spectrum around cusp --> scattering length 17

51 Summary Summary 1 We study the KN-πΣ interaction and Λ(1405) based on chiral SU(3) symmetry and unitarity Chiral symmetry constrains the NG boson dynamics with hadrons. Unitarity should be taken into account for a strongly interacting system. Two poles for Λ(1405) <-- attractive KN and πσ interactions T. Hyodo, D. Jido, arxiv: , submitted to Prog. Part. Nucl. Phys. 18

52 Summary Summary 2 Recent developments to construct a realistic meson-baryon interaction New KN threshold data by SIDDAHRTA - systematic χ2 analysis with NLO terms Y. Ikeda, T. Hyodo, W. Weise, in preparation Threshold information of πσ channel - importance of πσ threshold behavior Y. Ikeda, T. Hyodo, D. Jido, H. Kamano, T. Sato, K. Yazaki, arxiv: [nucl-th], to appear in Prog. Theor. Phys. - scattering length from Λc decay T. Hyodo, M. Oka, arxiv: [nucl-th] 19

Chiral dynamics and baryon resonances

Chiral dynamics and baryon resonances Tetsuo Hyodo a Tokyo Institute of Technology a supported by Global Center of Excellence Program Nanoscience and Quantum Physics 2009, June 5th 1 Contents Contents