Structure and compositeness of hadrons

Transcription

1 Structure and compositeness of hadrons Tetsuo Hyodo Yukawa Institute for Theoretical Physics, Kyoto Univ. 2014, Feb. 27th 1

2 Contents Contents Introduction: structure of Λ(1405) - Comparison of model and data - Not a simple issue! Compositeness of hadrons - Field renormalization constant Z - Negative effective range re T. Hyodo, Phys. Rev. Lett. 111, (2013) T. Hyodo, Int. J. Mod. Phys. A 28, (2013) 2

3 Introduction : structure of Λ(1405) Exotic structure of hadrons Various excitations of baryons conventional exotic M B energy internal excitation qq pair creation multiquark hadronic molecule Physical state: superposition of 3q, 5q, MB,... (1405) i = N 3q uds i + N 5q uds q q i + N KN KN i + How can we identify the structure of hadrons? 3

4 Introduction : structure of Λ(1405) Λ(1405) in quark model Baryon excited states in a constituent quark model N. Isgur, G. Karl, Phys. Rev. D18, 4187 (1978) Experiments Quark model Λ(1405) Prediction does not fit experimental data of Λ(1405) 4

5 Introduction : structure of Λ(1405) Λ(1405) in hadron molecule model Dynamical coupled-channel scattering model R.H. Dalitz, T.C. Wong, G. Rajasekaran, Phys. Rev. 153, 1617 (1967) Molecule model Experiment M B Λ(1405) M.H. Alston et al., Phys. Rev. Lett. 6, (1961) Good description of the spectrum (mass and width) 5

6 Introduction : structure of Λ(1405) qqq v.s. molecule Comparison with experimental data M B Quark model Molecule model The model prediction contradicts/agrees with data. (hidden) assumption: - Model space <--> structure of the predicted state Is this so simple? 6

7 Introduction : structure of Λ(1405) Improvement of models Quark model with more interactions (large Nc expansion) C.L. Schat, J.L. Goity, N.N. Scoccola, Phys. Rev. Lett. 88, (2002); J.L. Goity, C.L. Schat, N.N. Scoccola, Phys. Rev. D 66, (2002) Experiments improved quark model (15 parameters) B M Λ(1405) Simple quark model (Isgur-Karl) 7

8 Introduction : structure of Λ(1405) Chiral unitary model Ambiguity in the molecule model M = B LEC cutoff - Resonance saturation in low energy constants (LEC) G. Ecker, J. Gasser, A. Pich, E. de Rafael, Nucl. Phys. B 321, 311 (1989) - CDD pole contributions L. Castillejo, R.H. Dalitz, F.J. Dyson, Phys. Rev. 101, 453 (1956) G.F. Chew, S.C. Frautschi, Phys. Rev. 124, 264 (1961) T. Hyodo, D. Jido, A. Hosaka, Phys. Rev. C 78, (2008) 8

9 Introduction : structure of Λ(1405) Ambiguities in the model analysis Schematic picture: QCD ~ experiment hyperfine interaction M B LEC cutoff (CDD pole) Quark model Molecule model => model space structure of the predicted state 9

10 Introduction : structure of Λ(1405) Summary of introduction Model space structure of hadron What we need is a model-independent measure for the hadron structure. QCD ~ experiment Z ~ 1 Z ~ 0 M B 10

11 Compositeness of hadrons Compositeness of bound states Compositeness approach for a bound state B> S. Weinberg, Phys. Rev. 137, B672 (1965); T. Hyodo, IJMPA 28, (2013) H = H 0 + V H B i = B B i, h B B i = 1 Decompose H into free part + interaction Complete set for free Hamiltonian : bare B0 > + continuum Z 1 = B 0 ih B 0 + dp p ih p Z 1 = h B B 0 ih B 0 B i + dph B p ih p B i Z : elementary X : composite Energy In QCD, H0 : free hadrons V : hadron interaction Z, X : real and nonnegative --> probabilistic interpretation ) 0 apple Z apple 1, 0 apple X apple 1 11

12 Compositeness of hadrons Weak binding limit In general, Z depends on the choice of the potential V. - Z : model-(scheme-)dependent quantity 1 Z = a = Z h p V B i 2 dp (E p + B) 2 2(1 Z) 2 Z R + O(R typ), r e = V-dependent At the weak binding (R Rtyp), Z is related to observables. S. Weinberg, Phys. Rev. 137, B672 (1965); T. Hyodo, IJMPA 28, (2013) Z 1 Z R + O(R typ), a : scattering length, re : effective range R = (2μB) -1/2 : radius (binding energy) Rtyp : typical length scale of the interaction Criterion for the structure: ( a R typ r e (elementary dominance), a R r e R typ (composite dominance). Z ~ 1 Z ~ 0 (deuteron) 12

13 Compositeness of hadrons Interpretation of negative effective range For Z > 0, effective range is always negative. a = 2(1 Z) 2 Z R + O(R typ), r e = Z 1 Z R + O(R typ), ( a R typ r e (elementary dominance), a R r e R typ (composite dominance). Simple attraction (no barrier, energy-indep.,... ) : re > 0 --> only composite dominance is possible. re < 0 : energy- (momentum-)dependence of the potential D. Phillips, S. Beane, T.D. Cohen, Annals Phys. 264, 255 (1998) E. Braaten, M. Kusunoki, D. Zhang, Annals Phys. 323, 1770 (2008) <-- pole term/feshbach projection of coupled-channel effect Negative re --> Something other than p> : CDD pole 13

14 Compositeness of hadrons Generalization to resonances Compositeness approach of bound states 1 Z = Z h p V B i 2 dp (E p + B) 2 Extension to general resonances in chiral models T. Hyodo, D. Jido, A. Hosaka, Phys. Rev. C85, (2012) F. Aceti, E. Oset, Phys. Rev. D86, (2012) 1 Z = g 2 dg(w )! 1 Z = g 2 dg II (W ) II dw W!MB dw W!zR - Z is in general complex. Interpretation? h R R i! 1, h R R i = 1 Z 1 = h R B 0 ih B 0 R i + dph R p ih p R i complex h R B 0 i = h B 0 R i 6= h B 0 R i E R i R i R i 14

15 Compositeness of hadrons Generalization to resonances Compositeness approach at the weak binding: - Model-independent (no potential, wavefunction,... ) - Related to experimental observables What about near-threshold resonances (~ small binding)? shallow bound state: model-independent structure E bound state: model-dependent Z resonance: modeldependent complex Z 15

16 Compositeness of hadrons Poles of the amplitude Near-threshold phenomena: effective range expansion T. Hyodo, Phys. Rev. Lett. 111, (2013) with opposite sign of scattering length f(p) = 1 a + r2 e 2 p2 ip p ± = i ± 1 r 2re r e r e a 1 1 1/a! +1 bound state p Pole trajectories with a fixed re < 0 1/r e 1/a! 1 virtual state 2/r e resonance Resonance pole position <--> (a, re) 16

17 Compositeness of hadrons Example of resonance: Λc(2595) Pole position of Λc(2595) in πσc scattering - central values in PDG E = 0.67 MeV, a = p+ + p ip + p = 2.59 MeV - deduced threshold parameters of πσc scattering = 10.5 fm, r e = 2i p + + p = 19.5 fm - field renormalization constant: complex Z = i Large negative effective range p ± = p 2µ(E i /2) <-- substantial elementary contribution other than πσc (three-quark, other meson-baryon channel, or... ) Λc(2595) is not likely a πσc molecule 17

18 Summary Summary Composite/elementary nature of resonances Renormalization constant Z measures elementariness of a stable bound state. In general, Z of a resonance is complex. Negative effective range re : CDD pole Near-threshold resonance : pole position is related to re --> elementariness T. Hyodo, Phys. Rev. Lett. 111, (2013) T. Hyodo, Int. J. Mod. Phys. A 28, (2013) 18