Construction of K N potential and structure of Λ(1405) based on chiral unitary approach

Transcription

1 Construction of K N potential and structure of Λ(1405) based on chiral unitary approach Kenta Miyahara Kyoto Univ. Tetsuo Hyodo YITP NSTAR 2015, May

2 Contents 1. Motivation 2. Previous work (construction of potential) step1 experimental data chiral unitary approach step2 equivalent potential 3.This work (new potential) Improvement of construction procedure (step2) New constraint from SIDDHARTA (step1) 4.Discussion (structure of Λ(1405)) 5.Summary

3 Motivation Λ(1405) quasi bound state of K N. K N interaction is strongly attractive. Y. Akaishi and T. Yamazaki, Phys. Rev. C 65, (2002) T. Hyodo and D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012) molecular state of Λ(1405) Λ* K nuclei ex.) K K N N N ex.) deeply binding? compact state?

4 Motivation Theoretical calculation of K NN (I=1/2,Jp=0-) -100 πσn -50 K NN IKS 0 Re[E] [SGM] : Shevchenko, Gal, Mares, Phys. Rev. C 76, (2007) [YA] : Yamazaki, Akaishi, Phys. Rev. C 76, (2007) -50 YA IS DHW -100 Im[E] SGM [IS] : Ikeda, Sato, Phys. Rev. C 76, (2007) [DHW] : Dote, Hyodo, Weise, Phys. Rev. C 79, (2009) [IKS] : Ikeda, Kamano, Sato, Prog. Theor.Phys. 124, 3 (2010) Conclusive result has not been achieved in theoretical calculations

5 Motivation Theoretical calculation of K NN (I=1/2,Jp=0-) -100 πσn -50 K NN IKS 0 Re[E] [SGM] : Shevchenko, Gal, Mares, Phys. Rev. C 76, (2007) [YA] : Yamazaki, Akaishi, Phys. Rev. C 76, (2007) -50 YA IS DHW -100 Im[E] SGM [IS] : Ikeda, Sato, Phys. Rev. C 76, (2007) [DHW] : Dote, Hyodo, Weise, Phys. Rev. C 79, (2009) [IKS] : Ikeda, Kamano, Sato, Prog. Theor.Phys. e r a s t l u s e r t n e Differ n o i t c a r e t n i N caused by K 124, 3 (2010) Conclusive result has not been achieved in theoretical calculations

6 Motivation K N subthreshold amplitude πσ K N Borasoy et al. Phys. Rev. C 74, (2006) R.Nissler, Ph.D thesis (2007) (I=0) large uncertainty K-p subthreshold amplitude Ikeda, Hyodo, Weise Nucl. Phys. A 881, 98 (2012) (K-p) Bazzi et al. Phys. Lett. B 704, 113 (2011) SIDDHARTA Uncertainty is significantly reduced by SIDDHARTA

7 Motivation Construction of r-dep. local potential Chiral unitary approach experimental data SIDDHARTA high precision K N local potential reliable prediction equivalent potential precision in complex energy plane spatial structure of Λ(1405) few-body calculation

8 Previous work K N potential from Ch-U T. Hyodo and W. Weise, Phys. Rev. C 77, (2008) K N amplitude from chiral unitary approach chiral unitary approach T = + T Jido et al. Nucl. Phys. A 725, 181 (2003) Ch-PT channel coupling K N πσ in S=-1, I=0 sector Attractions in K N and πσ leads to double pole structure

9 equivalent local potential coupled-channel 1-channel interaction K N local potential K N amplitude chiral unitary approach Born approx. on K N threshold K N amplitude ( r-rep.) correction so that

10 equivalent local potential Gaussian : way to decide b Previous work This work Born approx. on K N threshold at resonance energy on K N threshold Consistent with original strategy Determination of b is improved

11 problem amplitude on almost reproduced analytic continuation of with to the complex energy plane pole of Λ(1405) i MeV i MeV iMeV from chiral unitary approach does not reproduce the pole structure of

12 This work Improvement (K N pole) deviation of the amplitude on the real axis change ΔV and fitting range HyodoWeise ΔV fit range [MeV] ΔFreal [%] Pole [MeV] Potential1 (This work) Chiral unitary real complex 1300~ ~1450 Hyodo-Weise (2008) precise region Potential i i i i and K N pole position are improved

13 Improvement (πσ pole) 1331MeV 1450MeV second pole did not appear πσ 1650MeV K N change fit range and polynomial type of Vequiv Potential1 Potential2 polynomial type in E 3rd order 10th order fit range [MeV] Pole [MeV] 1332~ ~ i i i Chiral unitary Potential i i πσ pole appears at correct position

14 Results with SIDDHARTA I=0 precise region b = 0.38 fm fit function : 10th order in fit range : 1332~1657 MeV pole : i MeV i MeV original pole i i I=1 ( with same framework ) Precise potential with SIDDHARTA

15 Discussion Wave function p : ~0.85fm K- : ~0.55fm cf. Λ(1405) N K ~1.44 fm N K ~0.3 fm K N ~1.4 fm

16 Summary We have improved the potential construction procedure by changing ΔV, fit range, and fit function is reproduced precisely in complex E plane We have constructed the new K N equivalent potentials in both I=0 and I=1 channels with SIDDHARTA constraint We have discussed the structure of Λ(1405) K molecular state of Λ(1405) N

17 Future work Examine the influence of the ambiguity of the potential by evaluating from various potentials with different spatial structure. Study the pole stability against the change of FK N in connection with the experimental uncertainty. Calculate K NN system with the new equivalent potential. Construct K N-πΣ coupled-channel equivalent potential to treat πσ-channel explicitly.