THE INTERACTION AND 1 RESONANCE STATES BETWEEN CHARMED BARYON AND NUCLEON Saori Maeda Makoto Oka Tokyo Institute of technology MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
2 CONTENTS β’ Introduction π π Interaction & Binding energy β’ π β’ Resonance states β’ Summary MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
3 INTRODUCTION ο We have obtained many experimental data related to hypernuclei and hyperon-nucleon(YN) interactions. Approaching to charm nuclei structure the next stage with theoretical knowledge β’ Interesting properties of charm nuclei γ» Heavy quark symmetry γ» Channel coupling including higher state than strange sector. MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
4 INTRODUCTION Strange Charm Ξ£ β 1385 β 2518 Ξ£ π (s,u,u)(s,u,d) (c,u,u)(c,u,d) 12 12 12 12 (s,d,d) (c,d,d) 64 [πππ] ο We have obtained many experimental data related to Ξ£ π 2454 hypernuclei and hyperon-nucleon(YN) interactions. 6 (c,u,u)(c,u,d) 196 (c,d,d) [πππ] Approaching to charm nuclei structure the next stage 168 with theoretical knowledge Ξ£ 1189 [πππ] 6 (s,u,u)(s,u,d) 73 [πππ] (s,d,d) Ξ 1116 Ξ π 2286 2 2 (s,u,d) (c,u,d) β’ Interesting properties of charm nuclei γ» Heavy quark symmetry γ» Channel coupling including higher state than strange sector. MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
5 π π INTERACTION π β ) π π potential ( π β’ π π = Ξ π , Ξ£ π , Ξ£ π In this study, we construct a hybrid potential using a hadron model and a quark model γ» One Boson Exchange potential [Y.R.Liu, M.Oka, Phys. Rev. D 85, 014015 (2012)] γ» Quark Cluster Model [M.Oka, Nuclear Physics A 881 (2012) 6 β 13] π π π) = π ππΆπΉπ + π (π π π·π β’ Channel coupling MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
6 π π INTERACTION π β’ One Boson Exchange potential We assume that the pion and π (π β² ) π the sigma meson exchange between the charm baryon and the nucleon. πΊ π At the vertices, we introduce the form factor πΊ π as follows Ξ 2 βπ 2 π π ( Τ¦ π) πΊ π = Ξ 2 βπ 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
7 π π INTERACTION π β’ One Boson Exchange potential We assume that the pion and π (π β² ) π the sigma meson exchange between the charm baryon and the nucleon. πΊ π At the vertices, we introduce the form factor πΊ π as follows Ξ 2 βπ 2 π π ( Τ¦ π) πΊ π = Ξ 2 βπ 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
8 π π INTERACTION π β’ Quark Cluster Model (QCM) The QCM considers two baryon clusters each made of three quarks . When two baryons overlap completely, r=0, all the six quarks occupy the lowest energy orbit with a single center. b Potential equation 0 π βπ 2 r π π π·π = π π 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
9 π π INTERACTION π β’ Quark Cluster Model (QCM) The QCM considers two baryon clusters each made of three quarks . When two baryons overlap completely, r=0, all the six π π = 0 β< 6π πΌ 6π > β2 < 3π πΌ 3π > quarks occupy the lowest energy orbit with a single center. b Potential equation 0 π βπ 2 r π π π·π = π π 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
10 π π INTERACTION π β’ Parameter fix we determine the parameters of the potential so as to reproduce the NN interaction data using the same model. YcN-CTNN γ» Fixed parameter Pi-baryon coupling constants, Range parameter of QCM γ» Determined parameter Cutoff parameter ( Ξ π , Ξ π ), sigma-baryon coupling constants MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
11 π π INTERACTION π β’ Parameter fix π π πΆ -Corresponding To NN we determine the parameters of the potential so as to reproduce the NN interaction data using the same model. YcN-CTNN γ» Fixed parameter Pi-baryon coupling constants, Range parameter of QCM γ» Determined parameter [Prog. Theor. Exp. Phys. (2016) 023D02] Cutoff parameter ( Ξ π , Ξ π ), sigma-baryon coupling constants MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
12 π π INTERACTION π β’ Result of binding energy and scattering length MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
13 π π INTERACTION π β’ Resonance In the previous calculation, Charm we consider only the state β π 3457 Ξ£ π under the Ξ π π threshold. (c,u,u)(c,u,d) 12 12 64 [πππ] (c,d,d) Ξ£ π π 3393 6 (c,u,u)(c,u,d) So, we calculate with the (c,d,d) Complex scaling method 168 [πππ] [J. Aguilar, J.M. Combes, Commun. Math. Phys. 22 (1971) 269.] to search the state above the Ξ π π 3225 2 Ξ π π threshold with π π π -CTNN (c,u,d) d-potential. MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
14 π π INTERACTION π β’ Resonance γ» πΎ π = 2 + Ξ π π and Ξ£ π π channel have no S-wave because of the rule of total angular momentum. The S-wave and G-wave are the characteristic 3 β having the spin = behavior of Ξ£ π 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
15 π π INTERACTION π β’ Resonance γ» Result MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
16 π π INTERACTION π πΎ π = 1 + πΎ π = 2 + πΎ π = 0 + β’ Resonance γ» Result β π Ξ£ π Ξ£ π π Ξ π π MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
17 π π INTERACTION π β’ Resonance γ» Result with partial channel coupling Ξ£ π π threshold: 167.10 MeV β π threshold: 231.51 MeV Ξ£ π π² πΈ = π + (π» π πΆ) π² πΈ = π + (π» π πΆ) π² πΈ = π + (π» π π² πΈ = π + (π» π β πΆ) β πΆ) potential CTNN-d 2.22[MeV] 14.28[MeV] 7.67[MeV] 17.68[MeV] MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
18 π π INTERACTION π β’ Resonance γ» Heavy quark limit β π are doublet, so we set the We assume Ξ£ π π and Ξ£ π β π threshold. π π π threshold in substitute for Ξ£ π π and Ξ£ π β π 3457 Ξ£ π (c,u,u)(c,u,d) (c,d,d) π π π 3414 Ξ£ π π 3393 (c,u,u)(c,u,d) (c,u,u)(c,u,d) (c,d,d) (c,d,d) Ξ π π 3225 Ξ π π 3225 (c,u,d) (c,u,d) MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
19 π π INTERACTION π β’ Resonance γ» Result MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
20 π π INTERACTION π πΎ π = 1 + πΎ π = 2 + πΎ π = 0 + β’ Resonance γ» Result π π π Ξ π π MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
21 SUMMARY β’ We propose the π π π potential model based on the hadron model and the quark model, and find four parameter set to reproduce experimental data of NN system. β’ Calculating the π π π 2-body system, we get not only the shallow bound state but also resonance states for several potential models. MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016
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