RESONANCE STATES BETWEEN CHARMED BARYON AND NUCLEON Saori Maeda - PowerPoint PPT Presentation

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 • Introduction 𝑑 𝑂 Interaction & Binding energy • 𝑍 • Resonance states • Summary MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

3 INTRODUCTION  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 • Interesting properties of charm nuclei ・ Heavy quark symmetry ・ Channel coupling including higher state than strange sector. MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

4 INTRODUCTION Strange Charm Σ ∗ 1385 ∗ 2518 Σ 𝑑 (s,u,u)(s,u,d) (c,u,u)(c,u,d) 12 12 12 12 (s,d,d) (c,d,d) 64 [𝑁𝑓𝑊]  We have obtained many experimental data related to Σ 𝑑 2454 hypernuclei and hyperon-nucleon(YN) interactions. 6 (c,u,u)(c,u,d) 196 (c,d,d) [𝑁𝑓𝑊] Approaching to charm nuclei structure the next stage 168 with theoretical knowledge Σ 1189 [𝑁𝑓𝑊] 6 (s,u,u)(s,u,d) 73 [𝑁𝑓𝑊] (s,d,d) Λ 1116 Λ 𝑑 2286 2 2 (s,u,d) (c,u,d) • Interesting properties of charm nuclei ・ Heavy quark symmetry ・ Channel coupling including higher state than strange sector. MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

5 𝑑 𝑂 INTERACTION 𝑍 ∗ ) 𝑑 𝑂 potential ( 𝑍 • 𝑍 𝑑 = Λ 𝑑 , Σ 𝑑 , Σ 𝑑 In this study, we construct a hybrid potential using a hadron model and a quark model ・ One Boson Exchange potential [Y.R.Liu, M.Oka, Phys. Rev. D 85, 014015 (2012)] ・ Quark Cluster Model [M.Oka, Nuclear Physics A 881 (2012) 6 – 13] 𝑊 𝑑 𝑂) = 𝑊 𝑃𝐶𝐹𝑄 + 𝑊 (𝑍 𝑅𝐷𝑁 • Channel coupling MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

6 𝑑 𝑂 INTERACTION 𝑍 • One Boson Exchange potential We assume that the pion and 𝑑 (𝑞 ′ ) 𝑍 the sigma meson exchange between the charm baryon and the nucleon. 𝐺 𝑟 At the vertices, we introduce the form factor 𝐺 𝑟 as follows Λ 2 −𝑛 2 𝑍 𝑑 ( Ԧ 𝑞) 𝐺 𝑟 = Λ 2 −𝑟 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

7 𝑑 𝑂 INTERACTION 𝑍 • One Boson Exchange potential We assume that the pion and 𝑑 (𝑞 ′ ) 𝑍 the sigma meson exchange between the charm baryon and the nucleon. 𝐺 𝑟 At the vertices, we introduce the form factor 𝐺 𝑟 as follows Λ 2 −𝑛 2 𝑍 𝑑 ( Ԧ 𝑞) 𝐺 𝑟 = Λ 2 −𝑟 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

8 𝑑 𝑂 INTERACTION 𝑍 • 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 𝑓 −𝑠 2 r 𝑊 𝑅𝐷𝑁 = 𝑊 𝑐 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

9 𝑑 𝑂 INTERACTION 𝑍 • 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 𝑊 𝑠 = 0 ≈< 6𝑟 𝐼 6𝑟 > −2 < 3𝑟 𝐼 3𝑟 > quarks occupy the lowest energy orbit with a single center. b Potential equation 0 𝑓 −𝑠 2 r 𝑊 𝑅𝐷𝑁 = 𝑊 𝑐 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

10 𝑑 𝑂 INTERACTION 𝑍 • Parameter fix we determine the parameters of the potential so as to reproduce the NN interaction data using the same model. YcN-CTNN ・ Fixed parameter Pi-baryon coupling constants, Range parameter of QCM ・ Determined parameter Cutoff parameter ( Λ 𝜌 , Λ 𝜏 ), sigma-baryon coupling constants MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

11 𝑑 𝑂 INTERACTION 𝑍 • Parameter fix 𝒁 𝒅 𝑶 -Corresponding To NN we determine the parameters of the potential so as to reproduce the NN interaction data using the same model. YcN-CTNN ・ Fixed parameter Pi-baryon coupling constants, Range parameter of QCM ・ Determined parameter [Prog. Theor. Exp. Phys. (2016) 023D02] Cutoff parameter ( Λ 𝜌 , Λ 𝜏 ), sigma-baryon coupling constants MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

12 𝑑 𝑂 INTERACTION 𝑍 • Result of binding energy and scattering length MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

13 𝑑 𝑂 INTERACTION 𝑍 • Resonance In the previous calculation, Charm we consider only the state ∗ 𝑂 3457 Σ 𝑑 under the Λ 𝑑 𝑂 threshold. (c,u,u)(c,u,d) 12 12 64 [𝑁𝑓𝑊] (c,d,d) Σ 𝑑 𝑂 3393 6 (c,u,u)(c,u,d) So, we calculate with the (c,d,d) Complex scaling method 168 [𝑁𝑓𝑊] [J. Aguilar, J.M. Combes, Commun. Math. Phys. 22 (1971) 269.] to search the state above the Λ 𝑑 𝑂 3225 2 Λ 𝑑 𝑂 threshold with 𝑍 𝑑 𝑂 -CTNN (c,u,d) d-potential. MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

14 𝑑 𝑂 INTERACTION 𝑍 • Resonance ・ 𝐾 𝑄 = 2 + Λ 𝑑 𝑂 and Σ 𝑑 𝑂 channel have no S-wave because of the rule of total angular momentum. The S-wave and G-wave are the characteristic 3 ∗ having the spin = behavior of Σ 𝑑 2 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

15 𝑑 𝑂 INTERACTION 𝑍 • Resonance ・ Result MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

16 𝑑 𝑂 INTERACTION 𝑍 𝐾 𝑄 = 1 + 𝐾 𝑄 = 2 + 𝐾 𝑄 = 0 + • Resonance ・ Result ∗ 𝑂 Σ 𝑑 Σ 𝑑 𝑂 Λ 𝑑 𝑂 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

17 𝑑 𝑂 INTERACTION 𝑍 • Resonance ・ Result with partial channel coupling Σ 𝑑 𝑂 threshold: 167.10 MeV ∗ 𝑂 threshold: 231.51 MeV Σ 𝑑 𝑲 𝑸 = 𝟏 + (𝚻 𝒅 𝑶) 𝑲 𝑸 = 𝟐 + (𝚻 𝒅 𝑶) 𝑲 𝑸 = 𝟐 + (𝚻 𝒅 𝑲 𝑸 = 𝟑 + (𝚻 𝒅 ∗ 𝑶) ∗ 𝑶) 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 𝑑 𝑂 INTERACTION 𝑍 • Resonance ・ Heavy quark limit ∗ 𝑂 are doublet, so we set the We assume Σ 𝑑 𝑂 and Σ 𝑑 ∗ 𝑂 threshold. 𝑍 𝑑 𝑂 threshold in substitute for Σ 𝑑 𝑂 and Σ 𝑑 ∗ 𝑂 3457 Σ 𝑑 (c,u,u)(c,u,d) (c,d,d) 𝑍 𝑑 𝑂 3414 Σ 𝑑 𝑂 3393 (c,u,u)(c,u,d) (c,u,u)(c,u,d) (c,d,d) (c,d,d) Λ 𝑑 𝑂 3225 Λ 𝑑 𝑂 3225 (c,u,d) (c,u,d) MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

19 𝑑 𝑂 INTERACTION 𝑍 • Resonance ・ Result MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

20 𝑑 𝑂 INTERACTION 𝑍 𝐾 𝑄 = 1 + 𝐾 𝑄 = 2 + 𝐾 𝑄 = 0 + • Resonance ・ Result 𝑍 𝑑 𝑂 Λ 𝑑 𝑂 MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016

21 SUMMARY • We propose the 𝑍 𝑑 𝑂 potential model based on the hadron model and the quark model, and find four parameter set to reproduce experimental data of NN system. • Calculating the 𝑍 𝑑 𝑂 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