Electromagnetic Form Factors of Electromagnetic Form Factors of - PowerPoint PPT Presentation

Electromagnetic Form Factors of Electromagnetic Form Factors of Electromagnetic Form Factors of Electromagnetic Form Factors of Λ(1405) in Chiral Dynamics Λ(1405) in Chiral Dynamics in Chiral Dynamics in Chiral Dynamics arXiv:0803.4068 [nucl nucl- -th th] ] arXiv:0803.4068 [ （ Kyoto Univ. ） Takayasu Sekihara （ Kyoto Univ. ） Takayasu Sekihara Kyoto Univ. Takayasu Sekihara Takayasu Sekihara Kyoto Univ. in Collaboration with in Collaboration with in Collaboration with in Collaboration with （ YITP and Tech. Univ. ） and Daisuke Jido （ YITP ） Tetsuo Hyodo Tetsuo Hyodo （ YITP and Tech. Univ. YITP and Tech. Univ. M Mü ünchen nchen nchen ） and Daisuke Jido and Daisuke Jido （ YITP YITP ） Tetsuo Hyodo Tetsuo Hyodo YITP and Tech. Univ. nchen and Daisuke Jido YITP Λ(1405) and Introduction: Λ(1405) 1. Introduction: 1. Introduction: and and Chiral Chiral Unitary Model ( Chiral Unitary Model ( Unitary Model (ChUM ChUM ChUM) ) ) 1. 1. Introduction: and Chiral Unitary Model ( ChUM ) 2. Electromagn 2. Electromagnetic In etic Interaction in teraction in Ch Ch ChUM UM 2. Electromagnetic In 2. Electromagn etic Interaction in teraction in ChUM UM 3. Electromagnetic Form Factors and Mean Square 3. Electromagnetic Form Factors and Mean Squared Radii d Radii d Radii 3. Electromagnetic Form Factors and Mean Square 3. Electromagnetic Form Factors and Mean Square d Radii 4. Conclusions 4. Conclusions 4. Conclusions 4. Conclusions 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ 代々木オリンピックセンター '08 @ (Aug. 19 - (Aug. 19 - 24, 2008 24, 2008 ） 24, 2008 '08 @ (Aug. 19 24, 2008

1. Introduction 1. Introduction 1. Introduction 1. Introduction Λ (1405) Excited baryon Λ ++ Excited baryon (1405) ++ ++ ++ ・ Λ Λ (1405) ± 4 MeV, width = 50 ± 2 ・ = 1406 ± 4 MeV, width = 50 ± (1405) --- --- mass mass = 1406 2 MeV MeV (PDG), (PDG), P = 1/2 = 1/2 － － . the lightest excited baryon with J P . the lightest excited baryon with J ー > ー > quasi bound state of quasi bound state of KN KN ??? ??? ？ ？ ーー ー > < ー > < Λ (1405) It is difficult to observe Λ ー It is difficult to observe < ー directly, < (1405) directly, Λ (1405) because Λ stands below the KN KN threshold threshold. . because (1405) stands below the Λ (1405) for Λ Therefore, theoretical studies theoretical studies are important are important for . Therefore, (1405) . 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ '08 @ 代々木オリンピックセンター (Aug. 19 - (Aug. 19 - 24, 2008 24, 2008 24, 2008 ） 2 '08 @ (Aug. 19 24, 2008 2

1. Introduction 1. Introduction 1. Introduction 1. Introduction ++ Λ Λ (1405) (1405) and and kaonic kaonic nuclei ++ nuclei ++ ++ Λ (1405) It is considered that Λ ・ It is considered that ・ (1405) plays an important role for plays an important role for the kaonic kaonic nuclei nuclei (cf. (cf. KNN KNN state state). ). the ー > ー > The structure of the The structure of the KN KN system system, , Λ (1405), which strongly couples to Λ which strongly couples to (1405), might be essential to essential to might be the properties of kaonic kaonic nuclei nuclei. . the properties of ・ Also in this point of view, ・ Also in this point of view, Λ (1405) the structure of Λ we want to know the structure of we want to know (1405) as dynamically generated KN KN quasi bound state quasi bound state. . as dynamically generated 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ 代々木オリンピックセンター '08 @ (Aug. 19 (Aug. 19 - - 24, 2008 24, 2008 24, 2008 ） 3 '08 @ (Aug. 19 24, 2008 3

1. Introduction 1. Introduction 1. Introduction 1. Introduction ++ Dynamics based on chiral chiral symmetry symmetry ++ ++ ++ Dynamics based on ・ Low energy ・ Low energy KN KN interaction interaction in coupled channel approach in coupled channel approach: : --- Tree Tree- -level interaction level interaction based on based on chiral chiral symmetry symmetry. . --- --- Satisfying Satisfying elastic elastic unitarity unitarity ( ( N/D N/D method). method). --- ー > ー > chiral chiral unitary model unitary model. . Kaiser, Siegel, Weise Weise, , Nucl. Phys Nucl. Phys . . A594 A594 (1995) 325, Oset, Ramos, (1995) 325, Oset, Ramos, Nucl. Phys. Nucl. Phys. A635 A635 (1998) 99, (1998) 99, Kaiser, Siegel, (1999) 074023, Oller, Mei β β ner, Oller, Oset, Phys. Rev. Phys. Rev. D60 D60 (1999) 074023, Oller, Mei ner, Phys. Lett. Phys. Lett. B500 B500 (2001) 263. (2001) 263. Oller, Oset, 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ 代々木オリンピックセンター '08 @ (Aug. 19 - (Aug. 19 - 24, 2008 24, 2008 24, 2008 ） 4 '08 @ (Aug. 19 24, 2008 4

1. Introduction 1. Introduction 1. Introduction 1. Introduction ++ Dynamics based on chiral chiral symmetry symmetry ++ ++ ++ Dynamics based on ・ Scatt ・ Scatt. Amp. . Amp. T T ij is written as following argeblaic argeblaic form: form: ij is written as following --- Weinberg Weinberg- -Tomozawa Tomozawa term term (from (from chiral chiral symmetry) symmetry) --- --- Loop integral --- Loop integral, which contains , which contains parameter parameter of of chiral chiral unitary model, unitary model, . . 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ '08 @ 代々木オリンピックセンター (Aug. 19 (Aug. 19 - - 24, 2008 24, 2008 24, 2008 ） 5 '08 @ (Aug. 19 24, 2008 5

1. Introduction 1. Introduction 1. Introduction 1. Introduction Λ (1405) ++ Chiral unitary model and Λ ++ ++ Chiral unitary model and (1405) ++ ・ The model reproduce ・ The model reproduce total cross sections of total cross sections of K - - p p ー ー > several channels > several channels. . K Kaiser, Siegel, Weise Weise, , Nucl. Phys Nucl. Phys . . A594 A594 (1995) 325, (1995) 325, Oset Oset, Ramos, , Ramos, Nucl. Phys. Nucl. Phys. A635 A635 (1998) 99. (1998) 99. Kaiser, Siegel, 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ 代々木オリンピックセンター '08 @ (Aug. 19 - (Aug. 19 - 24, 2008 24, 2008 ） 24, 2008 6 '08 @ (Aug. 19 24, 2008 6

1. Introduction 1. Introduction 1. Introduction 1. Introduction Λ (1405) ++ Chiral unitary model and Λ ++ ++ Chiral unitary model and (1405) ++ mass distribution of Λ Λ (1405) ・ The model reproduce ・ The model reproduce mass distribution of . (1405) . Kaiser, Siegel, Kaiser, Siegel, Weise Weise, , Nucl. Phys Nucl. Phys . . A594 A594 (1995) 325, (1995) 325, Oset Oset, Ramos, , Ramos, Nucl. Phys. Nucl. Phys. A635 A635 (1998) 99. (1998) 99. 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ 代々木オリンピックセンター '08 @ (Aug. 19 - (Aug. 19 - 24, 2008 24, 2008 ） 24, 2008 7 '08 @ (Aug. 19 24, 2008 7

1. Introduction 1. Introduction 1. Introduction 1. Introduction Λ (1405) ++ Chiral unitary model and Λ ++ ++ Chiral unitary model and (1405) ++ ・ The model ・ The model dynamically generates poles dynamically generates poles, which , which correspond to excited baryons, in , in Scatt Scatt. Amp. . Amp. correspond to excited baryons Mei β β ner Oller, , Mei ner, , Phys. Phys. Lett Lett. . B500 B500 (2001) 263, (2001) 263, Oller Oset, Ramos and Oset , Ramos and Bennhold Bennhold, , Phys. Phys. Lett Lett. . B527 B527 (2002) 99, (2002) 99, β ner Mei β Jido, , Oller Oller, , Oset Oset, Ramos, , Ramos, Mei ner, , Nucl. Phys. Nucl. Phys. A725 A725 (2003) 181. (2003) 181. Jido 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ 代々木オリンピックセンター '08 @ (Aug. 19 - (Aug. 19 - 24, 2008 24, 2008 ） 24, 2008 8 '08 @ (Aug. 19 24, 2008 8

2. Electromagnetic Interactions in ChUM 2. Electromagnetic Interactions in ChUM ChUM 2. Electromagnetic Interactions in 2. Electromagnetic Interactions in ChUM Λ (1405) ++ EM interactions of Λ (1405) ++ ++ ++ EM interactions of electromagnetic interactions of Λ Λ (1405) ・ We want to know ・ We want to know electromagnetic interactions of . (1405) . ー Photo < ー Photo- -couplings to couplings to Scatt Scatt. Amp. . Amp. T T ij : . < ij : . ー > ー > --- Photo Photo- -couplings to couplings to meson meson, , baryon baryon and and WT term WT term. . --- ・ Following ・ Following three diagrams three diagrams contribute to the form factors. contribute to the form factors. 夏の学校 '08 @ 代々木オリンピックセンター (Aug. 19 ） 夏の学校 '08 @ 代々木オリンピックセンター '08 @ (Aug. 19 - (Aug. 19 - 24, 2008 24, 2008 ） 24, 2008 9 '08 @ (Aug. 19 24, 2008 9