What we know about the Λ(1405)

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1 What we know about the Λ(1405) Tetsuo Hyodo Yukawa Institute for Theoretical Physics, Kyoto Univ. 2015, Sep. 15th 1

2 Contents Contents Current status of Λ(1405) and K N interaction - Recent experimental achievements - Systematic analysis in chiral dynamics Y. Ikeda, T. Hyodo, W. Weise, PLB 706, 63 (2011); NPA (2012) - Λ(1405) in πσ spectrum S. Ohnishi, Y. Ikeda, T. Hyodo, E. Hiyama, W. Weise, J. Phys. Conf. Ser. 569, (2014) + in preprataion; K. Miyahara, T. Hyodo, E. Oset, arxiv: [nucl-th] Structure of Λ(1405) - K N molecule? K. Miyahara, T. Hyodo, arxiv: [nucl-th]; Y. Kamiya, T. Hyodo, arxiv: [hep-ph] 2

3 Introduction K meson and K N interaction Two aspects of K(K ) meson - NG boson of chiral SU(3)R SU(3)L > SU(3)V - massive by strange quark: mk ~ 496 MeV > spontaneous/explicit symmetry breaking 3

4 Introduction Two aspects of K(K ) meson K meson and K N interaction - NG boson of chiral SU(3)R SU(3)L > SU(3)V - massive by strange quark: mk ~ 496 MeV > spontaneous/explicit symmetry breaking K N interaction... T. Hyodo, D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012) K N energy 3

5 Introduction K meson and K N interaction Two aspects of K(K ) meson - NG boson of chiral SU(3)R SU(3)L > SU(3)V - massive by strange quark: mk ~ 496 MeV > spontaneous/explicit symmetry breaking K N interaction... T. Hyodo, D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012) - is coupled with πσ channel energy K N πσ 3

6 Introduction K meson and K N interaction Two aspects of K(K ) meson - NG boson of chiral SU(3)R SU(3)L > SU(3)V - massive by strange quark: mk ~ 496 MeV > spontaneous/explicit symmetry breaking K N interaction... T. Hyodo, D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012) - is coupled with πσ channel - generates Λ(1405) below threshold energy K N Λ(1405) πσ M B molecule three-quark 3

7 Introduction K meson and K N interaction Two aspects of K(K ) meson - NG boson of chiral SU(3)R SU(3)L > SU(3)V - massive by strange quark: mk ~ 496 MeV > spontaneous/explicit symmetry breaking K N interaction... T. Hyodo, D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012) - is coupled with πσ channel - generates Λ(1405) below threshold energy K N Λ(1405) πσ M B molecule three-quark - is fundamental building block for K -nuclei, K in medium,... 3

8 Recent experimental achievements SIDDHARTA measurement Precise measurement of the kaonic hydrogen X-rays M. Bazzi, et al., Phys. Lett. B704, 113 (2011); Nucl. Phys. A881, 88 (2012) EM int. p Talk by Marton 6D4 K- binding energy EM value 4

9 Recent experimental achievements SIDDHARTA measurement Precise measurement of the kaonic hydrogen X-rays M. Bazzi, et al., Phys. Lett. B704, 113 (2011); Nucl. Phys. A881, 88 (2012) EM int. p Talk by Marton 6D4 K- strong int. binding energy exp. EM value E 4

10 Recent experimental achievements SIDDHARTA measurement Precise measurement of the kaonic hydrogen X-rays M. Bazzi, et al., Phys. Lett. B704, 113 (2011); Nucl. Phys. A881, 88 (2012) EM int. p Talk by Marton 6D4 K- strong int. binding energy exp. EM value E - shift and width of atomic state < > K-p scattering length U.-G. Meissner, U. Raha, A. Rusetsky, Eur. Phys. J. C35, 349 (2004) Direct constraint on the K N interaction at fixed energy 4

11 Recent experimental achievements πσ invarint mass spectra πσ spectrum before 2008: single mode, no absolute values R.J. Hemingway, Nucl. Phys. B253, 742 (1985) R.J. Hemingway / Production of A(1405) I I I 240 o % 120 oj I: Srei -Wig, ti~.~ K- Matrix Fit "O 40 7t 'l e- o, I./,0 I./,5 Mass( +~ -) GeV mass distribution of the ~: + ~r- system from the reaction K-p ~ + 5

12 Recent experimental achievements πσ invarint mass spectra πσ spectrum before 2008: single mode, no absolute values R.J. Hemingway, Nucl. Phys. B253, 742 (1985) After 2008: γp -> K + (πσ) 0 LEPS, CLAS, pp -> K + p(πσ) 0 HADES M. Niiyama, et al., Phys. Rev. C78, (2008); ) 2 counts / (0.01 GeV/c K. Moriya, et al., Phys. Rev. C87, (2013); G. Agakishiev, et al., Phys. Rev. C87, (2013) (a) Σ + π - o % 120 oj "O + MM (K ) (GeV/c e- o, LEPS 2 ) 40 R.J. Hemingway / Production of A(1405) ) 2 dσ/dm (µb/gev) counts / (0.01 GeV/c (b) I I I Σ - π + 0 7t MM (K ) (GeV/c ) 'l 0 I: Srei -Wig, ti~.~ K- Matrix Fit I./,0 I./, Mass( +~ -) GeV CLAS HADES mass distribution of the ~: + ~r- Σπ system Invariant from Mass (GeV/c 2 the reaction ) K-p ~ + Σ Cross sections in different charge modes are available. + π - Σ - π + dσ/dm [µb/(mev/c 2 )] dσ/dm [µb/(mev/c 2 )] (a) Σ + π - data Λ(1405) Σ(1385) Λ(1520) Σ π non. res. total fit (b) Σ - π + 5

13 Systematic analysis in chiral dynamics Strategy for K N interaction Above the K N threshold: direct constraints - K-p total cross sections (old data) - K N threshold branching ratios (old data) - K-p scattering length (new data: SIDDHARTA) Below the K N threshold: indirect constraints - πσ mass spectra (new data: LEPS, CLAS, HADES, ) K N Λ(1405) πσ energy 6

14 Systematic analysis in chiral dynamics Strategy for K N interaction Above the K N threshold: direct constraints - K-p total cross sections (old data) - K N threshold branching ratios (old data) - K-p scattering length (new data: SIDDHARTA) Below the K N threshold: indirect constraints - πσ mass spectra (new data: LEPS, CLAS, HADES, ) K N Λ(1405) πσ energy 6

15 Systematic analysis in chiral dynamics Construction of the realistic amplitude Chiral coupled-channel approach with systematic χ 2 fitting Y. Ikeda, T. Hyodo, W. Weise, Phys. Lett. B706, 63 (2011); Nucl. Phys. A (2012) = + T V V T 7

16 Systematic analysis in chiral dynamics Construction of the realistic amplitude Chiral coupled-channel approach with systematic χ 2 fitting Y. Ikeda, T. Hyodo, W. Weise, Phys. Lett. B706, 63 (2011); Nucl. Phys. A (2012) = + T V V T Chiral perturbation theory 1) TW term 2) Born terms 3) NLO terms O(p) 6 cutoffs O(p) O(p 2 ) 7 LECs 7

17 Systematic analysis in chiral dynamics Construction of the realistic amplitude Chiral coupled-channel approach with systematic χ 2 fitting Y. Ikeda, T. Hyodo, W. Weise, Phys. Lett. B706, 63 (2011); Nucl. Phys. A (2012) = + T V V T Chiral perturbation theory 1) TW term 2) Born terms 3) NLO terms O(p) 6 cutoffs O(p) O(p 2 ) 7 LECs TW model 7

18 Systematic analysis in chiral dynamics Construction of the realistic amplitude Chiral coupled-channel approach with systematic χ 2 fitting Y. Ikeda, T. Hyodo, W. Weise, Phys. Lett. B706, 63 (2011); Nucl. Phys. A (2012) = + T V V T Chiral perturbation theory 1) TW term 2) Born terms 3) NLO terms O(p) 6 cutoffs O(p) O(p 2 ) 7 LECs TW model TWB model 7

19 Systematic analysis in chiral dynamics Construction of the realistic amplitude Chiral coupled-channel approach with systematic χ 2 fitting Y. Ikeda, T. Hyodo, W. Weise, Phys. Lett. B706, 63 (2011); Nucl. Phys. A (2012) = + T V V T Chiral perturbation theory 1) TW term 2) Born terms 3) NLO terms O(p) 6 cutoffs O(p) O(p 2 ) 7 LECs TW model TWB model NLO model 7

20 Systematic analysis in chiral dynamics Best-fit results SIDDHARTA Branching ratios ( ( TW TWB NLO Experiment E [ev] ± 36 ± 6 [10] [ev] ± 89 ± 22 [10] ± 0.04 [11] R n ± [11] R c ± [11] 2 /d.o.f cross sections ) [mb] (K p K p) [mb] + (K p TW TWB NLO (K p K 0 n) [mb] P lab [MeV/c] P lab [MeV/c] P lab TW TWB NLO [MeV/c] 0 0 ) [mb] (K p P lab TW TWB NLO TW TWB NLO [MeV/c] 0 0 (K p ) [mb] + (K p ) [mb] P lab P lab TW TWB NLO [MeV/c] TW TWB NLO [MeV/c] SIDDHARTA is consistent with cross sections (c.f. DEAR). 8

21 Systematic analysis in chiral dynamics Comparison with SIDDHARTA 800 TW TWB NLO χ 2 /d.o.f SIDDHARTA Width Γ [ev] KEK-PS DEAR Shift E [ev] TW and TWB are reasonable, while best-fit requires NLO. 9

22 Systematic analysis in chiral dynamics Subthreshold extrapolation Behavior of K-p > K-p amplitude below threshold SIDDHARTA - c.f. K N > K N (I=0) without SIDDHARTA R. Nissler, Doctoral Thesis (2007) Subthreshold extrapolation is better controlled KN KN

23 Systematic analysis in chiral dynamics Extrapolation to complex energy: two poles Two poles: superposition of two states J. A. Oller, U. G. Meissner, Phys. Lett. B500, 263 (2001); D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 723, 205 (2003); T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) - Higher energy pole at 1420 MeV, not at 1405 MeV - Attractions of WT in 1 and 8 (K N and πσ) channels!"#$%& #(' +,+&#-.'"(% #(' #(% #(% #(" #($ #(" #($!"%#!""#!"#$%&#'"(%!"$#!"## &'# &%# &"# )*#$%&#'"(% &$# 11

24 Systematic analysis in chiral dynamics Extrapolation to complex energy: two poles Two poles: superposition of two states J. A. Oller, U. G. Meissner, Phys. Lett. B500, 263 (2001); D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 723, 205 (2003); T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) - Higher energy pole at 1420 MeV, not at 1405 MeV - Attractions of WT in 1 and 8 (K N and πσ) channels +,+&#-.'"(% #(' #(%!"#$%& #(' #(% #(" #($ Im z [MeV] TW TWB NLO #(" -100 #($ &'# -120 &%# &"# )*#$%&#'"(%!"%# -140!""#!"$# &$# !"#$%&#'"(%!"## Re z [MeV] NLO analysis confirms the two-pole structure

25 Systematic analysis in chiral dynamics Remaining ambiguity K N interaction has two isospin components (I=0, I=1). a(k p) = 1 2 a(i = 0) + 1 a(i = 1) +..., a(k n) = a(i = 1)

26 Systematic analysis in chiral dynamics Remaining ambiguity K N interaction has two isospin components (I=0, I=1). a(k p) = 1 2 a(i = 0) + 1 a(i = 1) +..., a(k n) = a(i = 1) a(k n) = i0.76 fm (TW), a(k n) = i0.74 fm (TWB), a(k n) = i0.73 fm (NLO). 12

27 Systematic analysis in chiral dynamics Remaining ambiguity K N interaction has two isospin components (I=0, I=1). a(k p) = 1 2 a(i = 0) + 1 a(i = 1) +..., a(k n) = a(i = 1) a(k n) = i0.76 fm (TW), a(k n) = i0.74 fm (TWB), a(k n) = i0.73 fm (NLO). Some deviation: constraint on I=1 (< kaonic deuterium?) 12

28 Systematic analysis in chiral dynamics Analyses by other groups Further studies with NLO + χ 2 analysis + SIDDHARTA data - Bonn group M. Mai, U.-G. Meissner, Nucl. Phys. A900, 51 (2013) - Murcia group Z.H. Guo, J.A. Oller, Phys. Rev. C87, (2013) I GUO AND J. A. OLLER PHYSICAL REVIEW C 87, (2013) σ(k p K p) (mb) K p K p Fit I Fit I S p Lab K σ(k p K 0 n) (mb) (MeV) (a) plab K K p K 0 n (MeV) (b) (K p π + Σ ) (mb) K p π Σ + ) (mb) K p π + Σ 60 K p π Σ

29 Systematic analysis in chiral dynamics Analyses by other groups Further studies with NLO + χ 2 analysis + SIDDHARTA data - Bonn group M. Mai, U.-G. Meissner, Nucl. Phys. A900, 51 (2013) M. Mai, U.-G. Meißner / Nuclear Physics A 900 (2013) Murcia group Z.H. Guo, J.A. Oller, Phys. Rev. C87, (2013) I GUO AND J. A. OLLER PHYSICAL REVIEW C 87, (2013) σ(k p K p) (mb) (K p π + Σ ) (mb) K p K p Fit I Fit I S σ(k p K 0 n) (mb) K p π Σ + ) (mb) K p K 0 n Fig. 5. Contour plot of the absolute value of the scattering amplitude for isospin I = 0inthecomplexW Riemann sheets R Σπ and R KN are glued together along the KN threshold line. The pole positio models are presented in the plot via squares [13], circles[6,7] and crosses [5]. T ij g ig j s s R, where g i and g j are coupling constants of the in- and out-going states, respectiv pole (isospin I = 0) we extract the coupling constants to the KN and πσ channel 20 W 1 : g 80 KN =3.02 and g πσ =1.61, 10 W 2 : g KN 40 =1.89 and g πσ = At the position of the first pole (the one located at the smaller imaginary value coupling to the KN channel is nearly twice as large as to the πσ channel. For th p Lab K (MeV) (a) plab K (MeV) (b) this pattern is reversed. Qualitatively both observations agree quite nicely with the 100 Refs. [4,14]. 200 Having presented the main results of our approach, we wish to comment on diff ~13 parameters 120 K p π + Σ > several local 60 K p minima π Σ results compared with the outcome of the recent analysis by Ikeda et al. [6,7].Them + difference is the different behavior of the K p scattering amplitude in the subthr region which is of course caused by the different pole positions compared to Ik exotic 40 solution by Bonn 20 group (second have investigatedpole the origin of these above observations qualitatively. K N)? First, from the an scattering in the same framework, see Ref. [9], itisknownthatoff-shelleffect 13

30 Systematic analysis in chiral dynamics Constraints from the πσ spectrum Combined analysis of scattering data + πσ spectrum M. Mai, U.-G. Meissner, Eur. Phys. J. A 51, 30 (2015) - a simple model for the photoproduction γp -> K + (πσ) 0 - CLAS data of the πσ spectrum M W B T M inv = X10 i=1 C i ( W )G i (M inv )f i, 0+ (M inv) 14

Systematic analysis in chiral dynamics Constraints from the πσ spectrum Combined analysis of scattering data + πσ spectrum M. Mai, U.-G. Meissner, Eur. Phys. J.

31 Systematic analysis in chiral dynamics Constraints from the πσ spectrum Combined analysis of scattering data + πσ spectrum M. Mai, U.-G. Meissner, Eur. Phys. J. A 51, 30 (2015) - a simple model for the photoproduction γp -> K + (πσ) 0 - CLAS data of the πσ spectrum M W B T M inv = X10 i=1 C i ( W )G i (M inv )f i, 0+ (M inv) > The exotic solution is excluded. 14

32 Systematic analysis in chiral dynamics Pole positions of Λ(1405) Mini-review prepared for PDG Pole structure of the Λ(1405) Ulf-G. Meißner, Tetsuo Hyodo February 4, 2015 The Λ(1405) resonance emerges in the meson-baryon scattering amplitude with the strangeness S = 1 andisospini = 0. It is the archetype of [11,12] Ikeda-Hyodo-Weise, [14] Guo-Oller, [15] Mai-Meissner approach pole 1 [MeV] pole 2 [MeV] Ref. [11, 12] NLO i i Ref. [14] Fit I i i Ref. [14] Fit II i i Ref. [15] solution # i i Ref. [15] solution # i i converge around 1420 still some deviations c.f. comprehensive analysis of the CLAS data (at LO) L. Roca, E. Oset, Phys. Rev. C 87, (2013); C 88, (2013) 15

33 Λ(1405) in πσ spectrum πσ spectra and K N interaction Can πσ spectra constrain the MB amplitude? - Yes, but not directly. 16

34 Λ(1405) in πσ spectrum πσ spectra and K N interaction Can πσ spectra constrain the MB amplitude? - Yes, but not directly. Λ(1405) in production (general): Emitted particle(s) Initial state M B T MB amplitude ( πσ spectrum 16

35 Λ(1405) in πσ spectrum πσ spectra and K N interaction Can πσ spectra constrain the MB amplitude? - Yes, but not directly. Λ(1405) in production (general): Emitted particle(s) Initial state M reaction model B T MB amplitude ( πσ spectrum - πσ spectra depend on the reaction (ratio of K N/πΣ in the intermediate state, interference with I=1, ). > Detailed model analysis for each reaction 16

36 Λ(1405) in πσ spectrum J-PARC E31 experiment: K-d -> n(πσ) = 1 GeV - two-step approaches K-d reaction D. Jido, E. Oset, T. Sekihara, Eur. Phys. J. A42, 257 (2009); A47, 42 (2011); K. Miyagawa, J. Haidenbauer, Phys. Rev. C85, (2012); J. Yamagata-Sekihara, T. Sekihara, D. Jido, PTEP 043D02 (2013) K d p T n K d N T N K T n 17

37 Λ(1405) in πσ spectrum K-d reaction J-PARC E31 experiment: K-d -> n(πσ) = 1 GeV - two-step approaches D. Jido, E. Oset, T. Sekihara, Eur. Phys. J. A42, 257 (2009); A47, 42 (2011); K. Miyagawa, J. Haidenbauer, Phys. Rev. C85, (2012); J. Yamagata-Sekihara, T. Sekihara, D. Jido, PTEP 043D02 (2013) K d p T n K d N Full Faddeev(AGS) calculation with relativistic kinematics K d N T N T + infinitely many diagrams T S. Ohnishi, Y. Ikeda, T. Hyodo, E. Hiyama, W. Weise, J. Phys. Conf. Ser. 569, (2014) + in preprataion n T N K T d 2 σ/dm πσ dcosθ(µb/mev) n (a) θ=0 π + Σ - π - Σ + π 0 Σ 0 E-dep M πσ (MeV) 17

38 Λ(1405) in πσ spectrum Λc decay Weak decay of Λc > π + MB (MB=πΣ, K N) K. Miyahara, T. Hyodo, E. Oset, arxiv: [nucl-th] - final state interaction of MB generates Λ(1405) 18

39 Λ(1405) in πσ spectrum Λc decay Weak decay of Λc > π + MB (MB=πΣ, K N) K. Miyahara, T. Hyodo, E. Oset, arxiv: [nucl-th] - final state interaction of MB generates Λ(1405) - dominant process (CKM, Nc counting, diquark correlation) filters the MB pair in I=0. I=0 18

Λ(1405) in πσ spectrum Λc decay Weak decay of Λc > π + MB (MB=πΣ, K N) K. Miyahara, T. Hyodo, E. Oset, arxiv:1508.

40 Λ(1405) in πσ spectrum Λc decay Weak decay of Λc > π + MB (MB=πΣ, K N) K. Miyahara, T. Hyodo, E. Oset, arxiv: [nucl-th] - final state interaction of MB generates Λ(1405) - dominant process (CKM, Nc counting, diquark correlation) filters the MB pair in I=0. I=0 Clean Λ(1405) signal can be found in the charged πσ modes. 18

41 K N molecule? K N molecule Structure of Λ(1405): three-quark or meson-baryon? - constituent quark model: too light? N. Isgur, G. Karl, Phys. Rev. D 18, 4187 (1978) - vector meson exchange: well reproduce R.H. Dalitz, T.C. Wong, G. Rajasekaran Phys. Rev. 153, 1617 (1967) K N 19

42 K N molecule? K N molecule Structure of Λ(1405): three-quark or meson-baryon? - constituent quark model: too light? N. Isgur, G. Karl, Phys. Rev. D 18, 4187 (1978) - vector meson exchange: well reproduce R.H. Dalitz, T.C. Wong, G. Rajasekaran Phys. Rev. 153, 1617 (1967) Recent lattice QCD study J. Hall, et al., Phys. Rev. Lett. 114, (2015) K N K N M N light sector strange sector strange magnetic FF overlaps in Hamiltonian model m 2 GeV c 2 19

43 K N molecule? K N potential Local K N potential > wave function T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) - Equivalent amplitude on the real axis - Single-channel, complex, energy-dependent 20

44 K N molecule? K N potential Local K N potential > wave function T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) - Equivalent amplitude on the real axis - Single-channel, complex, energy-dependent Realistic K N potential for NLO with SIDDHARTA (χ 2 /dof ~ 1) K. Miyahara, T. Hyodo, arxiv: [nucl-th] density potential 20

45 K N molecule? K N potential Local K N potential > wave function T. Hyodo, W. Weise, Phys. Rev. C 77, (2008) - Equivalent amplitude on the real axis - Single-channel, complex, energy-dependent Realistic K N potential for NLO with SIDDHARTA (χ 2 /dof ~ 1) K. Miyahara, T. Hyodo, arxiv: [nucl-th] - Substantial distribution at r > 1 fm density - root mean squared radius p hr2 i =1.44 fm potential The size of Λ(1405) is much larger than ordinary hadrons. 20

46 K N molecule? Compositeness Model-independent relation of compositeness X < (B, a0) S. Weinberg, Phys. Rev. 137, B672 (1965); V. Baru, et al., Phys. Lett. B 586, 53 (2004) 21

47 K N molecule? Compositeness Model-independent relation of compositeness X < (B, a0) S. Weinberg, Phys. Rev. 137, B672 (1965); V. Baru, et al., Phys. Lett. B 586, 53 (2004) - Generalization to quasi-bound states Talk by Kamiya 2B2 Y. Kamiya, T. Hyodo, arxiv: [hep-ph] ( s 2X a 0 = R 1+X + O Rtyp µ R + 03 ) µ 3 O l 3 R, R =1/ p 2µE QB 21

48 K N molecule? Compositeness Model-independent relation of compositeness X < (B, a0) S. Weinberg, Phys. Rev. 137, B672 (1965); V. Baru, et al., Phys. Lett. B 586, 53 (2004) - Generalization to quasi-bound states Talk by Kamiya 2B2 Y. Kamiya, T. Hyodo, arxiv: [hep-ph] ( s 2X a 0 = R 1+X + O Rtyp µ R + 03 ) µ 3 O l 3 R, R =1/ p 2µE QB - NLO Analyses of Λ(1405) with SIDDHARTA (χ 2 /d.o.f. ~ 1) Ref. E QB (MeV) a 0 (fm) X KN X KN U r e /a 0 [43] 10 i i i [44] 4 i i i [45] 13 i i i [46] 2 i i i [46] 3 i i i [43] Ikeda-Hyodo-Weise, [44,46] Mai-Meissner, [45] Guo-Oller Λ(1405) is a K N molecule. < observable quantities 21

49 Summary Summary: Λ(1405) The Λ(1405) in K N scattering is well understood by NLO chiral coupled-channel approach with accurate K-p scattering length. Reliable reaction model will be important to analyze precise πσ mass spectra. Various analyses (lattice, realistic potential, compositeness relation) consistently indicate!"#$%& that the Λ(1405) is a K N molecule. #(' K N +,+&#-.'"(% #(' #(% #(" #($!"%#!""#!"#$%&#'"(%!"$#!"## #(% #(" #($ &'# &%# &"# )*#$%&#'"(% &$# 22

Meson-baryon interactions and baryon resonances

Meson-baryon interactions and baryon resonances Tetsuo Hyodo Tokyo Institute of Technology supported by Global Center of Excellence Program Nanoscience and Quantum Physics 2011, June 16th 1 Contents Contents