Λ(1405) supported by Global Center of Excellence Program Nanoscience and Quantum Physics 2009, Aug. 5th 1
S KN Λ(1405) Λ(1405) CDD Nc 2
L = q(i/ m)q P L = 1 2 (1 γ 5), P R = 1 2 (1 + γ 5), q L P L q, q R P R q L = q L i/ q L + q R i/ q R q L mq R q R mq L m=0 q R exp{i N F a=0 t a θ a R}q R, q L exp{i N F a=0 t a θ a L}q L G = U(N F ) R U(N F ) L = U(1) V U(1) A SU(N F ) R SU(N F ) L 3
QCD QCD u, d, s => G = SU(3) R SU(3) L - - c.f. 0 qq 0 = 0 q L q R + q R q L 0 = v 0 u,d -(250 MeV) 3 SU(3) R SU(3) L SU(3) V 4
- Nambu-Goldstone (NG) m π 140 MeV - M p 1 GeV 3M q, M q 300 MeV v.s. m q 3-7 MeV - NG <-- ChPT SU(3) R SU(3) L SU(3) V QCD <==> 5
s NG (Ad)- (T) s : Weinberg-Tomozawa Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) V ij = C ij 4f 2 (ω i + ω j ) π C ij = α π (gv=1) C α,t ( 8 T α I Mi,Y Mi I Ti,Y Ti I, Y )( 8 T α I Mj,Y Mj I Tj,Y Tj I, Y ) C α,t = 2F T F Ad = C 2 (T ) C 2 (α)+3 SU(3) : 6
-NG - <-- Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) - <-- R.H. Dalitz, T.C. Wong, G. Rajasekaran, Phys. Rev. 153, 1617 (1967) T = 1 V 1 G T = + -> N. Kaiser, P. B. Siegel, W. Weise, Nucl. Phys. A594, 325 (1995); E. Oset, A. Ramos, Nucl. Phys. A635, 99 (1998); J. A. Oller, U. G. Meissner, Phys. Lett. B500, 263 (2001); M.F.M. Lutz, E. E. Kolomeitsev, Nucl. Phys. A700, 193 (2002);... many others - - V V G T 7
S Im [T 1 (s)] = ρ(s) 2 T 1 ( s)= i R i s Wi +ã(s 0 )+ s s 0 2π s + ds 0 ρ(s 0 ) (s 0 s)(s 0 s 0 ) Ri, Wi, a <- = G V -1 T ( s)= 1 V 1 ( s) G( s; a) V T T (1) = V (1), T (2) = V (2), T (3) = V (3) V (1) GV (1),... T 8
KN Λ(1405) 200 150 K - p KN K-p 70 200 60 0 + % # 150 50 γ Rc Rn! T [mb] 100 40 30 100 exp. 2.36 0.664 0.189 50 20 10 50 theo. 1.80 0.624 0.225! T [mb] 0 60 50 40 30 20 10 0 100 200 100 200 Plab [MeV/c] K 0 n 300 300 0 60 50 40 30 20 10 0 100 200 100 200 Plab [MeV/c] 0 0 T. Hyodo, S.I. Nam, D. Jido, A. Hosaka, Phys. Rev. C68, 018201 (2003); T. Hyodo, S.I. Nam, D. Jido, A. Hosaka, Prog. Theor. Phys. 112, 73 (2004) 300 300 0 80 60 40 20 0 100 200 100 200 Plab [MeV/c] % + 30 30 πσ mass distribution πσ 1360 Λ(1405) 1380 1400 s [MeV] 1420 1440 KN 9
KN Λ(1405) KN Λ(1405) (PDG) 1406.5 ± 4.0 MeV 50 ± 2 MeV 100% p ~1600 MeV? N. Isgur, G. Karl, PRD18, 4187 (1978) M B R.H. Dalitz, T.C. Wong, G. Rajasekaran, PR153, 1617 (1967) KN T. Hyodo, W. Weise, PRC 77, 035204 (2008) --> KN K A. Dote, T. Hyodo, W. Weise, NPA804, 197 (2008); PRC 79, 014003 (2009); Talk by KN πσ? Λ(1405) KN 10
KN Λ(1405) T ij ( s) g i g j s MR + iγ R /2! (1405) /2 Λ(1405) T 1.5 1.0 0.5 1440 1420 1400 1380 1360 Re[z] -80-60 -40-20 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, 035204 (2008) Im[z] 1.5 1.0 0.5 11
Λ(1405) CDD (a)... - M B (b) CDD L. Castillejo, R.H. Dalitz, F.J. Dyson, Phys. Rev. 101, 453 (1956)... 3 -> (a) 12
Λ(1405) CDD T = 1 V 1 G V G V CDD G CDD G CDD T. Hyodo, D. Jido, A. Hosaka, Phys. Rev. C78, 025203 (2008) CDD KN Λ(1405) --> πn N(1535) --> CDD '()*)+,-./ #!&# *!4 * 84 )5)8601217 0 )5)!60%#17!%#!$#!"# *!4 & )5)!60%#17 021# 0%## 0%1# 01## 011# 3-)*)+,-./ 0$## 0$1# 13
Λ(1405) Nc QCD Nc Nc Nc J.R. Pelaez, Phys. Rev. Lett. 92, 102001 (2004) qqq Nc M R O(N c ), Γ R O(1) Γ R O(1) Im W [MeV] 0-50 -100-150 -200-250 -100 z 2 (Nc=3) z 1 (Nc=3) 0 100 Re W - M N - m K [MeV] --> Λ(1405) -qqq z 1 (12) z 2 (12) 200 T. Hyodo, D. Jido, L. Roca, Phys. Rev. D77, 056010 (2008); L. Roca, T. Hyodo, D. Jido, Nucl. Phys. A809, 65-87 (2008) 14
Λ(1405) <-- r 2 E =0.33 [fm 2 ] Λ(1405) c.f. -0.12 [fm 2 ] --> - T. Sekihara, T. Hyodo, D. Jido, Phys. Lett. B669, 133-138 (2008); T. Sekihara, T. Hyodo, D. Jido, in preparation 15
QCD S QCD => - e.g. KN Λ(1405) 16
Λ(1405) Λ(1405) CDD => - T. Hyodo, D. Jido, A. Hosaka Nc => qqq T. Hyodo, D. Jido, L. Roca => T. Sekihara, T. Hyodo, D. Jido Λ(1405) B - M 17