.... D 1 in collaboration with 1, 2, 1 RCNP 1, KEK 2
. Exotic hadron qqq q q Θ + Λ(1405) etc. uudd s? KN quasi-bound state?
. D(B)-N bound state { { D D0 ( cu) B = D ( cd), B = + ( bu) B 0 ( bd) D(B)-N bound state Qq + qqq Previous work DN Yasui,Sudoh 1 π DN,BN 1 S.Yasui and K.Sudoh, Phys Rev. D 80, 034008 (2009)
. Heavy meson and Heavy quark symmetry Heavy quark symmetry 2 (HQS) Isuger Wise 2 m Q Heavy quark spin symmetry Spin-spin interaction 0 { Heavy pseudoscalar meson D(0 ) Heavy vector meson D (1 ) P P { md m D 140 MeV m B m B 45 MeV P N mixing 2 N.Isuger and M.B.Wise, Phys. Rev. Lett. 66,1130(1990)
. P N mixing and π exchange interaction P l = 0 N m K m K 400 MeV P π l = 2 π l = 0 N { md m D 140 MeV m B m B 45 MeV Couple P N channel with P N system P N P N mixing π
...... HQS π, ρ, ω S
. Interactions Heavy quark effective theory 3 L πhh = ig π Tr [ H b γ µ γ 5 A µ ba H a ] L vhh = iβtr [ H b v µ (ρ µ ) ba Ha ] + iλtr [ Hb σ µν F µν (ρ) ba Ha ] H a = 1+ v 2 [ P a µ γ µ P a γ 5], Ha = γ 0 H a γ 0 vector pseudoscalar A ν = i ν ˆπ, ρ µ = ig v ˆρ µ, F µν (ρ) = µ ρ ν ν ρ µ f π 2 Bonn model 4 L πnn = ig πnn Nb γ 5 N ( aˆπ ba L vnn = g vnn Nb γ µ (ˆρ µ ) ba + κ ) σ µν ν (ˆρ µ ) ba N a 2m N H π, ρ, ω H N N 3 R.Casalbuoni,et al. Phys Rept.,281 (1997) 145 4 R.Machleidt,et al. Phys Rept.,149 (1987) 1
. P N and P N system We investigate J P = 1/2 and 3/2 state. Various coupled channels for J P = 1/2, 3/2 state. { P N (1) J P = 1/2 state 2 S 1/2 P N 2 S 1/2, 4 3-channels D 1/2 { P N (2) J P = 3/2 state 2 D 3/2 P N 4 S 3/2, 4 D 3/2, 2 4-channels D 3/2
. P N and P N system We investigate J P = 1/2 and 3/2 state. Various coupled channels for J P = 1/2, 3/2 state. { P N (1) J P = 1/2 state 2 S 1/2 P N 2 S 1/2, 4 3-channels D 1/2 bound state (I = 0) { P N (2) J P = 3/2 state 2 D 3/2 P N 4 S 3/2, 4 D 3/2, 2 4-channels D 3/2 no bound state
. P N and P N system We investigate J P = 1/2 and 3/2 state. Various coupled channels for J P = 1/2, 3/2 state. { P N (1) J P = 1/2 state 2 S 1/2 P N 2 S 1/2, 4 3-channels D 1/2 bound state (I = 0) { P N (2) J P = 3/2 state 2 D 3/2 P N 4 S 3/2, 4 D 3/2, 2 4-channels D 3/2 resonance?
. P N and P N system We investigate J P = 1/2 and 3/2 state. Various coupled channels for J P = 1/2, 3/2 state. { P N (1) J P = 1/2 state 2 S 1/2 P N 2 S 1/2, 4 3-channels D 1/2 bound state (I = 0) { P N (2) J P = 3/2 state 2 D 3/2 P N 4 S 3/2, 4 D 3/2, 2 4-channels D 3/2 resonance? Solve coupled channel equation!
Result for J P = 1/2 state
. The bound state with (I, J P ) = (0, 1/2 ) The bound states exist in (I, J P ) = (0, 1/2 ) state. Table: Binding energy and root mean square radii in (I, J P ) = (0, 1/2 ) state. DN(π) DN(πρ ω) BN(π) BN(πρ ω) E B [MeV] 1.60 2.13 19.50 23.04 r 2 1/2 [fm] 3.5 3.2 1.3 1.2 π π, ρ, ω π D N mixing B N mixing
Result for J P = 3/2 state
. The scattering state with (I, J P ) = (0, 3/2 ) J P = 3/2 Phase shift
. The scattering state with (I, J P ) = (0, 3/2 ) J P = 3/2 Phase shift Phase shift for DN( 2 D 3/2 ) Phase shift for BN( 2 D 3/2 ) 4 4 δ [rad] 3 2 DN( 2 D 3/2 ) δ [rad] 3 2 BN( 2 D 3/2 ) 1 1 0 0 50 100 150 200 250 300 E [MeV] 0 0 10 20 30 40 50 E [MeV]
. The scattering state with (I, J P ) = (0, 3/2 ) J P = 3/2 Phase shift Phase shift for DN( 2 D 3/2 ) Phase shift for BN( 2 D 3/2 ) 4 4 δ [rad] 3 2 π/2 DN( 2 D 3/2 ) δ [rad] 3 2 BN( 2 D 3/2 ) 1 1 0 0 50 100 150 200 250 300 E [MeV] 0 0 10 20 30 40 50 E [MeV] Phase shifts cross π/2 Resonant state
. The scattering state with (I, J P ) = (0, 3/2 )! Phase shift for DN( 2 D 3/2 ) Phase shift for BN( 2 D 3/2 ) 4 4 δ [rad] 3 2 1 DN( 2 D 3/2 ) E re = 113.19 MeV Γ = 17.72 MeV δ [rad] 3 2 1 BN( 2 D 3/2 ) E re = 6.93 MeV Γ = 0.095 MeV 0 0 50 100 150 200 250 300 E [MeV] 0 0 10 20 30 40 50 E [MeV] Phase shifts cross π/2 Resonant state
. The resonance in (I, J P ) = (0, 3/2 ) channel P N P N { P N J P = 3/2 state 2 D 3/2 Ignored P N 4 S 3/2, 4 D 3/2, 2 3-channels D 3/2
. The resonance in (I, J P ) = (0, 3/2 ) channel P N P N { P N J P = 3/2 state 2 D 3/2 Ignored P N 4 S 3/2, 4 D 3/2, 2 3-channels D 3/2 P N Table: Bounding energy for P N system Binding energy [MeV] D N 11.50 B N 21.67 Feshbach
. The resonance in (I, J P ) = (0, 3/2 ) channel E D N bound state D N Feshbach resonance 140 MeV DN( 2 D 3/2 )
. The resonance in (I, J P ) = (0, 3/2 ) channel E D N D N quasi-bound state (Resonance) ////////////////////////////// E re = 113.5 MeV Γ = 17.7 MeV 140 MeV Feshbach resonance DN( 2 D 3/2 )
. The resonance in (I, J P ) = (0, 3/2 ) channel E D N D N quasi-bound state (Resonance) ////////////////////////////// E re = 113.5 MeV Γ = 17.7 MeV 140 MeV DN( 2 D 3/2 ) Feshbach resonance D N mixing < B N mixing 45 MeV B N B N quasi-bound state (Resonance) ////////////////////////////// E re = 6.9 MeV Γ = 0.09 MeV BN( 2 D 3/2 )
. Summary Heavy quark symmetry DN BN (I, J P ) = (0, 3/2 ) Feshbach P N π
. F Λ vertex F α (Λ, q ) = Λ2 m 2 α Λ 2 + q 2 vertex Λ N Bonn potential Deuteron vertex Λ P Λ D = 1.35Λ N Λ B = 1.29Λ N Table: Cutoff parameter. Potential Λ N [MeV] Λ D [MeV] Λ B [MeV] π 830 1121 1070 π, ρ, ω 846 1142 1091