反D中間子と核子のエキゾチックな 束縛状態と散乱状態の解析
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1 .... D 1 in collaboration with 1, 2, 1 RCNP 1, KEK 2
2 . Exotic hadron qqq q q Θ + Λ(1405) etc. uudd s? KN quasi-bound state?
3 . 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, (2009)
4 . 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)
5 . 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
6 HQS π, ρ, ω S
7 . 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) R.Machleidt,et al. Phys Rept.,149 (1987) 1
8 . 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
9 . 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
10 . 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?
11 . 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!
12 Result for J P = 1/2 state
13 . 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] r 2 1/2 [fm] π π, ρ, ω π D N mixing B N mixing
14 Result for J P = 3/2 state
15 . The scattering state with (I, J P ) = (0, 3/2 ) J P = 3/2 Phase shift
16 . 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 ) E [MeV] E [MeV]
17 . 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 ) E [MeV] E [MeV] Phase shifts cross π/2 Resonant state
18 . 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] DN( 2 D 3/2 ) E re = MeV Γ = MeV δ [rad] BN( 2 D 3/2 ) E re = 6.93 MeV Γ = MeV E [MeV] E [MeV] Phase shifts cross π/2 Resonant state
19 . 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
20 . 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 B N Feshbach
21 . 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 )
22 . The resonance in (I, J P ) = (0, 3/2 ) channel E D N D N quasi-bound state (Resonance) ////////////////////////////// E re = MeV Γ = 17.7 MeV 140 MeV Feshbach resonance DN( 2 D 3/2 )
23 . The resonance in (I, J P ) = (0, 3/2 ) channel E D N D N quasi-bound state (Resonance) ////////////////////////////// E re = 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 )
24 . Summary Heavy quark symmetry DN BN (I, J P ) = (0, 3/2 ) Feshbach P N π
25 . 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 π, ρ, ω
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医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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