j-parc におけるチャーム原子核生成
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J-PARC におけるチャーム原子核生成. 須藤 和敬 ( 二松学舎大学 ) ストレンジネス核物理 2010, KEK December 2, 2010. In collaboration with 安井 繁宏 (KEK). Reference: Phys. Rev. D 80, 034008 (2009). Introduction Exotic DN/BN Nuclei Production Cross Section @J-PARC, GSI Summary. Chiral Symmetry. SU(3) L x SU(3) R. - PowerPoint PPT PresentationTRANSCRIPT
J-PARC におけるチャーム原子核生成J-PARC におけるチャーム原子核生成
須藤 和敬 ( 二松学舎大学 )ストレンジネス核物理 2010, KEK
December 2, 2010
I. Introduction
II. Exotic DN/BN Nuclei
III. Production Cross Section @J-PARC, GSI
IV. Summary
In collaboration with 安井 繁宏 (KEK)
Reference: Phys. Rev. D 80, 034008 (2009).
K. Sudoh (Nishogakusha Univ.) Page-2
Introduction
• Exotic nuclei:– 原子核と strange, charm, bottom などを含むハドロンとの束縛状態– Λ(1405) - KbarN の束縛状態? Hyper nuclei, Kaonic nuclei, …
• Why charm/bottom?– 新しいエネルギースケール( mc, mb )の導入 ≫ ΛQCD
– 新しい対称性( heavy quark symmetry )– QCD に基づいた有効理論( HQET, NRQCD, pNRQCD, … )
charm/bottom を含むメソン( D/B )と核子との相互作用を求め、これらが束縛状態を形成するか否かを調べる。
これまでのストレンジネスの物理とは本質的に異なる可能性がある
Chiral Symmetry
SU(3)L x SU(3)R
Heavy Quark (Spin & Flavor) Symmetry
SU(2)spin x SU(Nh)flavor
u d s c bMass[MeV]ΛQCD
3 5 150 200 1500 4700Mass scale of quarks
K. Sudoh (Nishogakusha Univ.) Page-3
Bottom
Bottom Nuclei
Multi-Favored Nuclear Chart
Charm
Charmed Nuclei
K. Sudoh (Nishogakusha Univ.) Page-4
What are Charm/Bottom Nuclei?
Nucleusproton
neutron
Charm/Bottom
This is our subjectin this talk!
Mesons D, D*, B, B*, …
K. Sudoh (Nishogakusha Univ.) Page-5
DN/BN Potential
Q. What is the interaction between D/B and N ?
N
D/B
??
K. Sudoh (Nishogakusha Univ.) Page-6
Conventional Approach
• これまでの解析は主に SU(N) フレーバー対称性を用いた解析– Hoffmann-Lutz (2005), Mizutani-Ramos (2006), …
– カイラル対称性を尊重したコンタクト相互作用( Weinberg-Tomozawa )
– D, B メソンを π, K メソンと同様に NG ボソンとして取り扱えるか?– カイラルダイナミクスはさほど重要ではない → Heavy quark dynamics
SU(3)NK
K NStrangeness
ND
D N
SU(4)
Charm
NB
B N
SU(5)
Bottom
K. Sudoh (Nishogakusha Univ.) Page-7
Heavy Quark Symmetry
• Charm/Bottom の物理においては Heavy Quark Symmetry が重要– Pseudoscalar と Vector が縮退
D*/B* are new fundamental d.o.f.
Chiral dynamics Heavy quark dynamics
K
K*
400 MeV
500 MeVD
D*
140 MeV
1870 MeVB
B*45 MeV
5280 MeV
K* is almost irrelevant in dynamics.
K. Sudoh (Nishogakusha Univ.) Page-8
DN/BN Interaction
• One pion exchange interaction– KN 相互作用では KK coupling が存在しない。(短距離相互作用の
み)– DN/BN の場合は D*/B* を通じての pion exchange が存在
Weinberg-Tomozawa Heavy Meson Effective Theory
NK
K N
ND(*)
D(*) N
NB(*)
B(*) N
pion exchange is absent.(short range force)
pion exchange is present.(long range force)
K. Sudoh (Nishogakusha Univ.) Page-9
DN/BN Potential
• PN-P*N and P*N-P*N potentials– Based on heavy quark (meson) effective theory
G. Burdman and J.F. Donoghue (1992)M.B. Wise (1992)T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.C. Lin and H.-L. Yu (1997)
withvector pseudoscalar
P=D or B
OPEP S. Yasui and K. S., PRD80, 034008 (2009)P(*)
P(*)
N
N
K. Sudoh (Nishogakusha Univ.) Page-10
DN/BN Potential
• PN-P*N and P*N-P*N potentials– OPEP + short range repulsion (, )
P(*)
P(*)
N
N
→ Approximation by a contact interaction
Bonn A Bonn B
cI=0 [fm2]
cI=1 [fm2]
2.77
7.79
1.62
8.68
cNNI=0 = 17.8 [fm2] for A, 18.1 [fm2] for B
cf. smaller than NN contact interaction
3 31 2 0,1( ) ( )Ic c r c r
K. Sudoh (Nishogakusha Univ.) Page-11
DN/BN Bound States
Q. Are there bound states of D/B and N ?
N
D/B
??
D(cq)-N(qqq)B(bq)-N(qqq)
* No annihilation process
K. Sudoh (Nishogakusha Univ.) Page-12
Classification of State
• Classification of states
Case 1. JP=1/2- (I=0 or 1)
|PN; 2S1/2 > + |P*N; 2S1/2 > + |P*N; 4D1/2 >
NP
s-wave0 1/2
NP*
s-wave1 1/2
NP*
d-wave1 1/2
+ +
This plays an important role.
|state> = |PN>+ |P*N> P=Dbar (cbarq), B (bbarq)
* No annihilation process
S. Yasui and K. S., PRD80, 034008 (2009)
K. Sudoh (Nishogakusha Univ.) Page-13
• JP=1/2-, I=0:
Numerical Results
|PN; 2S1/2 > + |P*N; 2S1/2 > + |P*N; 4D1/2 >
DN +cont.A +cont.B
B.E. [MeV]
radius [fm]
10.8 6.6 8.2
1.7 2.1 1.9
OPEP + contact interaction
wav
e fu
nctio
ns
[fm
-3/2] |PN; 2S1/2 >
|P*N; 2S1/2 >
|P*N; 4D1/2 >
strong mixing by tensor coupling
PRELIMINARY
K. Sudoh (Nishogakusha Univ.) Page-14
Production Cross Section
• Factorization theorem: cross section can be factorized in pQCD– Inclusive hadron production:
2 2 2
, ,
ˆ( , ) ( , ) ( ) ( , )ha a b b c
a b c
f x Q f x Q ab cX D z Q
pp h X
PDFs and FFs:Determined using experimental data
Amplitude:Calculable in pQCD
K. Sudoh (Nishogakusha Univ.) Page-15
Charm Production @J-PARC
• Subprocesses for D/D production – O(s2) 2→2 tree-level channels in LO
qq cc gg cc
well-calculated in perturbation theory in αs
NLO → K factor x LO
J-PARC → pp
GSI → pp
gg dominance
qq dominance
K. Sudoh (Nishogakusha Univ.) Page-16
Numerical Results:
• Cross section of D production:
• Total cross section at the energies of J-PARC and GSI-FAIR.
3
3
( , 30GeV) 0.23 10 [nb]
( , 50GeV) 0.98 10 [nb]
Dbeam
Dbeam
pp E
pp E
( , )D pp pp DX
3
3
( , 15GeV) 0.42 10 [nb]
( , 15GeV, 3.5GeV) 7.03 10 [nb]
D pPANDA beam
D p pPAX beam beam
pp E
pp E E
J-PARC
GSI PANDA, PAX
D
Yield: N=σ ・ L ・ Br ・ ε
LJ-PARC = 3.6 x 106 nb-1/week
LGSI = 6.3 x 104 nb-1/week
Br(D-→K+π-π-) = 0.094 from PDG09
ε 〜 0.2
N = 15.5x106 /weekN = 66.0x106 /week
N = 0.50x106 /week
N = 8.33x106 /week
√s=8 GeV
√s=10 GeV
√s=5.5 GeV
√s=14.5 GeV
K. Sudoh (Nishogakusha Univ.) Page-17
• DN cross section is estimated as follows.
• Total cross section at the energies of J-PARC and GSI-FAIR.
( , 30GeV) 0.35 [nb]
( , 50GeV) 1.48 [nb]
DNbeam
DNbeam
pp E
pp E
2
3
( )(0)DN DN
D
pp DX
M
( , 15GeV) 0.63 [nb]
( , 15GeV, 3.5GeV) 10.62 [nb]
DN pPANDA beam
DN p pPAX beam beam
pp E
pp E E
J-PARC
GSI PANDA, PAX
Numerical Results: DN
N = 23.7x103 /week
N = 100.0 x103 /week
N = 0.75x103 /week
N = 12.58x103 /week
π + contact B
K. Sudoh (Nishogakusha Univ.) Page-18
Summary
• DN bound states are discussed with respecting to the heavy quark
symmetry.
– OPEP + contact repulsive interaction
– JP=1/2- with I=0 のチャネルのみ束縛解が存在 ( cf. (1405) )
• Charmed nuclei will be studied in experiments (J-PARC, GSI, …)
– 摂動計算により DN の生成断面積を見積もった。
– 強い相互作用による崩壊は存在しない。
– 弱崩壊が支配的( e.g. D–p → K––p ) →狭い崩壊幅
• Lots more coming!!
JP=1/2-,I=0 set A set B
B.E. [MeV]
radius [fm]
6.6 8.2
2.1 1.9