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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. 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.

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J-PARC におけるチャーム原子核生成

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  1. 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

  2. Chiral Symmetry SU(3)L x SU(3)R Mass scale of quarks 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 3 5 150 200 1500 4700 Mass [MeV] u d c b s ΛQCD Heavy Quark (Spin & Flavor) Symmetry SU(2)spin x SU(Nh)flavor 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, …）

  3. Charm Charmed Nuclei Bottom Bottom Nuclei Multi-Favored Nuclear Chart

  4. What are Charm/Bottom Nuclei? Mesons D, D*, B, B*, … This is our subject in this talk! Charm/Bottom neutron proton Nucleus

  5. DN/BN Potential D/B ?? N Q. What is the interaction between D/B and N ?

  6. K N D N B N Strangeness Charm Bottom K N D N B N SU(4) SU(5) SU(3) 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

  7. K* 400 MeV D* B* 140 MeV 45 MeV D B K 500 MeV 1870 MeV 5280 MeV 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 K* is almost irrelevant in dynamics. D*/B* are new fundamental d.o.f. Chiral dynamics Heavy quark dynamics

  8. p, w, r p, w, r p, w, r DN/BN Interaction • One pion exchange interaction • KN相互作用ではpKK 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 B(*) K D(*) N N N K N B(*) D(*) N N pion exchange is absent. (short range force) pion exchange is present. (long range force) Weinberg-Tomozawa Heavy Meson Effective Theory

  9. N with pseudoscalar vector N 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) P(*) p P(*) OPEP S. Yasui and K. S., PRD80, 034008 (2009) P=D or B

  10. P(*) N p, w, r P(*) N DN/BN Potential • PN-P*N and P*N-P*N potentials • OPEP + short range repulsion (w, r) → Approximation by a contact interaction Bonn A Bonn B cI=0 [fm2] 2.77 1.62 cI=1[fm2] 7.79 8.68 cf. smaller than NN contact interaction cNNI=0 = 17.8 [fm2] for A, 18.1 [fm2] for B

  11. DN/BN Bound States D/B ?? N D(cq)-N(qqq) B(bq)-N(qqq) * No annihilation process Q. Are there bound states of D/B and N ?

  12. Classification of State • Classification of states S. Yasui and K. S., PRD80, 034008 (2009) |state> = |PN>+ |P*N> P=Dbar(cbarq), B (bbarq) * No annihilation process Case 1. JP=1/2- (I=0 or 1) |PN; 2S1/2 > + |P*N; 2S1/2 > + |P*N; 4D1/2 > 1 1/2 0 1/2 1 1/2 d-wave s-wave s-wave + + N N N P* P P* This plays an important role.

  13. strong mixing by tensor coupling Numerical Results |PN; 2S1/2 > + |P*N; 2S1/2 > + |P*N; 4D1/2 > • JP=1/2-, I=0: OPEP + contact interaction |PN; 2S1/2 > wave functions [fm-3/2] |P*N; 2S1/2 > |P*N; 4D1/2 > PRELIMINARY

  14. Production Cross Section • Factorization theorem: cross section can be factorized in pQCD • Inclusive hadron production: PDFs and FFs: Determined using experimental data Amplitude: Calculable in pQCD

  15. J-PARC → pp gg dominance GSI → pp qq dominance Charm Production @J-PARC • Subprocesses for D/D production • O(as2) 2→2 tree-level channels in LO NLO → K factor x LO well-calculated inperturbation theory in αs

  16. Yield: N=σ・L・Br・ε LJ-PARC = 3.6 x 106 nb-1/week Br(D-→K+π-π-) = 0.094 from PDG09 LGSI = 6.3 x 104 nb-1/week ε 〜 0.2 Numerical Results: • Cross section of D production: • Total cross section at the energies of J-PARC and GSI-FAIR. J-PARC √s=8 GeV N = 15.5x106 /week N = 66.0x106 /week √s=10 GeV GSI PANDA, PAX √s=5.5 GeV N = 0.50x106 /week N = 8.33x106 /week √s=14.5 GeV

  17. Numerical Results: • DN cross section is estimated as follows. • Total cross section at the energies of J-PARC and GSI-FAIR. π + contact B J-PARC N = 23.7x103 /week N = 100.0 x103 /week GSI PANDA, PAX N = 0.75x103 /week N = 12.58x103 /week

  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. L(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–p–p） →狭い崩壊幅 • Lots more coming!!

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