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 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

Introduction Exotic nuclei: Why charm/bottom? 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, …） 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 u d s c b Mass [MeV] ΛQCD 3 5 150 200 1500 4700 Mass scale of quarks Chiral Symmetry SU(3)L x SU(3)R Heavy Quark (Spin & Flavor) Symmetry SU(2)spin x SU(Nh)flavor 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。

Multi-Favored Nuclear Chart Charm Charmed Nuclei Bottom Bottom Nuclei

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

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

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

Heavy Quark Symmetry D*/B* are new fundamental d.o.f. Charm/Bottomの物理においてはHeavy Quark Symmetryが重要 PseudoscalarとVectorが縮退 K K* 400 MeV 500 MeV K* is almost irrelevant in dynamics. D*/B* are new fundamental d.o.f. D D* 140 MeV 1870 MeV B B* 45 MeV 5280 MeV Chiral dynamics Heavy quark dynamics

DN/BN Interaction One pion exchange interaction N K p, w, r p, w, r N 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 N K p, w, r p, w, r N D(*) p, w, r N B(*) pion exchange is absent. (short range force) pion exchange is present. (long range force) Weinberg-Tomozawa Heavy Meson Effective Theory

DN/BN Potential PN-P*N and P*N-P*N potentials P(*) p N OPEP P=D or B 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 N with vector pseudoscalar OPEP S. Yasui and K. S., PRD80, 034008 (2009) P=D or B

DN/BN Potential PN-P*N and P*N-P*N potentials OPEP + short range repulsion (w, r) → Approximation by a contact interaction P(*) N p, w, r 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 　　　

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

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 > N P s-wave 1/2 P* 1 d-wave + This plays an important role.

Numerical Results JP=1/2-, I=0: |PN; 2S1/2 > + |P*N; 2S1/2 > + |P*N; 4D1/2 > OPEP + contact interaction strong mixing by tensor coupling DN p +cont.A +cont.B B.E. [MeV] radius [fm] 10.8 6.6 8.2 1.7 2.1 1.9 |PN; 2S1/2 > wave functions [fm-3/2] |P*N; 2S1/2 > |P*N; 4D1/2 > PRELIMINARY

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

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 in perturbation theory in αs J-PARC → pp GSI → pp gg dominance qq dominance

Numerical Results: √s=8 GeV N = 15.5x106 /week √s=10 GeV 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 √s=10 GeV N = 66.0x106 /week GSI PANDA, PAX √s=5.5 GeV N = 0.50x106 /week N = 8.33x106 /week √s=14.5 GeV 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

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

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!! JP=1/2-,I=0 set A set B B.E. [MeV] radius [fm] 6.6 8.2 2.1 1.9