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


Bottom

Bottom Nuclei

Multi-Favored Nuclear Chart

Charm

Charmed Nuclei


What are Charm/Bottom Nuclei?

Nucleusproton

neutron

Charm/Bottom

This is our subjectin this talk!

Mesons D, D*, B, B*, …


DN/BN Potential

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

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)NK

K NStrangeness

ND

D N

SU(4)

Charm

NB

B N

SU(5)

Bottom


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.


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)


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


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


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


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)


• 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


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


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


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


• 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


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

J-PARC におけるチャーム原子核生成

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