チャーム・ボトムのエキゾチックハドロン物理の最近の発展

安井 繁宏∈ 佐々木グループ ⊂ WPI-SKCM2 ⊂ 広島大学

瀬戸内サマーインスティチュートSSI2023@広島大学, 20-22 Sep. 2023

1

International Institute for Sustainability with Knotted Chiral Meta Matter/SKCM2World Premier International Research Center Initiative/WPI at Hiroshima University✔️ Cross-pollinates mathematical knot
theory and chirality knowledge acrossdisciplines and scales✔️ Creation of designable artificial knotlike particles that exhibit highly unusual
and technologically useful properties

Hadron & nuclear physics group
PI: Chihiro SASAKI (HU, Uni. of Wroclaw)
PI: Kenta SHIGAKI (HU)
coPI: Chiho NONAKA (HU)

coPI: Muneto NITTA (HU, Keio Uni.)
2

Keywords

Tetraquark
Spectroscopy
Heavy quarkCharm
symmetry
Heavy hadroneffective theory
BottomPentaquark

Exotic

XYZ

Spin

3

この講義の目標

1. ハドロン物理学の基本的知識を理解して用語を説明できること2. ハドロン現象論の基本的なモデルの特徴を理解しうて説明できること
3. エキゾチックハドロンの性質について実験データ
あるいは理論に基づいて説明できること

4https://www.jps.or.jp/books/gakkaishi/files/71-09_70fushigi.pdf

5

内容
1. イントロダクション
1.1 ハドロンの基本的性質
1.2 なぜ重いハドロンを研究するのか？
2. 重いクォークのスピン対称性と有効理論
2.1 スピン対称性とハドロンスペクトロスコピー
2.2 重いクォークの有効理論
2.3 重いハドロンの有効理論
3. 重いエキゾチックハドロン -ハドロン相互作用の観点から3.1 なぜエキゾチックハドロンが面白いのか？
3.2 チャームメソン：X, Y, Zc
3.3 ボトムメソン：Zb
3.4 チャームペンタクォーク：Pc, Pcs
3.5 ダブルチャームメソン：Tcc
3.6 フルチャームメソン：Xcc
3.7 反応論ー重イオン衝突によるエキゾチックハドロン生成ー

7

内容
1. イントロダクション
1.1 ハドロンの基本的性質
1.2 なぜ重いハドロンを研究するのか？
2. 重いクォークのスピン対称性と有効理論
2.1 スピン対称性とハドロンスペクトロスコピー
2.2 重いクォークの有効理論
2.3 重いハドロンの有効理論
3. 重いエキゾチックハドロン -ハドロン相互作用の観点から3.1 なぜエキゾチックハドロンが面白いのか？
3.2 チャームメソン：X, Y, Zc
3.3 ボトムメソン：Zb
3.4 チャームペンタクォーク：Pc, Pcs
3.5 ダブルチャームメソン：Tcc
3.6 フルチャームメソン：Xcc
3.7 反応論ー重イオン衝突によるエキゾチックハドロン生成ー

8物質とは？
HiggsTan.com

9

力とは？
万物の理論？？
大統一理論？

電弱力

強い力

電磁気力

弱い力

重力

原子核・ハドロン 原子・分子 ニュートリノ 天体・宇宙

10

1. Introduction
基本問題

核子間に働く力(核力)とは？

？

中性子

陽子
13

1. Introduction
電気力と核力の性質の違い
電気力

電子

核力

湯川秀樹
（1907-1981）

光子 (フォトン)の交換
・ほどほどの強さ(α=/137)
・無限に遠くまで届く

陽子

中性子
陽子

中間子(メソン)の交換
・かなり強い(電気力の100倍以上)
・短い距離しか届かない (数fm以下)
14

1. Introduction

中性子
陽子

中間子(メソン)の交換

原子核はメソン交換による力(核力)で核子(陽子・中性子)が集まってできた物質である。

15

1. Introduction

Potential Energy [MeV]

中性子

斥力

陽子

（短距離）

中間子(メソン)の交換

引力
（長距離）
σ, ρ, ω, ...

斥力芯

π

π
重いメソン(σ,ρ,ω,...)の交換

Δr [fm]π

軽いメソン(π)の交換
16

1 fm = 10-15 m

1. Introduction

π, σ, ρ, ω, ...って何？
(パイ)

(シグマ)

(ロー)

(オメガ)

クォークqと反クォークq
の束縛状態
反クォーク

π, σ, ρ, ω, ...

クォーク

17

1. Introduction

From nucleus to quark
Condensed matter, Chemistry, Biology 〜104 K
1 μeV〜 100 keV

1 meV

surface vibration/rotation

Nucleus

1 eV

PlasmaNuclear & Hadron

1 keV〜 100 MeV

1 MeV
excited hadron

1 GeV

1 MeV = 106 eV
1 GeV = 109 eV
Elementary Particle
1 TeV〜 100 GeV

quark

Hadronproton/neutron(baryon)pion(meson)

Quark
Gluon

Quark

18

1. Introduction

From nucleus to quark
Condensed matter, Chemistry, Biology 〜104 K
1 μeV〜 100 keV

1 meV

Plasma1 eVsurface vibration/rotation

1 keV〜 100 MeV
HadronNucleus
Superfluidity/Superconductivity
Rotational symmetry
Meson exchange(Yukawa theory)

H. Yukawa(1907-1981)

Nuclear & Hadron
1 MeV

1 GeV

1 MeV = 106 eV
1 GeV = 109 eV
Elementary Particle
1 TeV〜 100 GeV

excited hadron
D. Gross(1941-)

quark

F. Wilczek H. D. Politzer(1949-)(1951-)

Asymptotic freedom
proton/neutron(baryon)
Quark
Color confinement
pion
Gluon
(meson)Chiral symmetry breaking

Y. Nambu(1921-2015)

Quark

19
Can we understand nucleus/hadron by quarks and gluons?

1. Introduction

Questions
・How do quarks compose hadrons?

quarkshadrons20

1. Introduction
How do quarks move?

ma = F

Gluon
gluon
quark

quark

HiggsTan.com

gluon
21

1. Introduction“Law of motion” of quarks and gluons

Quantum Chromodynamics(QCD)𝜓𝑓: quark field (flavor 𝑓)
𝐴𝜇, 𝐹𝜇𝜈: gluon field

𝑔𝑠: coupling between
quarks and gluons22

1. Introduction

Why is hadron physics difficult?
Answer: strong coupling in low energy← Break-down ofperturbation
D. Gross F. WilczekH. D. Politzer
Asymptotic freedom

Quarks arenearly free.

Confined quarks

Hadron Physics(Quarks are NOT visible.)

0.01(=10 MeV)

free quarks

0.1(=100 MeV)

Non-perturative effects in low energy
Origin of a variety of matter states?

24

1. Introduction

Fundamental

4 Questions in Hadron Physics① Why are quarks confined?

Confined quarks③ Why is chiral symmetry broken?

② What is hadron interaction?

Nuclear force④ What is phase diagram?

25

1. Introduction

Properties of QCD① Color charge (red, blue, green)26

1. Introduction
Color charge (review)

QED
U(1) symmetryelectron e-

QCD
SU(3) symmetry
T8quark qT3-e“Minus sign”

positron e++e

T8antiquark q
T327

1. Introduction
Color charge (review)

Hadrons are colorless (white: T3=T8=0)

meson (qq)+baryon (qqq)+28

1. Introduction

Properties of QCD① Color charge (red, blue, green)② Gluon exchange in inter-quark
Time

gluon

quark

protonneutronprotonneutron29

1. Introduction

Properties of QCD① Color charge (red, blue, green)② Gluon exchange in inter-quark③ Asymptotic freedom④ “Structure” of QCD vacuum(small coupling at high energy)- quarks are confined- chiral symmetry is broken“Big problem” in strong interaction!!

30

1. Introduction“Structure” of QCD vacuum?

Nothing？

31

1. Introduction“Structure” of QCD vacuum?
Many particles in QCD vacuum!

HiggsTan.com”Non-perturbative vacuum”(Condensate by interaction is realized by stability of energy.)32

1. Introduction“Structure” of QCD vacuum?
Many particles in QCD vacuum!

HiggsTan.com”Non-perturbative vacuum”(Condensate by interaction is realized by stability of energy.)33

1. Introduction“Structure” of QCD vacuum?
Many particles in QCD vacuum!

HiggsTan.com”Non-perturbative vacuum”(Condensate by interaction is realized by stability of energy.)34

1. Introduction“Structure” of QCD vacuum?
Many particles in QCD vacuum!

“Vacuum” ≠ Nothingin field theory35

1. Introduction“Structure” of QCD vacuum?
Many particles in QCD vacuum!

Most“Vacuum” = StableStatein field theory

Nothing

36
L. Álvarez-Gaumé, J. Ellis, Nature Physics 7, 2–3 (2011)

1. Introduction“Structure” of QCD vacuum?
What happens in QCD vacuum?

Dynamical symmetry
breaking induceszero-mass boson(Nambu-Goldstone (NG) boson)

Origin of light mass of pion(mπ=140 MeV << mN=940 MeV)π
43
L. Álvarez-Gaumé, J. Ellis, Nature Physics 7, 2–3 (2011)

1. Introduction“Structure” of QCD vacuum?
What happens in QCD vacuum?

Dynamical symmetry
breaking induceszero-mass boson

Origin of light mass of pion(mπ=140 MeV << mN=940 MeV)

(Nambu-Goldstone (NG) boson)

Chiral symmetry breaking

〜1fm

〜1fm

1/mπ〜1.5fm
Exchange ofvirtual π(qq)Y. Nambu(1921-2015)

Inter-hadroninteraction
at long-range

Hadron (proton)

Hadron (neutron)

π exchange interaction is dominant at long distance.
44

1. Introduction“Structure” of QCD vacuum?
What happens in QCD vacuum?

color confinement

Can we separate two quarks？

𝑞 𝑞ത

𝑞

𝑞ത

𝑞 𝑞ത𝑞 𝑞ത

𝑞 𝑞ത 𝑞 𝑞ത

meson

potential
increases
linearly𝑞𝑞ത pair iscreatedfromvacuumtwomesons45

baryons with the excitation energy abthat the lowest hybrid baryon, which
1. Introduction
picture, has a large m ass of about 2 G
Together with the recent lattice resenergy ∆ E Q Q̄ ≡ VQe.Q̄s. − VQg Q̄. s. for th
What happens in1G
QCD
vacuum?
eV , thepresent result seems to su
H. Suganuma, H. Ichie, T.T. Takahashi,
about 1G
eVConfinementin term sandof Hadrons
the constitue
Color
in
Quantum Chromodynamics (2004)
G.S. Bali, Phys. Rep. 343 (2001) 1
4
2. 6. O th er R ecen t Stu d i es on the 3Q P oten ti a l

To clarify the current status of the 3Q potential, we introduce two recent
studies on the 3Q potential.

d e For cr an d ’s g r ou p : R ecently, de Forcrand’s group, who supported∆ -A nsatz in lattice QCD , 16 seems to change their opinion from ∆ -A nsatz
to Y -A nsatz17 except for a very short distance, where the linear potential
seem s negligible com pared with the Coulomb contribution. (A s a problemof their argum ent, they relied on the continuum Coulomb potential even forthe subtle argum ent at the very short distance, where the lattice Coulomb
potential should be used.)“Structure” of QCD vacuum?
C or n w al l : One of the theoretical basis of ∆ -A nsatz was Cornwall’s conjecture based on the vortex vacuum m odel. 18 Very recently, m otivated by ourstudies, Cornwall re-examined his previous work and found an error in his
model calculation. H is corrected answer is Y -A nsatz instead of ∆ -A nsatz. 19
I n this way, Y -A nsatz for the static 3Q potential seem s alm ost settled
both in lattice QCD and in analytic framework.
3. Y -ty p e F l u x -T u b e For m ati on i n L atti ce Q C D

Linear-type(confinement)𝑞Coloumb-type𝑞ത

3Q potential [GeV] (b=5.8)

R ecently, as a clear evidence for Y -A nsatz, Y -type ﬂux-tube form ation is
actually observed in the maxim ally-A belian projected QCD from the direct
measurem ent for the action density of the gluon ﬁ eld in the spatially-ﬁ xed
3Q system. 20, 21, 22 (See F ig.5)
20

18
16
14
12
10
8

3

6
17.5

20

22.5

25

27.5

30

32.5

F igure 5. T he lattice Q C D result for Y -typ e ﬂ ux-tub e form ation in the spatially-ﬁ xed
3Q system in m ax im ally-A b elian proj ected Q C D . T he distance b etween the j unction andeach quark is ab out 0.5 fm .

2
G.S.
1st E.S.

10

F igure 6.

0.5

Lmin [fm]1

1.5

T he lattice Q C D results of the gr

Quarks are always confined
inside hadrons.
46
and the 1st excited-state 3Q p otential V e. s.
3Q1. Introduction

color confinement𝑞𝑞ത

Quarks have to make white (colorless) objects.
47

1. Introduction
Main subject in this lecture:

Formation mechanism of hadrons by quarks

HADRON
quarkshadrons✔︎ Mass✔︎ Interaction✔︎ Many-body problem48

1. Introduction
Quark

Anti-Quark

249

1. Introduction
Quark

Quark

3

Quark

50

1. Introduction
Quark

Anti-Quark

Quark

Anti-Quark

451

1. Introduction
Quark

Quark

Anti-Quark

5

Quark

Quark

52

QuarkQuark

1. Introduction

653

1. Introduction

To be continued54

1. Introduction

Variety of Hadrons

2

4

3

5

6
55

1. Introduction

Variety of Hadrons

mesonbaryontetraquark pentaquark

hexaquark56

1. Introduction
How many hadrons were discovered?

57

1. Introduction

about

Particle Data Group

58

1. Introduction59

1. Introduction

Quarks have flavors？
60

1. Introduction

Quarks have flavors

HiggsTan.com

61

1. Introduction

Flavors
electric
charge

1st

2nd

3rd

Q=+2/3

up

charm

top

2 MeV

1300 MeV

173000 MeV

down

strangebottom

5 MeV

100 MeV

4200 MeV

Q=-1/3

HiggsTan.com

weak interaction:different flavors are interchanged by W and Z bosons (very slow process).
62

1. Introduction

Flavors
electric
charge

1st

2nd

3rd

Q=+2/3

up

charm

top

2 MeV

1300 MeV

173000 MeV

down

strangebottom

5 MeV

100 MeV

4200 MeV

Q=-1/3

HiggsTan.com

weak interaction:different flavors are interchanged by W and Z bosons (very slow process).
63

1. Introduction
Hadrons made of up, down, strange quarks

𝐾0
𝜋−

𝐾+

𝑛

𝜋 0 𝜂 𝜂' 𝜋 +

Σ−

𝑝
Σ0 Λ

Σ+
Y (=B+S)

𝐾−
𝐾 ∗0
𝜌−

ഥ0
𝐾
𝐾 ∗+

𝜌0 ω ϕ
𝐾 ∗−

ഥ ∗0
𝐾

𝜌+

Δ−

Ξ−

Ξ0

Δ0

Δ+

Σ ∗−

Σ ∗0

Ξ∗−

Iz

Δ++

Σ ∗+
Ξ∗0

Ω−

64

1. Introduction

Flavors
electric
charge

1st

2nd

3rd

Q=+2/3

up

charm

top

2 MeV

1300 MeV

173000 MeV

down

strangebottom

5 MeV

100 MeV

4200 MeV

Q=-1/3

HiggsTan.com

weak interaction:different flavors are interchanged by W and Z bosons (very slow process).
67

1. Introduction

Flavors
electric
charge

1st

2nd

3rd

Q=+2/3

up

charm

top

2 MeV

1300 MeV

173000 MeV

down

strangebottom

5 MeV

100 MeV

4200 MeV

Q=-1/3

HiggsTan.com

weak interaction:different flavors are interchanged by W and Z bosons (very slow process).
68

1. Introduction
Charm/bottom quarks

mc/mu,d = 200-400
mb/mu,d = 900-1400
69

SU (4) f weight diagram s.
lattice that the m is-m atch between the excitation spectrum predicted by the standard quark m odel
and experim ental observations is due to inappropriate degrees of freedom in the quark m odel.

1. Introduction

15.5.2 C har med
and bottom
yons
Hadronsmadeof barup,
down, strange, charm quarks

T he nam ing schem e for baryons with c or b quarks follows that of the light baryons: the » is an
isosinglet and the À an isotriplet with one heavy (s, c or b) quark. T he … is an isodoublet whichcontains two heavy quarks, and the œ an isosinglet with three heavy quarks. T he number of c orb quarks is indicated by the subscripts c or b. H yperons are baryons with at least one s quark.
- For charm ed baryons the addition of the c quark to the light quarks extends the ﬂavor sym m etryto SU (4) f . D ue to the large m ass of the c quark, this sym m etry is much m ore strongly broken
than the SU (3) f of the three light quarks. N evertheless, the SU (4) f representation is still usefulfor bookkeeping purposes. W ith the additive charm quantum number C the baryons are classiﬁ ed
in a 3-dim ensional representation with the three coordinates ( I z , Y , C ). F igure 15.5 Pshows the +SU (4) f weight diagram s.

mesonbaryonJP=0

J =1/2

F igure 15.5: SU (4) f multiplets of ground state baryons m ad
spin 12 20-plet extends the charmless SU (3) f octet to C = 1,2;
SU (3) f decuplet to C = 1, 2, 3.

JP=1-

J =3/2

P decom+pose
W ith four quarks the 64 possible conﬁ gurations4 ¢ 4 ¢ 4 = 4̄A ü 20S ü 20M S ü 2(for a review on SU(N ) symmetries see e.g. [69]). T he subscrip
and antisymm etry properties of the ﬂavor wave functions. T hassociated with spin-32 baryons, contains the charmless SU (3) f
20M S and 20M A multiplets correspond to the m ixed symmetri
wave functions of the spin-12 baryons, with the charmless octet
70
are two dsc and two usc spin-12 states, labeled …c0 , …cÕ0 and …
F igure 15.5: SU (4) f multiplets of ground state baryons made of u, d, s, and c quarks. (a) T he

1. Introduction71

1. Introduction

Variety of Hadrons

mesonbaryontetraquark pentaquark

hexaquark72

1. Introduction

Variety of Hadrons

mesonbaryontetraquark pentaquark

hexaquark73

1. Introduction
What is “exotic”?

74

1. Introduction
What is “exotic”?

1. Difference from (conventional) quark modelmeson baryon

normal hadrontetraquark

pentaquark

Exotic hadron“simple”(qq, qqq)

not so simple75

1. Introduction
What is “exotic”?

2. Quantum numbers (charge, JPC)
meson

tetraquark
or

ccbar

ccbarqqbar

76

1. Introduction
What is “exotic”?

2. Quantum numbers (charge, JPC)
meson

tetraquarkorElectric charge

ccbar

ccbarudbar

0

+1

77

1. Introduction
What is “exotic”?

2. Quantum numbers (charge, JPC)
meson

tetraquarkor

Exotic JPC
E+-, O-+

ccbar

ccbarqqbar

prohibitedallowed

E=0, 2, 4, ...
O=1, 3, 5, ...

78

1. Introduction
How many X, Y, Z are discovered so far?
Normal hadron
about

300

about
79

1. Introduction

How can we research exotic hadrons？

80

GSI-FAIR

BNL-RHICBESI,II,III
CERN-LHC

81

ELPH(Research Center for Electron Photon Science)

KEK (BelleI,II)

J-PARC(Japan Proton Accelerator Research Complex)

S-Pring 8(Super Photon ring-8 GeV)82

1. Introduction
Productions of exotic hadrons in Belle@KEK

e-

q
γ

e+

q

Quark-antiquark pairs are created through electron-positron collisions.
q = charm, bottom
83

q

eγ

e+

1. Introduction
Variety of reactions at KEK

q84

1. Introduction

S. L. Olsen, T. Skwarnicki, D. Ziemninska,
Rev. Mod. Phys. 90, 015003 (2018)

Tables of X, Y, Z discovered so far

85

86

and more!

87

1. Introduction
Conventional rule of naming

Hadrons whose properties are different from quark model.

JPC=1--

Electrically charged (±)

88

1. Introduction
Conventional rule of naming

However, all XYZ are “X” in Particle Data Group.

891. Introduction

What are structures of

cc
u
d

(
)
D*

Compact multiquark

gluonic excitation modes?

cc “string excitation”
Σ, Π, Δ, Φ, ...
(S, P, D, F, ...)()
D*

Hadronic molecule

J/ψ
Λb

N

χ cJ
N
Λ∗
(a)

Λb

D s∗∗
Λ∗c

K

(b

Kinematic effect
K
¯(∗)

90

1. Introduction

Brief review of early studies on exotic hadron:lessons from “ancient” researches

Confucius (孔子)(551BC-479BC)

子曰、温故而知新、可以為師矣
If we can keep the old traditions alive
and acquire new knowledge, we will
be able to become teachers.
91

1. Introduction
Classical Papers of Exotic Hadrons

quark model93

1. Introduction
Classical Papers of Exotic Hadrons
CERN-TH-401 (1964)

quark model94

1. Introduction
Classical Papers of Exotic Hadrons
Λ(uds)Λ(uds) >> H(uuddss) hexaquark"Pcs" (uudsc)
Note: recently discovered Pcs
is different from "Pcs" by Lipkin.

95

1. Introduction
Classical Papers of Exotic Hadrons96

1. Introduction
Classical Papers of Exotic Hadrons97

1. Introduction

Analysis method based on QCD
Lattice QCD

S. Aoki et al., Phys. Rev. Lett. 84, 238 (2000)
S. Durr et al., Science 322, 1224 (2008)

QCD sum rules

Correlation function

M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B147, 385 (1979), ibid. 448 (1979)
L. J. Reinders, H. Reubinstein, S. Yazaki, Phys. Rep. 127, 1 (1985)

ρ(s) spectral function: particle energy and width
peak
continuum states1. Introduction

Hadron models ... since early days

What is the essential picture？

A variety of hadron models have been used up to now.
They are very useful to calculate some physical quantities
and to provide concrete pictures of hadron dynamics.
Pablo Ruiz Picasso (1881-1973)

complex(realism)

simple(abstract)99

1. Introduction

Hadron models ... since early days

Skyrme model

Hadron molecule model

Hadrons are fundamental degrees of freedom
deuteron:Λ(1405):N N

σ meson:K N + π Σ

T. H. R. Skyrme, Nuclear Physics 31, 556, (1962)

Describing fermion in terms of bosonππN(1535):(nucleon)

Topological quantity: R3(S3)→SU(2)(S3)= baryon number

η N

Soliton solution: dynamically stable
G. S. Adkins, C. R. Nappi, E. Witten,
Nucl. Phys. B228, 552 (1983)

R. H. Dalitz, S. F. Tuan, Phys. Rev. Lett. 2, 425 (1959)

Bag model

Diquark model

A. Chodos, et al., Phys. Rev. D9, 3471 (1974)

M. Ida, R. Kobayashi, Prog. Thor. Phys. 36, 846 (1966)

Massless quark (no chiralsymmetry breaking inside bag)

A pair of quarks = diquark
Baryon = quark+diquark(π)

H-dibaryon = diquark×3 (?)

strong attraction
color 3cbar

Bag pressure B (energy density
outside bag)bag

Confinement of quark byboundary condition

QCD vacuum

Quark model

String model

A. De. Rujula, H. Georgi, S. L. Gkashow, Phys. Rev. D12, 147 (1975)

R. Giles, S.-H H. Tye, Phys. Rev. Lett. 37, 1175 (1976)

inter-quark potential:

m: dynamical quark mass
(300-400 MeV)
Color Coulomb potential
Confinement (linear) potentialqq

Excitation of ”gluon”
Flux tube model
Constituent gluon model...
→ Later example

1. Introduction

Hadron models ... since early days

Skyrme model

Hadron molecule model

Hadrons are fundamental degrees of freedom
deuteron:Λ(1405):N N

σ meson:K N + π Σ

T. H. R. Skyrme, Nuclear Physics 31, 556, (1962)

Describing fermion in terms of bosonππN(1535):(nucleon)

Topological quantity: R3(S3)→SU(2)(S3)= baryon number

η N

Soliton solution: dynamically stable
G. S. Adkins, C. R. Nappi, E. Witten,
Nucl. Phys. B228, 552 (1983)

R. H. Dalitz, S. F. Tuan, Phys. Rev. Lett. 2, 425 (1959)

Bag model

Diquark model

A. Chodos, et al., Phys. Rev. D9, 3471 (1974)

M. Ida, R. Kobayashi, Prog. Thor. Phys. 36, 846 (1966)

Massless quark (no chiralsymmetry breaking inside bag)

A pair of quarks = diquark
Baryon = quark+diquark(π)

H-dibaryon = diquark×3 (?)

strong attraction
color 3cbar

Bag pressure B (energy density
outside bag)bag

Confinement of quark byboundary condition

QCD vacuum

Quark model

String model

A. De. Rujula, H. Georgi, S. L. Gkashow, Phys. Rev. D12, 147 (1975)

R. Giles, S.-H H. Tye, Phys. Rev. Lett. 37, 1175 (1976)

inter-quark potential:

m: dynamical quark mass
(300-400 MeV)
Color Coulomb potential
Confinement (linear) potentialqq

Excitation of ”gluon”
Flux tube model
Constituent gluon model...
→ Later example

1. Introduction
Diquark

Meson

Diquarkcolor singlet

color anti-triplet/sextet

q
q

102

1. Introduction
Diquark

Meson

Diquarkqqqq

color singlet

color anti-triplet/sextet
NO asymptotic state: not “visible”

103

1. Introduction
Diquarkcolor electricLight-light diquark
color magnetic (color-spin)color jcolor lgluon

i, j, k, l = 1, 2, 3
distance between
two quarks
color icolor k104

1. Introduction
Diquark

Light-light diquark
color-spin

S=1+“bad”diquark
spin 1, isospin 1+ 50 MeV(repulsion)- 150 MeV
(attraction)

S=0“good”diquark
spin 0, isospin 0→ Is ”good” diquark favored inside hadrons ?

105

1. Introduction
Diquark

Light-light diquark
color-spin

The hadrons where we may see diquarks...

① Scalar meson JP=0+② Charm/bottom baryon (C, B=1)
③ Exotic hadrons: mass spectrum of colorful state④ Double charm baryon (C=2)

106

1. Introduction
Diquark

Light-light diquark
color-spin

The hadrons where we may see diquarks...

① Scalar meson JP=0+② Charm/bottom baryon (C, B=1)
③ Exotic hadrons: mass spectrum of colorful state④ Double charm baryon (C=2)

107

1. Introduction
Diquark② Charm/botttom baryon (C, B=1)
[MeV]

Light-light diquark

HQS doublet

repulsivecolor-spin

q S=1
q

a.v.
2502 MeVQ

58 MeVHQS doubletg.s.

HQS doublet

a.v.
5828 MeV

52 MeV(repulsion)(repulsion)

175 MeV

157 MeV(attraction)

HQS singlet

attractive

Λc(udc)[MeV]Σc(uuc, udc, ddc)

S=0 q
q

HQS doublet(attraction)g.s.

HQS singletQΛb(udb)Σb(uub, udb, ddb)109

1. Introduction
Diquarks in lattice QCD

See, e.g., this recent review paper to know more on diquarks.
117

1. Introduction“Diquark” in lattice QCD
A. Francis, P. de Forcrand, R. Lewis, K. Mlatman, JHEP05 (2022) 062“bad”-“good” diquarks
mass difference1181. Introduction
So far we have briefly reviewed how to understand hadrons by means of simple models.
Pablo Ruiz Picasso (1881-1973)

1191. Introduction120

1. Introduction

more about

Heavy Hadrons121

1. Introduction

more about

Heavy Hadrons
Charmonium

cc

122

of possible theoretical explanations (Fig. 8.3, left). Only 10 days after the initial
discovery, a second narrowstate,the ψ ′— now called ψ(2S)— was observed in
1.
Introductione+ e− collisions about 600 M eV above the J / ψ. Figure 8.3 (right) shows a pictorial
Charmonium
event display from the M ARKI experiment at SPEAR of the ψ ′decaying intoJ / ψ π + π− , with J / ψ → e+ e− . The observation of the ψ ′was soon followed by
the discovery of higher lying states at SPEAR and at DORIS/DESY (for an excellent
review on the history of the charm quark discovery see [5]).

cc

CERN courier, April 1975 (Amsler's textbook)

SLAC MARK I detector 1974

Fig. 8.3 Left: The J / ψ discovery triggered a ﬂood of theoretical specul ations (sketch by J.D.
124
Jackson, credit CERN courier, April 1975). Right: event display from the M ARK I detector at

1. Introduction
Charmonium Mass Spectrum

cc

Quark model A. De. Rujula, H. Georgi, S. L. Gkashow, Phys. Rev. D12, 147 (1975)cCf. T. Barnes, S. Godfrey, E. S. Swanson, Phys. Rev. D72, 054026 (2005)c
Coulomb pot.
Confinement pot.

potential V(r)(gluon)Spin-spin pot.

L-S pot.

Tensor pot.

Tensor operator
δ function (smearing)125

1. Introduction
Charmonium

cc

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV++

mass: 3511 MeV
width: 0.84 MeV++

mass: 3556 MeV
width: 1.9 MeV

126

1. Introduction
Charmonium

cc

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV

PC
J

++

mass: 3511 MeV
width: 0.84 MeV++

mass: 3556 MeV
width: 1.9 MeV

127

1. Introduction
Charmonium

cc

Angular momentum L
Parity (-1)L

Parity +1

PC
J

c

c

Parity -1

Total spin S=0 or 1

☑︎ Total angular momentum J=L, L ±1
☑ Total parity P=(+1)(-1)(-1)L=(-1)L+1☑ C parity (charge conjugate): C=(-1)L+S
Proof:
128

1. Introduction

PC
J

J ... total momentum spin (0, 1/2, 1, 3/2, ...)P ... parity (±)
C ... charge conjugate (±)

129

1. Introduction

PC
J

QQ (quark and antiquark) case ...
J ... total momentum spin (0, 1, ...) ← L±S

P ... parity (±) ← (-1)L+1
C ... charge conjugate (±) ← (-1)L+S

130

1. Introduction

PC
J

QQ (quark and antiquark) case ...

L02n (n≥1)

2n-1 (n≥1)

S

0

1

0

1

0

1

J

0

1

2n

2n, 2n±12n-12n-2, 2n-1, 2n

P

C

-1

+1

-1

+1

-1

+1

-1

-1

+1

JPC 0-+ 1--

E-+E--, O--

O+-

O++, E++

Note: E+- and O-+ are impossible for QQbar.

131

1. Introduction
Charmonium

cc

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV++

mass: 3511 MeV
width: 0.84 MeV++

mass: 3556 MeV
width: 1.9 MeV

132

1. Introduction
Charmonium

cc

L=0

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV++

mass: 3511 MeV
width: 0.84 MeV++

mass: 3556 MeV
width: 1.9 MeV

S=0

L+S
J=0, P=-1, C=(-1) =+1133

1. Introduction
Charmonium

cc

L=0

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV++

mass: 3511 MeV
width: 0.84 MeV++

mass: 3556 MeV
width: 1.9 MeV

S=1

L+S
J=1, P=-1, C=(-1) =-1134

1. Introduction
Charmonium

cc L=1

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV++

mass: 3511 MeV
width: 0.84 MeV++

mass: 3556 MeV
width: 1.9 MeV

S=0

L+S
J=1, P=+1, C=(-1) =-1135

1. Introduction
Charmonium

cc L=1

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV

S=1

++

mass: 3511 MeV
width: 0.84 MeV

S=1

++

mass: 3556 MeV
width: 1.9 MeV

S=1

L+S
J=0,1,2,P=+1,C=(-1) =+1136

1. Introduction
Charmonium

cc

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

1--

mass: 3097 MeV
width: 93 keV+-

mass: 3525MeV
width: 0.7 MeV++

mass: 3415 MeV
width: 10 MeV++

mass: 3511 MeV
width: 0.84 MeV++

mass: 3556 MeV
width: 1.9 MeV

137

1. Introduction
Charmonium

cc

𝜒
𝑐2
𝜒
𝑐1
𝜒
𝑐0
ℎ
2
𝑐
𝐽/𝜓
1
𝜂𝑐
0
1
0-+

mass: 2983 MeV
width: 32 MeV

𝜂
mass: 550 MeV
width: 1.3 keV

1--

mass: 3097 MeV
width: 93 keV

𝜙mass: 1020 MeV
width: 4.3 MeV+-

mass: 3525MeV
width: 0.7 MeVℎ1

mass: 1170 MeV
width: 375 MeV++

mass: 3415 MeV
width: 10 MeV

𝑓0

mass: 980 MeV
width: 100 MeV++

mass: 3511 MeV
width: 0.84 MeV

𝑓1
mass: 1280 MeV
width: 23 MeV++

mass: 3556 MeV
width: 1.9 MeV

𝑓2

mass: 1275 MeV
width: 187 MeV

138

1. Introduction
Charmonium
Quiz: what is JPC？

𝜂𝑐mass: 2983 MeV
width: 32 MeV

139

1. Introduction
Charmonium
Quiz: what is JPC？

𝜂𝑐0-+

mass: 2983 MeV
width: 32 MeV

140

1. Introduction
Charmonium
Quiz: what is JPC？

𝐽/𝜓
mass: 3097 MeV
width: 93 keV

141

1. Introduction
Charmonium
Quiz: what is JPC？

𝐽/𝜓
1--

mass: 3097 MeV
width: 93 keV

142

1. Introduction
Charmonium
Quiz: what is JPC？

ℎ𝑐mass: 3525 MeV
width: 0.7 MeV

143

1. Introduction
Charmonium
Quiz: what is JPC？

ℎ𝑐1+-

mass: 3525 MeV
width: 0.7 MeV

144

1. Introduction
Charmonium
Quiz: what is JPC？

𝜒𝑐0
mass: 3415 MeV
width: 10 MeV

145

1. Introduction
Charmonium
Quiz: what is JPC？

𝜒𝑐0
0++

mass: 3415 MeV
width: 10 MeV

146

1. Introduction
Charmonium
Quiz: what is JPC？

𝜒𝑐1
mass: 3511 MeV
width: 0.84 MeV

147

1. Introduction
Charmonium
Quiz: what is JPC？

𝜒𝑐1
1++

mass: 3511 MeV
width: 0.84 MeV

148

1. Introduction
Charmonium
Quiz: what is JPC？

𝜒𝑐2
mass: 3556 MeV
width: 1.9 MeV

149

1. Introduction
Charmonium
Quiz: what is JPC？

𝜒𝑐2
2++

mass: 3556 MeV
width: 1.9 MeV

150

1. Introduction
Bottomonium

bb

𝜂𝑏
0-+
mass: 9399 MeV
width: 10 MeV

𝜒
𝑏2
𝜒
𝑏1
𝜒
𝑏0
ℎ
Υ 𝑏 0 1 2
1--

mass: 9460 MeV
width: 54 keV

1+-

mass: 9899 MeV
width: ???

++mass: 9859 MeV
width: ???

++mass: 9893 MeV
width: ???

++mass: 9912 MeV
width: ???

151

1. Introduction152

1. Introduction
T. Barnes, S. Godfrey, E. S. Swanson,
Phys. Rev. D72, 054026 (2005)c c

Not consistent withquark model
prediction153

1. Introduction
Quarkonium Mass Spectrum

QQ
Scattering states

We need to understandheavy-light mesons.

open threshold (ex. DDbar)

mass

154

1. Introduction
Names of heavy-light mesons

D
0
D cu
+
D cd
meson

+2/3

-2/3

+2/3

+1/3

Charm

pseudoscalar

D
0
D cu
D cd
meson

-2/3

+2/3

-2/3

-1/3

155

1. Introduction
Names of heavy-light mesons

*
D

Charm
vector

meson

*
D

meson

*0
D cu

*0
D cu

*+
D cd

*D cd

+2/3

-2/3

+2/3

+1/3

-2/3

+2/3

-2/3

-1/3
156

1. Introduction
Names of heavy-light mesons

B
B bu
0
B bd
meson

-1/3

-2/3

-1/3

+1/3

Bottompseudoscalar

B
+
B bu
0
B bd
meson

+1/3

+2/3

+1/3

-1/3

157

1. Introduction
Names of heavy-light mesons*
B

Bottommeson

vector

*
B

meson

*B bu

*+
B bu

*0
B bd

*0
B bd

-1/3

-2/3

-1/3

+1/3

+1/3

+2/3

+1/3

-1/3
158

1. Introduction
Experiment ⇄ Theory

Hadron Spectroscopy
Production

Mass
mass

Decay
mass

He
av
2 0 1 7 /0 2 /2 7 1 5 : 5 6

2 0 1 7 /0 2 /2 7 1 5 : 5 6
20
01
17
7 /0
/0 2
2 /2
/2 7
7 1
15
5 :: 5
56
6
2

y
159

List of related review papers
Exotic heavy hadrons

・ The new heavy mesons: A status report:
E. S. Swanson, Phys. Rep. 429, 243 (2006)
・ Charmonium:
M. B. Voloshin, Prog. Part. Nucl. Phys. 61, 455 (2008)
・ Heavy quarkonium: progress, puzzles, and opportunities:
N. Brambilla et al., Eur. Phys. J. C71, 1534 (2011)
・ QCD and strongly coupled gauge theories: challenges and future perspectives:
N. Brambilla et al., Eur. Phys. J. C74, 2981 (2014)
・ The hidden charm pentaquark and tetraquark states:
H.-X Chen, W. Chen, X. Liu, S.-L. Zhu, Phys. Rep. 639, 1 (2016)
・ Exotic hadrons with heavy flavors: X, Y, Z, and related states:
A. Hosaka, T. Iijima, K. Miyabayashi, Y. Sakai, S. Yasui, PTEP 2016, 062C01 (2016)
・ Heavy-Quark QCD Exotica:
R. F. Lebed, R. E. Mitchel, E. S. Swanson, Prog. Part. Nucl. Phys. 93, 143 (2017)
・ Multiquark resonances:
A. Esposito, A. Pilloni, A. D. Plolsa, Phys. Rep. 668, 1 (2017)
・ Exotics: Heavy pentaquarks and tetraquarks:
A. Ali, J. S. Lange, S. Stone, Prog. Part. Nucl. Phys. 97, 123 (2017)
・ Nonstandard heavy mesons and baryons: Experimental evidence:
S.L. Olsen, T. Skwamick, D. Zieminska, Rev. Mod. Phys. 90, 015003 (2018)
・ Hadronic molecules:
F.-G. Guo, C. Hanhart, U.-G. Meissner, Q. Qang, Q. Zhao, B.-S. Zou, Rev. Mod. Phys. 90, 015004 (2018)
・ Pentaquark and Tetraquark States:
Y.-R. Liu, H.-Z. Chen, W. Chen, Prog. Part. Nucl. Phys. 107, 237 (2019)
・ The XYZ states: experimental and theoretical status and perspectives:
N. Brambilla, et al., Phys. Rep. 873 (2020) 1
・ Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners:
160
Y. Yamaguchi, et al., J. Phys. G: Nucl. Part. Phys. 47 (2020) 053001

List of related review papers
Exotic hadrons from heavy ion collisions

・ Exotic hadrons from heavy ion collisions:S. Cho et al. [ExHIC collaboration], Prog. Part. Nucl. Phys. 95, 279 (2017)

Heavy hadrons in nuclear matter・ Heavy hadrons in nuclear matter:
A. Hosaka, T. Hyodo, K. Sudoh, Y. Yamaguchi, S. Yasui, Prog. Part. Nucl. Phys. 96, 88 (2017)
・ Nuclear-bound quarkonia and heavy-flavor hadrons:
G. Krein, A.W. Thomas, K. Tushima,, Prog. Part. Nucl. Phys. 100, 161 (2018)161

Recommended text books (hadron phenomenology)162

Do you have questions?

163