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

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

2

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

33. Heavy exotic hadrons -X, Y, Z hadronsCharm/bottom exotic hadrons

T
P
cc
c
Y
XZ
4

3. Heavy exotic hadrons -X, Y, Z hadrons-53. Heavy exotic hadrons -X, Y, Z hadrons-

Exotic Hadrons

cc
u
d

(
)
D*

Compact multiquark

gluonic excitation modescc “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
¯(∗)

7

3. Heavy exotic hadrons -X, Y, Z hadronsCharm
TetraquarkX(3872)Y(4230) aka Y(4260)

Zc(4430)+
X(4140)X(4274)X(4500)X(4700)Zc(3900)+

Zc(4200)+

Zc(4020)+

Zc(4050)+
Zc(4250)+

Pc(4338) Pcs(4338)
Pc(4380) Pcs(4455)

Pc(4450) Pcs(4468)

Yb(10860)
Zb(10610)+
Zb(10650)+
BottomTetraquarkX(5568)Multicharm
Tetraquark

Tcc(3880)
Xcc(6900)

Charm
Pentaquark
10

3. Heavy exotic hadrons -X, Y, Z hadrons-

Charm
Tetraquark

11

3. Heavy exotic hadrons -X, Y, Z hadrons-X(3872)12

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
S. K. Choi et al. [Belle Collaboration], Phys. Rev. Lett. 91, 262001 (2003)> 2600 citations

13

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
198

X(3872)→J/ψπ+π- seen in different reactions
16 M ultiquark Statesa) Choi,
S.-K., et al.:
262001
Fig. 16.4 Observation of theX (3872)→ Phys.
J / ψRev.
π +Lett.
π−91,
; (a)
by (2003)
Belle in B + → K + J / ψ π+ π−b) Acosta,−D., et al.: Phys. Rev. Lett. 93, 072001 (2004)(including the charge conjugatedB decay) [11]; (b) by CDF, the strong peak at 3686 M eV stemsc) Chatrchyan, S., et al.: JHEP 04, 154 (2013)
from the ψ(2S), the bottomCf.distributionshows
the wrongchargecombinations
J / ψ π±π ± [12];Amsler, "The Quark
Structuresof Hadrons",
Springer(2018)(c) by CM S, the top blue curve is the ﬁ t, the bottom dotted red curve is the background subtracted
14
signal (enhanced in the inset) [13]

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Mass of X(3872) is very close to DD*bar threshold.

Observed 2P state

𝜒𝑐0 ′(3860)

𝜒𝑐2 ′(3930)

𝜒𝑐0 ′

Note:
𝜒𝑐1 ′ 2P and ℎ𝑐′ 2P not
observed yet

15

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Mass of X(3872) is very close to DD*bar threshold.

Observed 2P state

𝜒𝑐0 ′(3860)

𝜒𝑐2 ′(3930)
Note:𝜒𝑐1 ′ 2P and ℎ𝑐′ 2P not
observed yet𝜒𝑐0 ′D+D*-(D-D*+) 3879.84±0.14 MeV

isospinX(3872) 3871.65±0.06 MeV symmetry
breaking

D0D*0bar

3871.68±0.10 MeV

Note: the X(3872) mass observed in DD* channel
seems slightly heavier than the mass in J/ψππ channel.

16

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
What is quantum number (JPC)？
V. Bhardwaj et al. [Belle], Phys. Rev. Lett. 107, 091803 (2011)(Cf. B. Aubert et al. [BaBar], Phys. Rev. Lett. 102, 132001 (2009))① photon decay

C=-1

C=-1

X(3872) C=+1
No signature for C=-1: J/ψη(PTEP2014,
043C01 (2014)) and χc1(2P) (PRL111, 032001 (2013))② angular distribution of decay products
A. Abulencia et al. [CDF], Phys. Rev. Lett. 98, 132002 (2007)
B. S.-K. Choi et al. [Belle], Phys. Rev. D 84, 052004 (2011)
R. Aaij et al. [LHCb], Phys. Rev. Lett. 110, 222001 (2013)→
P. del Amo Sanchez et al. [BaBar], Phys. Rev. D 82, 011101 (2010)→
17
X(3872) JPC=1++ or 2-+
JPC=1++

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
L. Maiani, F. Piccinini, A. D. Polosa,
V. Riquer, Phys. Rev. D 71,
Tetrquark interpretation and014028 (2005)① Isospin symmetry breaking → particle eigenstates (isospin sym. discarded)

If isospin eigenstate exists…
I=0

I=1

② Mixing of uubar and ddbar via gluon exchange (interaction strength 𝛿)𝑞

Hamiltonian:③ Eigenstates of Hamiltonian: two states appear

𝑞ത

𝑞′

gluon

𝑞ത ′

𝛿: flavor-blind coupling(same for 𝑢𝑢ത and 𝑑 𝑑)ҧ

mass difference:18

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Tetrquark interpretation
Searching two states in B decays (by experiments)(Replacing u and d)mass difference
B. Aubert et al. [BaBar], Phys. Rev. D 77, 111101 (2008)

S.-K. Choi et al. [Belle], Phys. Rev. D 84, 052004 (2011)

No mass difference → Inconsistent with tetraquark...
Charged state？
(？) No signature in experiments.
S.-K. Choi et al. [Belle], Phys. Rev. D 84, 052004 (2011)19

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Dominance of D0D*0bar component？
X(3872)?

Excess at D0D*0bar threshold was found.
≈ 10×
Branching fraction B(channel):
T. Aushev et al. [Belle], Phys. Rev. D 81, 031103 (2010)
the ration of the decay width by the specific (cf. B. Aubert et al. [BaBar], Phys. Rev. D 77, 01110220(2008))
channel against the total decay width3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
D0D*0bar molecule interpretation
D+D*-(D-D*+) 3879.84±0.14 MeV

isospinsymmetry
X(3872) 3871.65±0.06 MeV breaking

D0D*0bar

3871.68±0.10 MeV

The energy from threshold is less than 0.1 MeV...

inter-distance ≥ 10 fm!

0
D

0
D*

208Pb

21
Such fragile particle must be difficult to be produced in ppbar collisions...

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Likely NOT a simple D0D*0bar molecule... What is this?
R. Aaij et al. [LHCb], Phys. Rev. Lett.
110, 222001 (2013)

Hint: absence of χc1(2P)

Observed by Belle, Phys. Rev.
Lett. 96, 082003 (2006)

DD*barDDbar?
χc0(2P) =χc0(3915)
Observed by Belle, Phys. Rev.
Lett. 104, 092001 (2010)

Under the debates:
・ Suppression in decay
to DDbar in experiments
・ccbarssbar tetraquark？

No observation of χc1(2P)

Is X(3872) mixed withχc1(2P) ?
DD*bar (S-wave) can easily
couple to χc1(1++).
V(r)centrifugal potential
L(L+1)/2μr2r
S-waveno centrifugal force223. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Admixture of D0D*0bar molecule and χc1(2P)

Eichiten et al., PRD73,014014(2006); A. M. Badalian et al., PRD85,031103(2012)
Model setting (simple!) E.M.J.Takizawa
and S. Takeuchi, Prog. Theor. Exp. Phys. 2013, 093D01 (2013)① Wave function as a superposition② Coupling between D0D*0bar (D+D*-) and χc1(2P): DD*bar ⇄ χc1(2P)③ Hamiltonian (3×3 matrix)

g: coupling constant
Λ: momentum cutoff

Parameter set: 0.3 GeV ≤ Λ ≤ 1.0 GeV (g is fixed to reproduce 3872 MeV mass.)23

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Admixture of D0D*0bar molecule and χc1(2P)

Result① Components in wave function

M. Takizawa and S. Takeuchi,
Prog. Theor. Exp. Phys.
2013, 093D01 (2013)[GeV]

D0D*0bar
D+D*c1,2,3 do not depend strongly in cutoff Λ.

1/Λ

0
D

D0

“shallow state”

0D*

0
D * “deep state”

24

3. Heavy exotic hadrons -X, Y, Z hadronsX(3872)
Admixture of D0D*0bar molecule and χc1(2P)

Result
Where is this χc1(2P)?
② Spectrum

M. Takizawa and S. Takeuchi,
Prog. Theor. Exp. Phys.
2013, 093D01 (2013)

Spectral function of X(3872)“χc1(2P)” exists
as a broad peak.

X(3872)bound state + cusp“χc1(2P)”
This explains naturally
no confirmation ofχc1(2P) in experiments.
25

mass

= 2.46 ±0.64(stat) ±0.29(sys) (4.4σ)(LHCb[7]).
3. Heavy exotic
hadrons -X, Y, Z hadronsX(3872)
The data from these three experiments seem not to be inconsistent, though BaBar and LHCb preferaX(3872)larger value whereas Belle prefers a smaller one. It is important to investigate the above
ratio in orderψ(2S)𝛾
to understand the nature of theRadiative
X(3872), the most decay
well-investigated exotic meson. The theoretical𝛾

works have been done with an assumption that the X(3872) is a bound state [8–11]. InJ/ψ
this work, we
Branchingratios (Rγ):
X(3872)→ψ(2S)γ, J/ψγ
study the radiative decays of the X(3872) with the above hybrid model. Our approach here-- enables++us
1
Aubertspectrum
et al. [BaBar],to deal with the X(3872) as a resonance and to produce theB. massof J/ψγ and ψ(2S)γ. 1
Phys. Rev. Lett. 102, 132001 (2009)

2. ModelV. Bhardwaj et al. [Belle],
Phys. Rev. Lett. 107, 091803 (2011)∗0+ ∗−In the present model, the X(3872) consists of D0 D , D D , J/ψω, J/ψρ, and the cc(1P) (χc1 (1P))
R. Aaij et al. [LHCb], Nucl. Phys.
and cc(2P) components. The radiative decay can occur from each of thesecomponents. Here we
B886, 665 (2014)
assume that the decay occurs only from the cc(nP) components and neglect the other ones as a ﬁrst
step [8].suggest
The present results, especially the absolute values, may change when the decay from theThosetwo-meson components are included. We, however, consider that the characteristic feature found in
B(X(3872)→ψ(2S)γ)
3 × B(X(3872)→J/ψγ)
the decay energy spectrum
will probably remain≈unchanged
if the other decay modes are included.
The the E1 transition from the cc components in the bound X(3872) to the ﬁnal ψ, which stands
for J/ψ or ψ(2S ), can be written as
S. Takeuchi, M. Takizawa, K. Shimizu,
X(3872)=χc1(1P)+χc1(2P)+D0D*0bar+D+/-D*-/+bar
arXiv:1602.04297[hep-ph]Table II. The probabilityof the cc componentsintheX(3872),the radiative decay
width Γ in keV, and3Eω24γ ψ A01, and A10.
2 set, A00,
ratio RΓγ are
shown
for
each
parameterX(3872) → ψ + γ = |Qc | α
Zcc(1P) ⟨ψ| r |cc(1P)⟩ + Zcc(2P) ⟨ψ| r |cc(2P)⟩
(3)
9
MX
model

gcc(1P)−DD

2
Zcc(1P)2
Zcc(2P)Γ(X → J/ψ)

Γ(X →ψ(2S ))R

R (spectrum)γγ
where Qc is the electric charge of the charm quark, α is the ﬁne-structure constant,ωγ and Eγ is the
2
A00
0
0
0.036
0.6
2.1
3.6
3.4
energy of the ﬁnal γ and ψ, respectively, MX is the X(3872) mass, Zcc(nP) is the probabilityof each1
A01component
0.001 0.036
1.1
2.0
1.8
1.9
10 gcc(2P)−DD
cc(nP)
in the X(3872).
26
A10−gcc(2P)−DD
0.011 ⟨ψ|r|cc(nP)⟩
0.060
1.0 model1.1wave function
The transfer
matrix elementis 6.1
calculated by 6.2
using the quark3. Heavy exotic hadrons -X, Y, Z hadrons-ψ(4230)aka Y(4260)
27

3. Heavy exotic hadrons -X, Y, Z hadronswas searching X(3872)
ψ(4230) aka Y(4260) BaBarin 1 . They did not find--

too many ψ’?

4S establishedX(3872), but found Y(4260).

energy scan

← new state between
ψ(3S) and ψ(4S)

3S established
2S

B. Aubert et al. [BaBar], Phys. Rev. Lett. 95, 142001 (2005)
C. Z. Yuan et al. [Belle], Phys. Rev. Lett. 99, 182004 (2007)
Z. Q. Liu et al. [Belle], Phys. Rev. Lett. 110, 252002 (2013)

π+ π Y(4260)

1S28

3. Heavy exotic hadrons -X, Y, Z hadronswas searching X(3872)
ψ(4230) aka Y(4260) BaBarin 1 . They did not find--

too many ψ’?

4S established← new state between
ψ(3S) and ψ(4S)

X(3872), but found Y(4260).

energy scan

3S established2Sπ+ π -1S

B. Aubert et al. [BaBar], Phys. Rev. Lett. 95, 142001 (2005)
C. Z. Yuan et al. [Belle], Phys. Rev. Lett. 99, 182004 (2007)
Z. Q. Liu et al. [Belle], Phys. Rev. Lett. 110, 252002 (2013)
M. Abikim et al. (BESSIII), Phys. Rev. Lett. 118, 092001 (2017)

Higher statistics(1) Asymmetry in the cross section(2) Shift-position of the peak mass to
the lower: ψ(4230)

29

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
mystery of decay patterns
Y(4260) should decay to DDbar, but...

However, this decay
is not observed...

?DDbar“Fall-apart process”

Seeming contradictory…

Note: ψ’’(3770) (JPC=1--), whosemass is slightly above DDbar,
decays to DDbar dominantly (B.R.
93% !) rather than to J/ψπ+π-.

30

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
mystery of decay patterns
Y(4260) can decay to DDbar, but...
There is no decay from Y(4260) to DDbar.

=Y(4260)

From Olsen et al. Rev. Mod. Phys. 90, 015003 (2018)
Original figure: BESS, Phys. Rev. Lett. 88, 101802 (2002)31

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
Hybrid state???
F. E. Close and P. R. Page, 2005, Phys. Lett. B 628, 215 (2005)
E. Kou and O. Pene, 2005, Phys. Lett. B 631, 164 (2005)
S.-L. Zhu, 2005, Phys. Lett. B 625, 212 (2005)

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

ccg hybrid
Gluons appear as dynamical d.o.f.
Candidate observed in lattice calculations:
Liu, L., G. Moir, M. Peardon, S. M. Ryan, C. E. Thomas, P. Vilaseca, J. J. Dudek, R. G.
Edwards, B. Joo, and D. G. Richards (Hadron Spectrum), 2012, J. High Energy Phys. 07 126

32

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
Hybrid state???
QQbar potential

J. Kuti, Nucl. Phys. B Proc. Suppl. 73, 72 (1999)

D u,
9 P
u
+
8 Su
7 Sg
6 Dg
5 Pg

10

10

c

,
+
Sg
3 Su

r0 [ EG (r) - E S+g (r0)]

4

2

5

10
9
8
6

c

Pu

7

5 4
3
2

-

Pu

10

7
9

0

1

V(r)

8

4

5

Wilson (small-a)

1

4

N=

3

N=

2

2

perturbation
theory

-5
0

N=

3

6

+
Sg

separations less thanclusion does not con
gluonic excitation modes
ground state energy
as 0.5 fm . A linearly
ily indicative of a str
exam ples. For r Q Q“stringsom
excitation”
e tantalizing sig
Σ, Π, Δ, Φ, ...
yet signi(S,form
P, D, F,ation,...)m ain. To what degr
explained in term s om ode
spectrum aris
conventionalmodes
rotation of the quark and anfect) is currently un
For reasons expla
principal
and number
reserved onrep
33
son loops in lower diN

2r/(2r 0)

3

=1

Sg
+
Su
Du
,
Pu
Su
Dg
,
+
Sg

c

Pg
Pu

4

c

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
Hybrid state???
QQbar potential K. J. Juge, J. Kuti, C. Morningstar, Phys. Rev. Lett. 16, 161601 (2003)(Cf. G. S. Bali, A. Pineda, Phys. Rev. D 69, 094001 (2004))

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

conventional modes
rotationccprincipal number34

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
Hybrid state???
gluon-excited 𝒄ത𝒄 potential

K.J. Juge, J. Kuti, C.J. Morningstar,Phys. Rev. Lett. 82, 4400 (1999)

mass spectracchybrid states!
Hybridinter-quark potentials

wave functions

𝒄ത𝒄 wave function in
hybrid states!

36

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
Hybrid state???
M. Berwein, N. Brambilla, J.T. Castela, A. Vairo, Phys. Rev. D92, 114019 (2015)

ExperimentY(4260)

Theoretical results→ 𝜒𝑐1 (4140)→ ψ(4160)→ ψ(4360)→ ψ(4660)

See for early applications to Y(4260):: Suppression to DDbar decay (?)
F. E. Close and P. R. Page, Phys. Lett. B 628, 215 (2005)
E. Kou and O. Pene, Phys. Lett. B 631, 164 (2005)
Cf. review: C. A. Meyer, E. S. Swanson, Prog. Part. Nucl. Phys. 82, 21 (2015)37

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
No single Breit-Wigner shape (reanalysis by higher statistics)
BESIII, Phys. Rev. Lett. 118, 092001 (2017)

BESIII, Phys. Rev. Lett. 118, 092002 (2017)

Newest “Y(4260)” up to date“Y(4260)”
Olsen et al. Rev. Mod. Phys. 90, 015003 (2018)“Y(4360)”
38

3. Heavy exotic hadrons -X, Y, Z hadronsψ(4230) aka Y(4260)
Lattice QCD (𝑚𝜋 ≈ 400 MeV)

Liu et al. JHEP07(2012)125

Hybrid (4285)

JPC exotic
1-+

c
c

JPC exotic
0+-, 2+-

Exp.
Charmonium

HybridHybrid (ground state)
Hybrid (excited state)𝑀𝜂𝑐 = 2984 MeV

Mass of the hybrid (4285) seems consistent
with 𝝍(𝟒𝟐𝟑𝟎) aka 𝝍(𝟒𝟐𝟔𝟎)!
→ We should explore the other hybrids including JPC exotics!!

39

Lattice computation of light meson spectrum@mπ=392 MeVHybridHybridHybridHybrids

JPC exotic

1-+, 0+-, 2+scalar mesons
𝒇𝟎 (𝟗𝟖𝟎), 𝒂𝟎 (𝟗𝟖𝟎), …
𝜔JPC

red: compatible with qqbar assignment
blue: hybrids (qqbar+gluon excitation)

𝜋

J.J. Dudek, R.G. Edwards, P. Guo, C.E. Thomas, Phys. Rev. D 88, 094505 (2013)
Cf. M.R. Stephaerd, J.J. Dudeck, R E. Mirchell, Nat. Phys. 534, 487 (2016)40

3. Heavy exotic hadrons -X, Y, Z hadrons-+
Zc(4430)

41

3. Heavy exotic hadrons -X, Y, Z hadronsZc(4430)+
Charged charmonium

First observation of genuinely “four-quark”

cc
u
d

cc

Charged (+)

Charge neutral

Four quarks at least

Note: ccbar should be contained, because the final state of Zc(4430) includes a charmonum.

42

3. Heavy exotic hadrons -X, Y, Z hadronsZc(4430)+
S. K. Choi et al. [Belle],
Charged charmonium

Phys. Rev. Lett. 100, 142001 (2008)
B. Aubert et al. [BaBar],
Phys. Rev. D 79, 112001 (2009)ccudCharged (+)

Zc(4430)+

What is the quantum number (JP)?
K. Chilikin et al. [Belle], Phys. Rev. D 88, 074026 (2013)
R. Aaij et al. [LHCb], Phys. Rev. Lett. 112, 222002 (2014)

JP = 0-, 1+, 1-, 2+43

3. Heavy exotic hadrons -X, Y, Z hadronsZc(4430)+
Does this peak really indicate a resonance?
Argand plot (ψ’π+)

R. Aaij et al. [LHCb],
Phys. Rev. Lett. 112, 222002 (2014)

Yes, this is consistent to be a resonance!!
(Necessary condition for being a resonance: If resonance, then circle in Argand plot.)44

3. Heavy exotic hadrons -X, Y, Z hadronsZc(4430)+
Does this peal really indicate a resonance?

Klaus Peters (GSI)
Argand plot (review) Slide byCharm2006

Introducing Partial Waves
Klaus Peters - PWA Primer• Schrödinger‘s Equation

Angular Amplitude: scattering wave
Dynamic Amplitude
1845

3. Heavy exotic hadrons -X, Y, Z hadronsAngular Amplitude+
Zc(4430)
Does this peal really indicate a resonance?

Klaus Peters (GSI)
Argand plot (review) Slide byCharm2006

Dynamic Amplitude

Standard Breit-Wigner

Klaus Peters - PWA Primer

18• Full circle in the

Argand PlotIntensity I=ΨΨ*

Phase δSpeed dφ/dm

Argand Plot

• Phase motion
from 0 to πδ=π/2

Resonance

21

46

3. Heavy exotic hadrons -X, Y, Z hadronsOther charged states: Zc(4200)+, Zc(4050)+, Zc(4250)+
LHCb, Phys. Rev. Lett. 112, 222002 (2014)

LHCb, Phys. Rev. D 92, 112009 (2015)

Belle, Phys. Rev. D 78, 072004 (2008)

Argand's plot for Zc(4200)
Belle, Phys. Rev. D 90, 112009 (2014)
Cf. Olsen et al. Rev. Mod. Phys. 90, 015003 (2018)

What exactly are they？
47

3. Heavy exotic hadrons -X, Y, Z hadrons-+
Zc(3900)48

3. Heavy exotic hadrons -X, Y, Z hadronsZc(3900)+
Z. Q. Liu et al. [Belle],
Charged charmoniumccudPhys. Rev. Lett. 110, 252002 (2013)
Cf. M. Ablikim et al. [BESSIII],
Phys. Rev. Lett. 110, 252001 (2013)

Zc(3900)+

Chargedcc
Charge neutral49

3. Heavy exotic hadrons -X, Y, Z hadronsZc(3900)+
Charged charmonium

BESIII, Phys. Rev. Lett. 112, 022001 (2014)

JP=1+

Neutral partner: Zc(3900)0cc
cc
cc
ud uu+dd duZc(3900)+

Zc(3900)０

Zc(3900)-

BESIII, Phys. Rev. Lett. 115, 112003 (2015)

BESIII, Phys. Rev. Lett. 115, 112002 (2015)↪︎Cf. Olsen et al. Rev. Mod. Phys. 90, 015003 (2018) 50

3. Heavy exotic hadrons -X, Y, Z hadronsrelated state: Zc(4020)+
Charged charmonium

BESIII, PRL111, 242001 (2013)

BESIII, PRL113, 212002 (2014)

BESIII, PRL112, 132001 (2014)

Bottom version

Zc(3900)+
Zc(4020)+

paired states？
(See next page.)Zb(10610)+
Zb(10650)+
We will discuss Zb’s in detail later.

Cf. Olsen et al. Rev. Mod. Phys. 90, 015003 (2018)51

3. Heavy exotic hadrons -X, Y, Z hadronsBrief summary of charged Zc’s

Zc(3900)+~DD*
Zc(4020)+~D*D*
Their masses are close to the D(*)D* thresholds.
Does this suggest the hadronic molecules？
52
From Olsen et al. Rev. Mod. Phys. 90, 015003 (2018)

3. Heavy exotic hadrons -X, Y, Z hadronsZc(3900)+
Lattice QCD

S. Prelovsek and L. Leskovec, Phys. Lett. B 727, 172 (2013)
S. Prelovsek, C. B. Lang, L. Leskovec, and D. Mohler, Phys. Rev. D 91, 014504 (2015)
Y. Chen et al., Phys. Rev. D 89, 094506 (2014)
Y. Ikeda et al., Phys. Rev. Lett. 117, 242001 (2016)ccu

DD*bar scatteringdρηc scattering
π J/ψ scattering53

3. Heavy exotic hadrons -X, Y, Z hadronsZc(3900)+
Lattice QCD

S. Prelovsek and L. Leskovec, Phys. Lett. B 727, 172 (2013)
S. Prelovsek, C. B. Lang, L. Leskovec, and D. Mohler, Phys. Rev. D 91, 014504 (2015)
Y. Chen et al., Phys. Rev. D 89, 094506 (2014)
Y. Ikeda et al., Phys. Rev. Lett. 117, 242001 (2016)“HAL QCD” method

N. Ishii, S. Aoki, and T. Hatsuda, Phys. Rev. Lett. 99, 022001 (2007)
S. Aoki, T. Hatsuda, and N. Ishii, Prog. Theor. Phys. 123, 89 (2010)① Calculate Nambu-Bethe-Salpeter wave function(correlation function)

hadron basis② Schrödinger equation (inverse problem)

inter-hadron potential 54

3. Heavy exotic hadrons -X, Y, Z hadronsZc(3900)+
Lattice QCD

Y. Ikeda et al., Phys. Rev. Lett. 117, 242001 (2016)→

Correct
thresholds

55

3. Heavy exotic hadrons -X, Y, Z hadronsZc(3900)+
Lattice QCD

Y. Ikeda et al., Phys. Rev. Lett. 117, 242001 (2016)

Strongest potential in c quark
exchange→ Not a simple DD*bar molecule

strongstrong56

3. Heavy exotic hadrons -X, Y, Z hadronsY. Ikeda et al.,Zc(3900)+
Phys. Rev. Lett. 117, 242001 (2016)

How about Zc(4020)+?
(possible partner)

Lattice QCD

J/ψπ→J/ψπ

DD*bar→DD*bar
ρηc→ρηcVery far from real axis....

Bump (cusp effect)57

3. Heavy exotic hadrons -X, Y, Z hadrons-

BottomTetraquark58

3. Heavy exotic hadrons -X, Y, Z hadronsBelle can search Υ(5S)
Belle’s main search:
Υ(4S) as BBbar factory59

3. Heavy exotic hadrons -X, Y, Z hadrons-

Yb(10860)
60

3. Heavy exotic hadrons -X, Y, Z hadronsYb(10860)
K.-F. Chen et al. [Belle],
Analogue of Y(4260)?
JP=1--

4416cc
D*D*barHybrid4040
4020

DD*bar

3880

DDbar

3740
3686

ccbar

11020

ψ(4S) 1319
Y(4260)ψ(3S) 943
923
783
643

ψ(2S) 589

Charmonium
3097

Phys. Rev. D 82, 091106 (2010)

J/ψ(1S)B*B*barBB*barBBbar

Υ(6S) 1560

“Υ(5S)” aka
Yb (10860)

10650
10604
10579
10558

Υ(4S)

1190
1144
1119
1098

10355

Υ(3S)

895

1. Above BBbar threshold?
2. Between Υ(nS) and Υ((n+1)S)?
10023

Υ(2S)

563

Bottomonium
0

9460

bbbar

Υ(1S) 610

3. Heavy exotic hadrons -X, Y, Z hadronsYb(10860)
Analogue of Y(4260)?

← Why is Y(5S) not just in the middle of Y(4S) and Y(6S)？

But Yb(10860) decays to BBbar (B.R.76%)
unlike Y(4260).

From Olsen et al. Rev. Mod. Phys. 90, 015003 (2018)62

3. Heavy exotic hadrons -X, Y, Z hadronsYb(10860)
K.-F. Chen et al. [Belle],
Analogue of Y(4260)?

Phys. Rev. D 82, 091106 (2010)

σ0: e+e-→μ+μ-← Why is Y(2S)ππ enhanced？
(Is Y(5S) not a simple bbbar?

Yb

Decays from Y(5S)← Enhanced
There should be some other components
except for bbbar (hybrid, or mixture with bbbar？)
Note: Yb(10860) decays to BBbar in contrast toY(4260).
63

3. Heavy exotic hadrons -X, Y, Z hadronshb(2P)
by-product...

I. Adachi et al. [Belle],
Phys. Rev. Lett. 108, 032001 (2012)(accidental) first discovery of hb(2P)64

3. Heavy exotic hadrons -X, Y, Z hadrons-+
Zb(10610)+
Zb(10650)
65

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
Charged bottomonium

Zb(10610)+

A. Bondar et al. [Belle],
Phys. Rev. Lett. 108, 122001 (2012)

Zb(10610)+
Zb(10650)+
Zb(10650)+

Zb(10610)+
Zb(10650)+

JP=1+ favored
JP=2+ unfavored66

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
Charged bottomonium

A. Bondar et al. [Belle],
Phys. Rev. Lett. 108, 122001 (2012)

Zb(10650)+
Zb(10610)+

Zb(10650)+
Zb(10610)+

67

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
Charged bottomonium

A. Bondar et al. [Belle],
Phys. Rev. Lett. 108, 122001 (2012)

summary table68

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
Charged bottomonium

B*B*bar10650

A. Bondar et al. [Belle],
Phys. Rev. Lett. 108, 122001 (2012)

Zb(10650)+

1- 1-① Isospin partner? Zb0② BB*bar, B*B*bar molecule?

BB*bar10604

Zb(10610)+

0- 1-

BBbar
0- 0-

10558

JP=1+

69

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
Charged bottomonium

P. Krokovny et al. [Belle],
Phys. Rev. D 88, 052016 (2013)① Isospin partner? Zb0
Zb(10610)0
Zb(10610)0

Zb(10610)0

C-parity of Zb(10610)0: C=-1 (ψ(JPC=1--)&π0(JPC=0-+))Zb(10610)0 was discovered, but Zb(10650)0 could not be seen due to low statistics...
70

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+

I. Adachi et al., [Belle],
arXiv:1209.6450 [hep-ex]

Charged bottomonium

Zb(10610)+② BB*bar, B*B*bar molecule?
Zb(10650)+
Zb(10650)+

Zb(10610)+ and Zb(10650)+ seem to contain much component of BB*bar and B*B*bar.

71

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
Charged bottomonium

I. Adachi et al., [Belle],
arXiv:1209.6450 [hep-ex]② BB*bar, B*B*bar molecule?
branching fraction %Zb(10610)+ and Zb(10650)+ seem to contain much component of BB*bar and B*B*bar.

→ Molecule picture?
72

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

Though Zb(10610)+ and Zb(10650)+ may not be simple hadronic molecules,
this picture provides us with a good starting point to under stand those properties.

Hint from experiments:
Are there equal weights for S=1 and S=0？

Br[Zb→Υπ] ≈ Br[Zb→hbπ]
QQbar spins

If Zb are B*B*bar and BB*bar molecules (QqbarQbarq),
QQbar

qqbar

heavy quark spins 1 and 0 should exist with same fraction!
A. E. Bondar, A. Garmash, A. I. Milstein, R. Mizuk, M. B. Voloshin, Phys. Rev. D 84, 054010 (2011)73

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation
Many papers…
A. E. Bondar, A. Garmash, A. I. Milstein, R. Mizuk, and M. B. Voloshin, Phys. Rev. D 84, 054010 (2011)
T. Mehen and J. W. Powell, Phys. Rev. D 84, 114013 (2011)
M. Cleven, F.-K. Guo, C. Hanhart, and U.-G. Meissner, Eur. Phys. J. A 47, 120 (2011)
J.-R. Zhang, M. Zhong, and M.-Q. Huang, Phys. Lett. B 704, 312 (2011)
D. V. Bugg, Europhys. Lett. 96, 11002 (2011)
J. Nieves and M. Pavon Valderrama, Phys. Rev. D 84, 056015 (2011)
Z.-F. Sun, J. He, X. Liu, Z.-G. Luo, and S.-L. Zhu, Phys. Rev. D 84, 054002 (2011)
M. B. Voloshin, Phys. Rev. D 84, 031502 (2011)
S. Ohkoda, Y. Yamaguchi, S. Yasui, K. Sudoh, and A. Hosaka, Phys. Rev. D 86, 014004 (2012)
Y. Yang, J. Ping, C. Deng, and H.-S. Zong, J. Phys. G 39, 105001 (2012)
C.-Y. Cui, Y.-L. Liu, and M.-Q. Huang, Phys. Rev. D 85, 074014 (2012)
S. Ohkoda, Y. Yamaguchi, S. Yasui, and A. Hosaka, Phys. Rev. D 86, 117502 (2012)
Y. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, J. Phys. G 40, 015002 (2013)
Z.-G. Wang, Eur. Phys. J. C 74, 2963 (2014)
Z.-G. Wang and T. Huang, Eur. Phys. J. C 74, 2891 (2014)
Z.-G. Wang and T. Huang, Nucl. Phys. A 930, 63 (2014)
S. Ohkoda, S. Yasui, and A. Hosaka, Phys. Rev. D 89, 074029 (2014)
J. M. Dias, F. Aceti, and E. Oset, Phys. Rev. D 91, 076001 (2015)... and more74

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

B*

B*

B*

10650 MeV

B
10604 MeV

same mass

B

B*
10604 MeV

B

B
10558 MeV75

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
mass

hadronic molecule interpretation

B

B
10558 MeV

76

threshold3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

mass

B

B* ± B*
10604 MeV

B

B
threshold

B10558 MeV

77

threshold3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

mass

B*

B*
10650 MeV

B

thresholdB* ± B*
10604 MeV

B

B
threshold

B10558 MeV

78

threshold3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation
Classification of B(*)B(*)bar states

S. Ohkoda, et al.,Phys. Rev. D86, 014004 (2012)

C-parity is defined only for Iz=0 (I=1)

79

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+

iφ

θ−

1
2

hadronic molecule interpretationosθei φe2i φC-parity of B(*)B(*)bar-1bar
CBC =B-1bar
CB*C =B*① BBbar: CBBbarC-1 = (CBC-1)(CBbarC-1) = BbarB = BBbar② BB*bar±B*Bbar:
C(BB*bar±B*Bbar)C-1= (CBC-1)(CB*barC-1)±(CB*C-1)(CBbarC-1)= BbarB*±B*bar(B)= ±(BB*bar±B*Bbar)③ B*B*bar: C(B*B*bar)S=0,1,2C-1= (-1)S B*B*barm e− i m φ

J = 0,1,2= (−1) J − j 1 − j 2 ⟨j 2 j 1 m 2 m 1 |j 2 j 1 JM ⟩ j1, j2 = 1⟨j 1 j 2 m 1 m 2 |j 1 j 2 JM ⟩80

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

JPC=1+-, I=1 from experiments

BBbar
0- 0-

spinP

angularmomentumJP

C-parity

0+

Swave

0+

+1

BB*bar±B*Bbar 1+
0- 11+
minus

Swave 1+
Dwave 1+,2+,3+±1 ✔

B*B*bar

0+

Swave

0+

+1

1+

Swave

1+

-1

✔

1+

Dwave

1+,2+,3+

-1

✔

2+

Swave

2+

+1

2+

Dwave

0+,1+,2+,3+,4+

+1

1-

1-

±1 ✔

81

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

If JPC=1++, I=1 …
BBbar
0- 0-

spinP

angularmomentumJP

C-parity

0+

Swave

0+

+1

BB*bar±B*Bbar 1+
0- 1plus
1+

Swave 1+
Dwave 1+,2+,3+±1 ✔

B*B*bar

0+

Swave

0+

+1

1+

Swave

1+

-1

1+

Dwave

1+,2+,3+

-1

2+

Swave

2+

+1

2+

Dwave

0+,1+,2+,3+,4+

+1 ✔

1-

1-

±1 ✔

82

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation
Classification of B(*)B(*)bar states

S. Ohkoda, et al.,Phys. Rev. D86, 014004 (2012)

C-parity is defined only for Iz=0 (I=1)

83

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation
The Schrödinger equation

light mesonexchange

B(*)

S. Ohkoda, et al.,Phys. Rev. D86, 014004 (2012)

B(*)

JPC=1+-,I=1

Ki : kinetic term, Vij : potential term (i,j=1,2,3,4)

What is the potential component Vij?
(light meson exchange potentials)

84

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

π, ω, ρ meson exchange potentials

S. Ohkoda, et al.,Phys. Rev. D86, 014004 (2012)π, ω, ρ

B*

B*

B*

- B*

π, ω, ρBπ, ω, ρB

What are the π, ω, ρ potentials？
85

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

HQS + chiral symmetry863. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation

central potential

tensor potential

HQS + chiral symmetry87

3. Heavy exotic hadrons -X, Y, Z hadronsReview: πB(*)B* coupling from effective theory② Constructing effective Lagrangian (leading order of mQ→∞)chiral covariant derivative:

Non-linear chiral transformation

invariant under HQS
and chiral symmetryNon-linear rep. of π field:

Vector current:

Axial-vector current:(even # of π)(odd # of π)

Example of vertex structure (axial-vector coupling)

B*

time

B

π
B

B*

π

π
B*

We will see details later.

B*88

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

2 questions① Why do we consider BB*bar(B*Bbar) and B*B*bar simultaneously?

BB*bar ± B*Bbar sector

HQS

B*B*bar sector

Answer: Heavy quark spin (HQS) symmetry make them mixed.

89

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

Transformation for heavy quark spin rotation

B meson:B* meson:① BB*bar ± B*Bbar sector:90

② B*B*bar :91

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

2 questions② Why do we consider S-wave and D-wave simultaneously?

BB*bar ± B*Bbar sector

HQS

B*B*bar sector923. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

2 questions② Why do we consider S-wave and D-wave simultaneously?

BB*bar ± B*Bbar sector

HQS

B*B*bar sector

Answer: Tensor potential mixes L and L±2 components.

93

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation
Tensor operator① OPEP for NN:

Tensor:π→N

N

S-wave and D-wave mixing (spin=1)② OPEP for B(*)B(*)bar:
Light spin triplet, S-wave
ExampleLight spin triplet, D-wave

πLight spin triplet, S-wave

Q qbarq Qbar94

(1) BB*bar→B*Bbar

B*

Bbar

(2) B*B*bar→B*B*bar B*π(3) BBbar→B*B*bar

π

B

B*bar

B*

B*bar

(4) BB*bar→B*B*bar

B*

B*bar

B*

B*bar

π
B

B*bar

π
Bbar

B

B*bar

Polarization vector (B*):
Spin 1 operator (B*):
Tensor operator:95

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

Summary table: mixing effects (HQS, tensor potential)
Components
Tensor

HQS

TensorTensorTensorTensor

HQS
Tensor

HQS

TensorTensor

HQS Tensor

TensorTensorTensorCentral potential:
Tensor potential:963. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation① Kinetic term

② OPEP

Tensor potential③ Vector-meson exchange potential973. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretationinteraction
interaction

B*B*barBB*bar10650

scattering
stateinteraction

B*B*barscattering
state

10604

BB*bar
BBbar

10558

scattering
state
BBbar

Solving scattering problem
with multi-channel
983. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

How to solve scattering problem? (review)

k

k

δl

θ

z

π/2

asymptotic state:(phase shift)① Partial wave decomposition

resonance↓kr② Resonance (definition by phase shift)

decay width:

Partial wave
amplitude

Pole ascomplex energy Matching (direct) method: finding δl(k) Complex scaling method: finding Er+iΓ/2

S. Aoyama T. Myo, K. Kato, K. Ikeda,
99
Prog. Theor. Phys. 116, 1 (2006)k

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

How to solve scattering problem? (review)

k

k

δl

θ

z

asymptotic state:(phase shift)

Typical mechanisms of resonances① Centrifugal potential② Feshbach resonanceπ/2resonance

↓

k

kr

③ E-dependent potential1003. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

How to solve scattering problem? (review)

k

k

δl

θ

z

asymptotic state:(phase shift)

Typical mechanisms of resonances① Centrifugal potential② Feshbach resonanceπ/2resonance

↓

k

kr

③ E-dependent potentialV(r)centrifugal potential
L(L+1)/2μr2

Veff(r)

r

V(r)

101

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

How to solve scattering problem? (review)

k

k

δl

θ

z

π/2

asymptotic state:(phase shift)

Typical mechanisms of resonances① Centrifugal potential② Feshbach resonanceV(r)resonance

↓

k

kr

③ E-dependent potential

Energycentrifugal potential
L(L+1)/2μr2

Veff(r)

V(r)

A’+B’

r

quasi-bound state(resonance)

A+B
A+B → A’+B’ → A+B
102

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
JPC=1+-,I=1
hadronic molecule interpretation

How to solve scattering problem? (review)

k

k

δl

θ

z

↓

π/2

asymptotic state:(phase shift)② Feshbach resonanceV(r)③ E-dependent potential

EnergyΛ(1405) baryon resonancecentrifugal potential
L(L+1)/2μr2

Veff(r)

V(r)

A’+B’

r

k

kr

Typical mechanisms of resonances① Centrifugal potential

resonance

quasi-bound state

Kbar

Σ

(resonance)

A+B

π

E

N

Weinberg-Tomozawa interaction(Chiral symmerty for NG boson)

A+B → A’+B’ → A+B
103

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)
( )+
( )

B*

hadronic molecule interpretation

B*

Hadronic molecule
Numerical result← bound state← resonant state

S. Ohkoda, et al.,Phys. Rev. D86, 014004 (2012)104

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation
Numerical resultexp.

✔

← resonant state✔

S. Ohkoda, et al.,Phys. Rev. D86, 014004 (2012)

✔

✔

✔
exp.
← bound state✔

Feshbach resonances

relevant
channels105

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation
Other effects?
① Υπ, hbπ loop

Method by M. R. Pennington and D. J. Wilson, Phys. Rev. D 76, 077502 (2007)

B. Dispersion relation:

C. Parametrization:
A. Loop propagator:
D. Numerical result- gn and gm are determined from Zb→Υπ, hbπ- s0 ≈ 9000 MeV

106
Mass is slightly shifted upwards.

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+
hadronic molecule interpretation
Other effects?

② Triangle diagram effect

S. Ohkoda, S. Yasui, and A. Hosaka, Phys. Rev. D 89, 074029 (2014)(decay width)

BB*bar or B*B*bar merging into the final state Υ(vector meson dominance)

Pion emission by B*bar

Zb’s dissociation into BB*bar or B*B*bar(form factor with cutoff ΛZ)

Zb(10610) decay width[MeV]

Zb(10650) decay width [MeV]It seems consistent with experiments.

107

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+

hadronic molecule interpretation③ Radiative decay (IZ=0)
Predictions for γ decay

0𝑙 −A. E. Bondar, A. Garmash, A. I. Milstein, R. Mizuk, and M. B. Voloshin, Phys. Rev. D84, 054010 (2011)
M. B. Voloshin, Phys. Rev. D 84, 031502 (2011)
S. Ohkoda, S. Yasui, and A. Hosaka, Phys. Rev. D 89, 074029 (2014)108

3. Heavy exotic hadrons -X, Y, Z hadronsZb(10610)+ & Zb(10650)+

hadronic molecule interpretation③ Radiative decay (IZ=0)
Predictions for γ decay

1.0

2.5

3.8

← prediction

1.0

2.6

4.1

← prediction

Branching ratios(including phase space factor)

A. E. Bondar, A. Garmash, A. I. Milstein, R. Mizuk, and M. B. Voloshin, Phys. Rev. D84, 054010 (2011)
M. B. Voloshin, Phys. Rev. D 84, 031502 (2011)
S. Ohkoda, S. Yasui, and A. Hosaka, Phys. Rev. D 89, 074029 (2014)109

3. Heavy exotic hadrons -X, Y, Z hadrons-110

3. Heavy exotic hadrons -X, Y, Z hadrons-

Charm

Pentaquark111

3. Heavy exotic hadrons -X, Y, Z hadrons-

Pc(4380)
Pc(4450)112

3. Heavy exotic hadrons -X, Y, Z hadronsPc(4380) & Pc(4450)
first charm pentaquark113

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14 Jul 2015

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Geneva, 14 July 2015. Today, the LHCb experim ent at CERN’s Large Hadron Collider has reported the
Safari 省電力

a class of particles know n as pentaquarks. The collaboration has subm itted a paper reporting
ク リ ッdiscovery
ク し て ofFlashプ ラ グイ ン を 開始
these findings to the journal Physical Review Letters .

“The pentaquark is not just any new particle,” said LHCb spokesperson Guy Wilkinson. “It represents a way
to aggregate quarks, namely the fundamental constituents of ordinary protons and neutrons, in a pattern thathas never been observed before in over f ifty years of experimental searches . Studying its properties may allow
Science& Environment
us to understandbetter how ordinary matter, the protons and neutrons from which we’re all made, isconstituted.”
Our understanding of the structure of m atter w as revolutionized in 1964 w hen Am erican physicist,

Large Hadron Collider discovers new
pentaquark particle

Murray Gell-Mann, proposed that a category of particles know n as baryons, w hich includes protons and

Top Stories

neutrons, are com prised of three fractionally charged objects called quarks, and that another category,im esons, are form ed of quark-antiquark pairs. Gell-Mann w as aw arded the Nobel Prize in physics for thisPlane part tested for MH370 linkw ork in 1969. This quark m odel also allow s the existence of other quark com posite states, such as

A Malaysia team is on its way to the
French Indian Ocean island of Reunion to
see whether washed up debris is frommissing Malaysia Airlines ﬂight MH370.

By Paulpentaquarks
Rincon com posed of four quarks and an antiquark. Until now , how ever, no conclusive evidence for
Science
editor, BBC
websitepentaquarks
hadNews
been seen.
LHCb researchers looked for pentaquark states by exam ining the decay of a baryon know n as Λ b

14 July 2015

Science & Environment

g

mfi

f

s

t

mfi

ns
h

(Lam bda b) into three other particles, a J/ψ - (J-psi), a proton and a charged kaon. Studying the spectrum

ツ イ ートof m asses of the J/ψ and the proton revealed that interm ediate states w ere som etim es involved in their++production. These have been nam ed P c (4450) and P c (4380) , the form er being clearly visible as a peakin the data, w ith the latter being required to describe the data fully .

“Benefitting from the large data set provided by the LHC, and the excellent precision of our detector, we haveexamined all possibilities for these signals, and conclude that they can only be explained by pentaquark
states”, says LHCb physicist Tom asz Skw arnicki of Syracuse University.

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w hereas LHCb conducted the search w ith the lights on, and from all angles. The next step in the analysis
w ill be to study how the quarks are bound together w ithin the pentaquarks.

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1900 citations

massesdecay widths
115

3. Heavy exotic hadrons -X, Y, Z hadronsPc(4380) & Pc(4450)
first charm pentaquark116

3. Heavy exotic hadrons -X, Y, Z hadronsLHCb, Phys. Rev. Lett. 115, 072001 (2015)

Pc(4380) Γ=205 MeV
Pc(4450) Γ=39 MeV

Note: Pc(4450) is now Pc(4457).

117

3. Heavy exotic hadrons -X, Y, Z hadronsArgand Plot

LHCb, Phys. Rev. Lett. 115, 072001 (2015)118

Thresholds of hadron states above 4 GeV
D*+Σc*

MeV

4500

D*+Σc

4465 1/2-, 3/2-

D+Λc*(1/2-)

4390 1/2-, 3/2-

D*+Λc

D+Σc

J/ψ+Δ

4325 1/2- 4329 1/2 , 3/2 , 5/2

4296 1/2-, 3/2-

D+Λc4156 1/2-

hc+N

Pc(4450)
5/2+ (?)

4216 3/2-

4100

4495 3/2+

4465 1/2+

ηc+Δ
4200

D+Λc*(3/2-)

D+Σc*

4400
4300

LHCb, Phys. Rev. Lett. 115, 072001 (2015)

4530 1/2-, 3/2-, 5/2-

Pc(4380)4463 1/2+

χc2+N4494 3/2+, 5/2+

χc1+N4448 1/2+, 3/2+

χc0+N4353 1/2+

3/2- (?)
Spin-parity JP ?
Mostly favored① 3/2-,

5/2+

J/ψ+N

4035 1/2-, 3/2-

4000
ηc+N

3921 1/2-

3090
119

Thresholds of hadron states above 4 GeV
D*+Σc*

MeV

4500

D*+Σc

4465 1/2-, 3/2-

D+Λc*(1/2-)

4390 1/2-, 3/2-

D*+Λc

D+Σc

J/ψ+Δ

4325 1/2- 4329 1/2 , 3/2 , 5/2

4296 1/2-, 3/2-

D+Λc4156 1/2-

hc+N

Pc(4450)
5/2- (?)

4216 3/2-

4100

4495 3/2+

4465 1/2+

ηc+Δ
4200

D+Λc*(3/2-)

D+Σc*

4400
4300

LHCb, Phys. Rev. Lett. 115, 072001 (2015)

4530 1/2-, 3/2-, 5/2-

Pc(4380)4463 1/2+

χc2+N4494 3/2+, 5/2+

χc1+N4448 1/2+, 3/2+

χc0+N4353 1/2+

3/2+ (?)
Spin-parity JP ?
Not excluded① 3/2-,② 3/2+,

5/2+
5/2-

J/ψ+N

4035 1/2-, 3/2-

4000
ηc+N

3921 1/2-

3090
120

Thresholds of hadron states above 4 GeV
D*+Σc*

MeV

4500

D*+Σc

4465 1/2-, 3/2-

D+Λc*(1/2-)

4390 1/2-, 3/2-

D*+Λc

D+Σc

J/ψ+Δ

4325 1/2- 4329 1/2 , 3/2 , 5/2

4296 1/2-, 3/2-

D+Λc4156 1/2-

J/ψ+N

hc+N

Pc(4457)
3/2- (?)

4216 3/2-

4100

4495 3/2+

4465 1/2+

ηc+Δ
4200

D+Λc*(3/2-)

D+Σc*

4400
4300

LHCb, Phys. Rev. Lett. 115, 072001 (2015)

4530 1/2-, 3/2-, 5/2-

Pc(4380)4463 1/2+

χc2+N4494 3/2+, 5/2+

χc1+N4448 1/2+, 3/2+

χc0+N4353 1/2+

5/2+ (?)
Spin-parity JP ?
Not excluded① 3/2-,② 3/2+,③ 5/2+,

5/2+
5/23/2-4035 1/2-, 3/2-

4000
ηc+N

3921 1/2-

3090
121

Pc should contain at least

ccuud
Hidden charm

So, what is the structure?
122

1. Pentaquark

Quark spin/orbital excitations
Inter-quark correlations (diquarks)

2. Hadronic moleculeInter-hadron correlations

3. Cusp effectKinematic anomaly

4. Other things?
Lattice QCD, AdS/QCD, …

123

1. Pentaquark

Quark spin/orbital excitations
Inter-quark correlations (diquarks)

124

Skyrme model (1992)

Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

Skyrmion (nucleon)

ηc

Motivation

1. What is cc-nucleon interaction?

bound-state approach

Volkovitsky (1992)
Color van der Waals force, Scale anomaly Kaidalov,Luke, Manohar, Savage (1992)

2. Flavor extension: N(1535)~ηN ⇒ Ncc(？)~ηcN
Gobbi, Riska, Nucl. Phys. A568, 779 (1994)

Ncc mass estimated to be 2800 MeV (too light?)
Binding energy ~ 1300 MeV (!)

What is the QCD mechanism
to prevent the too-deeply
bound state?
125Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

Skyrme model (1992)

Skyrmion (nucleon)

ηc
J/ψ, ηc-nucleon potential from lattice QCD
Sugiura, Ikeda, Ishii, arXix:1905.02336 [hep-lat]bound-state approach

Attractive!
But no bound state

Cf. Two-pion exchange in φN, HAL QCD, PRD106, 074507 (2022)

126Diquark model

Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

Maiani, Polosa,Lett. B749
(2015)
289
for the orbital excitationin X Riquer,, Y, ZPhys.
mesonsare
discusorbital excitation in X , Y, Z mesons
areanddiscussed
Therefore,
by isMestimaa non
in [11]the associatedenergydenoting
difference
Whyis the massdifferencePc(4380)small (~70 MeV)?
andQ.theassociatedenergydifference
amplitudec(4450)tobetween
beis∆ estimatedM (L= 0 →and
1)transition∼ P280M eV.
M (L = 0 → 1) ∼ 280 M eV. qq diquark
However, the mass difference between light-light
M |Hchaw|ver, the mass difference
light-light
di- s = 1, 0S=0quarkswith spin[12], estimated⟨P,
from
S=1 between
paritywith spin s = 1, 0 [12], estimatedfrom charmand Opposite
beautybaryon spectra, is of order 200 M eV, e
P+ M
to be in−the8⊕ 1 rΣ c (2455)(2286) ≃requires
170 M eV,Σ b (5811)
Λb(5620
auty baryon spectra, is of order
200 M −
eV,Λce.g.
the
190 −
MΛ
eV.
5) − Λc(2286) ≃ 170c M eV, Σ b (5811)
c well known SU(3) formulaeb(5620) ≃cc
If diquark
we assume the perfectly possible
compositions
cq
V.
8′
⊗L=1
8= 1⊕ 8⊕ 8⊕
Pc(4380)
Pc(4450)
L=0
−
′′
S=1
assumethe perfectly possible
compositions
S=1
P(3/2 ) = { c̄[cq]s= 1 [q q ]s= 1 , L = 0}8′
⊗ 10 = 8 ⊕ 10 ⊕
−
′′
′
+
′′
P(3/2 ) = { c̄[cq]s= 1 [q q ]s= 1 , L = 0} P(5/2 ) = { c̄[cq]s= 1 [q q ]s= 0 , L = 1}
P(5/2+ ) = { c̄[cq]s= 1 [q′q′′]s= the1}(5)is reduced
we see thatthe decay
canwh
be0, L =
orbitalgap
to about
100(14)
M eV,
Opposite parity →Angular-momentum
excitation
octet
orofdecuplet.
cabrings
it
back
to
the
range
spin-spin The
and ﬁrst
spin-orital gap is reduced to about 100
M
eV,
which
~ 500 MeV mass differenceand (2). However, decays su
corrections
indicated (1)by (4).
t back to the range of spin-spin andspin-orbit
N(940) 1/2+
N(1535) 1/2ons indicated by (4).
Λb → πP S1 0= − 1 → π(JL=2
F lavor SU ( 3) str u ctu r e of p en+taqSu=ar− k2 s
~500 MeVΛb → K P 1 0→K
L=1
F lavor SU ( 3) str u ctu r e of p en taqu ar~500
k s MeV
L=0
Pentaquarks realizing
thealsovalencemightoccurquark
whenstructure
the [ud] d
are of two types+ parity- parity
state
gets broken in the 127
decay.

quarks realizing the valence quark structure (3)Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

Diquark model

Maiani, Polosa,Lett. B749
(2015)
289
for the orbital excitationin X Riquer,, Y, ZPhys.
mesonsare
discusorbital excitation in X , Y, Z mesons
areanddiscussed
Therefore,
by isMestimaa non
in [11]the associatedenergydenoting
difference
Whyis the massdifferencePc(4380)small (~70 MeV)?
andQ.theassociatedenergydifference
amplitudec(4450)tobetween
beis∆ estimatedM (L= 0 →and
1)transition∼ P280M eV.
M (L = 0 → 1) ∼ 280 M eV. qq diquark
However, the mass difference between light-light
M |Hchaw|ver, the mass difference
light-light
di- s = 1, 0S=0quarkswith spin[12], estimated⟨P,
from
S=1 between
paritywith spin s = 1, 0 [12], estimatedfrom charmand Opposite
beautybaryon spectra, is of order 200 M eV, e
P+ M
to be in−the8⊕ 1 rΣ c (2455)(2286) ≃requires
170 M eV,Σ b (5811)
Λb(5620
auty baryon spectra, is of order
200 M −
eV,Λce.g.
the
190 −
MΛ
eV.
5) − Λc(2286) ≃ 170c M eV, Σ b (5811)
c well known SU(3) formulaeb(5620) ≃cc
If diquark
we assume the perfectly possible
compositions
cq
V.
8′
⊗L=1
8= 1⊕ 8⊕ 8⊕
Pc(4380)
Pc(4450)
L=0
−
′′
S=1
assumethe perfectly possible
compositions
S=1
P(3/2 ) = { c̄[cq]s= 1 [q q ]s= 1 , L = 0}8′
⊗ 10 = 8 ⊕ 10 ⊕
−
′′
′
+
′′
P(3/2 ) = { c̄[cq]s= 1 [q q ]s= 1 , L = 0} P(5/2 ) = { c̄[cq]s= 1 [q q ]s= 0 , L = 1}
P(5/2+ ) = { c̄[cq]s= 1 [q′q′′]s= the1}(5)is reduced
we see thatthe decay
canwh
be0, L =
orbitalgap
to about
100(14)
M eV,+)-M(3/2-) = ΔM
octetorofdecuplet.
The
ca
M(5/2
ΔM
it back
to+therange
spin-spinand ﬁrst
spin-orspin
anglular
momentumital gap is reduced to about brings
100 M eV,which
and (2). However, decays su
corrections
indicated (1)by (4).
t back to the range of spin-spinand spin-orbit

ons indicated by (4).

Λb → πP S1 0= − 1 → π(JF lavor SU ( 3) str u ctu r e of p en+taqSu=ar− k2 s

F lavor SU ( 3) str u ctu r e of p en taqu ar k s

Λb → KP10→KPentaquarks realizing
thealsovalencemightoccurquark
whenstructure
the [ud] d128
are of two types
state
gets
brokeninthedecay.
quarks realizing the valence quark structure (3)unit of orbital angular momentum. The n
Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV
In this note, we comment on the two pentaquarksof the lighter
state in (4) reﬂects just the ps the logical extension of the pictureforalready
proposed
Maiani, Polosa,
Phys.
B749
(2015)
289
valence
antiquark(3)Lett.
andthepositivethe orbital excitationin
X Riquer,, Y, Zin
mesonsare
discusn [2], andfor the beautyin [3], for
exoticorbitalexcitationin X , sector
Y, Z mesons
arethediscussed
denotingby isMestima
a non
nextTherefore,
stateenergy
is naturallyinterpreted
as
the
in
[11]
and
the
associateddifferencemesons, X , Y, Z , whereby the latter particles are deorbital,= 1,Mexcitation.
ParityorderingQ.theWhy
is the massdifferencePc(4380)
andsmall (~70
MeV)?
and
associatedenergydifference
estimated
amplitudec(4450)tobetween
beis∆bound
M (L
= 0→
1)transition∼ PL280eV.
cribed using diquarks as colored subunits,bythat we have just recalled, and in X , Y, Z
M (Lcolor= 0forces.
→ 1) See∼ 280
However,the mass
difference between light-light
qq diquark
QCD
also M
theeV.
discussionsin [4].
PC++
the opposite, the X (3872) withJ=
1
⟨P, M |Hcha
w|
ver,
mass
difference
betweenlight-light
di- sthanLightthescalarmesonsas fourstateshave
beenquarkswithconspin= Y1,(4260),0[12],
estimated
S=0
S=1quarkwith
J P C = 1− −from. This fea
parityideredin [5] sand= further
studiedin [6,
7].Opposite
Heavy-lightwith spin
1, 0 [12],estimated
from
charm
and
beautybaryonreﬂects
spectra,is thatof order200noMvalenceeV, ethe fact
there areiquarks
as building
blocks ofcharm
or beauty
P+ M
to be
8⊕ 1 rthe≃requires
familiar
twoin
quark-antiquΣ c (2455)(2286)
170 MbaryonseV,Σ band(5811)−theΛb(5620auty
baryonspectra,is hiddenof order200M−
eV,Λexce.g.
tic mesons have been introduced in [2, 3]. Pentaquarks
thewellXknown
SU(3)formulaelowestlying, Z mesons,as required
by
190
M
eV.
5)
−
Λ
(2286)
≃
170
M
eV,
Σ
(5811)−
Λ(5620)≃cccbbrom light diquarks are described
in
[8,
9]
see
also
[10].
c
c
picture.
If
weassumetheperfectly
possiblecompositionscq
diquark
V.In the particular case of the
newly discovered pen8′⊗L=1
8= 1⊕ 8⊕ 8⊕
Pc(4380)
Pc(4450)
L=0 (color 3̄) units−′′
S=1
aquarks,
we
led to identify
assumetheareperfectly
possiblecompositions
S=1 the basic
P(3/2 ) = { c̄[cq]s= 1 [q q ]s= 1 , L = 0}s: the charm
antiquarkc̄,
oneheavy-lightdiquark,[cq], +
8h′′
⊗e m10=d i8ffer⊕ en10
⊕
−
′
′
′
′
T
ass
ce
) = { c̄[cq][q′qq′′] ](q,,, Lq′′=denote0} P(5/2) = { c̄[cq]s= 1 [q q ]s= 0 , L = 1}
s= 1[qs= q
1′
nd P(3/2
one light-lightdiquark,light+ we restric at ﬁrst
′ beuarks,
whichthethe u,
orbitalexcitationinwe
X , seeY, Z thatmesonsare
discussed
Ther
P(5/2
) = { c̄[cq]s= 1 [q′q′to]s=for1}d quarks,(5)is reduced
the
decay
(14)
can
be
0, L =
theorbital
gap
to
about
100
M
eV,
wh
At
ﬁrst
sight,
the
near
70
M
eV
differen
in
[11]
and
the
associatedenergydifferenceisestimated
tran
xtending later to +the ﬂavor SU(3) triplet,
u,
d,
s).
octet
orofdoes
decuplet.
The
ﬁrst
it(L backrange
spin-spin
andspin-ormasses(4)
notmomentum
go wellwiththe caenebe ∆MMeV,
=spin
0 →to
1) the∼ 280
MineV.
anglular
ital gap is reduced to about tobrings
100
which
(1)
and
(2). However,decayssu
to orbital
excitation.
One orbital
excitacorrectionsby (4).
However, theindicatedmass difference
betweenlight-light
dit back to the range of spin-spin
andspin-orbit
carries anenergydifference
quarks with spin s = and1, 0 baryons[12], estimated
from
charm
requ
ons
indicated by (4).
S =exempliﬁed−
1cally ofisorder
300
Mbyand beauty
baryonof order
Mas
eV,
e.g.
W e refer to the original article [1] for experimental
errorsand spectra,
Λb 200
→eV,
πP
→
π(J
1 0 ∼ ≃290 MtheΣ c (2455) − Λc(2286) ≃ ferenceeV,Σ b (5811)−−Λ(1116)
more details.
inΛ(1405)eV. wb(5620)F lavor SU (170
3) M
str
u ctu
r e of pΛ
en
taq
u
ar
k
s
190
M eV.
c(qq)
c(qq)S=0(uds)
ΛL=1
K + L=0
P S1 0= − 2 → K
S=1
b → (uds)
If wearassumeF lavor SU ( 3) str u ctu r e of p en taquk s the perfectly possible compositions

Diquark modelM(5/2 )-M(3/2 ) = ΔM

+ ΔM

= (-200 MeV) + 300 MeV′′′
Pentaquarks
thevalenceP(3/2− ) realizing= { c̄[cq]]s= 1occur, L = quark0}whenstructure
might
the [ud] ds= 1 [q qalso+′′
are of two
types
P(5/2
) = { c̄[cq]q ′]s= 0broken, L = 1} in the(5)129we sstate
decay.
s= 1 [q getsquarks realizing the valence quark structure (3)unit of orbital angular momentum. The n
Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV
In this note, we comment on the two pentaquarksof the lighter
state in (4) reﬂects just the ps the logical extension of the pictureforalready
proposed
Maiani, Polosa,
Phys.
B749
(2015)
289
valence
antiquark(3)Lett.
andthepositivethe orbital excitationin
X Riquer,, Y, Zin
mesonsare
discusn [2], andfor the beautyin [3], for
exoticorbitalexcitationin X , sector
Y, Z mesons
arethediscussed
denotingby isMestima
a non
nextTherefore,
stateenergy
is naturallyinterpreted
as
the
in
[11]
and
the
associateddifferencemesons, X , Y, Z , whereby the latter particles are deorbital,= 1,Mexcitation.
ParityorderingQ.theWhy
is the massdifferencePc(4380)
andsmall (~70
MeV)?
and
associatedenergydifference
estimated
amplitudec(4450)tobetween
beis∆bound
M (L
= 0→
1)transition∼ PL280eV.
cribed using diquarks as colored subunits,bythat we have just recalled, and in X , Y, Z
M (Lcolor= 0forces.
→ 1) See∼ 280
However,the mass
difference between light-light
qq diquark
QCD
also M
theeV.
discussionsin [4].
PC++
the opposite, the X (3872) withJ=
1
⟨P, M |Hcha
w|
ver,
mass
difference
betweenlight-light
di- sthanLightthescalarmesonsas fourstateshave
beenquarkswithconspin= Y1,(4260),0[12],
estimated
S=0
S=1quarkwith
J P C = 1− −from. This fea
parityideredin [5] sand= further
studiedin [6,
7].Opposite
Heavy-lightwith spin
1, 0 [12],estimated
from
charm
and
beautybaryonreﬂects
spectra,is thatof order200noMvalenceeV, ethe fact
there areiquarks
as building
blocks ofcharm
or beauty
P+ M
to be
8⊕ 1 rthe≃requires
familiar
twoin
quark-antiquΣ c (2455)(2286)
170 MbaryonseV,Σ band(5811)−theΛb(5620auty
baryonspectra,is hiddenof order200M−
eV,Λexce.g.
tic mesons have been introduced in [2, 3]. Pentaquarks
thewellXknown
SU(3)formulaelowestlying, Z mesons,as required
by
190
M
eV.
5)
−
Λ
(2286)
≃
170
M
eV,
Σ
(5811)−
Λ(5620)≃cccbbrom light diquarks are described
in
[8,
9]
see
also
[10].
c
c
picture.
If
weassumetheperfectly
possiblecompositionscq
diquark
V.In the particular case of the
newly discovered pen8′⊗L=1
8= 1⊕ 8⊕ 8⊕
Pc(4380)
Pc(4450)
L=0 (color 3̄) units−′′
S=1
aquarks,
we
led to identify
assumetheareperfectly
possiblecompositions
S=1 the basic
P(3/2 ) = { c̄[cq]s= 1 [q q ]s= 1 , L = 0}s: the charm
antiquarkc̄,
oneheavy-lightdiquark,[cq], +
8h′′
⊗e m10=d i8ffer⊕ en10
⊕
−
′
′
′
′
T
ass
ce
) = { c̄[cq][q′qq′′] ](q,,, Lq′′=denote0} P(5/2) = { c̄[cq]s= 1 [q q ]s= 0 , L = 1}
s= 1[qs= q
1′
nd P(3/2
one light-lightdiquark,light+ we restric at ﬁrst
′ beuarks,
whichthethe u,
orbitalexcitationinwe
X , seeY, Z thatmesonsare
discussed
Ther
P(5/2
) = { c̄[cq]s= 1 [q′q′to]s=for1}d quarks,(5)is reduced
the
decay
(14)
can
be
0, L =
theorbital
gap
to
about
100
M
eV,
wh
At
ﬁrst
sight,
the
near
70
M
eV
differen
in
[11]
and
the
associatedenergydifferenceisestimated
tran
xtending later to +the ﬂavor SU(3) triplet,
u,
d,
s).
octet
orofdoes
decuplet.
The
ﬁrst
it(L backrange
spin-spin
andspin-ormasses(4)
notmomentum
go wellwiththe caenebe ∆MMeV,
=spin
0 →to
1) the∼ 280
MineV.
anglular
ital gap is reduced to about tobrings
100
which
(1)
and
(2). However,decayssu
to orbital
excitation.
One orbital
excitacorrectionsby (4).
However, theindicatedmass difference
betweenlight-light
dit back to the range of spin-spin
andspin-orbit
carries anenergydifference
quarks with spin s = and1, 0 baryons[12], estimated
from
charm
requ
ons
indicated by (4).
S =exempliﬁed−
1cally ofisorder
300
Mbyand beauty
baryonof order
Mas
eV,
e.g.
W e refer to the original article [1] for experimental
errorsand spectra,
Λb 200
→eV,
πP
→
π(J
1 0 ∼ ≃290 MtheΣ c (2455) − Λc(2286) ≃ ferenceeV,Σ b (5811)−−Λ(1116)
more details.
inΛ(1405)eV. wb(5620)F lavor SU (170
3) M
str
u ctu
r e of pΛ
en
taq
u
ar
k
s
190
M eV.
c(qq)
c(qq)S=0(uds)
ΛL=1
K + L=0
P S1 0= − 2 → K
S=1
b → (uds)
If wearassumeF lavor SU ( 3) str u ctu r e of p en taquk s the perfectly possible compositions

Diquark modelM(5/2 )-M(3/2 ) = ΔM

+ ΔM

= (-200 MeV) + 300 MeV

thevalence=Pentaquarks
100
MeV
(~70
P(3/2
) realizing= { c̄[cq][q qalso]MeV), L = quark0}whenstructure
might
occur
the [ud] d−+
are of two
types
P(5/2
)=
quarks realizing the valence quark structure (3)

′′
′
s= 1
exp.
′′
′
{ c̄[cq]s= 1 [q q ]s= 0 , L =s= 11} in the(5)130we sstate gets broken
decay.

sPentaquarks realizing the valence quark structure (3)Maiani, Polosa,Lett. B749
(2015)
289
for the orbital excitationin X Riquer,, Y, ZPhys.
mesonsare
discusDiquarkmodel
are of two
orbital excitationin X ,types
Y, Z mesons
areanddiscussed
Therefore,
by isMestimaa non
in [11]the associatedenergydenoting
differencev
Whyis the massdifference
betweenPc(4380)
andP280
small (~70 MeV)?
andQ.theassociatedenergydifference
estimatedtransition
amplitude
αbeβ γisc(4450)
to
∆
M
(L
=
0
→
1)
∼
M
eV.
Pu = ϵc̄α [cu]β , s= 0, 1 [ud]γ , s= 0, 1
(6)
M (L = 0 → 1) ∼ 280 M eV. qq diquark
However, the mass difference between light-lightt
α βlight-lightγ
M |Hchawr|ver, the mass difference
betweenP=ϵc̄αwith[cd]spin(7)quarks
1, 0
from
S=0
S=1 d
βdi, s= s0, 1= [uu]γ [12],, s= 1 estimated⟨P,
Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

paritywith spin s = 1, 0 [12], estimatedfrom charmand Opposite
beautybaryon spectra, is of order 200 M eV, e
P+ M
to be
the 8⊕ 1 r
where
greek
areM forcolor, ≃requires
diquarks
in intheΣ c (2455)−(2286)
170 M eV,Σareauty baryon
spectra,is ofindices
order
200
eV,Λce.g.
b (5811) − Λb(5620
the
SU(3)
formulaecolor
antisymmetric,
conﬁ guration
andknown
overallanti190 −M3̄,ΛeV.
5) − Λc(2286)≃ 170≃
c M eV, Σ b (5811)
c wellb(5620)cc
If diquark
we assumethe perfectly
possiblecompositions incqV.
symmetry requires
ﬂavor
symmetric
light-lightdiquark8′′⊗L=1
8= 1⊕ 8⊕ 8⊕
Pc(4380)
Pc(4450)
L=0
−
′
S=1
assumetheperfectly
possiblecompositions
S=1
with s = 1.
P(3/2 ) = { c̄[cq]s= 1 [q q ]s= 1 , L = 0}
t
8
⊗
10
=
8
⊕
10
⊕
′′
′′
′
we+ )havetwos= distinct
P(3/2− ) E= xtending{ c̄[cq]s= 1 [qtoq ′]ﬂavor0} (3),
P(5/2= { c̄[cq]L = 1}
s= 1 , L =SU
1 [q q ]s= 0 ,series
light-lightsymmeP(5/2+of) =pentaquarks{ c̄[cq]s= 1 [q′q′′according]s= the1} the(5)is reduced
we seediquarkthatthe decay
canwh
be0, L =
orbitalgap
to about
100(14)
M eV,
If thistry
is true, we can makebrings
an extension
from
SU(2)
flavorsymmetrytoSU(3).
octet
orofdecuplet.
The
ﬁrst
ca
it
back
to
the
range
spin-spin
andspin-orital gap is reduced to about 100 M eV, whichw
and (2). However, decays su
indicated′(1)byα β γcorrections′′(4).
t back to the range of spin-spinand spin-orbit

PA = ϵ{ c̄α [cq]β , s= 0, 1 [q q ]γ , s= 0 , L } =rons indicated by (4).
S= − 1Λb → πP 1 0 (8)→ π(Jd= 3 ⊗ 3̄ = 1 ⊕ 8
F lavor SU ( 3)′str
e of p en+taqSu=ar− k2 s
αβγ′
′u ctu r Λ
PS = ϵ{ c̄α [cq]β , s= 0, 1 [q q ]γ , s= 1 , Lb →} =K P 1 0 → Kw
F lavor SU ( 3) str u ctu r e of p en taqu ar k sEthevalencequark
structure= 3 ⊗ 6 Pentaquarks= 8 ⊕ 10 realizing(9)might also occur when the [ud] d131
are of two types
state
gets
brokeninthequarks realizing
valence thequarkﬁ structure
For theS-waves,
rst and (3)the second series give thedecay.

H =Ti − TG +Vi j ,(1) to test whether we could haveenwidely describedin theliterature
8, 27–30],
Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV
and B , andχ β (R
relativewaveandfunction of theucleonA B ) the [7,conﬁ guration is dominated byii,j
the reader
to thosereferencesHere
two clusters.
T hesymbol Aforis details.
the anti-symmetrizing
opgrefer
phase
H ere
we
performa dynamic
Wang, Huang, Zhang, Zou,
Phys.
Rev.
C84 015203(2011)
erator
deﬁ
ned
as
just
present
thesalient
featuresofthismodel.
T
he-nucleon
where Ti is the kinetic energy operator for the i th quark, and Λc D¯ states with isospin I
alas energy operator for the center-of-mass solving the RGM equation (EnsHamiltonian[24–
and isTGwritten
the kinetic
A ≡1 −Pi 4 ≡1 − 3P34 .
(15)uark inmotion.
V
represents
theinteractions
betweenquark- models as depicted in Sec. I I
i
j
Aij ,
H =
Ti − TG + i ∈V(1)and bostand the interaction proper
quark orquark-antiquark,ii,jdoscalar Substituting Ψ into the projection equation
states and to see whether ther
OGE
con f
M
Vi j
+operator
Vi j+for the, quark,(i j = qq)
del,or a Σ c D¯-Λc D¯ dynamically gere TtheM Viij thi is the kinetic energyDVi j =⟨δΨ|(H− E )|Ψ⟩ = 0,(16)
ourchiral quark models.
nets
are
O
G
E
con
f
d TG the kinetic energy
Vi j operator+ Vi j for, the center-of-mass
i j = qQ, qQ̄, Q Q̄Figure 1 shows the diagon
largelytion.
Vi j represents
thecoupledinteractions
between quarkwe obtain the
integro-differential
equation for the(2)Hamiltonian for the Σ c D¯ sys
d decuarkor quark-antiquark,relative
β as
where
qfunctionand Q χrepresent
light quark u or d and heavy dinate method (GCM ) [38] ca
DΣc-DΛ
methodc: resonating groupmodelsOGEΣeffective
c,f +respectively;
V(ii jj = qq)
is the OGE potential,Mc, ΛcgardedastheHamil
Vi Oj G E quark+ Vi conV,φ, N Ω̄,
j
i
j
M
′
′
′
′
[H β β ′(R , R ) − E N β β ′(R , R )]χ β ′(R ) dR = 0,=
clusters Σ c and D¯ qualitativ
OGE
con f
Vi j
+ βV
,
i j = qQ, qQ̄,1Q Q̄ π
′i j
1cludes the kinetic energy ofOGE) quarkVi j=
gi gj λ ci · λ cj−(2) δ( i j ) (17)the effective potential between
4
rij
2
namicalere q and Q
represent
light quarkkernelu or Hd and
where
the Hamiltonianand heavy
normalization kerthe generator coordinate which
OGE
s
in
the
nel N can,beark c, respectively;
Vi j respectively,
is the OGE
potential,
1 calculated
1
4byσi · σj
the distance between the two
×
+
+
,
(3)
), a wellFig. 1, one sees that Σ c and
m 2qi
m 2qj
3 m qi m qj
′
′
among
H1β β (R , Rc) c
1[φ̂ (ξπ, ξ ) φ̂ (ξ )] δ(R − R )other in the medium range fo
OGE=
A− 1 δ(2i j ) B
3 β
AB
V
=
g
g
λ
·
λ
′
i
j
j
i
j
ation i ofN4β β ′con
(R f, R )charm quark mass m c = 1.43
r i j nement
2
and
V
is
the
conﬁ
potential
which
providesijhe lightthe non-perturbative QCD effect in the long distance,
een the1
1
4 σi · σj
×
+
+
,
(3)
f 2
cm m
c
c
c0
s wherem 2qi Vi con
m
3
q
q
=
−
(λ
·
λ
)
a
r
+
a
(4)
i j
j ij ijqjji
ij .
rgies offenVi Mj conﬁ
represents
effective
quark-quarkdding
Vi conis thenement thepotential
which
provides potential inj
mass:
4.279-4.316
GeV Very good agreement with
132LHCb!
andets,
non-perturbative
QCD
effect inexchanges,
the long distance,
duced by
one-bosonand it is only considered

Quark model calculation

2. Hadronic moleculeInter-hadron correlations133

3̄ 3̄

3̄3̄

66

88

33

Meson-baryon coupling model

Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

144
244
344
Ξ+cc+
B [20]= − Ξ+cc of chiral
B [20]Ωcc . c constraints
low.BWe =emphasizethat thecombination
and= large-N[20]
9, 10) determine all coupling constants introduced in (6, 8).
is pointed out thattheη
relations(9,from the form of the inter- Hofmann, Lutz, Nucl. Phys. A763, 90 (2005)
η’N,
DΛfollowcN, DΣ
c, 10)
ction constructing(13). For completenesswe exchangespell out forces
the kinetic
term written
in terms
efore
the t-channel
it is rewarding
to dwell
a bit
the
SU(4)
multipletﬁelds:
ore on the coupling constants introduced in (1, 3). One may wonder whether
Lagrangian
with
SU(4)
symmetryannel
exchangeof thelight
orFlavor
heavy vector
mesons.
This importante results
obtainedarecompatible
with theapproximate
SU(4)piecesymmetry of(Isospin, Srangeness)formation
is
lost
in
(23).
CD that would 4arise in the limit of a light charm quark mass. As an amusing
SU (4)ji
L kin= 14exercise(∂we) (∂ µ Φj[16], i ) −thatm 2[16]theΦi[16],
sult
of
this
K
SFR
relation [30,31,32]µ Φwill[16], j demonstratej Φ[16],
his work we neglect
the t-dependence of the interaction kernel iinsisting
i ,j = 1
n=be0 derived
by insistingon SU(4)symmetric
coupling
constants.
The SU(4)in (21).
[11,13]the s-wave
projected
effective
scattering
4√ Following
(I
,S,C
)
[20]
i j writtenk
mmetric
downel, V( 1 s ), is readily+generalization
B¯i j k ofconstructed:
i ∂(1)/ − is
M readily.
(14)[20] B[20]

2

i ,j ,k = 1(I ,S,C )2√CV
m 2 symmetry iscontrast
constants
theassumptionofm̄a −
SU(4)SU )(4)√to ithe coupling(I ,S,C
µ ¯
¯
V
(
s
)
=
2
s
−
M
−
M
+
(
M
−
M
)
,(25)
L int = 4 g tr [(∂8µmΦ
2 [16]) , Φ[16]]− V[16] ,2m
ite nonsensical
for
the
meson
and
baryonmasses[34].
Thenotionof m [16]VVV ∈[16]d M [20] in⎛(14) is introduced only to√illustrate the normalizationof⎞√√the ﬁ elds.

1 are the2masses′
re M , M¯ andπ0m,m̄
of initialmeson2 D¯0√
2 π+ and ﬁnal baryon
2 Kand+⎜ + 3 η + 3 η (I ,S,C ) √⎟es.
The scattering
amplitudes,M( thes ), takethe simple
form vector⎜ section⎟e closethisby investigating
couplingof√√heavy√ mesons,⎜− 2 D¯− ⎟⎟⎟,[16] ⎜
√ −
√ 0
√
⎟
2
2
′
−
√
√
√
√
⎜
⎟
−
1
¯
¯
¯
√ )η +
2
K
2
−
η
2
D
(I , S,C ) ⎜(I ,S,C )(I ,S,C)K(I ,S,CM( ⎝s ) = 1 − V( s) J 7 ( s)V(26) s ⎟3 ( s) .3
⎠
√ 0
√ +
√ +
√
2D
2 Ds
2 ηc
√ − 2D
unitarity ⎛loop function, J (I ,S,C ) ( s ), is a diagonal matrix.
Each element⎞√ µ √mesonµ and√baryon,µµ intermediate
ends on the masses
of
ρ
+
ω
2
ρ
2
K
2 D¯0µ ⎟m and M , respec+
+
0
⎜
y:
⎜ √
√ µ √ µ ⎟µµ⎜µ2 ρ− −ρ0 + ω
2 K 0 − 2 D¯− ⎟
⎜
⎟
µ
⎜
⎟.
V√
(11)
√
√
√
[16] = ⎜ √
√ µ
µ 2
µ
s,µ ⎟
2
1/2
⎜
⎟
¯
¯
¯
2 D, − ⎟J( s ) = ⎜ M 2+ K(M− + p2cmK) ∗0 I ( 2 sφ) − I (µ)⎝ √⎠√ µ √ s,µ √
µ
µ
√
√
2
D
−
2
D
2
D
2
J/Ψ
+ s − 2p+√1
p0ss + 2ps
12 π−−π0 + √3 η +⎜Coupled-channel
equation
Φ
=⎜

cm

cm

2 ′
η
3

2K0

cm

< 4 GeV√ ln 1 −− ln 1 −16 π2sm2 + M 2
m2 + M 2√
2 interaction
e observe that1 mthewith (7)if andFig.and
1. I t (10)is shown
theDeeply
logarithm of the
diagonal Speed aa ( s ) for all channels+ M 2 m 2 − (11)M 2 is compatible
m2bound-state
134 where−ln+ 1 + I (0) resonances,(27)form with C = 0.
ly if the K+SFR
relation
2
2
2
2m −M
2s
M
I ( s) =a ameson.
bmomentum ofvectorT he Ca b(8)coefficien
gb =the) .
√lim (
P(4380)
Γ=205
MeV,
P(4450)
Γ=39 MeVTs→
P BbeandVB →V Bz thebyexchanging
aCoef
vec
R interactionaSU(4)
ac byccan
obtained
ClebschGordan− 1)
as:µregularize
it.
I
n
the
dim
ensional
regularization
schemeL P P V = −i g⟨V [P, ∂µ P ]⟩as shown
by fromthez Feynman
inthe
Fig.
1
cientswhich
we positions
take
Ref. these[14].diagramsWe listvalu
K Ξ
T meson,he states
obtainedpole
constants
R andofcoupling
these
and
modiﬁ
es
the
massesstates
only
I
n
o
g
g
one has [5, 12] ¯
a
b
µ√
µ
¯
T
=
.
(7)
T
he
effective
Lagrangians
fortheinteractions
invol
a
b
g
are
listedinTables
I
I
I
and
I
V
.
A
mong
six
states,
L
=
g(⟨
B
γ
[V
,
B
]⟩
+
⟨
B
γ
B
⟩⟨V
⟩)
(1)
of
the
C
coefficients
for
P
B
→
P
B
with
isospinan
α Wu, Molina,
BBVµµa bresults
slightly.
T he
are
given
in Tables
V and105
V I . 232001
W e do (2010),
states
0
Oset,
Zou,
Phys.
Rev. Lett.
s − zRDΣ
4, DΣc*, DΛc
four
of
them
coupleonly
toonechannelwhile
twostates
c
are
[12]:
d
q
1
1
not
consider the(Itransitions
betweenV BC84and015202
P B explicitly
statesstrangeness, S) = (1/2,0)Rev.
and
(0,
-1)
Phys.
(2011) resona
3
√in T
= use
i 2Mthe, ofB residue
2
2 + i ε q2 −2valueW eG canof −Taq)a 2todeterminethe4 (Pcoupletointwochannels.
becauseourt-channel
vectormeson
exchange
model
s=
(2π)
−
M
M
+
i
ε
where
P and
V stand for pseudoscalar
P2 V1 Band vectorP mesonsV2 ble I and Table I I, respectively.
Pexcept
1
1
g
,
for
a
globalphase.
T
hen,
the
other
couplingsµν
athey involveananomalous
V V P[Vvertex
is found to
nance
Lthe
=eV )i g⟨V, ∂ µ Vwhich
2MSU(4),
M B2
M P2 − M B2 + s M P2
V Vz Vtransitionν ]⟩ the coupled-channBof 2the 16-pletofrespectively.
W
ithpotential,
(
I
,
S)
g
R (M
a
are
derived
from
=
a
+
ln
+
ln
be
very
small
[15].
T
he
transitions
betweenV
B
andP
B
or Y ∗
0
µ
2
2
2
µ
+
¯
¯
16π
µ
2s
M
(1/2,through0) L Pmatrix
Σ[P,D− pseudoscalari g⟨V∂ µ mesonPΛby]⟩c solving
scattering
beDobtained
the coupleBc
Under the low energy approximation,
the threemo- states
Pt-channel
V = canexchanges
mass
g a Ta b√V*q¯ gV*
4269
2.85
0
3
=
lim
(
)
.
(8)
2
2
µ
µ
b
channelBethe-Salpeter
in+thefactoriz¯equationarealso foundto be very small.
A+ s anexamp
mentumversus+ the
mass
ofs→Bthemeson√ ln(s−√(M) + 2¯qcans) be neglected.
Lγ¯µΛ[V, Bexample,]⟩⟨B¯on-shell
γweBestiB B V = g(⟨ B D′⟩⟨V ⟩)ystoz R− MTPaa(0,the− 1)partialΞcD¯µΞstates¯Σ cD¯molecular
s our
c D
c
0
mate
decay
width
of
the aption
approach4213
of Refs.[3,1.37
5]
W e can just take the γ componentof√Eq. (1). T he threeheme
∗+
∗
∗
3.25
0
2
2
these
and
modiﬁ
these states
only
for these
new N
and Λ
NI ncc̄ order(4265)totolook
the J/ψ
p ﬁ nalpredictedstate throughthe t-channeltion t+ ln(s+ pole(M−esMthe) +masses
qands)ofcoupling
T he statesobtainedzR2¯
constants
Bpositions
Pexchanged
momentumandenergy
of
the
are
both
where
P
and
V
stand
for
pseudoscalarandvectormes(√ Vvector
0
0
2.64
−
1
0 4403slightly.
Theresults
are
given
in
Tables
and
V
I
.
W
e
do
states,weestimatetheproduction
cross
section
of
these
2
2
3(a,b)
gα Bare listedins −TablesI I IMand. A
mong six states, B2 pseudoscalar D meson
T exchange= [1 − VasG]shown
V by Fig. 2.
BP2) +BI V
−
ln(−
(M
−
2¯
q
s)
1
B
much smaller
thancouple
itstransitions
mass,
so between
its channel
propagatorof theata16-plet√
not 1ofconsiderthe
V Bwhileand PisBapproxstatesFA
I R . WofithSU
a p(4),¯ beam15ef.GeV/c
Following
similarapproachasrespectively.
inof R[17], onethehasparas sho
four
them
only
two
states resonances
2 to one2√
TA BL E I I I : Pole p ositions zR and coupling constants
g a for
(a)
(b)
−
ln(−
s
+
(M
−
M
)
+
2¯
q
s)
,
(5)
µ
ν
2
∗
B
P
,
becauset-channel
model
swith
= decay
5470
M
eVthe
, whichallowsonetoobserve
resotial
width
about
0.01
M eV
, which3N ordersof threeg /M. our
Tchannels.
henwith vector
g = Mmeson
the transition
being
functionof aismeson(P),ornism,
a vem
UG
nder
low
approximation,theV /2fexchange
to in
Vtwo
the
statesfrom
P Bisthe→Ploop
B .energy
εimatelycouple
Very
good
agreement
with
LHCb!
they
involveananomalousV
V
P
vertex
which
is
found
to
nancesinp¯X
production
up
to
a
mass
M
≃
4538
M
eV
magnitude
sm
aller
than
the
corresponding
decay
to
η
p
decay
X mesonpotential
corresponding
to the diagramsof Fig.
are
tor(V), anda baryon(B). Thepoles
in theamentumversusthe massof thecanTcbematrix
neglect
where
q is the four-momentumof the meson,
P the 1total
∗
be
[15].
T eV
hediagram
between
orofY23.4
hyperoninΛ̄Yproductionuptoa
M eV . zresonancestheN(IT, heS)smallzR (M)transitions
g a V B and2 P B
(I
,
S)
(M
eV
)
g
F I G .momentum
1: very
Feynm
an
s
of
pseudoscalar-baryon(a)Raof the meson and¯the baryon,s = P andWMe can
just
take
the
γ¯0e∗ component∗+∗ + of E q. (1). T he thr¯Λ +c exchanges¯
statesthrought-channel
pseudoscalar
meson
mass
≃
4355
M
eV
.
W
take
N
(4265)
as an
mined
(1/2,
0)
D
Σ
D
Y
(1/2,
0)
D
Σ
D
Λc
c
cc̄
c
or vectorbaryon(b) momentum
interactionofvia
exchangeof a vectorq¯ denotes
the threethethemeson
or baryon
(I
,
S)
M
Γ
Γ
iexchanged vector are b
momentumandenergyoftheare also found to 4269
besmall.
Asan
example,weestiexample.
Itslargestdecay
channelisηp.
Following− very0−∗−∗0in Tab
2.85
0
c
4418
2.75 ′0¯ or
m eson.
P 1center, P 2 isof Dmass, Dfram
V1 , V2 ¯isscale,D , D¯ (1/2,or 0)in thee. ¯Dµ sis+ ,a andregularization
πN
ηN
η N K∗ Ση∗ c N′
′
¯
∗
+
¯
¯
¯
¯
much
itswe
mass,
so itsisanism
appr
mate
D ΣD
the ∗approachas in R thanef. [18],
calculatecontribu(0,the− 1)partial decay width
Dofs ΛourΞcD Ξstatec molecular(0,− 1) smallerΞits
D 23.4Ξcc propagatorc ′c ∗s Λ c 3.9 D17.0
4261 56.9 3.8 D8.1
we1 ,take
to
eV
here.
ChangesintheD s∗ − ,whichB
B
is4213
Σbec , 1000
Λﬁ+cnal, MΞstate
or
Ω
,
and
V
is
ρ,
K
,
φ
∗+
2the
c, Ξ
cthe
c
µ
ν
2
Nand
(4265)
toJ/ψ
pthrought-channel
tion
to
p¯
p
→
p¯
p
η
throughprocesses
as
shown
in
Fig.
′
nism w
1.37
3.25
0
c/M K
1.23withcc̄
imatelyg 4370(0,− 1)πΣηΛ g3.14
η=Λ MKVΞ/2f
η0c Λthe transit
V .¯NT hen
are reabsorbed
in thesubtraction
constant
a to 3(a,b)
or ω.scale
pseudoscalar
D 0 4403
meson
exchange
by Fig.
and
also
those
from
the
conventional
mechanism
0.1µb,
0 as shown0
2.64 µ 2.
4550
0
0
2.53
4209 corresponding
32.4 15.8 2.9 to3.2the1.7
2.4 5.8of Fig.
potential
diagrams
1
make results scale independent.

arXi

µ
ν
Lthe
= Gi loopg⟨V[Vamplitudes, ∂µ Vaxis.
T heseclose twoto the
pole
VFor
Vreal
V the
ν ]⟩ behave
function,there
are usuallyways
toMeson-baryon coupling model

Following a similar approach as in R ef. [17], the paras shown in 4394
Fig. 43.3
3(c,d). 0 For10.6
the conventional
7.1 3.3 5.8mecha16.3
ThesecondwayforregularizationisbyputtingacutoffTA
E I I I : width
Pole pis
ositions
coupling
ga forTA BL
E IV: Polep ositionand coupling
constants
for theR andtialBLdecay
about z0.01
M eV, whichconstants
is 3 orders
of
nism
, the
ppη
is determ
ined fromthe partial(5)
c couplinginthethree-mom
T hecorresponding
formula is [3]:decay to η pthestatesfromP B entum.
→than
P B .theboundstatesV p¯B→. the(Γ),
TA BLE
V: M
ass(M),ptotalwidth
the partialwith
decaymagnitude
smallerdecay
width
offromηc →[1].V BFor
newandmechanism
c
∗+
width
from Pto
B →, within M eV .
i ) for the
totalgivenofby
23.4 M eV . Λ 2
theN cc̄(Γ(4265),
itsstates
couplings
ηc pP Bandπp units
are deter(I
,
S)
z
(M
eV
)
g
¯
d¯
q
2M
(ω
+
ω
Rq
a )
B
P
B
and
from its corresponding partial decay widths listed
G=(6) mined∗∗ +2
M statesΓ that we ﬁ nd have
Γ i zero width, we
(1/2,
D¯C
Λ)c + i ϵ)A(Is, S)
all the(I , S)0) M0 4πΓ2 ωP ωB (sΓD¯i ωB−Σac(ω
+
P
ryon
in
Table
V . I t is found that while the∗conventional
mechb ′
(1/2,
0)
ρN
ωN
K
Σ
J/ψN
(1/2,
0)
πN
ηN
η
N
K
Σ
η
N
4418
2.75
0
c
shouldtake
intoaccountsomedecay
mechanisms.
T hus,
V
=
(E
+
E
),
(2)
P
P
a
b(
P
B
→
P
B
)
1
2
1
1
2
2
cale,
anism gives4412
a cross
sectionabout
0.1nb,
the new mecha∗4f+ 2 3.9
∗ 2
∗23.4
′
2
47.3
3.2
10.4
13.7
19.2
4261
56.9
3.8
8.1
17.0
2
2
¯
¯
¯
(0, −ω
1)P =
D
Λ
D
Ξ
D
Ξ
where
q
¯
+
M
,
ω
=
q
¯
+
M
,
and
Λ
is
the
we
consider
the
decay
of
the
statestoalightbaryon∗+cc
P¯ B s cBthenism
resultsa cross(0,with− 1) the N cc̄ (4265)
K¯∗ NρΣ in ωΛφΛsectionK ∗ Ξ aboutJ/ψΛ(0, −parameter
1)
K three-momentum
N 1.23πΣηΛ 3.14η′Λof theK Ξ function
ηc Λ
4370
0
cutoffintheplus
either
a
light
m
eson
or
a
charmonium
throughheavy
C a b 3.2 1.7 2.4 5.8
0.1µb, about4368
3 orders
magnitudelarger.
de28.0 of13.9
3.1
0.3
4.0W ith
1.8 the 5.4
µ to
4209
32.4
15.8
2.9
V
=
(E
+
E
)⃗
ϵ
·
⃗
ϵ
,
(3)
4550
0
0
2.53
loop. a b( V 14394
charmedmeson
exchanges
by
means
of
box
diagrams
V
V
1
2
31
−
2
−
1
B 1 →VB)
12
22
signed luminosityof abouts for4544 36.6
0 108.8cm 9.1
0 the
5.0 p¯ beam
13.8 as
43.3
0
10.6
16.3
4f 2 7.1 the3.3free 5.8
For
these
two
types
of
G
function,parameters
it
was
done
in
[15,
16].
Coupling
tothese
additional
at FA I R [13], this corresponds to an event production
utoff
TA
BL
E in
I VE
: q.
Pole(5)p osition
andcoupling
constants
fora the
are
a
and
Λ
in
E
q.
(6).
W
e
chooseorchannels
thresholds
thethemasses
preTA
BLE
Vwith
I : M ass
(M ), totallower
width than(Γ), andpartialofdecay
TA
BL
E
V
:
M
ass
(
M
),
total
width
(Γ),
and
the
partial
decay
µ
µ
rate
of
where
the
a,
b
stand
bound
statesfrom
V B →forV B .different channels of P1 (V1 )B
1more than 80000 per day. W ith branching ratios(Γ i ) for
statesof
fromP B two→ P functions
B , with units
M eV .
width(Γobtained) fortheηππ,statesKfrom→in
M eVto.
+states+ decayΛwidthso thatthetheshapesthese
areinalmost
viously
bound
iK
for
ηc →
K¯π,
K −VπB+provides
π− V, B2πwith
2π−units
ofwidthsa few
and P2 (V2 )B 2 , respectively. T he E is the energy ofcor∗+
percent for each channel, the N cc̄ (4265) should be easily135(I , S) particle.
MΓΓ i polarization vector of(6)responding
T
he
⃗
ϵ
is
the
observed from the ηc p and ηc p¯ invariant mass spectra for
A s allzero width,(1/2,0) the states that
ρN we
ωNﬁ ndK ∗haveΣJ/ψNwesignedat FA
rate ofor ηcpercenobserv
the p¯ptor [1in theits larductiothe p¯pMeson-baryon coupling modelηcN, JψN, ηcΔ, JψΔ, DΛc, D*Λc

Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV
Garcia-Recio, Nieves, Romanetz, Salcedo, Tolos,
Phys. Rev. D87, 074034 (2013)

Many states around 4 GeV

136

a c quark,or makeevaluations
using wave functions of the quark model [63], substituting47] (Sec. I I .F) the 12 most general operators byallowedby SU(3)×
HQSS
inPc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV
the s quarkby the c ofquark.
m baryon-meson sector were already given. M oreover,theµ reduction
these
1
0
0
′
VVi j B=B−C(k Eq.
+ k ′(45))) ⃗ϵ ⃗ϵ gets, simpliﬁed in the approach,(46) where
γ matrixof thethere
vertex(see
ij
n no strangeness is involved was also discussed. The
I n thislatter case,2
4f theNieves,′neglect ′
Xiao,
Oset,
Phys.
Rev.
D88,
056012(2013)
wethethreemomentaversusmassoftheparticles
(in
this
case
the
baryon).
ent couplings, which determine the 11 LEC’s (µ s and λ s) introduced in0
only the γ becomes relevant, which can be taken as unity within the baryon states0*′DΣc,D*Σc, DΣc*,where
D*ΣkThus,, k 0 are the energies of the incoming and outgoing vector mesons, and Ci j numericalcof positive energy that we consider. Then the transition potential corresponding to thecoefficients evaluated as described above. The expression is the same for the pseudoscalar
0.3
2diagram of Fig. 2(b) is given by

Meson-baryon coupling model|T `D S | matrix elements for the same quark content of pseudoscalar and vector mesons,
E SC R I P T I O N O F T H E L O C A L H I Dbaryon
D E Nc G A U G E F O R M A L I SM
2omittingthe ⃗ϵ ⃗ϵ*|T`D S |′

factor.
1[b]
V−C(k 0 + k ′0 ) ⃗ϵ ⃗ϵ ′,(46)
i j =solving
i j theThe
scatteringmatrixisevaluatedby
2 coupled channels Bethe-Salpeter equa**|T|e the formalism of the hidden gauge interaction
for vector mesons which we
4f
`D Sc
0.2
tion in theon shellTfactorization
approachof [64–66]
see also useful Feynman
to SU(4).
heVLagrangian
P rules in [56])PextendedV0′0e interactionof vector mesons amongst themselvesby the energies of the incoming and outgoing vector mesons, and Ci j numerical
whereisk given, k are0.15−1
T = [1− V G](47)(q)(q)as describedcoefficients evaluatedabove.
TheV,expression is the same for the pseudoscalar
V
V
1
µ
ν
0.1
baryon matrix elements(37)for the same quark content of pseudoscalar and vector mesons,
L I I I = − ⟨Vµ ν V ⟩ ,4′with Gomitting
being 3000
theloop
functionofand a baryon, which we calculate in dimensionalthe ⃗ϵ ⃗ϵ Bfactor. a meson
B
B
B
2
0.05
regularization
using the formula[65] and|T`D
similarvaluesthe subtraction
constants.
scatteringmatrix isofevaluated
byS |solving
the forcoupledchannels Bethe-Salpeterequabol represents the trace in the SU(4) space
and VTheµ ν is given by
2
2500
|T
|
The
iterationofdiagrams
producedbytheSalpeterequation
in
the
case
of
the
`D S Bethe
tion
in
the
on
shell
factorization
approachof[64–66]
FI G.0 2. D iagrams obtained in the effective chiral Lagrangians for interaction of pseudoscalar[a] or 10|2 terms. Hence, the factor ⃗ϵ ⃗ϵ ′appearing in
3900 4000 4100
4200
4300
4400 g[V4500 ,vector
4600 4700
4800 keeps the ⃗ϵ ⃗ϵ ′factor`D S
mesonstheVν −the∂ν V(38) in each|Tof2000
ν = ∂ µwithµ − iorµ Vν ] , of baryons.
vector [b] Vmµesons
octet
decupletÖ̀s [M eV]
the potential V factorizes also in the T matrix
T =for[1the− VexternalG]− 1 0V, vector mesons. A consequence (47)MV
1500 is the pion decay
g of the theory given by g = P 2f wheref = is93that
M eV
this
the interaction is spin independent and one ﬁnds degenerate states having-aofcontact
G. 8. T hesquaredam
plitudesoftheJ = 1/2,
sector.
I=1/2,=1/2
T heinteractionof L I IJ
which
comes
I provides
P I = 1/2
−term
− from [Vµ , Vν ][Vµ , Vν ]J vectors= 1/2
J Pmeson=the
3/2. function
withofand
G 1000being
loop
of a meson and a baryon,
which we calculate in dimensional
magnitude Vµ is the SU(4) matrix of thethe
15-plet+10
2 In the[57]
regularization
using
the
formulaof[65]
andsimilarvaluesfor thesubtraction
present
work,inspirit
of
the
heavy
quark
symmetry,
we shallincludeconstants.
in the
g
(c)
µ ν
µ ν
500
L I I Riemann= coupled⟨Vµ sheet,Vν Vchannels
V
−
V
V
V
V
⟩
,
(40)
ng to these peaks in the second
and
ﬁ
nd
the
poles
at
ν
µ
I
20
of diagrams
produced by
the Bethe
Salpeterin thecase of the
dynamics,
the pseudoscalars,
vectors,baryonsof spinequation
J = 1/2 andbaryons⎛ 0⎞The iteration
2
4000
4200
4400
4600
4800
ρ
M eV , (4410.13+√
iω29.44)ρ+M eV , (4481.35+ D¯
i 28.91)
M
eV
.
T
he
couplings
∗+
∗0
′
′
√
+
K
mesonsthe⃗ϵ4300⃗ϵEqs.
factorin4600eachof4800
the terms. Hence, the factor ⃗ϵ ⃗ϵ appearing
inof J = vector
3/2 using
matricesof(29−34).
0 the keeps
2
2
3900
4000
4100
4200
4400
4500
4700
as
well
as
to
a
three
vectorvertexfrom⎜ for these poles are given in Table I .⎟From Table I we can see
pled channels
s
MeV
the
in
the
T
matrixfortheexternal
vectormesons.
A
consequence⎜⎟ potential V factorizes Ö̀salso[M eV]⎜(3V ) ρ0µ ν⎟µνω V −∗0∂ V )V∗−of⎟⟩thisis thatisstates having= i+g⟨(∂= i g⟨(V∂νthe
Vµ −interaction∂ν Vµ(a)V µ )V⟩ spin.
(41) and one ﬁnds degenerate⎜ ρ− L I I I− √
√
(b)
µ νK
ν µD V
P=3/2-independent
2
2
⎜
⎟
P
−
P
−
I=1/2,
J
ling constants
oles
in
the
J
=
1/2,
I
=
1/2
I V . EpJVA
L
U
A
T
I
O
N
O
F
T
H
E
H
Q
SS
L
E
C
’S
I
N
T
H
E
L
O
C
A
L
H
I
D
D
E
N
G
AUGE
Vµ = ⎜ of all channels corresp onded certain.
(39)⎟= 1/2 and J = 3/2 .
⎟I t is⎜worth
recallingtheanalogywiththecoupling
ofvectorstopseudoscalars
given
in
FI
G.
7. Tpresent
he resultsof theinJ the= 1/2,
I =of3/2
T hesymmetry,squared amweplitudesthree channels
the
work,
spiritthesector.
heavy(a):quark
shall ofinclude
in theR OACH⎜ K ∗−⎟InK¯∗0φ A PDPs∗−⎜ formalism by⎟
the same∗ ∗¯
exceptforJ/ψ∆ channel.
(b):
he real parts of vectors,
G functionin D Σofc spinchannel.
coupledchannels
dynamics,
theT pseudoscalars,baryons
J = 1/2 and baryons⎝⎠
L∗+V P P = −i g ⟨[P, ∂µ P ]V µ ⟩,
(42)
∗0
∗+
¯
∗
∗
∗
∗
of
3/2
using
Eqs. (29−34).
¯ΣusJµexamine
ﬁrstD¯thetheI = 1/2ofsector.
As an example let us take D Λc → D¯Λc andDD¯ΛcD D¯Σ c D s D¯ ΛLet
J/ψ
J/ψN
D=
Σ c matricescc∗∗where P is the SU(4) matrix of the pseudoscalarﬁ elds,¯ c →where
D¯ Λ
These
interactions
are equal as
is incanagreement
couplingof the resonanceto wethediscussed.
i channel. ThisAs onesee in Eq.with(65), gi gj
i is the0.76 − i 0.08⎛0.02 − i 0.02 3.12 − i 0.25 0.14D− iΛ
0.48 0.33−cg.i 0.68
0.16two− i 0.28⎞ (29) for J = 1/2 and I = 1/2, where both′0
thegeneral
HQSS
constraints
explicited
in
Eq.
η̃
η8
π
c
+ is the residue of T+i j at the pole.
0For a diagonal transitions we have√+ √+ √η̃12+ √c4
KI O N O F T HD¯
0.76
0.02
3.13
0.50 π I V . 0.75
alcedo.
E VA
L U equal
A T0.32
Es µH, Qand
SS itL EisCalso’S Iconsistent
N T H E Lwith
O C AtheL H
I D D E ND¯∗GΛA U G E
6matrixelements
are
to
the
LEC’
diagonal
′
⎜ 2
⎟
c
η̃c
√
η8
η̃c
π0
0
−2 2 ⎟
√
√
√
√
⎜
π−
−√
+
+
+
K
D
A PEq.
P R (31)OA
C(J
H = 3/2, I = 1/2). giSo= we
lim
T
(
s
−
s
).
(66)
2
6
12
4
entry
in
see
that
the
HQSS
is
respected
there
by
the
i
i
p
⎜
⎟
√
√
P = ⎜
s→. s p (43)
η̃c′
−
2η
η̃
⎟
−
0
c
−
8
¯
∗
∗
∗
∗
∗
∗
+D¯√Σ12c In+ √D sthe interactions
J/ψN ⎝ D¯Λc K 12
D¯Σ c
D¯
ΛcKhidden
D¯ gaugeΣ c √6results.
local
additionof D¯Σ c → D¯Σ c and D¯ PΣ c → D¯ -Σ c⎠4
η̃c′sector. As an example I=1/2,
3η̃=c 1/2
Let
usexamineus takeJofD¯=5/2
Λc →D¯Λcfound,and0++ﬁrst the I√√ gives as an idea of the let
D T3.05D−+
1.43 − 0.12 0.15 − i 0.10D 0.20 − i 0.05 0.17 − i 0.11
−
i
0.54
0.07
−
i
0.51
he
determinationofthecouplings
structurethestates
s
137
12
4
∗
∗
¯
¯
DsinceΛc →D Λc. Theseas we todiscussed.
is in agreementwithaccordingto [68,two72],interactions
the couplings
are related
the waveThis
functionat the originfor
14are equal
0.25

2 [a]

2

-2

|T| [M eV ]

c

c

*

c

*
c

2

Re G s-2|T| [M eV ]

*

1.44

0.18

0.20

0.20

3.10

0.51

′

Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

QCD sum ruleChen, Chen, Liu, Steele, Zhu, Phys. Rev. Lett. 115 (2015) 17

3/2-

5/2+

Very good agreement with LHCb!

Prediction for bottom analog:

1383. Cusp effectKinematic anomaly

139

Anomalous triangle singularity
Liu, Wang, Zhao, Phys. Lett. B757 (2016) 231

J/ψ
Λb

N

χ cJ

Λb

N
Λ∗
(a)

K

D s∗∗
D¯(∗)
Λ∗c

K

J/ψ
(b)

d dMJ Ψp arb. units

Pc(4380) Γ=205 MeV, Pc(4450) Γ=39 MeV

600
400

2700

PC(4380)

2573
3040

200
4.2

4.4

4.6

4.8

5.0

MJ Ψp GeV

¯(∗)

D

Σ ∗c

J/ψ
N

(c)

he loop diagram s as a consequence of F ig. 1 where the AT S and kinem atic CU SP can b e recognized.

d dMJ Ψp arb. units

K
Λb

s

2860

0
4.0

N

PC(4450) MD MeV

a

3
800

TA BL E I : T he χ cJ p thresholds which can b e enhanced by the AT S via F ig. 2 (a).
++T hreshold m asses [M eV ] χ c0 (1P ) 0 χ c1 (1P ) 1 χ c2 (1P ) 2
p 1/2+
4353 PC(4450)
4449
4494

MDs MeV
2860
2700
2573
3040

4.4

4.6

4.8

5.0

MJ Ψp GeV+

d dMJ Ψp arb. units

PC(4380)

1400
b
1200
1000
800
600
4
400
200
0
4.0
4.2

1500

MDs MeV

c

2860
2700

1000

g property of F ig. 2 (a) and (b) is that given the masses of the involved states located within certain
ow the internal states to be on-shell simultaneously. T his is different from the kinematic CU SP effects
appear as perturbative structures in the invariant m ass spectrum . W hen such a condition is satisﬁ ed,500
behavior of the integral will produce strong enhancem ents at the singular points of which the effects
in the experim ent. I n particular, the singular points will mostly locate in the vicinity of the two-body0
not necessarily to be exactly at the thresholds. I t should be realized that the singular property will 4.0
when higher partial waves contribute at the interaction vertices. T he reason is because the singulars be kept in the decomposition of the integrand in the Feynm an param etrization. I n another word,

2573
3040

4.2

4.4

4.6

MJ Ψp GeV

4.8 1405.0

4. Other things?
Lattice QCD, AdS/QCD, …

141

3. Heavy exotic hadrons -X, Y, Z hadronsRecent experiments
LHCb, Phys.Rev.Lett.115, 072001 (2015)

LHCb, Phys.Rev.Lett.122, 222001 (2019)

Pc(4380)?

Pc(4312)
Pc(4440)
Pc(4457)

same or different?

Pc(4450)
two peaks!

Three peak states

Pc(4380) Γ~200 MeV (very large)

Brambilla et al. Phys. Rep. 873 (2020) 1
142

3. Heavy exotic hadrons -X, Y, Z hadronsπ exchange pot. + short-range int.

(Yamaguchi etl al. (2020))

1. 1Attraction by 5q
2. π exchange pot.
→ Decay widths
Predictions

Very good agreement!

Y. Yamaguchi et al., Phys. Rev. D96, 114031 (2017)
Y. Yaamguchi et al. Phys. Rev. D101 (2020) 091502
Cf. Y. Shmizu, Y. Yamaguchi, M. Harada, Phys. Rev. D98, 014021 (2018)
Y. Shimizu, Y. Yamaguchi, M. Harada, PTEP2019 (2019) 123D01
Y. Shimizu, Y. Yamaguchi, M. Harada, arXiv:1904.00587 [hep-ph]143

3. Heavy exotic hadrons -X, Y, Z hadronsAren’t there more charm pentaquarks？

Yes, there are more!

144

3. Heavy exotic hadrons -X, Y, Z hadronsLHCb, Phys. Rev. Lett. 128 (2022) 062001

JP=1/2+

Pc(4338) positive parity (new)a few MeV below
Σc*Dbar thresholdΣc*Dbar dynamics (p-wave) may be relevant…

145

3. Heavy exotic hadrons -X, Y, Z hadronsCharm-strange pentaquark？

Pcs(udscc)
Pc

u u d

c c

Flavor Octet(I=1/2)c c

Flavor Singlet(I=0)

Pc(4380), Pc(4450)

Pcs

u d s
color octet

146

Brief summary of quark model
Three quarks in SU(6)flavor+spin symmetry

SU(6)flavor+spin representationΔ
Three quarks in SU(3)color symmetryN

Totally antisymmetric representation (fermion systems)
A: antisymmetric
S: symmetric
MA: mixed-antisymmetric
MS: mixed-symmetric

147

Brief summary of quark model
Three quarks in SU(6)flavor+spin symmetry

Colored qqq
SU(6)flavor+spin representation

Three quarks in SU(3)color symmetry

Totally antisymmetric representation (fermion systems)
A: antisymmetric
S: symmetric
MA: mixed-antisymmetric
MS: mixed-symmetric

Lowest-dimension:
Mostly attractive
in color-spin int.
𝝀⋅𝝀 𝝈⋅𝝈148the common value b for r 1 , r 2 , r 3 , because the wave
ofPhys.
theRev.
lightwil
Y. Irie,function
M. Oka, S.Y.,
D97, quarks
034006 (2018)

be distributed uniformly in space. In fact, as will be discussed later, the stability of thepentaquark considered here seems irrelevant to the diquark correlation between two lightquarks, but rather sensitive to the cc̄ correlations. I n this sense, we may justify to treat thecommon variational parameter b.

W ith the simpliﬁcations stated above, we assume the spatial part of the wave function
as
✓
◆
2
2
2
2
1
1
|R
|
|r
|
+
|r
|
+
|r
|
~
2 3). 3
. 1. T he coordinateof R− and ~r−i (i1 = 1, 2,
φ(RF, rI G,
1, r 2, r 3) =
3
9 exp
2
2
2
2
4a
2b
4
4
(2⇡ a ) ( ⇡ b )(7)which is normalized by integrating over the space. T he values of a and b will be determined

al part φ depends on the variables R and r i (i = 1, 2, 3) (Fig. 1). Herby variational calculation. Note that all the orbital angular momenta are zero.

ector from the c quark to the c̄ quark, and r i are the vectors for li
5

W e assume for simplicity that the internal angular momenta are S-wan the ground states.

own that the Jacobi coordinates are very useful to solve many-body p

149n the present discussion, however, we simplify the situation in thefoll

Y. Irie, M. Oka, S.Y., Phys. Rev. D97, 034006 (2018)

Quark model(5-body system)~ and ~F I G . 1. T he coordinate of R
r i (i = 1, 2, 3).

model A

(conventional
al part φ depends on the variables
R int.)
and r i (i = 1, 2, 3) (Fig. 1). Her+ from the c quark to the c̄ quark, and r i are the vectors for li
ector

W e assume for simplicity that the internal angular momenta are S-wan the ground states.

model B(+instanton-induced int.)

own that the Jacobi coordinates are very useful to solve many-body p

150
n the present discussion, however, we simplify the situation in thefollTA BLE V I . E xpectation

Y. Irie, M. Oka, S.Y., Phys. Rev. D97, 034006 (2018)
0 , P ⇤ ) and singlet-type
values for octet-type conﬁ guration (Pcs8 , Pcs8
cs8

0 , P ⇤ ).
conﬁ guration (Pcs1 , Pcs1
cs1

octet type singlet type
λ c · λ c̄

2
3

− 16
3

λq ·λqvariables R and r i (i = 1, 2, 3) (Fig. 1). Here R is the

− 23

− 83

o the c̄ quark, and r i are the vectors
for lightAλquarks
c ·λq
model

-2

0

-2
model A0~ and ~
coordinate of R
r i (i = 1, 2, 3).

that the internal angular momenta are S-wave because
λ c̄ · λ q

model
B in
dinates are very useful to solve many-bodyproblems

model Amodel B

← Pc(4450)← Pc(4380)

however, we simplify the situation in the following way.

s are sufficiently heavy, and that the midpoint of c andmodel Bof-mass of cc̄qqq system. I n this limiting case, we canors r i to be the center-of-mass of the system. W e noticethe cc̄ (or uds) cluster to the total system is neglected.
(I, JP)=(0, 1/2-)
ould be a reasonable approximation as long as the mass
those of light quarks.

(I, JP)=(0, 1/2-)c

we here consider only compact systems of ﬁ ve quarks
0.333 fm

0.521 fmh extension parameters a for R and b for r i . W e use

3,(I, J P)=(0, 3/2-)

0.316 fm

0.505 fm

0.336 fm

0.528 fmbecause the wave function of the lightcquarks will

I n fact, as will be discussed later, the stability of the

Pcs8

rrelevant to the diquark correlation between two lightc̄ correlations. I n this sense, we may justify to treat the

Pcs8’

Pcs8*
151

Y. Irie, M. Oka, S.Y., Phys. Rev. D97, 034006 (2018)(I, JP)=(0, 1/2-)

0.333 fm

(I, J P)=(0, 3/2-)(I, J P)=(0, 1/2-)

0.521 fm

0.316 fm

0.505 fm

0.336 fm

0.528 fm

~ and ~
coordinate of R
r i (i = 1, 2, 3).

Pcs8’

variables R and r i (i = 1, 2, 3) (Fig. 1). HerePRcs8is the

Pcs8*

model Ao the c̄ quark, and r i are the vectors
for lightAquarksmodel← Pc(4450)

that the internal angular momenta are S-wave because

F I G . 4. T he diagram s for the obtained values of the variational param eters a (red thick arrow)model Amodel B
← Pc(4380)
model
B
0
⇤
dinatesarevery
usefulto
solve
many-bodyproblems
inand b (thin black arrow) in the model B for Pcs8 , Pcs8 and Pcs8 (cf. Table V ).

however, we simplify the situation in the following way.

model Bs are sufficiently heavy, and that the midpoint of c andof-mass of cc̄qqq system. I n this limiting case, we canors r i to be the center-of-mass of the system. W
e noticeMasscc

the cc̄ (or uds) cluster to the total system is neglected.

ould be a reasonable approximation as long as the mass
those of light quarks.

uds

cc

h extension parameters a for R and b for r i . W e use

3,

because the wave function of the light quarks will

S=1

S=1/2

S=0
we here consider only compact systems of ﬁ ve quarks

Pcs8

uds

S=1/2

Pcs8*

cc

uds

S=1

S=1/2

I n fact, as will be discussed later, the stability of therrelevant to the diquark correlation between two lightc̄ correlations. I n this sense, we may justify to treat the

Pcs8’

152

Y. Irie, M. Oka, S.Y., Phys. Rev. D97, 034006 (2018)~ and ~
coordinate of R
r i (i = 1, 2, 3).

variables R and r i (i = 1, 2, 3) (Fig. 1). Here R is themodel Ao the c̄ quark, and r i are the vectors
for lightAquarksmodel← Pc(4450)

that the internal angular momenta are S-wave because

model
B in
dinates are very useful to solve many-bodyproblems

model Amodel Bcolor recomb.

however, we simplify the situation in the following
colorway.
recomb.

s are sufficiently heavy, and that the midpoint of c andmodel Bof-mass of cc̄qqq system. I n this limiting case, we cancolor
recomb.
ors r i to be the center-of-mass of the system.
W e noticethe cc̄ (or uds) cluster to the total system is neglected.

SU(3)flavor & HQS
ould be a reasonable approximation as longbreaking
as the mass

← Pc(4380)

color recomb.

color recomb.

SU(3)flavor breaking SU(3)flavor breaking

those of light quarks.
we here consider only compact systems of ﬁ ve quarks

h extension parameters a for R SU(3)and b flavor
for r ibreaking. W e use3,

because the wave function of the light quarks will

SU(3)flavor & HQS
breaking

SU(3)flavor & HQS
breaking

I n fact, as will be discussed later, the stability of therrelevant to the diquark correlation between two lightc̄ correlations. I n this sense, we may justify to treat the153

Y. Irie, M. Oka, S.Y., Phys. Rev. D97, 034006 (2018)~ and ~
coordinate of R
r i (i = 1, 2, 3).

variables R and r i (i = 1, 2, 3) (Fig. 1). Here R is themodel Ao the c̄ quark, and r i are the vectors
for lightAquarksmodel← Pc(4450)

that the internal angular momenta are S-wave because

model
B in
dinates are very useful to solve many-bodyproblems

model Amodel B

← Pc(4380)

however, we simplify the situation in the following way.

s are sufficiently heavy, and that the midpoint of c andmodel Bof-mass of cc̄qqq system. I n this limiting case, we canors r i to be the center-of-mass of the system. W e noticethe cc̄ (or uds) cluster to the total system is neglected.

Compact
quark model:
ould be a reasonable approximation as long as themass
S. G. Yuan et al., Eur. Phys. J A48 61 (2012)
those of light quarks.

we here consider only compact systems of ﬁ ve quarks

Hadronic molecule model:
J-J W. et al., PRL105, 232001 (2010)
PRC84, 015202 (2011)h extension parameters a for R and b for r i . W e use

3,

because the wave function of the light quarks will

I n fact, as will be discussed later, the stability of therrelevant to the diquark correlation between two lightc̄ correlations. I n this sense, we may justify to treat the154

3. Heavy exotic hadrons -X, Y, Z hadronsLHCb, Sci. Bull. 66 (2021) 1278

𝐵− → 𝐽/𝜓Λ𝑝ҧ

Pcs(4459)
two peaks？
(→next page)155

3. Heavy exotic hadrons -X, Y, Z hadronsLHCb, Sci. Bull. 66 (2021) 1278

𝐵− → 𝐽/𝜓Λ𝑝ҧ

two peaks？

Pcs(4459)
𝑀 = 4458.8 ± 2.9 MeV
Γ = 17.3 ± 6.5 MeV

Pcs(4455)

𝑀 = 4454.9 ± 2.7 MeV
Γ = 7.5 ± 9.7 MeV

Pcs(4468)
𝑀 = 4467.8 ± 3.7 MeV
Γ = 5.2 ± 5.3 MeV

cannot be distinguished statistically…

156

l
w
i
th
J/ψΛ
r
an
ce
Heavy
exotichadrons-X, Y, Z hadronsB‐3.J/
ψΛp
dec
a
ysesonψΛ r eson an ce
LHCb-PAPER-2022-031−

LHCb-PAPER-2022-031

𝐵 → 𝐽/𝜓Λ𝑝ҧ

ontributions:
Λ)
/ ψ)
ψΛ)

Branching ratio: [1]M ultibody decays of B m eson‐‐preliminary
good invariant mass resolution
high signal purity

preliminary‐ g ood place to search for narrow resonances‐ Exotic states‐ search for pentaquarks in J/ ψΛ and J/ ψp‐

PDG: Phys. Rev. D 98, 030001[1]

spin: 𝐽 = 1/2
parity: P = −1 favoreed

Elisabetta Spadaro Norella & Chen Chenity:etermined
vored, ½+ rejected @90% CL

14

CERN Seminar, July 5, 2022

preliminary

Pcs(4338) JP=1/2157

https://indico.cern.ch/event/1176505/attachments/2475130/4248283/CERN%20seminar_LHCb.pdf

Y. Irie, M. Oka, S.Y., Phys. Rev. D97, 034006 (2018)~ and ~
coordinate of R
r i (i = 1, 2, 3).

variables R and r i (i = 1, 2, 3) (Fig. 1). Here R is theo the c̄ quark, and r i are the vectors
for lightAquarks
modelthat the internal angular momenta are S-wave because

Pcs(4459)

model
B in
dinates are very useful to solve many-bodyproblems

JP=??
model Amodel Amodel B

← Pc(4450)← Pc(4380)

however, we simplify the situation in the following way.

P (4338)model Bs are sufficiently heavy, and that the midpoint ofcs
c and

JP=1/2-of-mass of cc̄qqq system. I n this limiting case, we canors r i to be the center-of-mass of the system. W e noticethe cc̄ (or uds) cluster to the total system is neglected.

Compact
quark model:
ould be a reasonable approximation as long as themass
S. G. Yuan et al., Eur. Phys. J A48 61 (2012)
those of light quarks.

we here consider only compact systems of ﬁ ve quarks

Hadronic molecule model:
J-J W. et al., PRL105, 232001 (2010)
PRC84, 015202 (2011)h extension parameters a for R and b for r i . W e use

3,

because the wave function of the light quarks will

It seems consistent partially with our prediction.

I n fact, as will be discussed later, the stability of therrelevant to the diquark correlation between two lightc̄ correlations. I n this sense, we may justify to treat the158

Giachino,Takizawa,
pretation of the experim ental analysis
by Hosaka,
LH CbSantopinto,[10]. WTakeuchi,
e
conﬁ
rm e
Yamaguchi, 2209.10413 [hpe-ph]suggest conducting a higher statistical data analysis in
hadronic
order to im proveHadronic
the statisticalsigniﬁ cancethose twoalm ost hmolecule+ ofquarkcore model
states.
It seems consistent with experiments. T he mversal phin variou
atom s an
disciplina
to im plem

T he cand ﬁ vem atrix a

Pcs(4459)
JP=??

JP=1/2-where H
5q
H159
forplings. T

Through researches of heavy hadrons...

~ and ~
coordinate of R
r i (i = 1, 2, 3).

variables R and r i (i = 1, 2, 3) (Fig. 1). Here R is thewe can accessthe colorful world!

o the c̄ quark, and r i are the vectors for light quarks
that the internal angular momenta are S-wave because

dinates are very useful to solve many-body problems in

however, we simplify the situation in the following way.

s are sufficiently heavy, and that the midpoint of c andof-mass of cc̄qqq system. I n this limiting case, we canors r i to be the center-of-mass of the system. W e noticethe cc̄ (or uds) cluster to the total system is neglected.

ould be a reasonable approximation as long as the mass
those of light quarks.
we here consider only compact systems of ﬁ ve quarks

h extension parameters a for R and b for r i . W e use

3,

because the wave function of the light quarks will

I n fact, as will be discussed later, the stability of therrelevant to the diquark correlation between two lightc̄ correlations. I n this sense, we may justify to treat the

160

3

diquark states as the basis states,[qq[15]q][6](3¯c , 2)[210]

12¯ (3c , 2)⟩ −5 |gq,3¯ (3c , 2)⟩[210]5 |bq,

0

3
5

2
5

3f

− 10/3Mqqqq

3f− 4Mqqqq

4
1
3
5
12

12
1
3
1
4

12

0
1
12

4
1
3
1
4

(15)
Exoticmassof colorful states[qq q][84](3¯ hadrons:
, 2)
=
|gq,
¯ (3
, 2)⟩ +
|bspectrumq,¯ (3 , 2)⟩
[15]

=

c

c

c

TABLE 4. [qqqq]3c States in a schematic diquark model

Diquark
content
Color magnetism favors one of the spin-1/2 multiplets (see Table 5). The two
spin-1/2
eigenstates are both linear superpositions of |bq⟩
¯ and |gq⟩:¯aa[qq[15]q]D¯ = − 2.421 (3c , 2)
[qq[15]q]D¯ = 2.754 (3c , 2)
TABLE 1. SU(3) representations relevant for bothcolor and ﬂavor. In the weight diagrams isospin multiplets (with the same baryon number, spin, and parity) shown in the same color can mix when SU(3) fsymmetry is broken. Multiplets in black do not mix.

ab

=
=

− 0.582 |gq,
¯ (3c , 2)⟩ + 0.813 |bq,¯ (3c , 2)⟩ bb(16)
0.813 |gq,
¯ (3c , 2)⟩ + 0.582 |bq,¯ (3c , 2)⟩ bb

R.L. Jaffe, Phys. Rev. D72, 074508 (2005)

Spin

SU (3) f Irrep“Mass”

0

3f

Mqqqq

1

3 f ⊕ 15 f

Mqqqq + DMqqqq

0⊕ 2

15 f

Mqqqq + 2DMqqqq

1

6 f ⊕ 15′f

Mqqqq + 2DMqqqq

Again the lightest state has spin-1/2, but it is considerably heavier than the lightest spin1/2 multiplet built of a and d diquarks (see eq. (13)). the Introduction.
The schematic diquark
The spectrum of [qqqq]3c
SU (3) Irrep
C
Weight Diagram
model ignores the g diquark
states in the colormag3 ↔
entirely
and therefore yields
netic model is sketched inonly one spin-1/2 multiplet
Fig. 2 and compared withandone spin-3/2 multithe spectrum obtained the
6 ↔
J=1
TABLE 1. SU(3) representations relevant for both
Since
thediagrams
b-diquarkcolorplet.
and ﬂavor.
In the weightisospin mul- is
schematic strongly corretiplets (with the same baryon number, spin, and parassumed
heavierthanthelated diquark model. Theity) shown in the same color can mix when SU(3)symmetry is broken. Multiplets in black do not mix.
a-diquark,
thismultipletordering of states in the col15 ↔
SU (3) Irrep
C
Weight Diagramis expected to be heavier
ormagnetic model follows
J=0
3 ↔
than
the [aq]¯ state foundthe simple “Hund’s Rule”
in the previous subsection.
of QCD[5]: Antisymmetric
156 ↔↔
Once again the schematic
ﬂavor irreps are favored.
diquark model mimics theWithin a multiplet withcolormagnetic model at
the same ﬂavor irrep, low
15 ↔ as far as the light states
least
spin is favored. The diquarkn the presence of SU (3) f violation because the multiplets with the same
3crcharge havetotal angular momentum.
aredifferent
concerned.
As before
scheme yields a similar, but
3: The¯ 3c states. The ﬁrst column shows2: The spectrum of [qqqq] states. The ﬁrst column shows
gnetic model the colorspin interaction matrix elements (which
we callspectrum of [qqq]distinction
not Theidentical
pattern.
[15]) arethe
determinedby eq. (7), between thecolormagnetic model splittings.
secondgives a sketch of colormagnetic model splittings. The second gives a sketch ofmodelslies
inthediquark
the ordering of statesEx.
in theDN
schematic
diquark model. SU(3) fThegroundstate mulD(a)= −[qq]
2Mqq
the orderingof statesin X(5568)
the schematic diquark
model.
SU (3)
c , 1)) =
Ex.
Λ
c
Ex.
=
[sud]
b
=
qqqqc
15
↔ ≡D([21](3
f
(8)
c
J=0
J=?
2
multipletsarelabeled
by
icons
of
their
weight diagrams.
content
of
the
light
state:
D(b) ≡D([15](3c , 3)) = + 3 Mqq .
tipletis thesame
in bothmultiplets are labeled by iconsof theirweightdiagrams.
(*)
inis theschematicmodel
it diquark
is model.
No experimentapproaches,thoughthe colΣc in the=[qq]
b diquarkheavier,as assumed
schematic
D0, PRL117,
022003(2016)
J=1c
nology ofthese states
is well known
from theanalogs in the charm intermixes the color-sextet
pureb-diquark,
while
colormagnetism
g-diquarkapproxiormagnetic scheme allows J = 1 as well as J = 0. In the schematic diquark model abine with the charm quark to make the lightest positive parity charm‡‡northehyperchargepresence
of (Y
SU(3)
violation
becausemultipletswith thesamemately2 relative
tothetheb-diquark)1
2/3:f statein the3 f joins
the
charm
quark
to makeJ = 1 3 f is nearby. If, as suggested in the Introduction, only the lightest multiplet(s) of
rchargedifferent
total angularmomentum.
The Y =have− 1/3
isodoublet
in the 3oftoc-quark toin
makespinf couples
The
spectrum[qq]
q¯
statesthetwomodelsissummarized
Fig. 3.are
In both[qqqq]3inc states
stablemodels
against falling apart into the [qqq]q3c continuum, then it will be
gnetic model
the colorspin
matrix inelements(whichwe alsocall
oweverthe spin-triplet
Y = interaction− 1/3 isodoublet
the ﬂavor
6 f can
161
[15])
are
determined
by
eq.
(7),
to make thea spin-1/2
Xc state.
When the strange
mass is “turned
lightest
multiplet
is a quark
degenerate
3 f and 6 f with spin-1/2. The spectra begin to differ′
ates mix to form the Xc and the Xc . Note that the a and b diquarks
D(a)≡D([21](3, 1)) = although− 2Mqqatthenext clevel,
even there the differences are minor.
c

f

c

4
3

f

10
3

f

16
3c

f

c

f

4
3

′
f
f

28
10
33

f

16
3

′
f

28
3

3. Heavy exotic hadrons -X, Y, Z hadrons-162

3. Heavy exotic hadrons -X, Y, Z hadrons-More X, Y, Z, ....?
I’m so full…

163

3. Heavy exotic hadrons -X, Y, Z hadronsY(4360) & Y(4660)
Cf. Y(4260)
too many ψ’?

Single peak?s...

Some confusions...

Double peaks?

c
i
t
s
ti

mass:
a
t
s
width:ss&mass:(relatively broad)leB. Aubert et al. [BaBar],

Phys. Rev. Lett. 98, 212001 (2007)

J. P. Lees et al. [BaBar],
Phys. Rev. D D89, 111103 (2014)

X. L. Wang et al. [Belle],
Phys. Rev. Lett. 99, 142002 (2007)

confirmed double peaks.
164

3. Heavy exotic hadrons -X, Y, Z hadronsZc(3885)+, Zc(4020)+, Zc(4025)+ Cf. Zc(3900)+
Other charged charmonium?

M. Ablikim et al. [BESSIII], Phys. Rev. Lett. 110, 252001 (2013)

Zc(3885)+

Zc(3885)+

Zc(4020)+

Zc(4025)+

M. Ablikim et al. [BESIII], Phys. Rev. Lett. 111, 242001 (2013)165
M. Ablikim et al. [BESIII], Phys. Rev. Lett. 112, 132001 (2014)

3. Heavy exotic hadrons -X, Y, Z hadronsLHCb, Phys. Rev. Lett. 118, 022003 (2017)

X(4140), X(4274), X(4500), X(4700)

J/ψ-φ scattering in lattice QCD
S. Ozaki, S. Sasaki, PRD87, 014506 (2013)

No bound/resonance statesb

ccss
Quartet state?

166

3. Heavy exotic hadrons -X, Y, Z hadrons5
X(5568)90

D0, PRL117, 022003 (2016)

N events / 8 MeV/c 2

D0 Run II, 10.4 fb-1

Background model w/o cone cut
Background model with cone cut
Fits to background function

80

(a)
DATA
Fit with background shape fixed70

Background60

Signal

50
40
30
20
10

p ±)

5.75

5.8

5.85

0
5.5
15

5.9
2

[GeV/c ]round for the m (B s0 π±) distriand the ﬁ t to that distributionnd without the cone cut.

tion gives a good description
ds, as seen in F ig. 2.
ass spectrum is shown inand (b) without the cone cut.
ear 5.57 G eV /c2 . To extract
distributions are ﬁ tted with ancludes two term s: the backth ﬁ xed shape param eters as
m F si g (m B π , M X , Γ X ), m od-W igner function convolved

Residuals (Data-Fit)

B

0
S

5.55

5.6

5.65

5.7

5.75

5.8

5.85

5.9

10
5
0
-5
-10

sbud
5.5

5.55

5.6

5.65

5.7

5.75

m (B0S p ±)

5.8

5.85

5.9

[GeV/c 2 ]120

D0 Run II, 10.4 fb-1

N events / 8 MeV/c 2

5.7

100

(b)

80

60

40

DATA

All different flavors!

Fit with background shape fixed20

Background167

3. Heavy exotic hadrons -X, Y, Z hadronsTalk file by E. S. Norella and C. Chen, CERN Seminar 5th July, 2022

https://indico.cern.ch/event/1176505/attachments/2475130/4248283/CERN%20seminar_LHCb.pdf

168

3. Heavy exotic hadrons -X, Y, Z hadrons-

169

DoubleCharm
3. Heavy exotic hadrons -X, Y, Z hadrons-

Tetraquark170

3. Heavy exotic hadrons -X, Y, Z hadrons-

Are exotic hadrons unstable in strong interaction？

Not necessarily! Some can be stable!

1713. Heavy exotic hadrons -X, Y, Z hadronsTcc
Double charm tetraquark

Zc

Tcc

ccud

ccud

Hidden charm

Double charm

𝐶=0|𝐶| = 2172

3. Heavy exotic hadrons -X, Y, Z hadronsJ.P. Ader, J.M. Richard and P. Taxil,
Tcc
Phys. Rev. D25, 2370 (1982)
Double charm tetraquark

I(JP)=0(1+)
strong ud
attraction

u c
c d

- Color confinement- Diquarkstrong decay？

u c +

c d

(fall-apart)Tcc can be stable!

Gluon exchange force induces color-spin interaction

ud pair 1/mC0 dominant attraction (3c, I=0, 1S0)
cu pair 1/mC

suppressed

cc pair 1/mC2 more suppressed (3c, 3S1)

173

3. Heavy exotic hadrons -X, Y, Z hadronsJ.P. Ader, J.M. Richard and P. Taxil,
Tcc
Phys. Rev. D25, 2370 (1982)
Double charm tetraquark

mass
Attractive ud diquark (S=0)

I(JP)=0(1+)

u c
c d

D

u c +

D*

c d

D+D* threshold 3880 MeV

174

3. Heavy exotic hadrons -X, Y, Z hadronsJ.P. Ader, J.M. Richard and P. Taxil,
Tcc
Phys. Rev. D25, 2370 (1982)
Double charm tetraquark

mass
Attractive ud diquark (S=0)

D

u c
c d

u c +

.: Charmedin heavy ion collisions+)
I(JP)=0(1exotics

D*

c d

D+D* threshold 3880 MeV

des of Tcc . I n the bottom row, we would observe the correand (K + π+ π+ π− )(K + π− )π− in the ﬁnal states. See the+ MD

Decay mode

Lifetime∗− ¯0DDweak decay:
D→Kπ
D¯0 D¯0 π−
D ∗− K + π− , D ∗− K + π+ π− π−hadronic decay
hadronic decay
0.41 × 10− 12 s
175
S.-H. Lee, S. Yasui, Eur. Phys. J. C64,283 (2009)
S.-H. Lee, S. Yasui, W. Liu, C.-M. Ko, Eur. Phys. J. C54, 259 (2008)

3. Heavy exotic hadrons -X, Y, Z hadronsF i g u r e 41. Spectrum of the doubly charm ed tetraquark states of I (J ) = 0(1 ) with
Recent review:di↵erent bases of operators: (A ) Tfull basis of meson-m eson and tetraquark operators,
cc
H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu,+P

only meson-m eson operators, (C) only m eson-m eson operators excluding one D D
S.-L. Zhu, 2204.02649(B)[hep-ph]Double charm tetraquark⇤

operator, and (D ) the operators as in C supplemented with the tetraquark operators.
Taken from R ef. [492].

Summary of theoretical studies (chronological table!)
+300

+300

Mass [MeV]

+200
+100
DD

not bound

*

-100

bound

⨯

⨯

-200

⨯
⨯
⨯
⨯
⨯
⨯⨯
⨯⨯ ⨯
⨯ ⨯
⨯
⨯
⨯
⨯⨯

-300
1970

+200
+100
DD

*

-100
-200
-300

1980

1990

2000

2010

2020

2030

Year

bound or not bound？

F i g u r e 42. T heoretical predictions on the m ass of the doubly charm ed tetraquark
state ccūd¯ with I (J P ) = 0(1+ ), with uncertainties (error bars) and without
176
uncertainties (crosses), calculated based on the com pact tetraquark picture through3. Heavy exotic hadrons -X, Y, Z hadronsTcc
Double charm tetraquark~100 MeV above DD*bar threshold

No bound state for Tcc？

177

3. Heavy exotic hadrons -X, Y, Z hadronsA.V. Manohar, M. B. Wise,
Tcc
Nucl. Phys. B399, 17 (1993)
Double charm tetraquark

mass

Hadron molecule
D
I(JP)=0(1+)

D*

u c +

c d
D+D* threshold 3880 MeV
DD* interaction

D

D*

u c

π,ρ,ω, ...

c d

DD* bound state

Basis:(HQS)

HQS & Tensor are important, à la Zb≈BBbar,B*B*bar,B*B*bar.

178

D(*)

3. Heavy exotic hadrons -X, Y, Z hadronsπ, ρ, ω
Tcc
D(*)

Double charm tetraquark

Hadronic molecule

Hadron molecule (I=0)
Hadron molecule (I=1)
Compact multiquark (cc: 3c)
Compact multiquark (cc: 6cbar)

S. Ohkoda, Y. Yamaguchi, S.Y., K. Sudoh,179
A. Hosaka, Phys. Rev. D86, 034019(2012)

3. Heavy exotic hadrons -X, Y, Z hadronsTcc
Double charm tetraquark

Lattice QCD simulation

Y. Ikeda (HAL Collaboration), PLB729, 85 (2014)mπ=700 MeV

mπ=410 MeV←Attraction!

c
c

u

d
180

3. Heavy exotic hadrons -X, Y, Z hadronsTcc
Double charm tetraquark

Lattice QCD simulation

Y. Ikeda (HAL Collaboration), PLB729, 85 (2014)

c
c

u

d

Attraction in DD* phase shifta>0

attractive→ However, the attraction is not sufficiently
strong to make a bound state....
(Due to the large pion mass?)181

3. Heavy exotic hadrons -X, Y, Z hadronsTcc
Double charm tetraquark

Tcc really exists in our world!

2022

182

3. Heavy exotic hadrons -X, Y, Z hadronsTcc
Double charm tetraquark

LHCb, Nature Phys. 18 (2022) 751, Nature Commun. 13 (2022) 3351

Bound state below D*+D0 threshold,

Very very shallow (keV)!
Anyway, we should explore
more on Tcc and related states.
Very hot topic ongoing.

183

3. Heavy exotic hadrons -X, Y, Z hadronsTcc
Double charm tetraquark

Ivan Polyakov (2021)

me!

184
https://indico.desy.de/event/28202/contributions/105627/attachments/67806/84639/EPS-HEP_2021_Polyakov_v5.pdf

0. Introduction to exotic hadrons

Tccc

Lattice QCD study of Tcc near physical point
Y. Ikeda, et al. (HAL Collaboration), PLB729, 85 (2014)：𝑚𝜋 = 410, 700 MeV
Y. Lyu, et al. (HAL Collaboration), 2302.04505: 𝑚𝜋 = 135 MeV (near physical point)

𝑬𝐩𝐨𝐥𝐞 = −𝟒𝟓 𝐤𝐞𝐕“virtual state”
Cf. LHCb (2022): below D*+D0 thresholdcu

Mass spectrumd3. Heavy exotic hadrons -X, Y, Z hadronsRecent lattice QCD study on T
Tbb
Meinel, Pflaumer, Wagner,
bb

Double bottom tetraquark

Phys. Rev. D106, 034507 (2022)

Recent result by HAL
Collaboration
83 MeV (2212.00202)

Binding energy ~ 100 MeV？
(deeply bound)Compact multiquark or
extended hadronic molecule?

Future experimental studies

186FullyCharm
3. Heavy exotic hadrons -X, Y, Z hadrons-

Tetraquark187

3. Heavy exotic hadrons -X, Y, Z hadronsLHCb, Science Bulletin 65 (2020) 1983

Assuming no interference…

Xcc(6900) Four-charm resonance
cccc

Assuming interference…

Compact state or extended state？
188

3. Heavy exotic hadrons -X, Y, Z hadronsBrief summary of X, Y, Z and Pc

A. Esposito, A. Pilloni, A. D. Plolsa,
Phys. Rep. 668, 1 (2017)189

3. Heavy exotic hadrons -X, Y, Z hadronsBrief summary of X, Y, Z and Pc

cc
u
d

(
)
B*

Compact multiquark

gluonic excitation modes

A. Esposito, A. Pilloni, A. D. Plolsa,
Phys. Rep. 668, 1 (2017)cc “string excitation”
Σ, Π, Δ, Φ, ...
(S, P, D, F, ...)()
B*

Hadronic molecule

J/ψ
Λb

N

χ cJ
N
Λ∗
(a)

Λb

D s∗∗
Λ∗c

K

(b

Kinematic effect
K
¯(∗)

190

3. Heavy exotic hadrons -X, Y, Z hadronsResearches continue....

T
P
cc
c
Y
XZ
191

3. Heavy exotic hadrons -X, Y, Z hadrons-

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?

192

3. Heavy exotic hadrons -X, Y, Z hadrons④ What is phase diagram?

① Finite temperature② Finite density193

3. Heavy exotic hadrons -X, Y, Z hadronstime-evolution in relativistic heavy ion collisions

Production of exotic hadrons?
More quark number than e+e- and pp → Can we see rare events？
(e.x. 20 ccbar from Pb+Pb, collision in LHC)

What is the hadron production mechanism？
How much are yields of hadrons？
194

3. Heavy exotic hadrons -X, Y, Z hadronsObservation of “anti-hypernuclei”

STAR, Science 328, 58 (2010)

Possible to produce quark many-body systems?

195

3. Heavy exotic hadrons -X, Y, Z hadrons-

Cf. ExHIC collaboration: Phys. Rev. C84 (2011) 064910; Prog. Part. Nucl. Phys. 95 (2017) 279 (review)196

3. Heavy exotic hadrons -X, Y, Z hadronsProduction process of exotic hadrons

Temperature

Quark
phase

Quark
coalescence
model

Critical (hadronization)
temperature

Early thermalization

1 fm/cQGP

nonequilibrium
as hadron gas

𝑇𝐶
𝑉𝐶

Hadron
phase
=
？

=

Hadronstatisticalmodel

Resonance/
Molecule
formation𝑇𝐻equilibrium as
𝑉𝐻 hadron gas

HadronInter-hadron
7 fm/c interaction
5 fm/cFreeze-out
𝐹 temperature

𝑇

time

17 fm/cFree quark gas, First order, Evolution with entropy conservation, ...
L. W. Chen, V. Greco, C. M. Ko, S. H. Lee, W. Liu, PLB 601, 34 (2004)

Hadronmolecule
coalescence197

3. Heavy exotic hadrons -X, Y, Z hadronsExotic hadrons to be explored

QGP
What is the
production yieldfor each hadron？

weak decay

Weak decay; some decays
outside the fireball (QGP).
weak decay

weak decay

weak decay
weak decay
weak decay

weak decay
weak decay
weak decay
weak decay198

3. Heavy exotic hadrons -X, Y, Z hadronsStatistical model
𝑇𝐻 𝛾ℎ
𝑉𝐻
antimatter (RHIC/STAR)

Key point:
Almost equilibrium state (temperature 𝑇𝐻 )Chemical-freezeout (fugacity 𝛾ℎ )Uniform volume (𝑉𝐻 )Those parameters are determined to reproduce normal hadrons.

A. Andronic et al.,Nucl. Phys. A772, 167 (2006)

Normal hadrons (LHC/ALICE)

What’s about exotic hadrons？
199

𝑝

3. Heavy exotic hadrons -X, Y, Z hadrons𝑓 𝑊 (𝑥, 𝑝)

Coalescence model𝑥𝑓(𝑥, 𝑝)
Key point: convolution of wave functions andthermal distributions in phase space (x, p)

V. Greco, C. M. Ko, P. Levai, PRL90, 202302 (2003)
L. W. Chen et al., PLB 601, 34 (2004)
L. W. Chen et al., PRC 76, 014906 (2007)

proton/pion ratio(quark coalescence model )① distribution function f(xi, pi) for particle i② Wigner function

What’s about exotic hadrons？
The same formula can be applied toHarmonic oscillator wave function (frequency ω) is used.
quark/hadron-molecule coalescence.
200
The value of ω is determined by normal hadron productions.

3. Heavy exotic hadrons -X, Y, Z hadronsParameters in statistical/coalescence models

Scenario 1: 𝑇𝐶 = 𝑇𝐻 , 𝑉𝐶 = 𝑉𝐻
𝜔: the hadron yields from the coalescence model at 𝑇𝐶= the hadron yields from the statistical modal at 𝑇𝐻 .
Scenario 2: 𝜔: the hadron yields at 𝑇𝐶 to reproduce RHIC/LHC data
𝑇𝐶 and 𝑉𝐶 :the hadron yields from the coalescence model at 𝑇𝐶= the hadron yields from the statistical modal at 𝑇𝐻 .
201

3. Heavy exotic hadrons -X, Y, Z hadronsnumerical results (# per collision)

The yields of exotic hadrons are much smaller
than those of normal hadrons (1~10), but not
negligible.

202

3. Heavy exotic hadrons -X, Y, Z hadronsThe statistical model v.s. the coalescence model

1. The yields of the compact multiquark are relatively suppressed.
2. The yields of the hadronic molecules depend on their spatial sizes.
203

3. Heavy exotic hadrons -X, Y, Z hadrons-X(3872)/ψ(2S)

X(3872) found in heavy ion collisions!
More produced than pp collisions.
Note: Loosely bound states are difficult tobe produced in pp collisions.

Many questions
1. Consistent with ExHIC’s prediction？
Supporting the hadronic molecule？
2. How is the 𝑝𝑇 dependence related tohadron structure？ (𝑝𝑇 trans. momentum)
Cf. Choi, Lee, PRC101, 024902 (2020)

3. Elliptic flow by X(3872)？
Cf. Zhang et al., PRL126, 012301 (2021)

4. What about 𝜒𝑐1 (2𝑃)？
(𝜒𝑐1 (2𝑃) is coupled to 𝑋(3872))
5. Other exotics？

204

Do you have questions?

205

206

Summary of this lecture
1. Exotic heavy hadrons (X,Y,Z,Pc,Tcc,…) are new
objects to be studied in hadron physics.
2. Hadron spectroscopy provides us with basic
tools to study internal structure of exotic hadrons.

3. Heavy hadrons in nuclear systems are importantin understanding the strong interaction.
4. Cooperation between experiments and theoryis important (KEK, J-PARC, RHIC, LHC, GSI-FAIR, BES, ...).

207

Keywords in the lecture

Tetraquark
Spectroscopy
Heavy quarkCharm
symmetry
Heavy hadroneffective theory
BottomPentaquark

ExoticXYZ

Spin

208