Pcs pentaquarks as a mixture state of hadronicmolecules and compact multiquarks
Yasuhiro Yamaguchi
Department of Physics, Nagoya University, Japanin collaboration with

Hugo García-Tecocoatzi ( INFN Genoa ), Alessandro Giachino ( INP, Cracow ),Atsushi Hosaka (RCNP, Osaka Univ.), Elena Santopinto (INFN Genoa),
Sachiko Takeuchi (Japan Coll. Social Work), Makoto Takizawa (Showa Pharmaceutical Univ.),

International symposium on Clustering as a Window on the Hierarchical
Structure of Quantum Systems (CLUSHIQ2022), Sendai, Japan
31 Oct - 3 Nov, 2022

Hadrons as a quark cluster▶ Hadron = Cluster system of the elementary particle “Quark”▶ Ordinary Hadrons: Baryon (qqq) and Meson (qq̄)#

Baryon(proton,nucleon,...)"

Y. Yamaguchi (Nagoya Univ)

Meson (ρ,K(∗) ,...)

CLUSHIQ2022 (2 Nov 2022)!

1 / 23

Hadrons as a quark cluster▶ Hadron = Cluster system of the elementary particle “Quark”▶ Ordinary Hadrons: Baryon (qqq) and Meson (qq̄)#

Baryon(proton,nucleon,...)"

Meson (ρ,K(∗) ,...)!

▶ Exotic Hadrons (̸= qqq, qq̄)Compact multiquark
cluster? Hadron cluster (= Hadronic molecule)?
'$

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

1 / 23

Today’s talkExotic hadrons as
hadronic molecule + compact state






⇐⇒

Mixture?

1. Introduction
Exotic hadron, Our mixture model

2. Numerical results: Pc (qqqcc̄) pentaquark
3. Numerical results: Pcs (qqscc̄) pentaquark
4. Summary
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

2 / 23Observations of exotic hadrons (̸= qq̄, qqq) containing cc̄
▶ e.g. cc̄ mesons (Charmonium) sector
one-g exchange+
Confinement
⇒
αs
+ cr
r
+...

V(r) = −N. Brambilla,et al. Eur.Phys.J.C 71(2011)1534, S. Godfrey and N. Isgur, PRD32(1985)189

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

3 / 23Observations of exotic hadrons (̸= qq̄, qqq) containing cc̄
▶ e.g. cc̄ mesons (Charmonium) sector and Unexpected X, Y, Z
one-g exchange+
Confinement
⇒
αs
+ cr
r
+...

V(r) = −N. Brambilla,et al. Eur.Phys.J.C 71(2011)1534, S. Godfrey and N. Isgur, PRD32(1985)189▶ Exotics ̸= cc̄ have been observed in the Experiments (BaBar, Belle,
BESIII, LHCb,...) since the discovery of X(3872) in 2003!
Q. What is their exotic structure? How do they form such
structure?
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

3 / 23

Recent reports of Exotic hadrons!
▷ X(6900) (ccc̄c̄?)▷ X0,1 (2900) (c̄s̄ud?)

LHCb, Science Bulletin 65 (2020) 1983

LHCb, PRL125, 242001 (2020), PRD102, 112003 (2020)▷ T+
cc (ccūd̄)▷ Pc (uudcc̄?),

LHCb, Nature Phys. 18 (2022) 751-754,

LHCb PRL115(2015)072001, PRL122(2019)222001

Nature Commun. 13 (2022) 3351

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

4 / 23

Recent reports of Exotic hadrons!
▷ X(6900) (ccc̄c̄?)▷ X0,1 (2900) (c̄s̄ud?)

LHCb, Science Bulletin 65 (2020) 1983

LHCb, PRL125, 242001 (2020), PRD102, 112003 (2020)▷ T+
cc (ccūd̄)▷ Pc (uudcc̄?), Pcs (udscc̄?)

LHCb, Nature Phys. 18 (2022) 751-754,

LHCb PRL115(2015)072001, PRL122(2019)222001

Nature Commun. 13 (2022) 3351

Sci.Bull.66(2021)1278

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

4 / 23

Candidates of Exotic structures?
















Compact multiquarks

Tetraquark

QQ̄g Hybrid

Pentaquark
Hadronic
moleculesTriangle Singularity



Near thresholds?

Meson-Meson
Y. Yamaguchi (Nagoya Univ)

Meson-Baryon
CLUSHIQ2022 (2 Nov 2022)

Near thresholds?

(w/o Resonance)
5 / 23

Pc pentaquarks

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

6 / 23Observation of two Pc pentaquarks in LHCb (2015)▶ Observation of the Hidden-charm Pentaquark (cc̄uud)in Λ0b → J/ψ K− p Decay? R.Aaij, et al. (LHCb collaboration) PRL115(2015)072001











Pc in Λ0b → J/ψpK− decay






cc̄uud state ? ⇒

Pc (4380):

M =4380 MeV
Γ= 205 MeV

Y. Yamaguchi (Nagoya Univ)

Pc (4450):

M =4449.8 MeV
Γ = 39 MeV

CLUSHIQ2022 (2 Nov 2022)

7 / 23

New LHCb analysis in 2019!
▶ R. Aaij, et al. Phys.Rev.Lett. 122 (2019) 222001▶ Pc (4450) in 2015 −→ Pc (4440) and Pc (4457)
Pc (4440): (M, Γ) = (4440.3, 20.6) MeV
Pc (4457): (M, Γ) = (4457.3, 6.4) MeV▶ Observation of New state!
Pc (4312): (M, Γ) = (4311.9, 9.8) MeV▶ Pc (4380) in 2015? “these fits can neither confirm
nor contradict the existence of the Pc (4380)+ ”

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

8 / 23

New LHCb analysis in 2019!
▶ R. Aaij, et al. Phys.Rev.Lett. 122 (2019) 222001▶ Pc (4450) in 2015 −→ Pc (4440) and Pc (4457)
Pc (4440): (M, Γ) = (4440.3, 20.6) MeV
Pc (4457): (M, Γ) = (4457.3, 6.4) MeV▶ Observation of New state!
Pc (4312): (M, Γ) = (4311.9, 9.8) MeV▶ Pc (4380) in 2015? “these fits can neither confirm
nor contradict the existence of the Pc (4380)+ ”▶ Complementary experiments: γ p → J/ψ p
in GlueX@J-Lab
GlueX Collaboration, PRL123(2019)072001.

→ No triangle singularity

No evidence of γ p → Pc → J/ψ p
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

8 / 23

What is the structure of the pentaquarks?









Proposals of various structures!

H.X.Chen, et al., Phys.Rept.639(2016)1, A.Esposito, et al.,Phys.Rept.668(2016)1, A.Ali,et al.,PPNP97(2017)123▶ Compact pentaquark (cc̄qqq)?
S.G.Yuan, et al. (2012), L.Maiani, et al, (2015),
J. Wu, et al. (2017), E. Hiyama, et al. (2018),

S.Takeuchi, et al, (2017),...

▶ Hadronic molecule (D̄Σ∗c , D̄∗ Σc ,...)?
J.-J.Wu et al., (2010) (2011), C. Garcia-Recio, et al. (2013),
R. Chen, et al. (2015), Y.Shimizu, et al. (2016-2019),
C. W. Xiao, et al. (2019), M.-Z. Liu, et al. (2019), M. L. Du, et al. (2019),...
▶ Triangle singularity?
(Non-resonant explanation)
F.K.Guo, et al. (2015), X.H.Liu, et al. (2016),
S.X.Nakamura PRD103, L111503 (2021),

Y. Yamaguchi (Nagoya Univ)...
CLUSHIQ2022 (2 Nov 2022)

9 / 23

Hadronic molecules?
▶ Exotics as Hadronic molecule ⇒ Hadron (quasi) bound state→ expected near the thresholds
baryon⌃(⇤)
cD̄ (⇤) meson

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

10 / 23

Hadronic molecules?
▶ Exotics as Hadronic molecule ⇒ Hadron (quasi) bound state→ expected near the thresholds
baryon⌃(⇤)
c

Analogous to DeuteronD̄ (⇤) meson

B = 2.2 MeV

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

10 / 23

Hadronic molecules?
▶ Exotics as Hadronic molecule ⇒ Hadron (quasi) bound state→ expected near the thresholds
baryon⌃(⇤)
c

Pc = D̄ (⇤) ⌃(⇤)
c molecules?

D̄(⇤) mesonD̄ ⇤ ⌃c (4463MeV)
6 MeV

23 MeVY. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

Pc (4457)

Pc (4440)

10 / 23

Hadronic molecules?
▶ Exotics as Hadronic molecule ⇒ Hadron (quasi) bound state→ expected near the thresholds
baryon⌃(⇤)
c

Pc = D̄ (⇤) ⌃(⇤)
c molecules?

D̄(⇤) mesonD̄ ⇤ ⌃c (4463MeV)
6 MeV

23 MeVPc (4457)

Pc (4440)▶ Exotic hadrons near thresholds▶ DD̄∗ : X(3872), Zc (3900),..., DD∗ : Tcc▶ BB̄∗ : Zb , Zb ′▶ D̄(∗) Σ(∗)
c : Pc F. K. Guo, et. al., Rev.Mod.Phys.90(2018)015004,Y. Y., et. al., J.Phys.G47(2020)053001,...
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

10 / 23

Hadronic molecules?
▶ Exotics as Hadronic molecule ⇒ Hadron (quasi) bound state→ expected near the thresholds
baryon⌃(⇤)
c

Pc = D̄ (⇤) ⌃(⇤)
c molecules?

D̄(⇤) mesonD̄ ⇤ ⌃c (4463MeV)
6 MeV

23 MeVPc (4457)

Pc (4440)▶ Exotic hadrons near thresholds▶ DD̄∗ : X(3872), Zc (3900),..., DD∗ : Tcc▶ BB̄∗ : Zb , Zb ′▶ D̄(∗) Σ(∗)
c : Pc F. K. Guo, et. al., Rev.Mod.Phys.90(2018)015004,Y. Y., et. al., J.Phys.G47(2020)053001,...

Q. What is an interaction binding the constituent hadrons?
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

10 / 23

Hadron interactions

Problem Hadron interactions are NOT established yet...

due to the lack of the hadron-scattering data(↔ Lattice QCD, Femtoscopy, etc near future!)
How can we describe hadron interactions?

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

11 / 23

Hadron interactions

Problem Hadron interactions are NOT established yet...

due to the lack of the hadron-scattering data(↔ Lattice QCD, Femtoscopy, etc near future!)
How can we describe hadron interactions?
Hint 1 One pion exchange potential (Long-range int.)• Long-range int. known in the nuclear force !
• Chiral and Heavy quark spin symmetries

baryon
⌃(⇤)
c

⇡ D̄

(⇤) meson

OPEP
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

11 / 23

Hadron interactions

Problem Hadron interactions are NOT established yet...

due to the lack of the hadron-scattering data(↔ Lattice QCD, Femtoscopy, etc near future!)
How can we describe hadron interactions?
Hint 1 One pion exchange potential (Long-range int.)• Long-range int. known in the nuclear force !
• Chiral and Heavy quark spin symmetries
Hint 2 Mixing of Hadronic molecule & Compact state⇒ Short-range int. between the constituent hadrons
baryon
⌃(⇤)
c

⇡ D̄

OPEP
Y. Yamaguchi (Nagoya Univ)(⇤) meson

5-quark potential
CLUSHIQ2022 (2 Nov 2022)

11 / 23

One pion exchange potential (OPEP)▶ e.g. D̄(∗) Yc interaction (D̄(∗) = D̄, D̄∗ and Yc = Λc , Σc , Σ∗c )
Yc

D̄(∗)
LπD̄(∗) D̄(∗)π

LπYc YcVπ (r) = −]gπ g1 [⃗ ⃗
S
·
S
C(r)
+
S
T(r)
1
2
S
S
1
2
3f 2π
(Contact term is removed)gπ = 0.59, g1 = 1.00 determined by the π emission

Yc

D̄(∗)

⇒ OPEP induces channel couplings among D̄Λc , D̄∗ Λc , D̄Σc , D̄Σ∗c , D̄∗ Σc ,and D̄∗ Σ∗c (6 meson-baryon channels!)▶ Form factor with Cutoff Λ (determined by the hadron size)F(⃗q2 ) =

Λ2 − m2π,
Λ2 + ⃗q2

ΛD̄ ∼ 1130 MeV, ΛYc ∼ 840 MeV

Y.Y, A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi, M. Takizawa, PRD96(2017)114031
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

12 / 23

Tensor force in NN (3 S1 −3 D1 )▶ Tensor force in Deuteron, NN(3 S1 −3 D1 )K. Ikeda, T. Myo, K. Kato and H. Toki, Lect. Notes Phys. 818, 165 (2010).

⇒ Tensor force produces a strong attraction▶ Tensor operator S12 (r̂) = 3(⃗S1 · r̂)(⃗S2 · r̂) − ⃗S1 · ⃗S2⇒ ⟨ψS |S12 T|ψD ⟩ ̸= 0!

(in general, ⟨ψL |S12 T|ψL±2 ⟩ ̸= 0)

Coupling to D−wave (L ̸= 0) components is important!
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

13 / 23

Mixture of the hadronic molecule and compact state▶ Hadronic molecule + Compact state (Massive)

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

14 / 23

Mixture of the hadronic molecule and compact state▶ Hadronic molecule + Compact state (Massive)⇒ Level repulsion generating an attraction in the hadronic molecules

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

14 / 23

Mixture of the hadronic molecule and compact state▶ Hadronic molecule + Compact state (Massive)⇒ Level repulsion generating an attraction in the hadronic molecules▶ Hadronic molecule coupling to Compact state ⇒ Effective hadroninteraction

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

14 / 23

Mixture of the hadronic molecule and compact state▶ Hadronic molecule + Compact state ⇒ Effective hadron interaction

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

15 / 23

Mixture of the hadronic molecule and compact state▶ Hadronic molecule + Compact state ⇒ Effective hadron interaction⇒ −fSi Sj e−αr

2

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

15 / 23

Mixture of the hadronic molecule and compact state▶ Hadronic molecule + Compact state ⇒ Effective hadron interaction⇒ −fSi Sj e−αr2Free Parameters
Strength f and Gaussian para. α (→ may be fixed in the future)(f is determined by the Pc data. α = 1 fm−2 is fixed.)

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

15 / 23

Mixture of the hadronic molecule and compact state▶ Hadronic molecule + Compact state ⇒ Effective hadron interaction⇒ −fSi Sj e−αr2Free Parameters
Strength f and Gaussian para. α (→ may be fixed in the future)(f is determined by the Pc data. α = 1 fm−2 is fixed.)

Relative strength Si(∗)(i, j = D̄(∗) Λc , D̄(∗) Σc )Spectroscopic factors ⇒ determined by the spin structure of 5q
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

15 / 23

Numerical Results for Hidden-charm sector+

Long range int.

Short range int.
(Gaussian)Bound state and Resonance▶ Coupled-channel Schrödinger equation for D̄Λc , D̄∗ Λc , D̄Σc , D̄Σ∗c ,D̄∗ Σc , D̄∗ Σ∗c (6 MB components).
▶ For JP = 1/2− , 3/2− , 5/2− (Negative parity)
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

16 / 23

For New Pc states by LHCb in 2019
Y.Y., H.Garcia-Tecocoatzi, A.Giachino, A.Hosaka, E.Santopinto, S.Takeuchi, M.Takizawa, PRD 101 (2020) 091502(R)(f0 = 6 MeV)

+Γ/2
M
-Γ/2

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

17 / 23

For New Pc states by LHCb in 2019
Y.Y., H.Garcia-Tecocoatzi, A.Giachino, A.Hosaka, E.Santopinto, S.Takeuchi, M.Takizawa, PRD 101 (2020) 091502(R)(f0 = 6 MeV)

+Γ/2
M
-Γ/2

▶ Agreement with Pc (4312), Pc (4440), and Pc (4457)

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

17 / 23

For New Pc states by LHCb in 2019
Y.Y., H.Garcia-Tecocoatzi, A.Giachino, A.Hosaka, E.Santopinto, S.Takeuchi, M.Takizawa, PRD 101 (2020) 091502(R)(f0 = 6 MeV)

+Γ/2
M
-Γ/2
Broad Pc(4380)▶ Agreement with Pc (4312), Pc (4440), and Pc (4457)▶ For Broad Pc (4380), we obtain the similar mass. But width...?
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

17 / 23

For New Pc states by LHCb in 2019
Y.Y., H.Garcia-Tecocoatzi, A.Giachino, A.Hosaka, E.Santopinto, S.Takeuchi, M.Takizawa, PRD 101 (2020) 091502(R)(f0 = 6 MeV)

+Γ/2
M
-Γ/2

▶ Agreement with Pc (4312), Pc (4440), and Pc (4457)▶ For Broad Pc (4380), we obtain the similar mass. But width...?
▶ Predictions: (1/2− , 3/2− , 5/2− ) states below D̄∗ Σ∗cY. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

17 / 23

For New Pc states by LHCb in 2019
Y.Y., H.Garcia-Tecocoatzi, A.Giachino, A.Hosaka, E.Santopinto, S.Takeuchi, M.Takizawa, PRD 101 (2020) 091502(R)(f0 = 6 MeV)

+Γ/2
M
-Γ/2

Pc

LHCb (M, Γ)JP

Pc (4312)
Pc (4380)
Pc (4440)
Pc (4457)
Pc
Pc
Pc(4312,9.8)(4380,205)(4440,21)(4457,6.4)
—
—
—

1/2−
3/2−
3/2−
1/2−
1/2−
3/2−
5/2−

Y. Yamaguchi (Nagoya Univ)

Ours
5q+OPEP

C. W. Xiao, et al.,
PRD100(2019)014021
Local hidden gauge

M. Z. Liu, et al.,PRL122(2019)242002
Cont (B)

M. L. Du, et al.,2102.07159
Cont+OPEP (IIB)(4299,9.4)(4350,5)(4415,15)(4462,3.2)(4521,2.8)(4511,14)(4468,18)(4306,15)(4374,14)(4452,3.0)(4453,23)(4520,22)(4519,14)(4519,0)4306
4371
4440 (input)
4457 (input)
4523
4517
4500

(4313,6)(4376,12)(4441,8)(4461,10)(4525,18)(4520,24)(4500,16)

CLUSHIQ2022 (2 Nov 2022)

17 / 23

Role of Interactions in Pc
4460

Pc (4457)?

4450

D̄⇤ ⌃c

1/2

E [MeV]

4440

4430

3/2

4420

Pc (4440)?

▷ Our JP assignment
Pc (4440): 3/2−
Pc (4457): 1/2−
E(1/2− ) > E(3/2− )

4410

4400

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

18 / 23

Role of Interactions in Pc
4460

Pc (4457)?

4450

D̄⇤ ⌃c

1/2

w/o Tensor▷ Our JP assignment
Pc (4440): 3/2−
Pc (4457): 1/2−

E [MeV]

4440

4430

3/2

4420

w/o Tensor

Pc (4440)?

E(1/2− ) > E(3/2− )

4410

4400

▶ with Tensor (original) vs without Tensor for Vπ⇒ Mass and Width are reduced!
1/2− : (E, Γ) = (4462, 1.6) [MeV] ⇒ (4462, 0.48) [MeV]
3/2− : (E, Γ) = (4415, 7.5) [MeV] ⇒ (4433, 0.88) [MeV]Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

18 / 23

Role of Interactions in Pc
4460

Pc (4457)?

4450

D̄⇤ ⌃c

1/2

w/o Tensor

E [MeV]

4440

Small

4430

3/2

4420

▷ Our JP assignment
Pc (4440): 3/2−
Pc (4457): 1/2−
E(1/2− ) > E(3/2− )w/o Tensor

Pc (4440)?
4410

4400

▶ with Tensor (original) vs without Tensor for Vπ⇒ Mass and Width are reduced!
1/2− : (E, Γ) = (4462, 1.6) [MeV] ⇒ (4462, 0.48) [MeV]
3/2− : (E, Γ) = (4415, 7.5) [MeV] ⇒ (4433, 0.88) [MeV]▷ V5q : Major role to determine Energy Levels

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

18 / 23

Role of Interactions in Pc
4460

Pc (4457)?

4450

D̄⇤ ⌃c

1/2

w/o Tensor

E [MeV]

4440

Small

4430

3/2

4420

▷ Our JP assignment
Pc (4440): 3/2−
Pc (4457): 1/2−
E(1/2− ) > E(3/2− )w/o Tensor

Pc (4440)?
4410

4400

▶ with Tensor (original) vs without Tensor for Vπ⇒ Mass and Width are reduced!
1/2− : (E, Γ) = (4462, 1.6) [MeV] ⇒ (4462, 0.48) [MeV]
3/2− : (E, Γ) = (4415, 7.5) [MeV] ⇒ (4433, 0.88) [MeV]▷ V5q : Major role to determine Energy Levels▷ Vπ : Major role to enhance Decay Width (Channel-coupling effect)
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

18 / 23

Today’s talkExotic hadrons as
hadronic molecule + compact state






⇐⇒

Mixture?

1. Introduction
Exotic hadron, Our mixture model

2. Numerical results: Pc (qqqcc̄) pentaquark
3. Numerical results: Pcs (qqscc̄) pentaquark
4. Summary
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

19 / 23

Strange partner Pcs (qqscc̄) in 2020 and 2022!
▶ Pcs (4459) in 2020 Ref. R.Aaij, et al. (LHCb), Sci. Bull. 66 (2021) 1278-1287,▷ One Pcs state ?
+8.0
M = 4458.8 ± 2.9+4.7−1.1 MeV, Γ = 17.3 ± 6.5−5.7 MeV(below the Ξ0c D̄∗0 threshold )▷ Two-peak structure hypothesis
M1 = 4454.9 ± 2.7 MeV, Γ1 = 7.5 ± 9.7 MeV
M2 = 4467.8 ± 3.7 MeV, Γ2 = 5.2 ± 5.3 MeV

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

20 / 23

Strange partner Pcs (qqscc̄) in 2020 and 2022!
▶ Pcs (4459) in 2020 Ref. R.Aaij, et al. (LHCb), Sci. Bull. 66 (2021) 1278-1287,▷ One Pcs state ?
+8.0
M = 4458.8 ± 2.9+4.7−1.1 MeV, Γ = 17.3 ± 6.5−5.7 MeV(below the Ξ0c D̄∗0 threshold )▶ Pcs (4338) in 2022

▷ Two-peak structure hypothesis
M1 = 4454.9 ± 2.7 MeV, Γ1 = 7.5 ± 9.7 MeV
M2 = 4467.8 ± 3.7 MeV, Γ2 = 5.2 ± 5.3 MeV

https://lhcb-outreach.web.cern.ch/2022/07/05/observation-of-a-strange-pentaquark-a-doubly-charged-tetraquark-and-its-neutral-partner/

M = 4338.2 ± 0.7 ± 0.4 MeV
Γ = 7.0 ± 1.2 ± 1.3 MeV(near the Ξc D̄ threshold)

The preferred quantum numbers are JP = 1/2− .
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

20 / 23

Numerical Results for Strange Hidden Charm+Long range int.

Short range int.
(Gaussian)Bound state and Resonance▶ Coupled-channel Schrödinger equation for D̄s Λc , D̄∗s Λc , D̄Ξc , D̄∗ Ξc ,D̄Ξ′c , D̄Ξ∗c , D̄∗ Ξ′c , D̄∗ Ξ∗c (8 MB components).
▶ Method: Gaussian expansion method + Complex scaling method▶ For JP = 1/2− , 3/2− , 5/2− (Negative parity)
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

21 / 23

Numerical results for JP = 1/2− , 3/2− , 5/2−
Comparing EXP with the predicted masses
A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi,
M. Takizawa, Y.Y, arXiv:2209.10413 [hep-ph]▶ Two Ξc D̄∗ bound states↔ Pcs (4468), Pcs (4455)?

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

22 / 23

Numerical results for JP = 1/2− , 3/2− , 5/2−
Comparing EXP with the predicted masses
A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi,
M. Takizawa, Y.Y, arXiv:2209.10413 [hep-ph]▶ Two Ξc D̄∗ bound states↔ Pcs (4468), Pcs (4455)?
▶ One Ξc D̄ bound state↔ Pcs (4338)?

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

22 / 23

Numerical results for JP = 1/2− , 3/2− , 5/2−
Comparing EXP with the predicted masses
A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi,
M. Takizawa, Y.Y, arXiv:2209.10413 [hep-ph]▶ Two Ξc D̄∗ bound states↔ Pcs (4468), Pcs (4455)?
▶ One Ξc D̄ bound state↔ Pcs (4338)?
▶ Four new predictions
Rich structure near the thresholds 

Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

22 / 23

Numerical results for JP = 1/2− , 3/2− , 5/2−
Comparing EXP with the predicted masses
A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi,
M. Takizawa, Y.Y, arXiv:2209.10413 [hep-ph]▶ Two Ξc D̄∗ bound states↔ Pcs (4468), Pcs (4455)?
▶ One Ξc D̄ bound state↔ Pcs (4338)?
▶ Four new predictions
Rich structure near the thresholds ▶ The short-range interaction plays the important role to generate theattraction → Without the short-range int, no bound state is found.
▶ π exchange dominates to determine Γ (Channel-coupling effect)
Y. Yamaguchi (Nagoya Univ)

CLUSHIQ2022 (2 Nov 2022)

22 / 23

Summary⇐⇒

Mixture?

▶ Many exotic hadrons have been reported in the experiments▶ Hadronic molecule + compact state model▶ Long-range int. : π exchange potential▶ Short-range int. : Coupling to the compact state▶ Pc and Pcs resonances are obtained near the thresholds.
▶ Short-range int. determining Ere▶ Long-range int. enhancing Γ
Y.Y, A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi, M. Takizawa, Phys. Rev. D 101 (2020) 091502(R),
A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi, M. Takizawa, Y.Y, arXiv:2209.10413 [hep-ph]Y. Yamaguchi (Nagoya Univ)

Thank you for yourkind attention.
CLUSHIQ2022 (2 Nov 2022)

23 / 23