Multi-Quark Hadrons in the Quark Model Makoto Oka Advanced Science - - PowerPoint PPT Presentation

Multi-Quark Hadrons 
 in the Quark Model

Makoto Oka

Advanced Science Research Center, JAEA
 March 2019, YITP

Makoto Oka (ASRC, JAEA)

Makoto Oka (ASRC, JAEA)

Contents

• 1. Introduction
• 2. Dibaryon d*= DΔ = ΔΔ (I=0, J=3)
• 3. Pentaquark Pcs (ccbaruds)
• 4. Pentaquark Pc (ccbaruud)
• 5. Conclusion

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Makoto Oka (ASRC, JAEA)

Introduction

Hadrons are made of quarks bound by gluonic forces. Dynamics of quarks and gluons are highly non-perturbative. Low-lying hadrons are described in terms (only) of valence, or constituent quarks. No hadron with constituent gluon is confirmed. The constituent quark seems to exhibit “non-relativistic” degrees

• f freedom even for light (chiral) quarks, i.e., orbital motion, spin,

flavor and color. The short-range interactions among the quarks are described by spin-color-flavor dependent two-body forces. The color Coulomb interaction and the color-magnetic interaction are dominant. At long distances, the color confinement is to be realized, but no consensus is reached for how the confinement is described by

• potentials. The pair production/annihilation of quarks are not

under control in the potential model.

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Color Interactions of Quarks

Makoto Oka (ASRC, JAEA)

Potential Quark Model

Linear confinement with color Casimir dependence
 
 OgE: Electric Coulomb interaction
 
 OgE: Magnetic spin-spin interaction
 
 Non-relativistic quarks with

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mu,d ∼ 300MeV

ms ∼ 500MeV

H =

• i

p2

i

2mi + Vconf + VOgE

q

q

λa 2 γµ

λa 2 γµ

Makoto Oka (ASRC, JAEA)

Spin dependence

Spin-spin interaction aka Color-Magnetic Interaction (CMI)

12 C2[SU(g)]([f1, f2, . . . , fg]) =

• i

fi(fi − 2i + g + 1) − N 2 g

VCMI = −

• i<j

(⇧ ⇤i · ⇧ ⇤j)(⇧ ⌅i · ⇧ ⌅j)f(rij) f(rij) ∼ ⇥(rij) VCMI⇥(0s)N = α f(r)⇥0s ∆

prefers symmetric color-spin states

∆CM ⇥ ⇤

• i<j

(⇤ i · ⇤ j)(⇤ ⇥i · ⇤ ⇥j)⌅color

∆CM = 8N − 2C2[SU(6)cs] + 4 3S(S + 1) + C2[SU(3)c]

C2[singlet] = 0 ∆CM = V0∆CM

Makoto Oka (ASRC, JAEA)

Spin dependence

CMI prefers color-spin symmetric states, i.e. flavor antisymmetric states.

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∆CM(10) − ∆CM(8) = 8 − (−8) = 16 ∆CM(H) − 2∆CM(Λ) = −24 − 2(−8) = −8 ∆CM(D∆) − 2∆CM(∆) = 16 − 2 × 8 = 0

∆CM = 8N − 2C2[SU(6)cs] + 4 3S(S + 1) + C2[SU(3)c]

M(∆) − M(N) = 16V0 ∼ 300 MeV V0 ∼ 300/16 ∼ 19 MeV DΔ (ΔΔ, I=0, S=3) H (ΛΛ+NΞ+ΣΣ, S=0)

From ABC to DΔ

Makoto Oka (ASRC, JAEA)

ABC effect

• A. Abashian, N.E. Booth, K.M. Crowe 


Possible anomaly in meson production in p+d collisions, PRL 5, 258 (1960)
 Anomaly in meson production in p+d collisions, PRL 7, 35 (1961)


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phase-space volume adjusted to the data phase space + π-π S-wave enhancement 
 for aI=0= 3.9 fm (exp.~0.2fm) p + d → 3He + π-π (I=0)
 Ep=624-743 MeV

Makoto Oka (ASRC, JAEA)

ABC effect

• A. Abashian, N.E. Booth, K.M. Crowe 


Possible anomaly in meson production in p+d collisions, PRL 5, 258 (1960)
 Anomaly in meson production in p+d collisions, PRL 7, 35 (1961) Low mass ππ enhancement observed in the inclusive production,
 p + d → 3He + X, 3H + X (Ep=624-743 MeV, Berkeley)
 X = ππ (I=0) for 3He
 ππ (I=1) for 3He and 3H As the beam energies correspond to ΔΔ excitation in nucleus, the ππ enhancement is attributed to the ΔΔ excitations.
 The π0π0 enhancement is much larger than estimate in ΔΔ production by Alvarez-Ruso, Oset, Hernandez, NPA 633 (1998) 519.
 An s-channel resonance at mR~2.36 GeV may explain the results. ABC effect in basic double-pionic fusion: A new resonance?
 WASA@COSY, PRL 106, 242302 (2011)
 p+d → d+π0+π0+pspectator at Tp=1.0, 1.2, 1.4 GeV

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Makoto Oka (ASRC, JAEA)

d* resonance

WASA@COSY, PRL 106, 242302 (2011)
 p + n(d) → d + π0 + π0 (+pspectator) at Tp=1.0, 1.2, 1.4 GeV A di-baryon resonance, d* (I=0, Jπ=3+) (in pn and ΔΔ) is suggested.

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ΔΔ contributions d* : s-channel resonance 
 mR=2.37 GeV and Γ=68 MeV

Makoto Oka (ASRC, JAEA)

d* resonance

WASA@COSY+SAID, PRL 112, 202301 (2014)
 Evidence for a new resonance from polarized n-p scattering
 d(↑) + p → np + pspectator
 np analyzing power, Ay(θ), at Tn=1.108-1.197 GeV
 A phase shift analysis of 3D3 (3+) amplitudes shows a narrow resonance at M=2380 MeV and Γ~70 MeV.

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Makoto Oka (ASRC, JAEA)

d* resonance

WASA@COSY+SAID, PRL 112, 202301 (2014)
 Evidence for a new resonance from polarized n-p scattering
 d(↑) + p → np + pspectator
 np analyzing power, Ay(θ), at Tn=1.108-1.197 GeV
 A phase shift analysis of 3D3 (3+) amplitudes shows a narrow resonance at M=2380 MeV and Γ~70 MeV.

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Makoto Oka (ASRC, JAEA)

DΔ (ΔΔ)I=0 di-baryon

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Makoto Oka (ASRC, JAEA)

Di-baryon

by M.O. (1980)

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Pauli Allowed channels Fermion statistics for Quarks

ΓCM ≡ −

• i<j

(λa

i λa j )(σk i σk j ) = 8n − 2C6 + 4

3S(S + 1)

4C6 C6 ≡ C2[SU(6)cs] =

• i

fi(fi − 2i + 7) − n2 6

R.L. Jaffe, PRL 38 (1977) 195

∆∆(I = 0, S = 3) V = V0 × 0 ∆∆(I = 3, S = 0) V = V0 × 32 H = ΛΛ(I = S = 0) V = V0 × (−8) V0 = 300/16 ∼ 18(MeV)

ΓCM(∆) = +8 ΓCM(N) = −8

Color Magnetic Interaction

Makoto Oka (ASRC, JAEA)

Spin dependence

CMI prefers color-spin symmetric states, i.e. flavor antisymmetric states.

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∆CM(10) − ∆CM(8) = 8 − (−8) = 16 ∆CM(H) − 2∆CM(Λ) = −24 − 2(−8) = −8 ∆CM(D∆) − 2∆CM(∆) = 16 − 2 × 8 = 0

∆CM = 8N − 2C2[SU(6)cs] + 4 3S(S + 1) + C2[SU(3)c]

M(∆) − M(N) = 16V0 ∼ 300 MeV V0 ∼ 300/16 ∼ 19 MeV DΔ (ΔΔ, I=0, S=3) H (ΛΛ+NΞ+ΣΣ, S=0)

Makoto Oka (ASRC, JAEA)

DΔ (ΔΔ)I=0 di-baryon

S=3, I=0 (Δ2) bound state

Relative wave function

No repulsive core

100 200 MeV

7S3 phase shift

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Makoto Oka (ASRC, JAEA)

Di-lepton enhancement

DLS puzzle: low energy di-lepton enhancement 
 in pA, AA collisions @ E~1GeV/A


• riginally found in DLS detector at Bevalac


PRL 79, 1229 (1997), PRC 57, 1865 (1998)
 confirmed by HADES@Darmstadt
 PLB 690 (2010) 118

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Makoto Oka (ASRC, JAEA)

Di-lepton enhancement

26 DLS PRC 57, 1865 (1998)

pd/pp ratio

Makoto Oka (ASRC, JAEA)

Di-lepton enhancement

27 PLB 690 (2010) 118

Enhancement at Mee ~ 0.3~0.6 GeV

Makoto Oka (ASRC, JAEA)

Di-lepton enhancement

The DΔ formation in the pn scattering may be the origin.


• M. Bashkanov, H. Clement, EPJ A50 (2014) 107


On a possible explanation of the DLS puzzle The isospin factor for the (ππ)I=0 formation from pp vanishes. So the enhancement is attributed to the DΔ resonance in p+n, which gives relevant energy dependence.

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NN → ∆∆ → NNππ → NNγ∗ → NNe+e−

(ππ)I=1 ∼ ρ0 → γ∗

   1/2 1 3/2 1/2 1 3/2 INN 1 Itot       1/2 1 3/2 1/2 1 3/2 1 1 1    = 0

Hidden-Charm Pentaquarks

Makoto Oka (ASRC, JAEA)

Exp: Hidden-Charm Pentaquark Pc

Pc → J/ψ+p (ccuud)
 LHCb (PRL 115 (2015) 07201) found two penta-quark states with hidden cc.
 
 


30 Pc(4450) (5/2-) Pc(4380) (3/2+)

Makoto Oka (ASRC, JAEA)

Hidden-Charm Pentaquarks

Constituent quark model analyses “Study of qqq cbar c five quark system with three kinds of quark- quark hyperfine interaction”,
 S.G. Yuan, K.W. Wei, J. He, H.S. Xu, B.S. Zou, 


• Eur. Phys. J. A 48 (2012) 61.

“The hidden charm pentaquarks are the hidden color-octet uud baryons?”
 Sachiko Takeuchi, Makoto Takizawa, Phys. Lett. B 764 (2017) 254. “Flavor-singlet hidden charm pentaquark”
 Yoya Irie, MO, Shigehiro Yasui, Phys. Rev. D 97 (2018) 034006 “Quark model estimate of hidden-charm pentaquark resonances”


• E. Hiyama, A. Hosaka, MO, J. M. Richard, Phys. Rev. C98 (2018)

045208.


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Makoto Oka (ASRC, JAEA)

Hidden-Charm Pentaquarks

color 1 cc
 56 = (8, 1/2) + (10, 3/2)
 (8,1/2) ΔCM = -8 Pc= cc uud = ηc or J/ψ + p
 (10,3/2) ΔCM = 8 color 8 cc
 70 = (1, 1/2) + (8, 1/2) + (8, 3/2) + (10, 1/2)
 (1,1/2) ΔCM = -14 Pcs= cc uds = η8/ψ8+ Λ8(singlet)
 (8,1/2) ΔCM = -2 η8/ψ8+ N8
 The most favored state with cc by CMI may not be J/ψ + p. Pcs family (I=0, Str= -1) 
 (cc)8,J=1 + (uds)8, J=1/2 Jπ＝1/2-, 3/2-
 (cc)8,J=0 + (uds)8, J=1/2 Jπ＝1/2-

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∆CM ⇥ ⇤

• i<j

(⇤ i · ⇤ j)(⇤ ⇥i · ⇤ ⇥j)⌅color

u d u c c

Makoto Oka (ASRC, JAEA)

Flavor Singlet Pentaquark Pcs

Potential Quark Model
 Linear confinement with color Casimir dependence
 
 Coulomb electric interaction from one-gluon-exchange
 
 Color magnetic spin-spin interaction from OGE
 
 Non-relativistic quarks with

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m(u, d) = 313 MeV m(s) = 522 MeV

Makoto Oka (ASRC, JAEA)

Instanton-Light quark coupling gives an effective interaction

Flavor Singlet Pentaquark Pcs

The 3-body III is repulsive in flavor singlet u-d-s systems 2-body III

3-body interaction 2-body interaction

[3]G. ‘t Hooft, Phys. Rev. Lett 37 (1976) 8 [4]G. ‘t Hooft, Phys. Rev. D14 (1976) 3432 [5]S. Takeuchi, M. Oka, Nuclear Physics A547 (1992) 283c-288c 34

Makoto Oka (ASRC, JAEA)

Flavor Singlet Pentaquark Pcs

Pcs family (I=0, Str= -1)

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u d s c c

8*

Energy Spectrum

The lowest energy state is 8’. The instanton induced interaction lowers the masses by about 80 MeV. Two 1/2- states mix by the CMI.

8 8’

• Y. Irie, MO, S. Yasui.

• Phys. Rev. D 97 (2018) 034006

A variational method is used for a qualitative evaluation of the spectrum.

8*

Energy Spectrum

The lowest energy state is 8’. The instanton induced interaction lowers the masses by about 80 MeV. Two 1/2- states mix by the CMI.

8 8’

• Y. Irie, MO, S. Yasui.

• Phys. Rev. D 97 (2018) 034006

A variational method is used for a qualitative evaluation of the spectrum.

8*

Decays

8 8’ Flavor SU(3)：suppressed (barely) allowed 8* : D-wave decay 8* : S-wave decay With Instantons → forbidden

• Y. Irie, MO, S. Yasui.

• Phys. Rev. D 97 (2018) 034006

no charge negative charge

Production

Pcs

Pcs

Makoto Oka (ASRC, JAEA)

Pentaquark Pc

• E. Hiyama, A. Hosaka, MO, J. M. Richard, 


“Quark model estimate of hidden-charm pentaquark resonances”, Phys. Rev. C98 (2018) 045208. Complete calculation of the Pentaquark ccuud (I=1/2, JP= 1/2-, 3/2-) in the NR potential quark model with two-body confining potential,

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Vconf = −a

• all(ij)pairs

(λ(i)

c

· λ(j)

c ) rp ij

• B. Silvestre-Brac, Few Body Syst. 20 (1996) 1-25

(p=1 or 2/3)

Makoto Oka (ASRC, JAEA)

Variational method 
 
 
 
 
 scattering channels confined channels Real scaling method
 scale the relative coordinate in channels C=1, 2 by 
 R(1,2) → α R(1,2) (α ~ 1.0 – 1.5) 
 As the ranges of the variational basis functions are finite, all the eigenstates are discrete. Under the real scaling, the energy

• f the scattering states will change (decrease) towards the

scattering threshold, but the compact state will stay.

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r(1) ρ

(1)

R(1) s(1)

C=1

q q q c c 1 4 5 r(2 ) ρ R(2) s(2)

(2)

1 2 3 4 5 q q c q c

C=2

r(3) R (3) ρ

(3)

s(3) 1 2 3 4 5 q q q c c

C=3

r(4) R(4) ρ

(4)

s(4) 1 2 3 4 5 q q q c c

C=4

2 3

Pentaquark Pc

Makoto Oka (ASRC, JAEA)

Energy levels before coupling to the scattering channels

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4000 4100 4200 4300 4400 4500 4600 4700

MeV

4119 4236 4497 4581 4593 4629 4679 4708 4221 4577 4617 4700 3900 4748 4711

c * + D* (4587)

+ N (4584)

c + D* (4505) c + D* (4323) c + D (4353) c + D (4171)

J + N (4040)

c + N (3920)

Thresholds

c + N (4555)

Jπ= 1/2-

3/2-

J/ψ + N

ηc + N

many thresholds

Pc(4380)

Pc(4450)

Pentaquark Pc

(α=1)

Makoto Oka (ASRC, JAEA)

Real scaling around 4100-4300 MeV for 1/2- Coupling of ηcN and J/ψN is weak because of the HQ spin symmetry

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4000 4100 4200 4300 4119 4236 3900

c c + D (

J + N (

c + N (

(J/ψ + N) scattering

(ηc + N) scattering

Pentaquark Pc

Makoto Oka (ASRC, JAEA)

At the end, most of the states are gone with the scattering channels and there remains a narrow 1/2- state at E=4690 MeV.

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Full calculation Free solutions

Pentaquark Pc

Estimated decay width from the level crossing is about 40 MeV.

Makoto Oka (ASRC, JAEA)

Pentaquark Pc

Another resonance structure at E=4920 MeV for Jπ=3/2-. No other (sharp) resonance is found for 1/2+-, 3/2+-, 5/2+- channels. Why do we not reproduce the LHCb pentaquark(s)? Choice 1: This model does not predict loosely-bound hadronic molecules, because it does not induce any long-range interaction between color singlet hadrons, that is, no meson exchange force. Thus the possibility remains that the LHCb pentaquark(s) are Σc + D* molecular resonance state(s). (Not very interesting?) Choice 2: This model does not have a correct (confinement) potential, so that it cannot be applied to the pentaquark systems.

44

Makoto Oka (ASRC, JAEA)

Conclusion

I have shown three cases of analyses in the constituent quark model. So far, the available spectroscopy data (including lattice QCD results) are consistent with the model whenever the color-spin interaction plays the dominant role. It is not confirmed (or may be even doubtful) that the confinement by the color-dependent two-body potential is correct. If the Pc pentaquark is a compact 5-quark state, then the model is not good enough to reproduce such a state.

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