multi-quark hadrons in the quark model
TRANSCRIPT
![Page 1: Multi-Quark Hadrons in the Quark Model](https://reader031.vdocuments.us/reader031/viewer/2022011817/61d54b384b9d493d96771cd0/html5/thumbnails/1.jpg)
Multi-Quark Hadrons in the Quark Model
Makoto Oka Advanced Science Research Center, JAEA
March 2019, YITP
Makoto Oka (ASRC, JAEA)
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Makoto Oka (ASRC, JAEA)
Contents1. Introduction
2. Dibaryon d*= DΔ = ΔΔ (I=0, J=3)
3. Pentaquark Pcs (ccbaruds)
4. Pentaquark Pc (ccbaruud)
5. Conclusion
2
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Makoto Oka (ASRC, JAEA)
IntroductionHadrons 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 of 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
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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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ms � 500MeV<latexit sha1_base64="n2pzVN/ZbBWFpiYKayiTi5E9Btk=">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</latexit><latexit sha1_base64="pgOi6Ta38bBiJByoZuVnPokSyWs=">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</latexit><latexit sha1_base64="pgOi6Ta38bBiJByoZuVnPokSyWs=">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</latexit><latexit sha1_base64="/JrrGapo85mld5TGn0chuURtHkQ=">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</latexit>
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2mi+ Vconf + VOgE
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�a
2�µ
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�a
2�µ
<latexit sha1_base64="N7Vxv9QRX2/y9ZGIr8vVSTw706c=">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</latexit><latexit sha1_base64="14qxnC+PBzJp6cBbEU0jOpLSNZw=">AAACinicjVFNLwNRFD3Gd3202EgIQipW8tqFz02TWlgqisRQb8ZrTTpfmZk2YdKljT9gYUViQbf8Aht/wMIPsBDLSmws3JkSRIg7mXnnnXvPeffOU2xdcz3G7hukxqbmlta29khHZ1d3NNbTu+ZaJUcVWdXSLWdD4a7QNVNkPc3TxYbtCG4oulhXiukgv14WjqtZ5qq3b4stgxdMLa+p3CMqFxuW8w5XfVknyS7f5hU/WZEL3DB4zpeNUiUXG0tMsjBG2A/wkRpLTQ2mH5JDO0tW7BIydmFBRQkGBEx4hHVwuPRsIgEGm7gt+MQ5hLQwL1BBhLQlqhJUwYkt0rdAu8131qR94OmGapVO0el1SDmCOLtjF6zGblmVPbJX8or/4uaHLkE3+7QqdbWwc9Gj/pWXf+gMWj3sfer+0ASde8hjJuxYownskAlmUesO5YPj2srcctwfZ2fsiaY4ZffshuYwy8/qeUYsnyDy9Rp+B2vJyQThDN1HCvVowwBGMUF/fRopLGIJWTr3EFVc4VrqlJLSrDRfL5Ua3jV9+BbSwhvdtZld</latexit><latexit sha1_base64="14qxnC+PBzJp6cBbEU0jOpLSNZw=">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</latexit><latexit sha1_base64="XOIlN2jCqeC0deuDseoPwyxDEUA=">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</latexit>
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Makoto Oka (ASRC, JAEA)
Spin dependenceSpin-spin interaction aka Color-Magnetic Interaction (CMI)
12
C2[SU(g)]([f1, f2, . . . , fg]) =�
i
fi(fi � 2i + g + 1)� N2
g
VCMI = ���
i<j
(⇧⇤i · ⇧⇤j)(⇧⌅i · ⇧⌅j)f(rij) f(rij) ⇥ ⇥(rij)VCMI = ���
i<j
(⇧⇤i · ⇧⇤j)(⇧⌅i · ⇧⌅j)f(rij) f(rij) ⇥ ⇥(rij)
�VCMI⇥(0s)N = � �f(r)⇥0s �cm
prefers symmetric color-spin states
�CM ⇥ ⇤��
i<j
(⇤�i · ⇤�j)(⇤⇥i · ⇤⇥j)⌅color singlet
= 8N � 2C2[SU(6)] +43S(S + 1)�CM = 8N � 2C2[SU(6)cs] +
43S(S + 1) + C2[SU(3)c]
C2[singlet] = 0
�CM = V0�CM
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Makoto Oka (ASRC, JAEA)
Spin dependenceCMI prefers color-spin symmetric states, i.e. flavor antisymmetric states.
13
�CM(10)��CM(8) = 8� (�8) = 16
�CM(H)� 2�CM(⇥) = �24� 2(�8) = �8
�CM(D�)� 2�CM(�) = 16� 2⇥ 8 = 0
�CM = 8N � 2C2[SU(6)cs] +43S(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)
![Page 8: Multi-Quark Hadrons in the Quark Model](https://reader031.vdocuments.us/reader031/viewer/2022011817/61d54b384b9d493d96771cd0/html5/thumbnails/8.jpg)
From ABC to DΔ
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Makoto Oka (ASRC, JAEA)
ABC effectA. 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
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Makoto Oka (ASRC, JAEA)
ABC effectA. 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
16
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Makoto Oka (ASRC, JAEA)
d* resonanceWASA@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.
17
ΔΔ contributions
d* : s-channel resonance mR=2.37 GeV and Γ=68 MeV
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Makoto Oka (ASRC, JAEA)
d* resonanceWASA@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.
18
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Makoto Oka (ASRC, JAEA)
d* resonanceWASA@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.
19
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Makoto Oka (ASRC, JAEA)
DΔ (ΔΔ)I=0 di-baryon
20
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Makoto Oka (ASRC, JAEA)
Di-baryonby M.O. (1980)
21
Pauli Allowed channels
Fermion statistics for Quarks
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�CM � ��
i<j
(�ai �a
j )(�ki �k
j ) = 8n� 2C6 +43S(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 = ��(I = S = 0) V = V0 � (�8)
V0 = 300/16 � 18(MeV)
�CM(�) = +8�CM(N) = �8
Color Magnetic Interaction
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Makoto Oka (ASRC, JAEA)
Spin dependenceCMI prefers color-spin symmetric states, i.e. flavor antisymmetric states.
23
�CM(10)��CM(8) = 8� (�8) = 16
�CM(H)� 2�CM(⇥) = �24� 2(�8) = �8
�CM(D�)� 2�CM(�) = 16� 2⇥ 8 = 0
�CM = 8N � 2C2[SU(6)cs] +43S(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)
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Makoto Oka (ASRC, JAEA)
DΔ (ΔΔ)I=0 di-baryonS=3, I=0 (Δ2) bound state
Relative wave function
No repulsive core100 200 MeV
7S3 phase shift
24
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Makoto Oka (ASRC, JAEA)
Di-lepton enhancementDLS puzzle: low energy di-lepton enhancement in pA, AA collisions @ E~1GeV/A originally found in DLS detector at Bevalac PRL 79, 1229 (1997), PRC 57, 1865 (1998) confirmed by HADES@Darmstadt PLB 690 (2010) 118
25
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Makoto Oka (ASRC, JAEA)
Di-lepton enhancement
26
DLS PRC 57, 1865 (1998)
pd/pp ratio
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Makoto Oka (ASRC, JAEA)
Di-lepton enhancement
27
PLB 690 (2010) 118
Enhancement at Mee ~ 0.3~0.6 GeV
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Makoto Oka (ASRC, JAEA)
Di-lepton enhancementThe 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.
28
NN � ��� NN�� � NN�� � NNe+e�
(��)I=1 � �0 � ��
��
�
1/2 1 3/21/2 1 3/2INN 1 Itot
��
�
��
�
1/2 1 3/21/2 1 3/21 1 1
��
� = 0
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Hidden-Charm Pentaquarks
![Page 24: Multi-Quark Hadrons in the Quark Model](https://reader031.vdocuments.us/reader031/viewer/2022011817/61d54b384b9d493d96771cd0/html5/thumbnails/24.jpg)
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+)
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Makoto Oka (ASRC, JAEA)
Hidden-Charm PentaquarksConstituent 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.
31
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Makoto Oka (ASRC, JAEA)
Hidden-Charm Pentaquarkscolor 1 cc56 = (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 cc70 = (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+ N8The 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-
32
�CM ⇥ ⇤��
i<j
(⇤�i · ⇤�j)(⇤⇥i · ⇤⇥j)⌅color singlet
= 8N � 2C2[SU(6)] +43S(S + 1)
u du
cc
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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
33
m(u, d) = 313 MeV m(s) = 522 MeV
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Makoto Oka (ASRC, JAEA)
Instanton-Light quark coupling gives an effective interaction
Flavor Singlet Pentaquark Pcs
The3-bodyIIIisrepulsiveinflavorsingletu-d-ssystems
2-bodyIII
3-bodyinteraction
2-bodyinteraction
[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
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Makoto Oka (ASRC, JAEA)
Flavor Singlet Pentaquark Pcs
Pcs family (I=0, Str= -1)
35
u ds
cc
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8*
Energy Spectrum
Thelowestenergystateis8’.
Theinstantoninducedinteractionlowersthemassesbyabout80MeV.
Two1/2-statesmixbytheCMI.8 8’
Y. Irie, MO, S. Yasui.Phys. Rev. D 97 (2018) 034006
Avariationalmethodisusedforaqualitativeevaluationofthespectrum.
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8*
Energy Spectrum
Thelowestenergystateis8’.
Theinstantoninducedinteractionlowersthemassesbyabout80MeV.
Two1/2-statesmixbytheCMI.
8 8’
Y. Irie, MO, S. Yasui.Phys. Rev. D 97 (2018) 034006
Avariationalmethodisusedforaqualitativeevaluationofthespectrum.
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8*
Decays
8 8’FlavorSU(3):suppressed
(barely)allowed8* :D-wavedecay
8* :S-wavedecayWithInstantons→forbidden
Y. Irie, MO, S. Yasui.Phys. Rev. D 97 (2018) 034006
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nocharge
negativecharge
Production
Pcs<latexit sha1_base64="batGNA8MHLZAu9BsmBiqKeLRLwM=">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</latexit><latexit sha1_base64="JVBE7hu+5gIXidMhv7mMV+vY+Vk=">AAACb3icjVFNS8NAEH2N3/Wr6kFBkKBUFKRMq6D1VPDisX60CioliVuNpklI0oKWXjx68ibqScGD+jO8+AcU/AeKJ1EQxIOTtCIeFGfZ3dk3897O7Kq2obse0X1IqqtvaGxqbgm3trV3dEa6urOuVXQ0kdEsw3KWVcUVhm6KjKd7hli2HaEUVEMsqdszfnypJBxXt8xFb8cWawVlw9TzuqZ4DGXTubLmVnKRIYpRYDLF4hNJSvhOIjlF40k5XgsNpXru3vceKmNpK3KJVazDgoYiChAw4bFvQIHLYwVxEGzG1lBmzGFPD+ICFYSZW+QswRkKo9u8bvBppYaafPY13YCt8S0GT4eZMqJ0Sxf0Qjd0RY/0wVrRX9TKgYpfzQ7vapUt7Fznft/C2z94Bd49bH7z/uD4lXvIYyqoWOcO7ADxe9GqCqXdw5eF6floeZjO6Im7OKV7uuY+zNKrdj4n5k8Q5m/4emv5dyebiMXZn+P/SKFqzejHIEb41SeRwizSyPC9WzjAEY5Dz1KvNCDJ1VQpVOP04IdJo59y75Ee</latexit><latexit sha1_base64="JVBE7hu+5gIXidMhv7mMV+vY+Vk=">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</latexit><latexit sha1_base64="kIIjPuMvJf4OFNorQ3x+Gx4tfdU=">AAACb3icjVFNS8NAEH2NX7V+VT0oCBIsFb2UaRW0ngpePNaPVkGlJHHV2DQJSVrQ4h/w5E3Uk4IH9Wd48Q946E8QT1LBiwcnaUQ8KM6yu7Nv5r2d2VVtQ3c9okZEamvv6OyKdsd6evv6B+KDQ0XXqjqaKGiWYTkbquIKQzdFwdM9Q2zYjlAqqiHW1fKiH1+vCcfVLXPNO7TFdkXZM/VdXVM8hor5Ul1zj0vxBKUoMJlS6dksZXwnk52nmaycDkMJhJa34nfYwg4saKiiAgETHvsGFLg8NpEGwWZsG3XGHPb0IC5wjBhzq5wlOENhtMzrHp82Q9Tks6/pBmyNbzF4OsyUkaQnuqUmPdI9PdMHayV/UasHKn41h7yrLbawSwMno6vv/+BVePew/837g+NX7mEX80HFOndgB4jfi9ZSqB2dNVcXVpL1SbqmF+7iihr0wH2YtTftZlmsXCLG3/D11vLvTjGTSrO/TIlcLvyQKMYwgSl+9TnksIQ8CnzvAU5xjovIqzQijUtyK1WKhJxh/DBp+hOlAozo</latexit>
Pcs<latexit sha1_base64="batGNA8MHLZAu9BsmBiqKeLRLwM=">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</latexit><latexit sha1_base64="JVBE7hu+5gIXidMhv7mMV+vY+Vk=">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</latexit><latexit sha1_base64="JVBE7hu+5gIXidMhv7mMV+vY+Vk=">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</latexit><latexit sha1_base64="kIIjPuMvJf4OFNorQ3x+Gx4tfdU=">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</latexit>
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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,
39
Vconf = �a�
all(ij)pairs
(�(i)c · �(j)
c ) rpij
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B. Silvestre-Brac, Few Body Syst. 20 (1996) 1-25
(p=1 or 2/3)
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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 of the scattering states will change (decrease) towards the scattering threshold, but the compact state will stay.
40
r(1)ρ (1)
R (1)s(1)
C=1
q
c
c
1 4
5
r(2 ) ρR (2) s (2)(2)
1
2
3
4 5
q
qc
q
c
C=2
r(3)R (3)
ρ (3)s(3)
1
2
3
45
q
q
q
cc
C=3
r(4) R (4) ρ(4)s(4)
1
2
3
45
q
q
q
cc
C=4
2 3
Pentaquark Pc
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Makoto Oka (ASRC, JAEA)
Energy levels before coupling to the scattering channels
41
4000
4100
4200
4300
4400
4500
4600
4700
MeV
4119
4236
4497
458145934629
46794708
4221
4577
4617
4700
3900
48004748
4711
4900
48364840
4896
JP =1 2 JP = 3 2
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/� + N<latexit sha1_base64="H0phQDUQOK1/S69w4nhQGI/u53Q=">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</latexit><latexit sha1_base64="TI/SXk9FJ6zWHgEuTsv4a2UUHT8=">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</latexit><latexit sha1_base64="TI/SXk9FJ6zWHgEuTsv4a2UUHT8=">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</latexit><latexit sha1_base64="TYkVxDx1/2RjOFwz9KIHStQbGrk=">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</latexit>
�c + N<latexit sha1_base64="lEm83f5224s8Dxp7tUfOLLGBJUA=">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</latexit><latexit sha1_base64="H9d/OXLkQZyNXjNyyKVj7OxA4yE=">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</latexit><latexit sha1_base64="H9d/OXLkQZyNXjNyyKVj7OxA4yE=">AAACcXicjVE9S8NQFD2N3/WjVRfFwaBUBKHcVq3VqeDiJH5VCyoliU8NpklIXgtanAVHFwddFBzUn+HiLDj4E8SxgouDN6kiDoo3JO+88+45ufc+3bVMXxI9RZSGxqbmlta2aHtHZ1cs3t2z6jtlzxB5w7Ecr6BrvrBMW+SlKS1RcD2hlXRLrOl7s8H5WkV4vunYK3LfFZslbcc2t01Dk0wVNoTUisbYfDE+TMnpbGZ8PKVSkjLpTHoyANM0kZ1SU0kKYzjXf1R0HgZrC078BhvYggMDZZQgYEMytqDB52cdKRBc5jZRZc5jZIbnAoeIsrbMWYIzNGb3+LvDu/VP1uZ94OmHaoP/YvHrsVJFgh7pmmp0T7f0TO/slfjFrRq6BNXs86rX1cItxo77lt/+oSvxKrH7rftDE1QusY1sWLHJHbghE/Ri1B0qB6e15ZmlRHWELumFu7igJ7rjPuzKq3G1KJbOEOVr+Jq1+jtYTSdTjBf5PnKoRysGMIRRnvoUcpjDAvLhtE9whvNITelXVGWonqpEPjW9+BHK2Ad6L5EC</latexit><latexit sha1_base64="UcoeJTr0QodAvva8Co/1pWh2PDw=">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</latexit>
many thresholds
Pc(4380)<latexit sha1_base64="KNS5XJ2wlFSQQq3SSSrhOim6HBE=">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</latexit><latexit sha1_base64="zlmtHJM2FvNggbH1N4Q/L4pw+Vo=">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</latexit><latexit sha1_base64="zlmtHJM2FvNggbH1N4Q/L4pw+Vo=">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</latexit><latexit sha1_base64="iOkfQ0CoVuuAKKoMqglXxc3PX/U=">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</latexit>
Pc(4450)<latexit sha1_base64="Ia2kc5me7nh7k+wc/tm0QDRi2sk=">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</latexit><latexit sha1_base64="wBBcm6SrWf5KApdcIRO+CGxOr/k=">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</latexit><latexit sha1_base64="wBBcm6SrWf5KApdcIRO+CGxOr/k=">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</latexit><latexit sha1_base64="RjhheNh7M//ks9CsOTzHVwHnSU0=">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</latexit>
Pentaquark Pc
(α=1)
![Page 37: Multi-Quark Hadrons in the Quark Model](https://reader031.vdocuments.us/reader031/viewer/2022011817/61d54b384b9d493d96771cd0/html5/thumbnails/37.jpg)
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
42
4000
4100
4200
4300
4400
4500
4600
4700
MeV
4119
4236
4497
458145934629
46794708
4221
4577
4617
4700
3900
48004748
4711
4900
48364840
4896
JP =1 2 JP = 3 2
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)
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(�c + N) scattering<latexit sha1_base64="Hjj/NKwVHe1+WDgHhxo/nRSTtbc=">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</latexit><latexit sha1_base64="Nvu7S7eENIj+KxtHmVr2wbyNfx0=">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</latexit><latexit sha1_base64="Nvu7S7eENIj+KxtHmVr2wbyNfx0=">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</latexit><latexit sha1_base64="JIRLZJuVddMLE8XOKoQOEIto0uQ=">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</latexit>
Pentaquark Pc
![Page 38: Multi-Quark Hadrons in the Quark Model](https://reader031.vdocuments.us/reader031/viewer/2022011817/61d54b384b9d493d96771cd0/html5/thumbnails/38.jpg)
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 calculationFree solutions
Pentaquark Pc
Estimated decay width from the level crossing is about 40 MeV.
![Page 39: Multi-Quark Hadrons in the Quark Model](https://reader031.vdocuments.us/reader031/viewer/2022011817/61d54b384b9d493d96771cd0/html5/thumbnails/39.jpg)
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.
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![Page 40: Multi-Quark Hadrons in the Quark Model](https://reader031.vdocuments.us/reader031/viewer/2022011817/61d54b384b9d493d96771cd0/html5/thumbnails/40.jpg)
Makoto Oka (ASRC, JAEA)
ConclusionI 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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