XYZ Theory

Eric Swanson

Sept, 2017[236/134]

D0D0

D0D⇤0DsDs

D⇤0D⇤0DsD⇤

s

D⇤sD

⇤s

⇤+c ⇤�

c

⌘c(1S)

J/ (1S)

�c0(1P )

�c1(1P )hc(1P )�c2(1P )

⌘c(2S) (2S)

(3770)(1D) 2(3823)(1D)

X(3872)

Y (4008)

Z0c (3900)

X(3915) �c2(2P )

X(3940)

Z0c (4020)

(4040)(3S)

Y (4140)X(4160)

(4160)(2D)

Y (4230)Y (4260)

Y (4274)

X(4350)Y (4360)

(4415)(4S)

X(4500)

X(4700)

X(4630)Y (4660)

0�+ 1�� 1+� 0++ 1++ 2++ 2�� ??

3000

3500

4000

4500

JPC

Mass(M

eV)

I=0 pi pi S-wave. Green: pole on the real axis at 758 MeV — bound state just below 2 mpi=782.

Briceno, R. A., J. J. Dudek, R. G. Edwards, and D. J. Wilson (2017a), Phys. Rev. Lett. 118 (2), 022002.

Raul A. Briceno, Jozef J. Dudek, and Ross D. Young, Scattering processes and resonances from lattice QCD, arXiv:1706.06223

Lattice Scattering

��J/� ��hc

�DD� �D�D�

���(nS)��hb(nP )

�K��

Zc(3900) Zc(4025) Zc(4200)

Zc(4475)

Z1(4050)Z2(4250)

Zb(10610)Zb(10650)

K��cJ K�J/�

�BB�

��(2S)

Zc(4240)

Zc(3900)

Attempt a “microscopic” cusp model.

Y (4260)� �DD� Y (4260)� ��J/�

gDD� · exp(��(s�Y )/�2�Y ) exp(��(sDD�)/�2

DD�)

[separable nonrelativistic model; solve exactly][iterate all bubbles]

D. V. Bugg, Europhys. Lett. 96, 11002 (2011)

D. V. Bugg, Int. J. Mod. Phys. A 24, 394 (2009)Zc(3900) & Loops

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-4 -3 -2 -1 0 1 2 3 4

ampl

itude

z

Im(Π)

Re(Π)

|Π|

⇔

(a) (b) (c) (d)

A

B C

D A

B

D

B

D

C

B

D

and are related to thresholds

E.S. Swanson, arXiv:1409.3291

D. V. Bugg, Europhys. Lett. 96, 11002 (2011)

D. V. Bugg, Int. J. Mod. Phys. A 24, 394 (2009)

E.P. Wigner, Phys. Rev. 73 (1948) 1002

Zc(3900) & Loops

E.S. Swanson,``Cusps and Exotic Charmonia,’' arXiv:1504.07952 [hep-ph].

Z.Y. Zhou and Z. Xiao, ``Distinguishing cusp effects and near-threshold-pole effects,’' arXiv:1505.05761 [hep-ph].

F.K. Guo, C. Hanhart, Q. Wang and Q. Zhao, `Could the near-threshold XYZ states be simply kinematic effects?,''   Phys. Rev. D {91}, no. 5, 051504 (2015)

Zc(3900) & Loops

A. Pilloni et al [JPAC] Amplitude analysis and the nature of the Zc(3900) arXiv:1612.06490

K-matrix with poles on the sheet closest to the real axisas above + logarithmic branch cut from a triangle singularityconstant K-matrix + triangleas above, but force any poles in t to be far removed (tests the triangle)

Zc(3900) & Loops

Unable to distinguish scenarios with only mass projections

Zc(3900) & Loops

A. Pilloni et al [JPAC] Amplitude analysis and the nature of the Zc(3900) arXiv:1612.06490

Y. Ikeda et al. [HAL QCD] Fate of the Tetraquark Candidate Zc(3900) from Lattice QCD arXiv:1602.03465v2 Phys. Rev. Lett. 117, 242001 (2016)

S. Prelovsek and L. Leskovec, Phys. Lett. B 727, 172 (2013); S. Prelovsek et al., Phys. Rev. D 91, no. 1, 014504 (2015).

from the Bethe-Salpeter equation. “HAL-QCD method” [not yet tested on conventional resonances!] Relate a correlator to a “Schroedinger-type equation” w/ velocity expansion.

⇡J/ , ⇢⌘c, DD⇤

Zc(3900) & Lattice

Unable to find Zc with local operators.

Examine channels and extract “interactions”

Plug into a T-matrix equation, determine that Zc is a threshold cusp effect.

Zc(3900) & Lattice

Xicc

Discovery of doubly-charmed Ξcc baryon implies a stable tetraquark

Assume colour/space factorize (as in weak coupling) so QQ interaction strength is 1/2 QQ~ . Take (ud) w/ I=0 S=0

Xicc & bb Tetraquarks

Marek Karliner and Jonathan L. Rosner arXiv:1707.07666

b

bu

d

3

bbudJP = 1+

3

3

Xicc & bb Tetraquarks

Marek Karliner and Jonathan L. Rosner arXiv:1707.07666

Predict a stable 1+ state at 10389, 215 MeV below BB* and 170 MeV below BBγ might be below threshold too

(bbud)!BD⇡+ Electroweak decay modes, eg

bbud

bcud

employ dq-DQ and BB* operators pions at 415, 299, 164 MeV

A. Francis et al., PRL 118, 142001 (2017)

JP = 1+, I = 0

Xicc & bb Tetraquarks

NRQCD for the b quarks

arXiv:1606.07895v1

B � KJ/��

LHCb Tetraquarks

LHCb Tetraquarks arXiv:1606.07895v1

PHYSICAL REVIEW D 91, 034009 (2015)

red: LHCb fitblack GIblue: PDGgreen: unconfirmed

LHCb Tetraquarks arXiv:1606.07895v1

� = 205± 18± 86 MeV� = 39± 5± 19 MeV

JP =32

±

JP =52

�

LHCb 1507.03414v2 Pc(4380)Pc(4450)

Pentaquarks

Pentaquarks

Pentaquarks

�b

�b

K

p

J/�K

Pc

�� J/�

p

b

c

sc

b cc

s

Production Mechanisms (tree)

Pentaquarks

�b �b �b

b

J/�

K

ps

c

p p

J/� J/�

K K

Ds

D

�c

�c

�c,�c

D�

�

�c1

p

c b b

c c

ssc

c

Production Mechanisms (loop)

1/N 1/N

Pentaquarks

diagonal onlyPentaquarks

J.M. Richard, A. Valcarce, J. Vijande, Stable heavy pentaquark in constituent models, July, 2017

Binding energy decreases going to bbqqq because threshold degeneracy is lost.

ccqqq

Pentaquarks

Quark model calculation of

E. Hiyama, M. Kamimura, A. Hosaka, H. Toki, M. Yahiro, Five-body calculation of resonance and scattering states of pentaquark system , Physics Letters B 633 (2006) 237–244

Pentaquarks

Quark model (IK) KN scattering computation.

� ⇠ 0.12 MeV � ⇠ 110 MeV

PHYSICAL REVIEW D 84, 014032 (2011) Exotic baryons from a heavy meson and a nucleon: Negative parity states Y Yamaguchi, S Ohkoda, S Yasui, and A Hosaka

one pion+ one vector exchange interactions

Pentaquarks

(I, JP ) = (0, 1/2�) (I, JP ) = (0, 3/2�)

Quarkonium h States As Arbiters of Exoticity arXiv:1705.03140 R.F. Lebed and E.S. Swanson

use “ultrafine splitting” to test for valence light quark degrees of freedom.

Ultrafine Splittings

Ultrafine SplittingsHeavy-Quark Hybrid Mass Splittings: Hyperfine and “Ultrafine”

arXiv:1708.02679

R.F. Lebed and E.S. Swanson

Questions: “Simple” quark models may be able to describe compact multiquark states (to be confirmed). The main issue is modelling the colour degrees of freedom. What about diquarks etc?

How should long range dynamics (molecules) be modelled? One pion exchange has issues with on-shell pions and the contact portion.

“Kinematical” effects are likely to be important in some cases. How can these be modelled and identified?

Gluonic degrees of freedom are required. How can these be modelled and identified?