XYZ States: theory overview

Eric Swanson

Sept, 201[

Cassidy, D.B.; Mills, A.P. (Jr.) (2007). "The production of molecular positronium". Nature 449 (7159): 195–197

Multi-electron States

1946: Wheeler suggests that Ps2 might be boundWheeler, J. A. Polyelectrons. Ann. NY Acad. Sci. 48, 219–238 (1946).

1946: Ore proves it is unbound

1947: Hylleraas & Ore prove it is boundHylleraas, E. A. & Ore, A. Binding energy of the positronium molecule. Phys. Rev.71, 493–496 (1947).

2007: Ps2 is observed

Multi-quark States

��J/� ��hc

�DD̄� �D�D̄�

���(nS)��hb(nP )

�K��

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

Zc(4475)

Z1(4050)Z2(4250)

Zb(10610)Zb(10650)

K��cJ K�J/�

�BB̄�

Multi-quark States

pJ/�

Pc(4380)Pc(4450)

Multi-quark States

LQED �

�

Multi-quark States

LQED �

�

pQCD

r (fm)

r0 (V(r)-V(r0))

QQ̄

Adiabatics K.J. Juge, J. Kuti and C.J. Morningstar, ``Ab initio study of hybrid anti-b g b mesons,'' Phys. Rev. Lett. {82}, 4400 (1999)

QQ̄

Loop Corrections

Gupta & Radford, PRD33, 777 (86)

QQ̄

V1(mq,mq̄, r) = −br − CF12r

α2s

π

!CF − CA

!ln

"(mqmq̄)1/2r

#+ γE

$$

V2(mq,mq̄, r) = −1rCF αs

%1 +

αs

π

%b0

2[ln (µr) + γE ] +

512

b0 −23CA +

12

!CF − CA

!ln

"(mqmq̄)1/2r

#+ γE

$$&&

V3(mq,mq̄, r) =3r3

CF αs

%1 +

αs

π

%b0

2[ln (µr) + γE − 4

3] +

512

b0 −23CA+

+12

'CA + 2CF − 2CA

'ln

"(mqmq̄)1/2r

#+ γE − 4

3

((&&

V4(mq,mq̄, r) =32αsσ3e−σ2r2

3√

π

V5(mq,mq̄, r) =1

4r3CF CA

α2s

πln

mq̄

mq(1)

Loop Corrections

QQ̄

Instantons

U. Loring, B.C. Metsch and H.R. Petry, ``The Light baryon spectrum in a relativistic quark model with instanton induced quark forces: The Strange baryon spectrum,'' Eur. Phys. J. A {10}, 447 (2001) [hep-ph/0103290].

QQ̄

Pion Exchange

L.Y. Glozman and D.O. Riska, ``The Spectrum of the nucleons and the strange hyperons and chiral dynamics,'' Phys. Rept. {268} (1996) 263

QQ̄

Spin-Dependence

N. Brambilla, A. Pineda, J. Soto, and A. Vairo, The QCD potential at O(1/m), Phys. Rev. D63 (2001) 014023, [hep-ph/0002250].

QQ̄

Y. Koma and M. Koma, ``Scaling study of the relativistic corrections to the static potential,'' PoS LAT {2009}, 122 (2009) [arXiv:0911.3204 [hep-lat]].

QQ̄

QQ̄g

A large collection of pre-LGT ideas: !

(i) flux tube excitation !(ii)constituent vector particle !(iii) string excitation !(iv)bag mode

N. Isgur and J. Paton, Phys. Rev. D31, 2910 (1985).

R. Giles and S. H. Tye, Phys. Rev. Lett. 37, 1175 (1976)

D. Horn and J. Mandula, Phys. Rev. D17, 898 (1978)

T. Barnes, Nucl. Phys. B158, 171 (1979); P. Hasenfratz, R.R. Horgan, J. Kuti and J.M. Richard, Phys. Lett. 95B, 299 (1980); F. de Viron and J. Weyers, Nucl. Phys. B185, 391 (1981); M.S. Chanowitz and S.R. Sharpe, Phys. Lett. B132, 413 (1983).

R.L. Jaffe and K. Johnson, Phys. Lett. 60B, 201 (1976)

J.J. Dudek, ``The lightest hybrid meson supermultiplet in QCD,'' Phys. Rev. D {84}, 074023 (2011)

QQ̄g

Lattice points to a quasi-gluonic excitation with and an excitation scale of order 1 GeV

JPC = 1+�

QQQ

H. Ichie, V. Bornyakov, T. Streuer and G. Schierholz, “The flux distribution of the three quark system in SU(3)”, arXiv:hep-lat/0212024.

C. Alexandrou, P. De Forcrand and A. Tsapalis, Phys. Rev. D 65, 054503 (2002).

T. T. Takahashi, H. Suganuma, Y. Nemoto and H. Matsufuru, Phys. Rev. D 65, 114509 (2002).

N. Cardoso and P. Bicudo, `Color fields of the static pentaquark system computed in SU(3) lattice QCD,'' Phys. Rev. D {87}, no. 3, 034504 (2013)

QQQ̄Q̄QQQQQ̄

S. Furui, A.M. Green and B. Masud, ``An analysis of four quark energies in SU(2) lattice Monte Carlo using the flux tube symmetry,'' Nucl. Phys. A {582}, 682 (1995)

L =g√2fπ

!d4xψ̄(x)γµγ5τ

aψ(x)∂µπa(x)

o�e

N.A. Tornqvist, ``From the deuteron to deusons, an analysis of deuteron-like meson meson bound states,'' Z. Phys. C {61}, 525 (1994)

F. Close, C. Downum, Phys. Rev. Lett. 102, 242003 (2009), 0905.2687 F. Close, C. Downum, C.E. Thomas, Phys. Rev. D81, 074033 (2010), 1001.2553

o�e

D� � [D�]P

D1 � [D�]S

There are channels with S-wave interactions!

E.E. Kolomeitsev and M.F.M. Lutz, ``On Heavy light meson resonances and chiral symmetry,'' Phys. Lett. B {582}, 39 (2004)

J. Nieves and E. Ruiz Arriola, ``Properties of the rho and sigma Mesons from Unitary Chiral Dynamics,'' Phys. Rev. D {80}, 045023 (2009)

u�PT

L. Roca, J. Nieves and E. Oset, ``The LHCb pentaquark as a $\bar{D}^*\Sigma_c-\bar{D}^*\Sigma_c^*$ molecular state,'' arXiv:1507.04249 [hep-ph].

more mesons

F.K. Guo, C. Hanhart, G. Li, U.G. Meissner and Q. Zhao, ``Effect of charmed meson loops on charmonium transitions,'' Phys. Rev. D {83}, 034013 (2011)

D. Diakonov, V. Petrov and M. Polyakov, Z. Phys. A 359, 305 (1997). !T.D. Cohen,``Chiral soliton models, large N(c) consistency and the theta + exotic baryon,'' Phys. Lett. B {581}, 175 (2004)

SU(3) chiral soliton model treated with collective quantization.

But, the theta has excitations that are finite in the large Nc limit, and hence are inconsistent with the DPP assumptions.

The standard analysis of SU(3) solitons is only justified in the large Nc limit which plays an essential role in two ways:

(i) It justifies the use of the classical static hedgehog configurations

(ii) effects of quantum fluctuations around the hedgehogs are suppressed by 1/Nc.

DPP argued that the anti-decuplet should not be dismissed as a large Nc artifact.

chiral solitons

M.A. Nowak, M. Rho and I. Zahed, ``Chiral doubling of heavy light hadrons: BABAR 2317-MeV/c**2 and CLEO 2463-MeV/c**2 discoveries,'' Acta Phys. Polon.B { 35}, 2377 (2004) !M.A. Nowak, M. Rho and I. Zahed, Phys. Rev.D48 (1993) 4370 (hep-ph/9209272). !Bardeen and C. T. Hill, Phys. Rev.D49(1994) 409 (hep-ph/9304265).

�0�1�

��

�0+

1+

�

m(D1)�m(D�) = m(D0)�m(D)

chiral doublers

O. Lakhina and E.S. Swanson, ``A Canonical Ds(2317)?,''Phys. Lett. B {650}, 159 (2007) [hep-ph/0608011].

Construct an effective field theory with (i) chiral symmetry (ii)heavy quark symmetry

S. Dubynskiy and M.B. Voloshin, ``Hadro-Charmonium,'' Phys. Lett. B {666}, 344 (2008)

(multipole expansion)

hadrocharmonium

M.E. Peskin, Nucl. Phys. B 156 (1979) 365;

O. Lakhina and E.S. Swanson, ``Hybrid meson potentials and the gluonic van der Waals force,'' Phys. Lett. B {582}, 172 (2004)

hadrocharmonium

|{qq}3̄c(A)3̄f (A)0+(A)⇤ |{qq}3̄c(A)6f (S)1+(S)⇤

‘good’ ‘bad’

repulsive

3� 3 = 3̄ + 6

(qqq) = [qq]3̄q � Q̄q

(qq̄qq̄) = [qq][q̄q̄]� QQ̄

(qqqqq̄) = [qq][qq]q̄ � QQq̄

diquarksR.L. Jaffe, hep-ph/0409065

M. Ida and R. Kobayashi, Prog. Theor. Phys. 36, 846 (1966)

D.B. Lichtenberg and L.J. Tassie, PR155, 1601 (1967)

A. Selem and F. Wilczek, hep-ph/0602128

R.L. Jaffe, PRD15, 267 (1977)

|0++⇥ = |[cq]S [c̄q̄]S ;J = 0⇥ (1)

|0++⇥⇥ = |[cq]V [c̄q̄]V ;J = 0⇥ (2)

|1++⇥ =1⌅2

(|[cq]S [c̄q̄]V ;J = 1⇥+ |[cq]V [c̄q̄]S ;J = 1⇥) (3)

|1+�⇥ =1⌅2

(|[cq]S [c̄q̄]V ;J = 1⇥ � |[cq]V [c̄q̄]S ;J = 1⇥) (4)

|1+�⇥⇥ = |[cq]V [c̄q̄]V ;J = 1⇥ (5)|2++⇥ = |[cq]V [c̄q̄]V ;J = 2⇥ (6)

Maiani, Riquer, Piccinini, Polosa; PRD72, 031502 (2005)

Maiani, Polosa, Riquer; PRL99, 182003 (2007)

Bigi, Maiani, Piccinini,Polosa, Riquer; PRD72, 114016 (2005)

Maiani, Polosa, Riquer; arXiv:0708.3997

Maiani, Piccinini,Polosa, Riquer; PRD71, 014028 (2005)

Assume a spin-spin interaction

Diquarks and the New Charmonia

M([cq]V ) = 1933M([cq]S) = 1933

diquarks

R.F. Lebed, ``A New Dynamical Picture for the Production and Decay of the XYZ Mesons,'' arXiv:1508.03320 [hep-ph]. !S.J. Brodsky and R.F. Lebed, Phys. Rev. D 91, 114025 (2015) [arXiv:1505.00803 [hep-ph]].

Hadronization occurs at large r, which enhances the coupling to 𝜓(2S) over J/𝜓, in agreement with experiment.

P+c = [c̄(ud)]3 [cu]3̄

diquarks

Similarly,

The diquarks separate to large distance, suppressing the “fall apart” decay mode.

Attempt a “microscopic” cusp model.

Y (4260)� �DD̄� Y (4260)� ��J/�

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

DD�)

[separable nonrelativistic model; solve exactly]

cusps

[iterate all bubbles]

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

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

0

10

20

30

40

50

60

70

4 4.02 4.04 4.06 4.08 4.1 4.12 4.14

even

ts

m(DD*) (GeV)

0

10

20

30

40

50

60

70

80

90

4 4.02 4.04 4.06 4.08 4.1 4.12 4.14

even

ts

m(DD*) (GeV)

no evidence for π D* dynamics, background, or bubble

�D�D� = 0.3 GeV

attractive bubble

repulsive bubble

�D�D� = 0.2 GeV

�D�D� = 0.4 GeV�D�D� = 0.3 GeV

cusps

**

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)

cusps

Conclusions

• many XYZs; not all of them are resonances! • cusp effects can be important and should be accounted

for when modelling • theory evolutionary landscape is largely unconstrained

(we rely on experiment and, increasingly, lattice for help)

✛ ÆRIC MEC HEHT GEWYRCAN