HEAVY-QUARK EXOTICSJ. Rosner (University of Chicago) – Kyoto, June 15, 2018

New Frontiers in QCD 2018: Recent Developments in Quark-Hadron Sciences

1964: M. Gell-Mann and G. Zweig proposed that the known mesonswere qq and baryons qqq, with quarks known at the time u (“up”), d(“down”), and s (“strange”) having charges (2/3,–1/3,–1/3). Mesonsand baryons would then have integral charges.

Mesons such as qqqq and baryons such as qqqqq would also haveintegral charges. Why weren’t they seen?

They have now been seen, as “molecules” of heavy-quark hadrons oras deeply bound states involving heavy quarks (charm and bottom).

Charm-anticharm and bottom-antibottom molecules; “pentaquark” asa charmed meson – baryon molecule; Ξ++

cc = ccu as the first doublycharmed baryon; ccs mass; stable bbud tetraquark; quark fusion

Thanks to Marek Karliner and Michael Gronau for many enjoyablecollaborations on these and other topics. Bibliography at end has manyreferences. Recent: M. Karliner, T. Skwarnicki, JLR, arXiv:1711.10626

2/33THREE-QUARK BARYONSOctet (spin 1/2) Decuplet (spin 3/2)

p = uud, n = udd ∆++ = uuu, Ω− = sss

u, d, s have charges 2/3,–1/3,–1/3 and strangeness 0,0,–1

No qqqqq baryons seen made of just these three quarks

“Pentaquark” uudds at 1540 MeV decaying to K0p orK+n claimed in early 2000’s; not confirmed subsequently

3/33QUARK-ANTIQUARK MESONSOctet (spin 0) Nonet (spin 1)

π+ = ud, K+ = us ρ+ = ud, K∗+ = us

No resonances made of u, d, s seen which would correspondto qqqq but not qq (e.g., uuds decaying to K+π+)

Situation changes with heavy quarks c (charm), b (bottom)

4/33EARLY HINT OF EXOTICSProcesses “dual” (JLR, 1968) to t-channel qq exchange:

s-channel resonances ⇔ t-channel Regge trajectories

In antiproton-proton scattering, qq dual to qqqq

Predicts “exotic” qqqq mesons, but where?

Do resonances form via qq annihilation? (JLR, 1972):

p∗ ≤ 350 MeV/c p ∗≤ 250 MeV/c p∗ ≤ 200 MeV/c?

5/33BARYON-ANTIBARYON EXOTICS(a) qq: Standard meson

(b) qqq: Standard baryon

(c) qqqq: Exotic meson

Freund-Waltz-JLR 1969, Imachi + 1974-7, Rossi-Veneziano 1977: decays occur via quark pair production(breaking of QCD string) ⇒ qqqq → baryon-antibaryon

Don’t see meson + baryon → baryon + (exotic meson)

Such exotics may fall apart into meson pairs and may betoo broad to show up as distinct resonant peaks

R. Jaffe (1976-8): extensive study of qqqq states withinbag model of QCD; light diquark-antidiquark states couldbe familiar ones with masses of a GeV or less

First “baryonium” candidate: the pion (Fermi-Yang 1949)

6/33pp THRESHOLD EFFECTFermilab E687: Dip in diffractive 6π photoproduction nearpp threshold (shading: amplitudes w/o interference)

1.6 1.8 2 2.2 2.40

20

40

60

80

100

120

M6π(GeV)

[

(Eve

nts/

Acc

epta

nce)

(M6π

2 )-1

](M

eV/c

2 )-1

Arbitrary U

nits

The pp channel is“robbing” the 6πchannel; rapid variationsuggests production inan S-wave, and couplingto a photon suggests a3S1 state: JPC = 1−−

Similar behavior in I = 0ππ S wave near 1 GeVwhen KK thresholdopens up near f0(980)

Solodov, Baldini (Bad Honnef, 4/18): Behavior in e+e− →(hadrons) near pp, ΛcΛc thresholds

7/33BEHAVIOR NEAR pp THRESHOLD

0

50

100

150

Evt

s/0.

005

GeV

/c2

0.00 0.10 0.20 0.30M(p p

-) - 2mp (GeV/c2)

0

400

800

Wei

ghte

d E

vts/

bin

0

20

40

60

80

100

120

2 2.5 3 3.5 4 4.5Mpp

_ (GeV/c2)dN

/ dM

pp_

(E

vent

s / (

GeV

/c2 ))

Eve

nts

/ (5

MeV

/c2 )

0

5

10

3 3.05 3.1 3.15

BES: M(pp) in J/ψ → γpp Belle: M(pp) in B+ → K+pp

Peak now seen also in J/ψ → γπ+π−η′:M(π+π−η′) = 1834 ± 7 MeV, Γ = 68 ± 21 MeV

Solodov (CMD-3): Dip at pp threshold now also seen ine+e− → K+K−π+π−

8/33THE CHARMED QUARK

Leptons:

(

νee−

)

,

(

νµµ−

)

(no stronginteractions)

1964: Bjorken–Glashow, ...: quark–lepton analogy;(

νee−

)

,

(

νµµ−

)

⇔(

u

d

)

,

(

c

s

)

Glashow–Iliopoulos–Maiani (1970): mc ≃ 2 GeV/c2;Gaillard-Lee (1973): electroweak role of charmed quark

1974: Charmed quark c in J/ψ = cc. J = “Ting” (co-discoverer). Charmonium (cc) spectrum is still evolving

Particles with one charmed quark: rich spectrum today

Large mc: nonrelativistic QM provides some insights

9/333RD QUARK-LEPTON FAMILYAt the same time as charm: the τ lepton (M. Perl, 1974)

Quark-lepton analogy:(

νe

e−

)(

νµ

µ−

)(

ντ

τ−

)

⇔(

u

d

)(

c

s

) (

t

b

)

Third lepton pair (ντ , τ−) ⇒ third quark pair (t [top], b

[bottom]), predicted by Kobayashi and Maskawa.

1977 (Fermilab): Υ family of spin–1 bb particles producedin proton-proton interactions, decaying to e+e−, µ+µ−

Rich bb spectroscopy; “B” mesons containing a single bquark. Decays of particles with b quarks: an active field.

Top (1994 at Fermilab Tevatron): mass Mt ≃ 173 GeV/c2

large so decays too rapidly to have interesting spectroscopy

10/33X(3872): GENUINE EXOTICState decaying to J/ψπ+π− discovered by Belle (2003) at3872 MeV (shown with ψ′(3686 MeV)); also seen by CDF(2004, left), D0 (2004, right), and BaBar (2008)

)2

Mass (GeV/c-π+πψJ/3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00

2C

andi

date

s/ 5

MeV

/c

0

500

1000

1500

2000

2500

3000

3.80 3.85 3.90 3.95

900

1000

1100

1200

1300

1400CDF II

)2

(GeV/c-µ+µ - M-π+π-µ+µM0.6 0.7 0.8 0.9 1

2C

and

idat

es /

10 M

eV/c

0

200

400

600

800 DØ

(2S)ψ

X(3872)

)2

(GeV/c-µ+µM2.9 3 3.1 3.2 3.3

2C

and

idat

es /

10 M

eV/c

0

10000

20000

ψJ/

Within ∼ 0.2 MeV of D0D∗0 threshold

11/33X(3872) PROPERTIESM(X) = (3871.69 ± 0.17) MeV ≃ M(D0) + M(D∗0) =(3871.68 ± 0.07) MeV ⇒ key role for that channel

Decay X → γJ/ψ seen; implies C(X) = + and someadmixture of cc in its wave functionAngular distribution of decay products implies JPC = 1++

as expected for S-wave state of D0D∗0 + c.c.

C invariance ⇒ C(π+π−) = − ⇒ π+π− in a ρ meson

Large M(D(∗)+ −D(∗)0) ⇒ little D(∗)± in wave function

Γ(X → ωJ/ψ) comparable to γ(X → J/ψρ), as onewould expect for a state with ccuu admixture

In addition to X(3872) (mixture of 23P1 cc state andJPC = 1++ ccuu state) one expects an orthogonal mixture(potential models: probably > 3900 MeV)

12/33THE BELLE Υ(nS)π PEAKSBelle: Υ(10865) → Υ(1S, 2S, 3S)π+π− ⇒ unexpectedstructures “Zb(10610, 10650)” in M [π±Υ(1S, 2S, 3S)]

0

20

40

60

80

10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8

M(Y(1S)π)max, (GeV/c2)

(Events/10 MeV/c2) (a)

0

20

40

60

80

100

10.4 10.45 10.5 10.55 10.6 10.65 10.7 10.75

M(Y(2S)π)max, (GeV/c2)

(Events/5 MeV/c2) (c)

0

20

40

60

80

100

120

10.58 10.62 10.66 10.70 10.74

M(Y(3S)π)max, (GeV/c2)

(Events/4 MeV/c2) (e)

M(Υ(1S)π) M(Υ(2S)π) M(Υ(3S)π)

All spectra: peaks at M(Υ(nS)π = 10.61 and 10.65 GeV

Within a few MeV ofM(B)+M(B∗) andM(B∗)+M(B∗)

Looks like S-wave molecules of BB∗(+c.c.) and B∗B∗

13/33PION EXCHANGE AND Xc,b

D0D∗0 +c.c. molecule BB∗ +c.c. molecule B∗B∗ molecule

Pion doesn’t couple to a pair of pseudoscalar mesons (P )

Implies no DD or BB molecules; doesn’t preclude genuinecc or bb resonances slightly above threshold (e.g., Υ(4S)

Potential: V ∼ ±(I1 · I2)(S1 · S2) for (qq, qq) interactions

Expect JPC = 1++ Xb (analogue of X(3872)) to haveI = 0 because M(B(∗)−) ≃M(B(∗)0)

Distinct from the Zbs which have I = 1; expect M(Xb) ∼10562–10585 MeV (χb(3

3P1)?)(Karliner + JLR, PR D 91)

14/33V EXPECTATION VALUESMost deeply bound DD∗, D∗D∗, BB∗, B∗B∗ states:

D∗D∗ or B∗B∗: 〈I1 · I2〉 = (−34,

12) for I = 0, 1;

〈S1 · S2〉 = (−2,−1, 1) for S = (0, 1, 2)

Hence 〈V 〉 = −(I1 · I2)(S1 ·S2) for D∗D∗ or B∗B∗ is mostattractive in the I = S = 0 channel

Zc(4020), Zb(10650) have I = 1; 〈V 〉 < 0 for S = 2;expect lower-mass I = S = 0 states

DD∗, BB∗: use basis (e.g.) [D0D∗0, D∗0D0, D+D∗−, D∗+D−]

Eigenstates of potential have definite C, I

Most attractive channel with 〈V 〉 = −3 in some units hasC = +, I = 0.

Zc(3900), Zb(10610) have I = 1; if their 〈V 〉 < 0 then itis 1/3 that for C = +, I = 0 state, and their C = −

15/33PENTAQUARK PcLHCb (PRL 115, 072001) sees bumps in J/ψ p invariantmass in the decay Λb → K−J/ψ p at 4380 and 4450 MeV

Λ∗ excitation Pc excitation

Dalitz plot: many K−p resonances (all I = 0: b → ccs is∆I = 0). May be missing high-M(K−p) states.

Prominent narrow band at M(J/ψ p) = 4449.8±1.7±2.5MeV with fitted width Γ = 39 ± 5 ± 8 MeV

Karliner + JLR (PRL 115, 122001): Pion exchange bindsΣc(2453) and D∗(2010) into a near-threshold bound state

16/33K−pJ/ψ DALITZ PLOT

Asymmetric behavior along M(J/ψ p) band indicatesinterference with an opposite-parity state

17/33AN INTERPRETATION

Red curves: phase space. Λ∗ resonances at low M(K−p)

Peak at M(J/ψ p) ≃ 4450 MeV: could be a ΣcD∗ S-wave

bound state with JP = 3/2−; quark content = ccuud

Further structure fitted by LHCb with resonance Pc(4380)(Γ ≃ 205 MeV) with opposite parity to Pc(4450)

18/33ARGAND PLOTS

Pc(4450): classic resonant behavior; Pc(4380) anomalous

No obvious molecular explanation for Pc(4380)

Σ∗c(2520)D∗(2010) channel above the Pc(4450) interfering

destructively with a suitable background? (P?)

Assumed JP = 5/2+ Assumed JP = 3/2−

19/33BARYONS WITH > 1 HEAVY QUARK

So far: QQqq′ or QQqqq′ (Q = heavy, q, q′ = light). Canwe predict masses of (simpler) QQ′q systems?

SELEX at Fermilab (2002-5) claimed Ξ++cc (3520) = ccu

and Ξ+cc(3460) = ccd; not confirmed by others

M. Karliner + JLR (PR D 90): Constituent-quark masses,hyperfine splittings, estimates of QQ′ binding (q = u, d):

State Quark content M(J = 1/2) M(J = 3/2)

Ξ(∗)cc ccq 3627±12 3690 ± 12

Ξ(∗)bc b[cq] 6914 ± 13 6969 ± 14

Ξ′bc b(cq) 6933 ± 12 –

Ξ(∗)bb bbq 10162 ± 12 10184 ± 12

LHCb PRL 119, 112001: M(Ξ++cc ) = 3621.40± 0.78 MeV

Other estimates (> 30): spread of at least 100 MeV

20/33ΛcK−π+π+ SPECTRUM

Similar peak seen in 8 TeV data; no ΛcK−π+ peak

We predicted τ(Ξ++,+cc ) = (185,53) fs; ΛcK

−π+ peakdisfavored by LHCb lifetime cut τ > 150 fs

LHCb (Novosibirsk, 5/22): τ(Ξ++cc ) = 256+24

−22 ± 14 fs

21/33INPUTSDescribe ground-state baryons containing u, d, s takingmbu = mb

d ≡ mbq = 363 MeV, mb

s = 538 MeV, and

hyperfine interaction term a/(mbq)

2 = 50 MeV

State (mass Spin Expression for mass Predictedin MeV) mass (MeV)

N(939) 1/2 3mbq − 3a/(mb

q)2 939

∆(1232) 3/2 3mbq + 3a/(mb

q)2 1239

Λ(1116) 1/2 2mbq +mb

s − 3a/(mbq)

2 1114Σ(1193) 1/2 2mb

q +mbs + a/(mb

q)2 − 4a/mb

qmbs 1179

Σ(1385) 3/2 2mbq +mb

s + a/(mbq)

2 + 2a/mbqm

bs 1381

Ξ(1318) 1/2 2mbs +mb

q + a/(mbs)

2 − 4a/mbqm

bs 1327

Ξ(1530) 3/2 2mbs +mb

q + a/(mbs)

2 + 2a/mbqm

bs 1529

Ω(1672) 3/2 3mbs + 3a/(mb

s)2 1682

Describe mesons with quark masses mmu,d,s ∼ 55 MeV less

M(Λc,b) −M(Λ) ⇒ mbc,b = (1710.5, 5043.5) MeV

22/33CHARMED & BOTTOM BARYONSAbove choices of mass sufficient to describe nonstrangebaryons with one c or b quark

When taking account of deeper cs or bs binding in baryonswith one or two strange quarks and one charm or bottomfit all baryons with one c or b

Charmed baryons Bottom baryonsState (M Spin Predicted State (M Spin Predictedin MeV) M (MeV) in MeV) M (MeV)

Λc(2286.5) 1/2 Input Λb(5619.5) 1/2 InputΣc(2453.4) 1/2 2444.0 Σb(5814.3) 1/2 5805.1Σ∗

c(2518.1) 3/2 2507.7 Σ∗b(5833.8) 3/2 5826.7

Ξc(2469.3) 1/2 2475.3 Ξb(5792.7) 1/2 5801.5Ξ′

c(2575.8) 1/2 2565.4 Ξ′b(−) 1/2 5921.3

Ξ∗c(2645.9) 3/2 2628.6 Ξ∗

b(5949.7) 3/2 5944.1Ωc(2695.2) 1/2 2692.1 Ωb(6046.4) 1/2 6042.8Ω∗

c(2765.9) 3/2 2762.8 Ω∗b(−) 3/2 6066.7

23/33HEAVY QUARK PAIR BINDINGQuark pair more deeply bound when neither is u or d

B(cs) = [3M(D∗s)+M(Ds)]/4−mm

s −mmc = −69.9 MeV

Assume B(cs)/B(cs) = 1/2 as for single-gluon exchange

Then B(cs) = −35 MeV; also find B(bs) = −41.8 MeV

Rescale hyperfine interactions when neither quark is u ord; take a cue from M(D∗

s) −M(Ds) ≃M(D∗) −M(D)

Now we are ready to deal with cc, cb, bb

Charm-anticharm binding: B(cc) = [3M(J/ψ) +M(ηc)]/4 − 2mm

c = −258 MeV, so B(cc) = −129 MeV

Similar calculations give B(bb) = −281.4 MeV andB(bc) = −167.8 ± 3.0 MeV (uncertainty in B∗

c mass)

24/33STABLE bbud TETRAQUARK

We looked at QQ′ud systems (Q = c or b) (PRL 119)

We found ccud unbound; it could decay to DD∗ or DDγ

Lowest-lying bcud state was near BDγ threshold and wecould not tell for sure whether it was bound or unbound

Predicted M(bbud) = 10, 389 ± 12 MeV, 215 MeV belowB−B∗0 threshold and 170 MeV below B−B0γ threshold

Regard bb as a color-3∗ diquark (transforming under QCDas an antiquark); fermi statistics require its spin to be 1

Lightest qq′ state (q, q′ = u, d) is a color-3 ud state withisospin zero; fermi statistics require its spin to be zero

Mass prediction then relies on accounting for constituent-quark masses, hyperfine interactions, and binding effects

25/33TETRAQUARKS QQ′udContributions (MeV) to mass of lightest tetraquark:

ccud, JP = 1+ bcud, JP = 0+ bbud, JP = 1+

Contribution Value Contribution Value Contribution Value

2mbc 3421.0 mb +mc 6754.0 2mb

b 10087.02mb

q 726.0 2mbq 726.0 2mb

q 726.0cc hyperfine 14.2 bc hyperfine −25.5 bb hyperfine 7.8−3a/(mb

q)2 −150.0 −3a/(mb

q)2 −150.0 −3a/(mb

q)2 −150.0

cc binding −129.0 bc binding −170.8 bb binding −281.4Total 3882±12 Total 7134±13 Total 10389 ± 12

Spin zero allowed for the bcud state, taking advantage ofthe attractive bc hyperfine interaction

Since M(ccud) > M(D0) +M(D+) = 3734 MeV, it candecay to D0D+γ (decay to D0D+ is forbidden)

M(bcud) < M(D0) + M(B0) = 7144 MeV?

Estimated lifetime of bbud state: 367 fs

26/33COMPARISON OF TQ MASSES

Distance in MeV of the ccud, bcud and bbud tetraquarkmasses from corresponding thresholds D0D+γ, B0D0, andB0B−γ, plotted against reduced masses of the doubly-heavy diquarks µ(QQ′), Q,Q′=c, b.

27/33HEAVY QUARK FUSIONMK + JLR, Nature 551, 89 (2017): ΛQ+ΛQ′ → ΞQQ′+N

Q,Q′ s, s c, c b, c b, b

ΞQQ′ Ξ Ξcc Ξbc Ξbb

∆E (MeV) −23 12 50 138 ± 12

28/33QQQQ STATESM. Karliner, S. Nussinov, JLR: Masses, production, decaysof cccc and bbbb states (PR D 95, 034011 (2017))

Compensate 55 MeV difference in effective quark massesin mesons and baryons with 165 MeV per “string junction”

M(cc)(cc) = 6192 ± 25 MeV, 225 ± 25 MeV above 2M(ηc)

M(bb)(bb) = 18826± 25 MeV, 28± 25 MeV above 2M(ηb),could exhibit non-hadronic decays if estimate is > 1σ high

Hadronic production of an extra QQ: probability ∼ 0.1%

CMS (JHEP 05 (2017) 013): double Υ(1S) production;38 events, each Υ → µ+µ−, [20.7 fb−1,

√s = 8 TeV]

S. Durgut (CMS, thesis, U. of Iowa, April 2018 APSMeeting): Excess in Υ(1S)ℓ+ℓ− at 18.5 ± 0.1 ± 0.2 GeV

29/33QQQQ DECAY

If M(0+) < 2m(ηQ), main decay to flavored meson pair:

QQ→ qq partial width of α2s order (tens of MeV)

Wave function overlap uncertain; could be very small

σ(pp→ Xbbbb[0++] → ℓ+1 ℓ

−1 ℓ

+2 ℓ

−2 ) ≤ 4 fb (LHC, 13 TeV) ;

upper limit attained only if little competition from

Xbbbb[0++] → BBX .

30/33PREDICTIONS FOR Ωcc = ccsStrange quark is about 175 MeV heavier than nonstrangebut more deeply bound to cc diquark than nonstrange

Ξcc = ccq Ωcc = ccsContribution Value (MeV) Contribution Value (MeV)

2mbc +mb

q 3789.0 2mbc +mb

s 3959.0cc binding −129.0 cc binding −129.0acc/(m

bc)

2 14.2 acc/(mbc)

2 14.2−4a/mb

qmbc −42.4 −4a′/mb

smbc −42.4

Total 3626.8 ± 12 Subtotal 3801.8 ± 12

Additional binding of s to cc: −109.4 ± 10.5 MeV, givingM(Ωcc) = 3692 ± 16 MeV, M(Ω∗

cc) = 3756 ± 16 MeV

Superscripts on quark masses: value in a baryon

Universal quark masses and 165 MeV “string junction”term for baryons: predict M(Ωcc) ∼ 40 MeV higher

31/33EXCITED Ωc STATES

Ground css states: Ωc(2695, 1/2+), Ω∗c(2766, 3/2+) (PDG)

LHCb (PRL 118): Five narrow Ω∗c states → Ξ+

c K−

Karliner + JLR (PR D 95): Five P-wave excitations?

32/33ALTERNATIVE ASSIGNMENT

In this case two JP = 1/2− states yet to be seen

One around 2904 MeV decaying to Ωcγ and/or Ωcπ0

The other around 2978 MeV → Ξ+c K

− in S-wave

33/33PROSPECTSExotic mesons and baryons (beyond qq and qqq) do exist;molecular configurations are at least part of the story

Heavy quarks have a lower kinetic energy and help tostabilize exotic configurations containing them

Techniques for mass estimation (constituent-quarkmasses, hyperfine interactions, binding effects) relativelystraightforward and starting to be tested for QQ′q baryons

Frontier: Q1Q2Q3Q4; any cccc lighter than 2M(ηc)? Anybbbb lighter than 2M(ηb)?

Can quark-level analogue of nuclear fusion be put to use?

Still to be known: What does it cost to produce one ormore extra heavy quarks via strong interactions? When dotwo heavy quarks end up in the same hadron?

34/33BIBLIOGRAPHYE. Fermi and C. N. Yang, Phys. Rev. 76, 1739 (1949).

M. Gell-Mann, Phys. Lett. 8, 214 (1964) (quark model)

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J. L. Rosner, Phys. Rev. Lett. 21, 950 (1968) (baryonium from duality)

H. Harari, Phys. Rev. Lett. 22, 562 (1969); J. L. Rosner, Phys. Rev.Lett. 22, 689 (1969) (duality diagrams)

P. G. O. Freund, R. Waltz, and J. L. Rosner, Nucl. Phys. B13, 237(1969) (selection rule).

J. L. Rosner, Phys. Rev. D 6, 2717 (1972) (resonance formation)

M. Imachi et al., Prog. Theor. Phys. 52, 341 (1974); 54, 280 (1975);55, 551 (1975); 57, 517 (1977) (strings)

R. L. Jaffe, Phys. Rev. D 15, 267, 281 (1977); 17, 1444 (1978)(multiquark hadrons; QQQQ states)

G. C. Rossi and G. Veneziano, Phys. Lett. 70B, 255 (1977); Nucl.Phys. B123, 507 (1977) (QCD-string models)

I. S. Shapiro, Sov. Phys. Usp. 21, 645-673 (1978) [Usp. Fiz. Nauk125 577-630 (1978)] (potential model)

35/33BIBLIOGRAPHY, CONTINUEDA. Antonelli et al. (FENICE Collaboration), Nucl. Phys. B517, 3(1998) (dip in e+e− → 6π cross section near 2mp)

P. L. Frabetti et al. (Fermilab E687), Phys. Lett. B 514, 240 (2001)(6π diffractive photoproduction)

M. Mattson et al. (SELEX), PRL 89, 112001 (2002); A. Ocherashviliet al. (SELEX), PL B 628, 18 (2005) (Ξcc)

T. Nakano et al. (LEPS), PRL 91, 012002 (2003) [Θ+(1540)]

J. Z. Bai et al. (BES), PRL 91, 022001 (2003) (narrow pp state)

S. K. Choi el. (Belle), PRL 91, 262001 (2003) (X(3872) discovery)

J. L. Rosner, Phys. Rev. D 68, 014004 (2003) (baryonia in B decays)

J. L. Rosner, PR D 69, 094014 (2004) (exotics in heavy meson decays)

D. Acosta et al. (CDF), PRL 93, 072001 (2004) (X(3872) signal)

V. M. Abazov et al. (D0), PRL 93, 262002 (2004) (X(3872) signal)

J. L. Rosner, Phys. Rev. D 74, 067006 (2006) (thresholds)

B. Aubert et al. (BaBar), PR D 77, 111101 (2008) (X(3872) signal)

36/33BIBLIOGRAPHY, CONTINUEDM. Gaspero al. (BaBar), PR D 78, 014015 (2008); AIP Conf. Proc.1257, 242 (2010) (JPC = 0−− state in D0 decay)

M. Karliner et al., Ann. Phys. 324, 2 (2009) (b baryons)

D. Ebert et al.. PR D 84, 014025 (2011) (excited Σc,bs)

A. Bondar et al. (Belle), PRL 108, 122001 (2012) (Zb states)

M. Karliner and J. L. Rosner, Phys. Rev. D 90, 094007 (2014) (QQ′q)

Z. S. Brown et al., PR D 90, 094507 (2014) (QQ′q on lattice)

S. L. Olsen, Front. Phys. 10, 221 (2015)

M. Karliner and JLR, PR D 91, 014014 (2015) (X(3872), Zbs)

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