Theoretical Interpretation of the XYZ Mesons

Home , Quarkonium

Eric Braaten Ohio State University

1 Theoretical Interpretation of the XYZ Mesons

Introduction

New results on XYZ states ...

... from hadron collider experiments Sebastien Neubert

... from e+e− collider experiments Changzheng Yuan

2 Theoretical Interpretation of the XYZ Mesons

Outline

Models for XYZ Mesons quarkonium quarkonium hybrids quarkonium tetraquarks

QCD Theory Lattice QCD Lattice NRQCD Born-Oppenheimer approximation

3 _ Discovery of Tetraquark bb Mesons!

+ + Zb (10610), Zb (10650) Belle 2011 + + both decay into Υ(nS) π and hb(nP)_ π _ ⟹ constituents are b b u d

120

) (e)

2 100

80 Zb

60 Zb′

20 (Events/4 MeV/c

0 10.58 10.62 10.66 10.70 10.74 2 M(Y(3S))max, (GeV/c )

4 _ Discovery of Tetraquark cc Mesons! + Zc (3900) BESIII April_ _2013 decays into J/ψ π+ ⟹ constituents are c c u d

Data 100 2 Zc Total fit Background fit 80 PHSP MC

Sideband 60

20 Events / 0.01 GeV/c

0 3.7 3.8 3.9 4.0 ± 2 Mmax( J/) (GeV/c ) + Zc (4020) BESIII June 2013_ _ + decays into hc(nP) π ⟹ constituents are c c u d 5 _ _ New cc Mesons above DD threshold TABLE I:

State M (MeV) (MeV) J PC Decay modes 1st observation neutral cc¯ mesons X(3823) 3823.1 1.9 < 24 ?? Belle 2013 ± c1 X(3872) 3871.68 0.17 < 1.21++ J/ ⇡+⇡ , J/ ⇡+⇡ ⇡0 Belle 2003 ± D0D¯ 0⇡0, D0D¯ 0 J/ , (2S) X(3915) 3917.5 1.9 20 50++ J/ !, Belle 2004 ± ± (2P ) 3927.2 2.6 24 62++ DD¯, Belle 2005 c2 ± ± +9 +27 ?+ ¯ X(3940) 3942 8 37 17 ? D⇤D Belle 2007 G(3900) 3943 21 52 11 1 DD¯ BABAR 2007 ± ± 15 neutral +121 + Y (4008) 4008 49 226 97 1 J/ ⇡ ⇡ Belle 2007 _ ± +11 ?+ Y (4140) 4144.5 2.6 15 7 ? J/ CDF 2009 ± cc mesons +29 +113 ?+ ¯ X(4160) 4156 25 139 65 ? D⇤D⇤ Belle 2007 +8 + 0 0 Y (4260) 4263 9 95 14 1 J/ ⇡ ⇡, J/ ⇡ ⇡ BABAR 2005 ± Zc(3900) ⇡ +8.4 +22 ?+ Y (4274) 4274.4 6.7 32 15 ? J/ CDF 2010 +4.6 +18.4 ++ X(4350) 4350.6 5.1 13.3 10.0 0/2 J/ , Belle 2009 Y (4360) 4361 13 74 18 1 (2S) ⇡+⇡ BABAR 2007 ± ± +9 +41 + X(4630) 4634 11 92 32 1 ⇤c ⇤c Belle 2007 Y (4660) 4664 12 48 15 1 (2S) ⇡+⇡ Belle 2007 ± ± charged cc¯ mesons Z+(3900) 3898 5 51 19 ?? J/ ⇡+ BESIII 2013 c ± ± 5 charged Z+(4020) 4021.8 2.75.7 3.6?? h (1P ) ⇡+, D D¯ BESIII 2013 _ c ± ± c ⇤ ⇤ + +24 +51 ?+ + Z1 (4050) 4051 43 82 55 ? c1(1P ) ⇡ Belle 2008 cc mesons + +185 +321 ?+ + Z2 (4250) 4248 45 177 72 ? c1(1P ) ⇡ Belle 2008 + +24 +113 + + Z (4430) 4443 18 107 71 1 (2S) ⇡ Belle 2007

1 _ _ New bb Mesons above BB threshold TABLE I:

PC st 1_ neutral State M (MeV) (MeV) J Decay modes 1 observation neutral b¯b mesons +8.9 + bb meson Yb(10888) 10888.4 3.0 30.7 7.7 1 ⌥(nS) ⇡ ⇡ Belle 2010 ± + + Zb (10610) ⇡, Zb (10610) ⇡ charged b¯b mesons 2_ charged Z+(10610) 10607.2 2.0 18.4 2.4 1+ ⌥(nS) ⇡+, h (nP ) ⇡+ Belle 2011 b ± ± b Z+(10650) 10652.2 1.5 11.5 2.2 1+ ⌥(nS) ⇡+, h (nP ) ⇡+ Belle 2011 bb mesons b ± ± b _ many unexpected _neutral QQ mesons several charged QQ mesons many of them are narrow

a major challenge to our understanding of the QCD spectrum!

1 Models for XYZ Mesons _ ● conventional quarkonium QQ

_ Q Q ● quarkonium hybrids g

_ Q q_ ● quarkonium tetraquarks q Q ● compact tetraquark ● meson molecule ● diquark-onium ● hadro-quarkonium

8 _ Models for XYZ Mesons quarkonium tetraquarks _ ● compact tetraquark Q q_ q Q _ _ ● meson molecule Qq qQ _ _ ● diquark-onium Qq qQ q _ ● hadro-quarkonium QQ_ q

● Born-Oppenheimer tetraquark! arXiv:1305.6905 9 Models for XYZ Mesons _ Conventional Quarkonium Q Q

● well-developed phenomenology based on potential models

● accurate below open-heavy-ﬂavor threshold! how accurate above?

● spin-symmetry multiplets S-wave: {0–+,1--} P-wave: {1+–,(0,1,2)++} D-wave: {2–+,(0,1,2)--}

10 Models for XYZ Mesons _ Q Q Quarkonium Hybrids _ g ● small_ wave function for QQ at the origin QQ in color-octet state ⟹ repulsive potential

● suppression of decays into S-wave + S-wave mesons S-wave + P-wave preferred (if kinematically accessible) Close & Page 1995, Kou and Pene 2005

● constituent gluon picture

● Born-Oppenheimer picture

11 Models for XYZ Mesons _ Quarkonium Hybrids ● constituent gluon picture Q Q gluon with quantum numbers 1+– spin-symmetry_ multiplets g S-wave QQ_: {1– –,(0,1,2)–+} P-wave QQ: {0++,1+–}, {1++,(0,1,2)+–}, {2++,(1,2,3)+–}

● Born-Oppenheimer picture_ – gluon field generated by QQ sources: Πu, Σu , ... spin-symmetry_ multiplets – – –+ ++ +– P-wave QQ_ in Πu field: {1 ,(0,1,2) }, {1 ,(0,1,2) } Σ – ++ +– S-wave QQ in u field: {0 ,1 } _ Q Q

12 Models for XYZ Mesons Charmonium Hybrid Y(4260) Babar 2005 ● 1- - + - ● produced very weakly in e e_ annihilation ⟹ small wavefunction for cc at the origin ● not observed in S-wave + S-wave charm mesons

2 40 104

103

30 102

10 identify as 1 charmonium hybrid 20 3.6 3.8 4 4.2 4.4 4.6 4.8 5 Events / 20 MeV/c Close and Page 2005

0 3.8 4 4.2 4.4 4.6 4.8 5 13 m(+-J/) (GeV/c2) Models for XYZ Mesons _ Q q Compact Tetraquark _

● spacially overlapping orbitals q Q

● 2-body potentials only ⟹ fall-apart decays into meson+meson unless mass is below all meson pair thresholds Vijande, Valcarce, Richard

● 3-body and higher potentials?

14 Models for XYZ Mesons _ _ Meson Molecule Q q q Q

● constituents must be narrow S-wave charm mesons: D, D*, Ds, Ds* P-wave charm mesons: D1, D2*, Ds0*, Ds1, Ds2*

● many XYZ mesons are near a charm-meson-pair threshold

Are XYZ mesons near thresholds just by coincidence? 25 nonstrange thresholds between 3770 and 5150 MeV! Are charm mesons bound by their interactions? π exchange between charm mesons Tornqvist 1993 isospin-0 bound_ states near threshold D*D_: 0–+,1++ D*D*: 0++, 0–+, 1+–, 2++

15 Models for XYZ Mesons Meson Molecules Universality of S-wave near-threshold resonances if a state is sufﬁciently close to a threshold within 10 MeV for charm mesons within 3 MeV for bottom mesons and if it has S-wave coupling to the threshold it is transformed by its interactions into a loosely bound molecule with universal properties determined by its small binding energy

large mean-square separation of constituents: 2 ⟨r ⟩ = 1/(4μ Ebinding) _ r _ Q q q Q

16 Models for XYZ Mesons Deﬁnitive Meson Molecule: X(3872)

X(3872) _ ● extremely close to threshold for D*0 D0 below threshold by 0.3±0.4 MeV Belle, CDF, LHCb ++ ● quantum numbers 1 LHCb _ ⟹ S-wave coupling to D*0 D0 must be loosely bound molecule_ _ superposition of D*0 D0 and D0 D*0 rms separation of charm mesons: 5 fm (if binding energy is 0.3 MeV)

5 fm _ D*0 D0

17 Models for XYZ Mesons Meson Molecules

Bottomonium tetraquarks Zb(10610), Zb(10650)

both decay into Υ(nS) π and hb(nP) π _ Zb(10610) is close to B*B_ threshold Zb(10650) is close to B*B* threshold (but they are above threshold and not close enough to be universal molecules) _ Assumption that Zb(10610) is B*B_ molecule and that Zb(10650) is B*B* molecule can explain why they both decay into Υ(nS) π and hb(nP) π Bondar, Garmash, Milstein, Mizuk, & Voloshin 2011

Is there a better explanation?

18 Models for XYZ Mesons _ _ Diquark-Onium Q q Q q

● diquark Qq: color anti-triplet, spin 0 or 1

● for q = u,d only degenerate isospin-0 and isospin-1 multiplets quantum numbers: 0++, 0++, 0++, 0++ 1+–, 1+–, 1++, 1++ 2++, 2++

● include q = s orbital excitations? radial excitations?

proliferation of predicted states!

19 Models for XYZ Mesons q _ Hadro-Quarkonium QQ _ _ ● light quarks bound to color-singlet QQ core q Dubynskiy & Voloshin 2008

● or light meson bound to quarkonium

● motivation: many XYZ mesons observed though single hadronic transition to speciﬁc charmonium and light meson

20 Models for XYZ Mesons Born-Oppenheimer Tetraquark

● quarkonium tetraquark can be described by the Born-Oppenheimer approximation just like quarkonium hybrids except that the gluons and light quarks are in a ﬂavor-nonsinglet state arXiv:1305.6905 _ q _ Q Q q _ ● Q and Q move adiabatically in B-O potentials deﬁned by energies of gluons and light quarks with isospin 1

21 QCD Theory Approaches

● Lattice QCD for charmonium S Prelovsek, Lattice QCD Review of Charmonium ... Spectroscopy, Saturday 14:00 C Thomas, Excited Charmonia ... from Lattice QCD, Sunday 9:40

● Lattice NRQCD for bottomonium

● Born-Oppenheimer approximation for charmonium and bottomonium

● QCD Sum Rules?

22 _ Lattice QCD for cc Mesons Dudek, Edwards, Mathur, Richards 2007 Hadron Spectrum Collaboration 2012 Lattice QCD ● anisotropic lattice: 243 x 128 ● lattice spacing: a = 0.12 fm ● light quark masses: mπ = 400 MeV caveat: no extrapolation to a = 0 no extrapolation to physical u,d quark masses

● determine masses of charmonium and charmonium hybrids from cross-correlators of many operators ● identiﬁed 46 states with various JPC: J up to 4, mass up to 4.6 GeV ● discriminate between charmonium and charmonium hybrids

23 Lattice QCD for charmonium Hadron Spectrum Collaboration 2012 charmonium hybrid candidates ﬁll out 4 spin-symmetry multiplets

{1++, (0,1,2)+-}, {0++, 1+-}, {2++, (1,2,3)+-} {1--, (0,1,2)-+} 1500 L 1000 DsDs MeV H c

h DD M -

M 500

exotic! exotic! 0 0-+ 1-- 2-+ 1-+ 0++ 1+- 1++ 2++ 3+- 0+- 2+-

24 Charmonium Hybrids ● Lattice QCD predicts one 1-- charmonium hybrid near 4300 MeV identify that state as Y(4260) Close and Page 2005

● extrapolations to a = 0 and to physical mπ will affect masses smaller effects on mass splittings? ● take mass of Y(4260) from experiment take mass splittings from Hadron Spectrum Collaboration predict masses for rest of ground-state hybrid multiplet 0–+: 4173±21 MeV 1–+: 4195±23 MeV 2–+: 4312±24 MeV arXiv:1305.6905 need deﬁnitive Lattice QCD calculations with extrapolations to a = 0 and physical mπ 25 _ Lattice NRQCD for bb Mesons _ mb too large use Lattice QCD to calculate bb meson spectrum must use an effective ﬁeld theory

Lattice NRQCD Juge, Kuti, Morningstar 1999 ● anisotropic lattice: 153 x 45 ● lattice spacing: a = 0.11 fm ● no dynamical quarks! lowest bottomonium hybrid spin-symmetry multiplets {1– –, (0,1,2)–+} {1++, (0,1,2)+–} {0++, 1+–} {1– –, (0,1,2)–+} (radial excitation)

need Lattice NRQCD calculations with dynamical light quarks!

26 Born-Oppenheimer approximation

● Born-Oppenheimer potentials Vn(R) deﬁned by energies of gluons_ and light quarks in presence of static Q and Q sources separated by distance R

_ Q Q _ ● Q and Q move adiabatically in B-O potential

● gluons and light quarks respond_ instantaneously to the motion of the Q and Q

27 Born-Oppenheimer approximation for hybrids

Juge, Kuti, Morningstar 1999

Born-Oppenheimer potentials labelled by component of Jlight and by (CP)light + - or by Σg , Πu, Σu , ... _ Q Q

+ ground state: Σg

- excited states: Πu, Σu , ...

28 Born-Oppenheimer approximation for hybrids Juge, Kuti, Morningstar 1999 calculate Born-Oppenheimer potentials + Σg : quarkonium potential - Πu, Σu , ...: hybrid potentials

Lattice QCD ● anisotropic lattice: 103 x 30 ● lattice spacing: a = 0.19 fm ● no dynamical quarks!

29 Born-Oppenheimer approximation for hybrids

Juge, Kuti, Morningstar 1999 solve Schroedinger_ equation for Q and Q in B-O potentials energy levels labelled by nL radial quantum number n = 1,2,3,... orbital angular momentum L = S,P,D,... quarkonium hybrid multiplets -- -+ ++ +- Πu(1P): {1 , (0,1,2) }, {1 , (0,1,2) } - ++ +- Σu (1S): {0 ,1 } -- -+ ++ +- Πu(2P): {1 , (0,1,2) }, {1 , (0,1,2) } challenge to Lattice QCD: calculate Born-Oppenheimer potentials with dynamical quarks

30 Born-Oppenheimer approximation for tetraquarks

● quarkonium tetraquarks can be treated using the Born-Oppenheimer approximation just like quarkonium hybrids except that the gluons and light quarks are in a ﬂavor-nonsinglet state arXiv:1305.6905 _ q _ Q Q q

challenge to Lattice QCD: calculate Born-Oppenheimer potentials for isospin 1

31 Born-Oppenheimer approximation for tetraquarks isospin-1 B-O potentials

simple possibility: ● same qualitative behavior as ﬂavor-singlet B-O potentials

discovery of Zb and Zc tetraquarks ⟹ shifted lower in energy lowest multiplets same as for quarkonium hybrids?

{1--, (0,1,2)-+}, {1++, (0,1,2)+-}, {0++,1+-}, ...

32 Conclusions discoveries of neutral XYZ mesons bottomonium tetraquarks Zb, Zb′ charmonium tetraquarks Zc, Zc′ have revealed a serious gap in our understanding of the QCD spectrum none of the proposed models for the XYZ mesons has yet presented a compelling pattern new proposal: Born-Oppenheimer hybrids and tetraquarks _ q _ Q Q q

33 Conclusions Conclusions _ What is needed from theory: ● definitive calculations_ of spectrum of cc mesons using Lattice QCD ● definitive calculations_ of spectrum of bb mesons using Lattice NRQCD ● calculation of B-O potentials using Lattice QCD for flavor-singlet and for isospin-1 ● development of phenomenological models for transitions between quarkonium, quarkonium hybrids, quarkonium tetraquarks _ _ _ q _ Q Q Q Q Q Q q

34 Conclusions _ Additional hints can be expected from experiment

● Intensity Frontier charm factory BEPCII bottom factory_ Super KEK-B PANDA: pp annihilation into charmonium

● Energy Frontier ATLAS and CMS LHCb

“Quarkonium at the Frontiers of High Energy Physics: A Snowmass White Paper” Bodwin, Braaten, Eichten, Olsen, Pedlar, and Russ, arXiv:1307.7425