Theoretical Interpretation of the XYZ Mesons 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′ 40 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 40 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) Γ(MeV) J PC Decay modes 1st observation neutral cc¯ mesons X(3823) 3823.1 1.9 < 24 ?? χ γ Belle 2013 ± − c1 X(3872) 3871.68 0.17 < 1.21++ J/ ⇡+⇡ , J/ ⇡+⇡ ⇡0 Belle 2003 ± − − D0D¯ 0⇡0, D0D¯ 0γ J/ γ, (2S) γ X(3915) 3917.5 1.9 20 50++ J/ !, γγ Belle 2004 ± ± χ (2P ) 3927.2 2.6 24 62++ DD¯, γγ 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/ φ 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/ φ CDF 2010 − − +4.6 +18.4 ++ X(4350) 4350.6 5.1 13.3 10.0 0/2 J/ φ, γγ 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 + ? + ¯ Zc (4020) 4021.8 2.75.7 3.6?− hc(1P ) ⇡ , D⇤D⇤ BESIII 2013 _ ± ± + +24 +51 ?+ + Z1 (4050) 4051 43 82 55 ? χc1(1P ) ⇡ Belle 2008 − − cc mesons + +185 +321 ?+ + Z2 (4250) 4248 45 177 72 ? χc1(1P ) ⇡ Belle 2008 − − + +24 +113 + + Z (4430) 4443 18 107 71 1 − (2S) ⇡ Belle 2007 − − 6 1 _ _ New bb Mesons above BB threshold TABLE I: State M (MeV) Γ(MeV) J PC Decay modes 1st observation 1_ neutral 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! 7 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 Q Q ● constituent gluon picture +– 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 10 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