Hunting for exotic QQQ¯Q¯ tetraquark states Wei Chen Sun Yat-Sen University ICNFP 2017, Kolymbari, Crete, Greece August 17 { 26, 2017 Wei Chen QQQ¯Q¯ states August 23, 2017 1 / 25 Outline 1 Background of the exotic hadron states 2 Briefly Introduction of QCD Sum Rules 3 Moment sum rule analyses for mass spectra 4 Decay properties of the QQQ¯Q¯ tetraquarks 5 Summary Wei Chen QQQ¯Q¯ states August 23, 2017 2 / 25 Why hadron spectroscopy? Three generations of quarks: up, down, strange, charm, bottom, top. Hadrons are bound states of quarks, via strong interaction. The mass of the universe is mainly due to hadrons (95% are baryonic matter): nucleons forming nuclei! Wei Chen QQQ¯Q¯ states August 23, 2017 3 / 25 Why hadron spectroscopy? Quark masses only accounts for a small fraction of the nucleon mass: 99% is generated by dynamics of QCD confinement Light quark visible mass is dominated by QCD effects Hadron spectroscopy: revealing the nature of the hadron masses Quantitative understand the QCD confinement and spontaneous chiral symmetry breaking. Important for understanding the QCD vacuum. Wei Chen QQQ¯Q¯ states August 23, 2017 4 / 25 Exotic Hadrons in QCD meson(qq¯) baryon(qqq) Quark model is established to classify hadrons:JPC quantum numbers and flavour quantum numbers. However, the hadron structures are more complicated in QCD. It may allow for hadrons which lie outside the naive quark model. Mesons with exotic JPC quantum numbers: JPC = 0−−; 0+−; 1−+; 2+−; ::: Baryons with exotic flavour quantum numbers: dibaryon, pentaquark,... Wei Chen QQQ¯Q¯ states August 23, 2017 5 / 25 Different configurations of exotic hadrons: d u s u d c π u u s d u¯ u c c¯ c¯ dibaryon pentaquark molecule g c¯ u u¯ c q¯ q g g tetraquark glueball hybrid Wei Chen QQQ¯Q¯ states August 23, 2017 6 / 25 Overview of XYZ States Experiments: Belle, BaBar, BESIII, CLEO, D0, LHCb... s γ − − c γ e c e ∓ c c π γ * γ * c Y (4260) b c Z ± c c + + γ q q e c e J /ψ X (3872) Y (4260) X (3940) X (3915) Zc (3900) Y (4008) X (4160) Y (3940) X (4350) Zc (4025) Z + (4430) Y (4360) Z(3930) Zc (4020) Z + (4051) Y (4630) Zc (3885) Z + (4248) Y (4660) Y (4140) Y (4274) + Zc (4200) Z + (4240) X (3823) H.X.Chen, W.Chen, X.Liu, S.L.Zhu, Phys.Rept.639(2016) 1-121. Wei Chen QQQ¯Q¯ states August 23, 2017 7 / 25 Overview of XYZ States S. L. Olsen, Front. Phys. 10 (2015) 101401 Many charmonium-like states were discovered above the open-charm thresholds. Their masses and decay modes are different from the pure cc¯ charmonium states. Some charged Zc states were observed, which are evidences for four-quark states (ccu¯ d¯). They are good candidates for exotic hadron states! Wei Chen QQQ¯Q¯ states August 23, 2017 8 / 25 Theoretical Models Theoretical configurations: tetraquark, molecule, hybrid,... Zc states: tetraquark, molecule It is difficult to distinguish these two intepretations. c π u c d¯ c¯ ¯ c¯ u d Wei Chen QQQ¯Q¯ states August 23, 2017 9 / 25 Pentaquarks: Pc (4380) and Pc (4450) In 2015, LHCb reported two hidden-charm pentaquark states 800 Pc (4380) and Pc (4450) in J= p 700 (b) LHCb invariant mass distribution via 600 Λ0 J= K −p decay (PRL115, b 500 072001(2015)! ) Events/(15 MeV) 400 300 M1 = (4380 8 29) MeV ; ± ± 200 Γ1 = (205 18 86) MeV ; ± ± 100 M2 = (4449:8 1:7 2:5) MeV ; 0 ± ± 4 4.2 4.4 4.6 4.8 5 m [GeV] Γ2 = (39 5 19) MeV : J/ψp ± ± P 3 − 5 + 3 + 5 − 5 + 3 − J (Pc (4380); Pc (4450)) = 2 ; 2 ; 2 ; 2 or 2 ; 2 Wei Chen QQQ¯Q¯ states August 23, 2017 10 / 25 Pentaquarks: Pc (4380) and Pc (4450) Two possible configurations: ?? It is the time to search for more exotic multiquark states! Wei Chen QQQ¯Q¯ states August 23, 2017 11 / 25 Doubly hidden-flavor tetraquarks: QQQ¯Q¯ QQQ¯Q¯ Tetraquarks: They are far away from the mass range of the observed conventional qq¯ hadrons. Can be clearly distinguished experimentally from the normal states. The light mesons (π; ρ, !; σ...) can not be exchanged between two charmonia/bottomonia. The binding force comes from the short-range gluon exchange. A molecule configuration is not favored and thus the QQQ¯Q¯ is a good candidate for compact tetraquark. Q¯ Q ¯ Q Q Wei Chen QQQ¯Q¯ states August 23, 2017 12 / 25 Theoretical works: Quark-Gluon models: Prog. Theor. Phys. 54, 492 (1975); Zeit. Phys. C7, 317 (1981). Potential model: Phys.Rev. D25, 2370 (1982); Phys. Lett. B123, 449 (1983). MIT bag model: Phys. Rev. D32, 755 (1985). Hyperspherical harmonic formalism: Phys. Rev. D73, 054004 (2006). BS or Schroedinger Eqs: Phys.Rev.D86, 034004 (2012); Phys.Lett.B718, 545 (2012). Recent studies: arXiv:1605.01134; 1605.01647; 1612.00012; PRD95, 034011 (2017); EPJC77, 432 (2017); arXiv:1706.07553. Experiments: J= J= pairs: Phys. Lett. B707, 52 (2012) (LHCb); JHEP 1409, 094(2014) (CMS); Phys. Rev. D90, 111101 (2014) (D0). J= Υ(1S) events: Phys. Rev. Lett. 116, 082002 (2016) (D0); K. Dilsiz's talk at APS April Meeting 2016 on behalf of CMS, see https://absuploads.aps.org/presentation.cfm?pid=11931. Υ(1S)Υ(1S) pairs: JHEP 05, 013 (2017) (CMS). Wei Chen QQQ¯Q¯ states August 23, 2017 13 / 25 Tetraquark Sum Rules Study two-point correlation function of current J(x) with the same quantum numbers with hadron state: Z Π(q2) = i d4xeiq·x Ω T [J(x)Jy(0)] Ω h j j i Classify states X by coupling to current Ω J(x) X = 0 j i h j j i 6 Currents are probes of spectrum and might not overlap with state Interpolating currents with JPC = 0++: Q¯ Q T ¯ ¯T J1 = Qa Cγ5QbQaγ5CQb ; ¯ Q T ¯ µ ¯T Q J2 = Qa Cγµγ5QbQaγ γ5CQb ; T ¯ µν ¯T J3 = Qa CσµνQbQaσ CQb ; T ¯ µ ¯T J4 = Qa CγµQbQaγ CQb ; T ¯ ¯T J5 = Qa CQbQaCQb ; Wei Chen QQQ¯Q¯ states August 23, 2017 14 / 25 Hadron level: described by the dispersion relation N−1 (q2)N Z ImΠ(s) X Π(q2) = ds + b (q2)n; π sN (s q2 i) n − − n=0 1 X ρ(s) = ImΠ(s) = δ(s m2) 0 J n n Jy 0 π n n − h j j ih j j i = f 2δ(s m2 ) + continuum; X − X Quark-gluon level: evaluated via operator product expansion(OPE) Π(s) = Πpert (s) + ΠhGGi(s) + :::; Wei Chen QQQ¯Q¯ states August 23, 2017 15 / 25 Define moments in Euclidean region Q2 = q2 > 0: − n 2 1 d 2 Mn(Q0 ) = Π(Q ) Q2=Q2 n! − dQ2 j 0 Z 1 2 ρ(s) fX 2 = 2 ds = 2 2 1 + δn(Q0 ) ; 2 (s + Q )n+1 (m + Q )n+1 mH 0 X 0 2 where δn(Q0 ) contains the higher states and continuum. Ratio of the moments 2 2 2 Mn(Q0 ) 2 2 1 + δn(Q0 ) r(n; Q0 ) 2 = mX + Q0 2 : ≡ Mn+1(Q0 ) 1 + δn+1(Q0 ) Predict hadron mass q 2 2 mX = r(n; Q ) Q 0 − 0 2 2 for sufficiently large n when δn(Q0 ) ∼= δn+1(Q0 ) for convergence. Wei Chen QQQ¯Q¯ states August 23, 2017 16 / 25 Limitations for (n; ξ) parameter space: 2 2 ξ = Q0 =16mc ; for ccc¯c¯ system; 2 2 ¯¯ ξ = Q0 =mb; for bbbb system: Small ξ: higher dimensional condensates give large contributions to 2 Mn(Q0 ), leading to bad OPE convergence. 2 Large ξ: slower convergence of δn(Q0 ). This can be compensated by taking higher derivative n for the lowest lying resonance to dominate. Large n: moving further away from the asymptotically free region. The OPE convergence would also become bad. hGGi pert Requiring Π (s) Π (s) to obtain an upper limit nmax , which will increase with respect≤ to ξ. Good (n; ξ) region: the lowest lying resonance dominates the moments while the OPE series has good convergence. nmax = 75; 76; 77; 78 for ξ = 0:2; 0:4; 0:6; 0:8 Wei Chen QQQ¯Q¯ states August 23, 2017 17 / 25 H¨older'sinequality: 2 2 Mn(Q0 ) R = 2 2 1 ; Mr (Q0 )M2n−r (Q0 ) ≤ R 1.000 80 0.995 60 0.990 0 n 1 40 Ξ 2 20 3 The boundary gives( n; ξ) = (48; 0:2); (49; 0:4); (49; 0:6); (50; 0:8). Wei Chen QQQ¯Q¯ states August 23, 2017 18 / 25 Mass for scalar bbb¯b¯ tetraquark: mass curves have plateaus at (n; ξ) = (48; 0:2); (49; 0:4); (49; 0:6); (50; 0:8) 20.1 Ξ=0.2 19.7 Ξ=0.4 Ξ=0.6 D 19.3 Ξ=0.8 GeV @ X 18.9 m 18.5 18.45 18.1 12 20 28 36 44 52 60 68 76 n mX = (18:45 0:15) GeV: b ± Wei Chen QQQ¯Q¯ states August 23, 2017 19 / 25 Mass spectra for the ccc¯c¯ and bbb¯b¯ tetraquarks: PC J Currents mXc (GeV) mXb (GeV) ++ 0 J1 6:44 0:15 18:45 0:15 ± ± J2 6:59 0:17 18:59 0:17 ± ± J3 6:47 0:16 18:49 0:16 ± ± J4 6:46 0:16 18:46 0:14 ± ± J5 6:82 0:18 19:64 0:14 ± ± 1++ J+ 6:40 0:19 18:33 0:17 1µ ± ± J+ 6:34 0:19 18:32 0:18 2µ ± ± 1+− J− 6:37 0:18 18:32 0:17 1µ ± ± J+ 6:51 0:15 18:54 0:15 2µ ± ± ++ 2 J1µν 6:51 0:15 18:53 0:15 ± ± J2µν 6:37 0:19 18:32 0:17 ± ± −+ + 0 J1 6:84 0:18 18:77 0:18 J+ 6:85 ± 0:18 18:79 ±0:18 2 ± ± 0−− J− 6:84 0:18 18:77 0:18 1 ± ± 1−+ J+ 6:84 0:18 18:80 0:18 1µ ± ± J+ 6:88 0:18 18:83 0:18 2µ ± ± 1−− J− 6:84 0:18 18:77 0:18 1µ ± ± J− 6:83 0:18 18:77 0:16 2µ ± ± Wei Chen QQQ¯Q¯ states August 23, 2017 20 / 25 24.00 20.00 16.00 12.00 Mass (GeV) 8.00 4.00 0 + ++ ++ + ++ + 0− 0 1−− 1 1 − 2 0−− 1− Wei Chen QQQ¯Q¯ states August 23, 2017 21 / 25 Decay behavior: ccc¯c¯ tetraquarks ccc¯c¯ (ccq) + (¯cc¯q¯): kinematically forbidden.