Physics of the Multiquark States

Transcription

1 Physics of the Multiquark States Ahmed Ali DESY, Hamburg Sept. 2, 2015 Corfu Summer School & Workshop Ahmed Ali (DESY, Hamburg) 1 / 44

2 Prologue Experimental Evidence for Multiquark states X, Y, Z Models for X, Y, Z Mesons The diquark model of Tetraquarks Charmonium-like and bottomonium-like Tetraquark Spectrum The LHCb Pentaquarks P ± (4380) and P ± (4450) Pentaquarks as Baryon-Meson molecules Pentaquarks as Diquark-Diquark-Antiquark baryons Summary Ahmed Ali (DESY, Hamburg) 2 / 44

3 Prologue It took some 40 years before Gell-Mann s prophecy of multiquark hadrons (q q q q) and (q q q q q) could be experimentally verified! Ahmed Ali (DESY, Hamburg) 3 / 44

4 X(3872) - the poster Child of the X, Y, Z Mesons Discovery Mode : B J/ψπ + π K M = ± 0.6 ± 0.5 MeV Γ < 2.3 MeV J PC = 1 ++ [LHCb] [PRL110, 22201(2013)] Ahmed Ali (DESY, Hamburg) 4 / 44

5 The charged four-quark state Z(4430) + First observed by Belle in B 0(+) ψ(2s)π + K (0) [PRL100, , (2008)] Confirmed by LHCb in 2014 Ahmed Ali (DESY, Hamburg) 5 / 44

6 Observation of Z c (3900) ± in the decay Y(4260) πz c (3900) Ahmed Ali (DESY, Hamburg) 6 / 44

7 Summary of Charmonia and Charmonium-like Hadrons (Olsen, ) Ahmed Ali (DESY, Hamburg) 7 / 44

8 Exotic states in the hidden bottom sector Enigmatic Υ(5S) Decays and a Y b (10890) close to Υ(5S) Ahmed Ali (DESY, Hamburg) 8 / 44

9 σ(e + e Υ(nS)π + π ) in the Υ(10860) and Υ(11020) resonance region [Belle] F Υ(nS)ππ = A 5S,n f 5S 2 + A 6S,n f 6S 2 + 2K n A 5S,n A 6S,n R[e iδ n f 5S f6s ] K n and δ n allowed to float Fit Values (MeV): M 5S = ± ; Γ S = M 5S (Υ(nS)ππ) M 5S (b b) = 9.2 ± 3.4 ± 1.9 MeV Ahmed Ali (DESY, Hamburg) 9 / 44

10 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? Ahmed Ali (DESY, Hamburg) 10 / 44

11 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? Ahmed Ali (DESY, Hamburg) 10 / 44

12 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? Ahmed Ali (DESY, Hamburg) 10 / 44

13 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? Ahmed Ali (DESY, Hamburg) 10 / 44

14 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? Ahmed Ali (DESY, Hamburg) 10 / 44

15 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? Ahmed Ali (DESY, Hamburg) 10 / 44

16 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? Ahmed Ali (DESY, Hamburg) 10 / 44

17 Dipion mass distributions in Υ(5S) Υ(nS)ππ decays? tetraquark & rescattering trying to explain data (unresolved so far) Ahmed Ali (DESY, Hamburg) 10 / 44

18 Evidence for Z b (10610) ± and Z b (10650) ± (Belle) Ahmed Ali (DESY, Hamburg) 11 / 44

19 Summary of Bottomonia and Bottomonium-like Hadrons (Olsen, ) Ahmed Ali (DESY, Hamburg) 12 / 44

20 Ahmed Ali (DESY, Hamburg) 13 / 44

21 Diquark Model of Tetraquarks Diquarks and Anti-diquarks are the building blocks of Tetraquarks Color representation: 3 3 = 3 6; only 3 is attractive; C 3 = 1/2 C 3 Interpolating diquark operators for the two spin-states of diquarks good : 0 + Q iα = ɛ αβγ ( b β c γ 5 q γ i q β i c γ 5 b γ ) α, β, γ: SU(3) C indices bad : 1 + Q iα = ɛ αβγ ( b β c γq γ i + q β i c γb γ ) Ahmed Ali (DESY, Hamburg) 14 / 44

22 Diquark Model of Tetraquarks Diquarks and Anti-diquarks are the building blocks of Tetraquarks Color representation: 3 3 = 3 6; only 3 is attractive; C 3 = 1/2 C 3 Interpolating diquark operators for the two spin-states of diquarks good : 0 + Q iα = ɛ αβγ ( b c β γ 5 q γ i q β i c γ 5 b γ ) α, β, γ: SU(3) C indices bad : 1 + Q iα = ɛ αβγ ( b c β γq γ i + q β i c γb γ ) NR limit: States parametrized by Pauli matrices : good : 0 + Γ 0 = σ 2 2 bad : 1 + Γ = σ 2 σ 2 Ahmed Ali (DESY, Hamburg) 14 / 44

23 Diquark Model of Tetraquarks Diquarks and Anti-diquarks are the building blocks of Tetraquarks Color representation: 3 3 = 3 6; only 3 is attractive; C 3 = 1/2 C 3 Interpolating diquark operators for the two spin-states of diquarks good : 0 + Q iα = ɛ αβγ ( b c β γ 5 q γ i q β i c γ 5 b γ ) α, β, γ: SU(3) C indices bad : 1 + Q iα = ɛ αβγ ( b c β γq γ i + q β i c γb γ ) NR limit: States parametrized by Pauli matrices : good : 0 + Γ 0 = σ 2 2 bad : 1 + Γ = σ 2 σ 2 Diquark spin s Q tetraquark total angular momentum J: Y [bq] = sq, s Q ; J Tetraquarks: 0 Q, 0 Q ; 0 J = Γ 0 Γ 0 1Q, 1 Q ; 0 J = 1 Γ i Γ i Q, 1 Q ; 1 J = Γ 0 Γ i Ahmed Ali (DESY, Hamburg) i 0 14 / 44

24 NR Hamiltonian for Tetraquarks with hidden charm States need to diagonalize Hamiltonian: H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL H eff (X, Y, Z) = 2m Q + B Q [ 2 L2 2a L S + 2κ qq sq s Q + s q s Q ] ( ) BQ = 2m Q aj(j + 1) a L(L + 1) + as(s + 1) 3κ qq + κ qq [ sqq (s qq + 1) + s q Q (s q Q + 1)] Ahmed Ali (DESY, Hamburg) 15 / 44

25 NR Hamiltonian for Tetraquarks with hidden charm States need to diagonalize Hamiltonian: H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL with constituent mass H eff (X, Y, Z) = 2m Q + B Q [ 2 L2 2a L S + 2κ qq sq s Q + s q s Q ] ( ) BQ = 2m Q aj(j + 1) a L(L + 1) + as(s + 1) 3κ qq + κ qq [ sqq (s qq + 1) + s q Q (s q Q + 1)] Ahmed Ali (DESY, Hamburg) 15 / 44

26 NR Hamiltonian for Tetraquarks with hidden charm States need to diagonalize Hamiltonian: H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL with qq spin coupling H (qq) SS = 2(K cq ) 3 [(S c S q ) + (S c S q )] H (q q) SS = 2(K c q )(S c S q + S c S q ) + 2K c c (S c S c ) + 2K q q (S q S q ) q q spin coupling H eff (X, Y, Z) = 2m Q + B Q [ 2 L2 2a L S + 2κ qq sq s Q + s q s Q ] ( ) BQ = 2m Q aj(j + 1) a L(L + 1) + as(s + 1) 3κ qq + κ qq [ sqq (s qq + 1) + s q Q (s q Q + 1)] Ahmed Ali (DESY, Hamburg) 15 / 44

27 NR Hamiltonian for Tetraquarks with hidden charm States need to diagonalize Hamiltonian: H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL with H (qq) SS = 2(K cq ) 3 [(S c S q ) + (S c S q )] H (q q) SS = 2(K c q )(S c S q + S c S q ) + 2K c c (S c S c ) + 2K q q (S q S q ) H SL = 2A Q (S Q L + S Q L) H LL = B Q L Q Q (L Q Q + 1) 2 LS coupling LL coupling H eff (X, Y, Z) = 2m Q + B Q [ 2 L2 2a L S + 2κ qq sq s Q + s q s Q ] ( ) BQ = 2m Q aj(j + 1) a L(L + 1) + as(s + 1) 3κ qq + κ qq [ sqq (s qq + 1) + s q Q (s q Q + 1)] Ahmed Ali (DESY, Hamburg) 15 / 44

28 Low-lying S- and P-wave Tetraquark States S-wave states In the s qq, s q Q ; S, L Jand s q q, s Q Q ; S, L J bases, the positive parity S-wave tetraquarks are given in terms of the six states listed below (charge conjugation is defined for neutral states) Label J PC s qq, s q Q ; S, L J s q q, s Q Q ; S, L J Mass X ( 0, 0; 0, 0 0 0, 0; 0, ) 3 1, 1; 0, 0 0 /2 M00 3κ qq X ( ) 1, 1; 0, , 0; 0, 0 0 1, 1; 0, 0 0 /2 M00 + κ qq X ( ) 1, 0; 1, , 1; 1, 0 1 / 2 1, 1; 1, L 1 M 00 κ qq Z 1 + ( ) ( 1, 0; 1, 0 1 0, 1; 1, 0 1 / 2 1, 0; 1, L 1 0, 1; 1, L ) 1 / 2 M00 κ qq Z 1 + ( 1, 1; 1, 0 1 1, 0; 1, L 1 + 0, 1; 1, L ) 1 / 2 M00 + κ qq X , 1; 2, 0 2 1, 1; 2, L 2 M 00 + κ qq P-wave (J PC = 1 ) states Label J PC s qq, s q Q ; S, L J s q q, s Q Q ; S, L J Mass Y 1 1 ( 0, 0; 0, 1 1 0, 0; 0, ) 3 1, 1; 0, 1 1 /2 M00 3κ qq + B Q Y 2 1 ( ) 1, 0; 1, , 1; 1, 1 1 / 2 1, 1; 1, L 1 M 00 κ qq + 2a + B Q Y 3 1 ( ) 1, 1; 0, , 0; 0, 1 1 1, 1; 0, 1 1 /2 M00 + κ qq + B Q Y 4 1 1, 1; 2, 1 1 1, 1; 2, L 1 M 00 + κ qq + 6a + B Q Y 5 1 1, 1; 2, 3 1 1, 1; 2, L 1 M 00 + κ qq + 16a + 6B Q Ahmed Ali (DESY, Hamburg) 16 / 44

29 Charmonium-like and Bottomonium-like Tetraquark Spectrum (with Satoshi Mishima) Parameters in the Mass Formula charmonium-like bottomonium-like M 00 [MeV] κ qq [MeV] B Q [MeV] a [MeV] charmonium-like bottomonium-like Label J PC State Mass [MeV] State Mass [MeV] X X X X(3872) Z 1 + Z c + (3900) 3890 Z+,0(10610) b Z 1 + Z c + (4020) 4024 Z+ (10650) b X Y 1 1 Y(4008) 4024 Y b (10891) Y 2 1 Y(4260) 4263 Y b (10987) Y 3 1 Y(4290) (or Y(4220)) Y 4 1 Y(4630) Y Ahmed Ali (DESY, Hamburg) 17 / 44

30 Comparison with current data in the Charmonium-like sector Our determination of the parameters M 00, κ qc, B C and a in the Charmonium-like sector close to the one by Maiani et al. (2014). Their results are shown below New; Old Quarks inside a Diquark are much more tightly bound than Diquarks in Baryons Ahmed Ali (DESY, Hamburg) 18 / 44

31 There are two or three recent experiments that find weak evidence for signals near the nominal masses, but there is simply no point in tabulating them in view of the overwhelming evidence that the claimed pentaquarks do not exist. The only advance in particle physics thought worthy of mention in the American Institute of Physics Physics News in 2003 was a false alarm. The whole story is a curious episode in the history of science. Ahmed Ali (DESY, Hamburg) 19 / 44 Pentaquarks Pentaquarks remained cursed under the shadow of the botched discoveries of Θ(1540), Φ(1860), Θ c (3100)! For example, the one-page review on Pentaquarks in PDG (2014) by C.G. Wohl states the following:

32 Elusive Pentaquark Comes into View! (R. Aaij et al., PRL 115, (2015) Ahmed Ali (DESY, Hamburg) 20 / 44

33 The Pentaquarks P c + (4380) and P c + (4450) as resonant J/ψp states Discovery Channel (LHC; s = 7 & 8 TeV; Ldt = 3 fb 1 ) pp b b Λ b X; Λ b K J/ψp Ahmed Ali (DESY, Hamburg) 21 / 44

34 Model fits with one P + c (4450) state with J P = 5/2 + Results of the fit with one J P = 5/2 + P c state. The m Kp projection is well described, but discrepencies remain in the m J/ψp projection Ahmed Ali (DESY, Hamburg) 22 / 44

35 Model fits with two [ P + c (4380) and P + c (4450)] states Fits with two P + c states. Acceptable fits found for several J P combinations The best fit yields J P = (3/2, 5/2 + ) for [P + c (4380), P + c (4450)] states. Both the m Kp and m J/ψp projections are well described Ahmed Ali (DESY, Hamburg) 23 / 44

36 Summary of the LHCb Pentaquark Measurements Higher mass state (statistical significance 12σ) M = ± 1.7 ± 2.5 MeV; Γ = 39 ± 5 ± 19 MeV Lower mass state (statistical significance 9σ) M = 4380 ± 8 ± 29 MeV; Γ = 205 ± 18 ± 86 MeV Fitted Values of the real and imaginary parts of the amplitudes For P + c (4450), fit shows a phase change in amplitudes consistent with a resonance Ahmed Ali (DESY, Hamburg) 24 / 44

37 Theoretical Interpretations of the LHCb Pentaquarks The new pentaquarks in the diquark model L. Maiani, A.D. Polosa, V. Riquer, arxiv: PLB The pentaquark candidates in the dynamical diquark picture Richard F. Lebed, arxiv: Some predictions of diquark model for hidden charm pentaquark discovered at the LHCb; Guan-Nan Li, Xiao-Gang He, Min He, arxiv: The LHCb pentaquark as a D Σc molecular state L. Roca, J. Nieves, E. Oset, arxiv: Is pentaquark doublet a hadronic molecule? A. Mironov, A. Morozov, arxiv: The D Σc and D Σ c interactions and the LHCb hidden-charmed pentaquarks Jun He, arxiv: How to reveal the exotic nature of the P c (4450) Feng-Kun Guo, Ulf-G.Meißner, Wei Wang, Zhi Yang, arxiv: Testing the χ c1 p composite nature of the P c (4450) Ulf-G. Meißner, Jose A. Oliver, arxiv: Towards exotic hidden-charm pentaquarks in QCD Hua-Xing Chen, Wei Chen, Xiang Liu, T.G. Steele, Shi-Lin Zhu, arxiv: Identifying exotic hidden-charm pentaquarks Rui Chen, Xiang-Liu, arxiv: PRL Understanding the newly observed heavy pentaquark candidates Xiao-Hai Liu, Qian Wang, Qiang Zhao, arxiv: Ahmed Ali (DESY, Hamburg) 25 / 44

38 Pentaquarks as hadronic molecular states [Rui Chen et al., arxiv: ] Identify P + c (4380) with Σ c (2455) D and P + c (4450) with Σ c (2520) D bound by a pion exchange Effective Lagrangians: L P = igtr [ H ( Q) a γ µ A µ ab γ 5H ( ] Q) b L S = 3 2 g 1ɛ µλνκ v κ Tr [ S µ A ν S λ ] H ( Q) a = [P ( Q) µ a γ µ P ( Q) a γ 5 ](1 /v)/2; v = (0, 1) is a pseudoscalar and vector charmed meson multiplet (D, D ); S µ = 1/3(γ µ + v µ )γ 5 B 6 + B6µ stands for the charmed baryon multiplet, with B 6 and B6µ corresponding to the JP = 1/2 + and J P = 3/2 + in 6 F flavor representation; A µ is an axial-vector current, containing a pion chiral multiplet Ahmed Ali (DESY, Hamburg) 26 / 44

39 Effective potentials for the Σ c D and Σ c D systems V Σc D = 1 gg 1 2 Y(Λ, m π, r)i 0 G 0 3 V Σ c D = 1 2 f 2 π gg 1 fπ 2 2 Y(Λ, m π, r)i 1 G 1 where Y(Λ, m, r) = 4π 1 r (exp mr exp Λr ) Λ2 m 2 8πΛ exp Λ r Λ is a phenomenological parameter; the coeffs. I i and G i are related to the isospin and 2S+1 L J quantum numbers, respectively Solving the Schrödinger equation, one reproduces the masses of the pentaquarks P c (4380)and P c (4450)as hidden-charm molecular states Σ c D with (I = 1/2, J = 3/2) and Σ c D with (I = 1/2, J = 5/2), respectively, for two different values of Λ Ahmed Ali (DESY, Hamburg) 27 / 44

40 Eff. potentials, energy levels & wave-functions of the Σ c ( ) D systems P c (4380)is a Σ c D (I = 1/2, J = 3/2) molecule P c (4450)is a Σ c D (I = 1/2, J = 5/2) molecule Predict two additional hidden-charm molecular pentaquark states, Σ c D (I = 3/2, J = 1/2) and Σ c D (I = 3/2, J = 1/2), which are isospin partners of P c (4380) and P c (4450), decaying into (1232)J/ψ and (1232)η c Ahmed A rich Ali pentaquark (DESY, Hamburg) spectrum of states for the 28 / 44

41 Effective Hamiltonian for Pentaquarks H eff (P) = H eff ([QQ]) + m c + κ c[qq] (s c S [QQ] ) 2a P (L P S P ) + B P 2 L P 2 S [QQ] is the spin of the tetraquark; s c is the spin of the c L P and S P are the orbital angular momentum and spin of the pentaquark, respectively Ahmed Ali (DESY, Hamburg) 29 / 44

42 Pentaquarks in the diquark model [Maiani et al., arxiv: ] Λ b (bud) P + K decaying according to P + J/Ψ + p P + carry a unit of baryonic number and have the valence quarks P + = ccuud Assume the assignments Mass difference: P + (3/2 ) = { c [cq] s=1 [q q ] s=1, L = 0 } P + (5/2 + ) = { c [cq] s=1 [q q ] s=0, L = 1 } Λ(1405) Λ(1116) 290 MeV, level spacing for L = 1 in light baryons; light-light diquark mass difference for S = 1: [qq ] s=1 [qq ] s=0 = Σ c (2455) Λ c (2286) 170 MeV, the orbital gap P + (3/2 ) P + (5/2 + ) is reduced to about 100 MeV, in agreement with data, 70 MeV Ahmed Ali (DESY, Hamburg) 30 / 44

43 Pentaquark production mechanisms in Λ 0 b K J/ψp Two possible mechanisms are proposed by Maiani et al.. In the first, the b-quark spin is shared between the K, and the c and [cu] components, the final [ud] diquark has spin-0, Fig. A In the second, the [ud] diquark is formed from the original d quark, and the u quark from the vacuum uū; angular momentum is shared among all components, and the diquark [ud] may have both spins, s = 0, 1, Fig. B Which of the two diagrams dominate is a dynamical question; semileptonic decays of Λ b hint that the mechanism in Fig. B is dynamically suppressed Ahmed Ali (DESY, Hamburg) 31 / 44

44 Flavor SU(3) structure of Pentaquarks Pentaquarks are of two types: P u = ɛ αβγ c α [cu] β,s=0,1 [ud] γ,s=0,1 P d = ɛ αβγ c α [cd] β,s=0,1 [uu] γ,s=1 This leads to two distinct SU(3) series of Pentaquarks P A = ɛ αβγ { c α [cq] β,s=0,1 [q q ] γ,s=0, L } = 3 3 = 1 8 P S = ɛ αβγ { c α [cq] β,s=0,1 [q q ] γ,s=1, L } = 3 6 = 8 10 For S waves, the first and the second series have the angular momenta (multipicity) P A (L = 0) : J = 1/2(2), 3/2(1) P A (L = 0) : J = 1/2(3), 3/2(3), 5/2(1) Maiani et al. propose to assign P(3/2 ) to the P A and P(5/2 + ) to the P S series of Pentaquarks Ahmed Ali (DESY, Hamburg) 32 / 44

45 SU(3) based analysis of Λ b P + K (J/ψ p)k With respect to flavor SU(3), Λ b (bud) 3, and is isosinglet I = 0 The weak non-leptonic Hamiltonian for b c cs decays is: H (3) W ( I = 0, S = 1) With M a nonet of SU(3) light mesons, P, M H W Λ b requires P + M to be in 8 1 representation Recalling the SU(3) group multiplication rule 8 8 = = the decay P, M H W Λ b can be realized with P in either an octet (8) or a decuplet (10) The discovery channel Λ b P + K J/ψpK corresponds to P in an octet (8) Ahmed Ali (DESY, Hamburg) 33 / 44

46 Weak decays with P in Decuplet representation Decays involving the decuplet (10) pentaquarks may also occur, if the light diquark pair having spin-0 [ud] s=0 in Λ b gets broken to produce a spin-1 light diquark [ud] s=1 Λ b πp (S= 1) 10 π(j/ψσ(1385)) Λ b K + P (S= 2) 10 K + (J/ψΞ (1530)) Ahmed Ali (DESY, Hamburg) 34 / 44

47 Weak decays with P in Decuplet representation - Contd. Apart from Λ b (bud), several b-baryons, such as Ξ 0 b (usb), Ξ b (dsb) and Ω b (ssb) undergo weak decays Examples of bottom-strange b-baryon in various charge combinations, respecting I = 0, S = 1 are: Ξ 0 b (5794) K(J/ψΣ(1385)) which corresponds to the formation of the pentaquarks with the spin configuration (q, q = u, d) P 10 ( c [cq] s=0,1 [q s] s=0,1 ) Ahmed Ali (DESY, Hamburg) 35 / 44

48 Weak decays with P in Decuplet representation - Contd. The s s pair in Ω b is in the symmetric (6) representation of flavor SU(3) with spin 1; expected to produce decuplet Pentaquarks in association with a φ or a Kaon Ω b (6049) φ(j/ψ Ω (1672)) Ω b (6049) K(J/ψ Ξ(1387)) These correspond, respectively, to the formation of the following pentaquarks ( q = u, d) P 10 ( c [cs] s=0,1 [ss] s=1 ) P 10 ( c [cq] s=0,1 [ss] s=1 ) These transitions are on firmer theoretical footings, as the initial [ss] diquark in Ω b is left unbroken; more transitions can be found relaxing this condition Ahmed Ali (DESY, Hamburg) 36 / 44

49 Summary A new facet of QCD is opened by the discovery of the exotic X, Y, Z, and the pentaquark states P(4380) and P(4450) Dedicated studies required to establish the nature of exotics in experiments and QCD Important puzzles remain in the complex: What is the nature of Y c (4260)? A tetraquark? or a c cg hybrid? What exactly is Υ(10888)? Is it just Υ(5S)? Does Y b (10890) still exist? Branching ratios at Υ(5S) are enigmatic Need detailed Dalitz distributions of Y(11020). Do Z b, Z b (and related excited states) play a role in the the decays of Y(11020)?. Recent Belle studies confirm that they do. There is a good case for having dedicated runs above Υ(4S)at KEK Super-B ; would be great if this machine can reach the Λ b Λ b energy threshold! We look forward to decisive experimental results from Belle-II and LHC Ahmed Ali (DESY, Hamburg) 37 / 44

50 Hidden-Beauty Charged Tetraquarks and Heavy Quark Spin Conservation A.A., L. Maiani, A.D. Polosa, V. Riquer; PR D91, (2015) Interpret the Z ±,0 (10610) = Z b b and Z ±,0 (10650) = Z b b as S-wave J PG = 1 ++ tetraquark states (in the notation s [bq], s [ b q] ) Z b = 1 bq, 0 b q 0 bq, 1 b q 2, Z b = 1 bq, 1 b q J=1 J P = 1 + multiplet is completed by X b, given by the C = +1 combination X b = 1 bq, 0 b q + 0 bq, 1 b q 2 Expect X b and Z b to be degenerate, with Z b heavier M(Z b ) M(Z b) = 2κ b A similar analysis for the hidden-charm charged tetraquarks Z c and Z c yields 2κ c = M(Z c) M(Z c ) 120 MeV QCD expectation: κ b : κ c = M c : M b. With M c M b = 0.30, yields 2κ b 36 MeV, fits OK with the observed Z b Z bmass difference ( 45 MeV) Ahmed Ali (DESY, Hamburg) 38 / 44

51 Heavy-Quark-Spin Flip in Υ(10890) Z b /Z b + π h b(1p, 2P)ππ In Υ(10890), S b b = 1. In h b (np), S b b = 0, so the above transition involves heavy-quark spin-flip, yet its rate is not suppressed, violating heavy-quark-spin conservation This contradiction is only apparent. Expressing the states Z b and Z b in the basis of definite b b and light quark q q spins, Z b = 1 q q, 0 b b 0 q q, 1 b b, Z b = 1 q q, 0 b b + 0 q q, 1 b b 2 2 More generally, admitting a subdominant spin-spin interaction, the above composition may be written as Z b = α 1 q q, 0 b b β 0 q q, 1 b b, Z b = β 1 q q, 0 b b + α 0 q q, 1 b b 2 2 Define g Z = g(υ Z b π)g(z b h b π) αβ h b Z b Z b Υ g Z = g(υ Z b π)g(z b h bπ) αβ h b Z b Z b Υ where g are the effective strong couplings at the vertices Υ Z b π and Z b h b π Therefore, independently from the values of the mixing coefficients, the above equation and heavy quark spin conservation require g Z = g Z Ahmed Ali (DESY, Hamburg) 39 / 44

52 Heavy-Quark-Spin Flip in Υ(10890) Z b /Z b + π h b(1p, 2P)ππ Relative normalizations and phases for s b b: 1 1 and 1 0 transitions Final State Υ(1S)π + π Υ(2S)π + π Υ(3S)π + π h b (1P)π + π h b (2P)π + π Rel. Norm ± ± ± ± Rel. Phase 58 ± ± ± Within errors, Belle data is consistent with heavy quark spin conservation To determine the coefficients α and β, one has to resort to s b b: 1 1 transitions Υ(10890) Z b /Z b + π Υ(nS)ππ (n = 1, 2, 3) The analogous effective couplings are f Z = f (Υ Z b π)f (Z b Υ(nS)π) β 2 Υ(nS) 0 q q, 1 b b 0 q q, 1 b b Υ f Z = f (Υ Z b π)f (Z b Υ(nS)π) α 2 Υ(nS) 0 q q, 1 b b 0 q q, 1 b b Υ Ahmed Ali (DESY, Hamburg) 40 / 44

53 Determination of α/β from Υ(10890) Z b /Z b + π Υ(nS)ππ (n = 1, 2, 3) Dalitz analysis indicate that Υ(10890) Z b /Z b + π Υ(nS)ππ (n = 1, 2, 3) proceed mainly through the resonances Z b and Z b, though Υ(10890) Υ(1S)ππ has a significant direct component, expected in tetraquark interpretation of Υ(10890) A comprehensive analysis of the Belle data including the direct and resonant components is required to test the underlying dynamics, yet to be carried out Parametrizing the amplitudes in terms of two Breit-Wigners, one can determine the ratio α/β s b b : 1 1 transition : Rel.Norm. = 0.85 ± 0.08 = α 2 / β 2 Rel.Phase = ( 8 ± 10) s b b : 1 0 transition : Rel.Norm. = 1.4 ± 0.3 Rel.Phase = (185 ± 42) Within errors, the tetraquark assignment with α = β = 1 is supported, i.e., Z b = 1 bq, 0 b q 0 bq, 1 b q 2, Z b = 1 bq, 1 b q J=1 Z b = 1q q, 0 b b 0q q, 1 b b 2, Z b = 1q q, 0 b b + 0q q, 1 b b 2 Ahmed Ali (DESY, Hamburg) 41 / 44