Multiquark Hadrons - the Next Frontier of QCD

Transcription

1 Multiquark Hadrons - the Next Frontier of QCD Ahmed Ali DESY, Hamburg 9. Nov CEPC Workshop, IHEP, Beijing Ahmed Ali (DESY, Hamburg) 1 / 45

2 Experimental Evidence for Multiquark states X, Y, Z and P c Models for X, Y, Z Mesons The Diquark model of Tetraquarks Mass Spectrum of the low-lying S and P Wave Tetraquark States A New Look at the excited Ω c and the Y States in the Diquark Model Doubly Heavy Tetraquarks - Prospects at a Mega-Z Factory The Pentaquarks P ± (4380) and P ± (4450) in the Diquark Model Summary Ahmed Ali (DESY, Hamburg) 2 / 45

3 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) 3 / 45

4 X, Y, Z, P c and Charmonium States [S.L. Olsen, T. Skwarnicki, D. Zieminska, arxiv: ] Ahmed Ali (DESY, Hamburg) 4 / 45

5 Bottomonium and Bottomonium-like States [S.L. Olsen, T. Skwarnicki, D. Zieminska, arxiv: ] Ahmed Ali (DESY, Hamburg) 5 / 45

6 Enigmatic Υ(5S) Decays! Is there a Y b (10890) close to Υ(5S)? If yes, what is it?? [AA, Hambrock, Ishtiaq Ahmed, Jamil Aslam, PLB 684 (2010) 28] Ahmed Ali (DESY, Hamburg) 6 / 45

7 The charged Z ± b (10610) and Z± b (10650) states [Belle, PRL 108, (2012)] Ahmed Ali (DESY, Hamburg) 7 / 45

8 Ahmed Ali (DESY, Hamburg) 8 / 45

9 Diquarks: Color Representation One gluon exchange model [Jaffe,Phys.Rept.(2005)] Color factor determines binding: Negative sign Attractive Ahmed Ali (DESY, Hamburg) 9 / 45

10 Diquarks: Color Representation One gluon exchange model [Jaffe,Phys.Rept.(2005)] Color factor determines binding: Negative sign Attractive Quarks in diquark transform as: 3 3 = 3 6 Ahmed Ali (DESY, Hamburg) 9 / 45

11 Diquarks: Color Representation One gluon exchange model [Jaffe,Phys.Rept.(2005)] Color factor determines binding: Negative sign Attractive Quarks in diquark transform as: qq bound state color factor: t a ij ta kl = = 3 6 (δ ij δ kl δ il δ kj )/2 + 1 }{{} 3 (δ ijδ kl + δ il δ kj )/2 }{{} antisymmetric: projects 3 symmetric: projects 6 Ahmed Ali (DESY, Hamburg) 9 / 45

12 Diquarks: Color Representation One gluon exchange model [Jaffe,Phys.Rept.(2005)] Color factor determines binding: Negative sign Attractive Quarks in diquark transform as: qq bound state color factor: t a ij ta kl = = 3 6 (δ ij δ kl δ il δ kj )/2 + 1 }{{} 3 (δ ijδ kl + δ il δ kj )/2 }{{} antisymmetric: projects 3 symmetric: projects 6 Ahmed Ali (DESY, Hamburg) 9 / 45

13 Diquarks: Color Representation One gluon exchange model [Jaffe,Phys.Rept.(2005)] Color factor determines binding: Negative sign Attractive Quarks in diquark transform as: qq bound state color factor: t a ij ta kl = = 3 6 (δ ij δ kl δ il δ kj )/2 + 1 }{{} 3 (δ ijδ kl + δ il δ kj )/2 }{{} antisymmetric: projects 3 symmetric: projects 6 Ahmed Ali (DESY, Hamburg) 9 / 45

14 Diquarks: Spin representation Ahmed Ali (DESY, Hamburg) 10 / 45

15 Diquarks: Spin representation Lattice simulations for light quarks [Alexandrou, Forcrand, Lucini, PRL (2006)] : Calculation of 2 quark correlation strength Decreasing distance Increasing strength for good diquarks Diquark size O(1fm) Ahmed Ali (DESY, Hamburg) 10 / 45

16 Diquarks: Spin representation Lattice simulations for light quarks [Alexandrou, Forcrand, Lucini, PRL (2006)] : Calculation of 2 quark correlation strength Decreasing distance Increasing strength for good diquarks Diquark size O(1fm) Ahmed Ali (DESY, Hamburg) Binding for good spin 0 diquarks No binding for bad spin 1 diquarks Spin decoupling in HQ-Limit Bad diquarks in b-sector might bind 10 / 45

17 Diquark Model of Tetra- and Pentaquarks 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 Scalar: 0 + Q iα = ɛ αβγ ( c β c γ 5 q γ i q β i c γ 5 c γ ) α, β, γ: SU(3) C indices Axial-Vector: 1 + Q iα = ɛ αβγ ( c β c γq γ i + q β i c γc γ ) Ahmed Ali (DESY, Hamburg) 11 / 45

18 Diquark Model of Tetra- and Pentaquarks 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 Scalar: 0 + Q iα = ɛ αβγ ( c c β γ 5 q γ i q β i c γ 5 c γ ) α, β, γ: SU(3) C indices Axial-Vector: 1 + Q iα = ɛ αβγ ( c c β γq γ i + q β i c γc γ ) NR limit: States parametrized by Pauli matrices : Scalar: 0 + Γ 0 = σ 2 2 Axial-Vector: 1 + Γ = σ 2 σ 2 Ahmed Ali (DESY, Hamburg) 11 / 45

19 Diquark Model of Tetra- and Pentaquarks 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 Scalar: 0 + Q iα = ɛ αβγ ( c c β γ 5 q γ i q β i c γ 5 c γ ) α, β, γ: SU(3) C indices Axial-Vector: 1 + Q iα = ɛ αβγ ( c c β γq γ i + q β i c γc γ ) NR limit: States parametrized by Pauli matrices : Scalar: 0 + Γ 0 = σ 2 2 Axial-Vector: 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 11 / 45

20 NR Hamiltonian for Tetraquarks with hidden charm Involves constituent diquark mass, spin-spin, spin-orbit, and tensor forces H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL + H T In the following, assume κ q q 0 H eff (X, Y, Z) = 2m Q + B Q [ ] S 2 L2 + 2A Q (L S) + 2κ qq sq s Q + s q s Q + 12 by 4 Ahmed Ali (DESY, Hamburg) 12 / 45

21 NR Hamiltonian for Tetraquarks with hidden charm Involves constituent diquark mass, spin-spin, spin-orbit, and tensor forces H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL + H T with constituent mass = b Y [ 3(SQ n)(s Q n) (S Q S Q )] ; (n = unit vector) In the following, assume κ q q 0 H eff (X, Y, Z) = 2m Q + B Q [ ] S 2 L2 + 2A Q (L S) + 2κ qq sq s Q + s q s Q + 12 by 4 Ahmed Ali (DESY, Hamburg) 12 / 45

22 NR Hamiltonian for Tetraquarks with hidden charm Involves constituent diquark mass, spin-spin, spin-orbit, and tensor forces H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL + H T 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 = b Y [ 3(SQ n)(s Q n) (S Q S Q )] ; (n = unit vector) In the following, assume κ q q 0 H eff (X, Y, Z) = 2m Q + B Q [ ] S 2 L2 + 2A Q (L S) + 2κ qq sq s Q + s q s Q + 12 by 4 Ahmed Ali (DESY, Hamburg) 12 / 45

23 NR Hamiltonian for Tetraquarks with hidden charm Involves constituent diquark mass, spin-spin, spin-orbit, and tensor forces H = 2m Q + H (qq) SS + H(q q) SS + H SL + H LL + H T with LS 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 ) H SL = 2A Q (S Q L + S Q L) H LL = B Q L Q Q (L Q Q + 1) 2 LL coupling = b Y [ 3(SQ n)(s Q n) (S Q S Q )] ; (n = unit vector) In the following, assume κ q q 0 H eff (X, Y, Z) = 2m Q + B Q [ ] S 2 L2 + 2A Q (L S) + 2κ qq sq s Q + s q s Q + 12 by 4 Ahmed Ali (DESY, Hamburg) 12 / 45

24 NR Hamiltonian for Tetraquarks with hidden charm Involves constituent diquark mass, spin-spin, spin-orbit, and tensor forces with H = 2m Q + H (qq) SS 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(q q) SS + H SL + H LL + H T L H LL = B Q Q (L Q Q + 1) Q 2 S H T = b 12 Y 4 = b [ Y 3(SQ n)(s Q n) (S Q S Q )] ; (n = unit vector) In the following, assume κ q q 0 H eff (X, Y, Z) = 2m Q + B Q [ ] S 2 L2 + 2A Q (L S) + 2κ qq sq s Q + s q s Q + 12 by 4 Ahmed Ali (DESY, Hamburg) 12 / 45

25 Low-lying S-Wave Tetraquark 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 listed below; M 00 = 2m Q 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, 0 1 M 00 κ qq Z 1 + ( ) ( ) 1, 0; 1, 0 1 0, 1; 1, 0 1 / 2 1, 0; 1, 0 1 0, 1; 1, 0 1 / 2 M00 κ qq Z 1 + ( ) 1, 1; 1, 0 1 1, 0; 1, , 1; 1, 0 1 / 2 M00 + κ qq X , 1; 2, 0 2 1, 1; 2, 0 2 M 00 + κ qq The spectrum of these states depends on just two parameters, M 00 (Q)and κ qq, Q = c, b, hence very predictive Some of the states, such as X 0, X 0, X 2, still missing and are being searched for at the LHC Ahmed Ali (DESY, Hamburg) 13 / 45

26 Charmonium-like and Bottomonium-like Tetraquark Spectrum Parameters in the Mass Formula charmonium-like bottomonium-like M 00 [MeV] κ qq [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 b (10610) Z 1 + Z c + (4020) 4024 Z + b (10650) X Ahmed Ali (DESY, Hamburg) 14 / 45

27 A new look at the Y tetraquarks and the excited Ω c states in the Diquark model Observation of 5 narrow excited Ω c baryons in Ω c Ξ + c K [LHCb, PRL 118, (2017)] Measured masses (in MeV) [LHCb] and plausible J P quantum numbers, assuming diquark model Ω c (= css) = c[ss] [M. Karliner, J.L. Rosner, PR D95, (2017)] M(Ω c (3000)) = ± 0.2 ± 0.1; J P = 1/2 M(Ω c (3050)) = ± 0.1 ± 0.1; J P = 1/2 M(Ω c (3066)) = ± 0.1 ± 0.3; J P = 3/2 M(Ω c (3090)) = ± 0.3 ± 0.5; J P = 3/2 M(Ω c (3119)) = ± 0.3 ± 0.9; J P = 5/2 For the P states, important to take into account the tensor couplings H eff = m c + m [ss] + κ ss S s S s + B Q 2 L2 + V SD, V SD = a 1 L S [ss] + a 2 L S c + b S c S [ss] S c Ahmed Ali (DESY, Hamburg) 15 / 45

28 Analysis of the excited Ω c states in the Diquark-Quark model b S 12 /4 represents the matrix element of the tensor interaction S 12 4 = Q(S 1, S 2 ) = 3(S 1 n)(s 2 n) (S 1 S 2 ) S 1 = S [ss] and S 2 = S c are the spins of the diquark and the charm quark, respectively, n = r/r is the unit vector along the radius vector The scalar operator above can be expressed as the convolution 3S i 1 Sj 2 N ij N ij = n i n j 1 3 δ ij Need matrix elements of this operator between the states with the same fixed value L of the angular momentum operator L, using an identity from Landau and Lifshitz : N ij = a(l)(l i L j + L j L i 2 3 δ ijl(l + 1)) where a(l) = 1 (2L 1)(2L+3) Q(S X, S X ) = 3 5 [2(L S X) 2 + (L S X ) 4 3 (S X S X )] where S X = S [ss], S c, S = S [ss] + S c Ahmed Ali (DESY, Hamburg) 16 / 45

29 Analysis of the excited Ω c states in the Diquark-Quark model-contd. For L = 1, and S [ss] = 1, all three terms are non-zero, as opposed to the charmonium case, and one has to calculate the matrix element L, S ; J L S X L, S; J S 12 2 = 2Q(S [ss], S c ) = Q(S, S) Q(S c, S c ) Q(S [ss], S [ss] ) Tensor operator mixes the two J = 1/2, and the two J = 3/2 states ( ) J = 1/2 : 4 S 12 = ( ) J = 3/2 : 4 S 12 = 2 5 J = 5/2 : 1 4 S 12 = Ahmed Ali (DESY, Hamburg) 17 / 45

30 Analysis of the excited Ω c states in the Diquark-Quark model- contd. Coeffs. determined from the masses of the J P states (in MeV) a 1 a 2 b c M M 0 m c + m [ss] + 2κ ss + B Q Ahmed Ali (DESY, Hamburg) 18 / 45

31 Analysis of the tetraquark Y states in the diquark model H eff = 2m Q + B Q S 2 L2 3κ cq + 2a Y L S + 12 b Y [ 4 + κ cq 2(Sq S c + S q S c ) + 3 ] ( ) 1 0 2/ 5 4 S 12 = 2/ 5 7/5 There are four L = 1 and one L = 3 tetraquark states with J PC = 1 Tensor couplings non-vanishing only for the states with S Q = S Q = 1 P-wave (J PC = 1 ) states Label J PC s qq, s q Q ; S, L J Mass Y 1 1 Y 2 1 0, 0; 0, 1 ( 1 ) 1, 0; 1, , 1; 1, 1 1 / 2 M 00 3κ qq + B Q M 00 M κ qq 2A Q Y 3 1 1, 1; 0, 1 1 M κ qq + E + Y 4 1 1, 1; 2, 1 1 M κ qq + E Y 5 1 1, 1; 2, 3 1 M Y2 + 2κ qq 14A Q + 5B Q 8/5b Y E ± = 1 10 ( 30A Q 7b Y 3 300A 2 Q + 140A Qb Y + 43b 2 Y ) Ahmed Ali (DESY, Hamburg) 19 / 45

32 Experimental situation with the tetraquark Y states rather confusing Summary of the Y states observed in Initial State Radiation (ISR) processes in e+ e annihilation [BaBaR, Belle, CLEO] e+ e γisr J/ψπ + π ; γisr ψ0 π + π = Y(4008), Y(4260), Y(4360), Y(4660) Ahmed Ali (DESY, Hamburg) 20 / 45

33 e + e J/ψπ + π cross section at s = ( ) GeV ( BESIII, PRL 118, (2017) Y(4008) is not confirmed; Y(4260) is split into 2 resonances: Y(4220) and Y(4320), with the Y(4220) probably the same as Y(4260) Ahmed Ali (DESY, Hamburg) 21 / 45

34 Two Experimental Scenarios for the Y States [AA, L. Maiani, A. Borisov, I. Ahmed, A. Rehman, M.J. Aslam, A. Parkhomenko, A.D. Polosa, arxiv: ] SI (Based on CLEO, BaBaR, Belle): Y(4008), Y(4260), Y(4360), Y(4660) SII ( BESIII, PRL 118, (2017): Y(4220), Y(4320), with Y(4390), Y(4660) the same as in SI a Y - κ cq Correlations SI 60 SII κcq [MeV] κcq [MeV] ay [MeV] ay [MeV] SII (based on BESIII data) is favored, with a Y and κ cq values similar to the Ω c analysis Ahmed Ali (DESY, Hamburg) 22 / 45

35 Correlations (Contd.) Fixing κ cq = 67 MeV(from the S states); fitted the two scenarios = clear preference for SII, with the following parameters (in MeV) Scenario M 00 a Y b Y χ 2 min /n.d.f. SI 4321 ± 79 2 ± ± /1 SII 4421 ± 6 22 ± ± 6 1.3/1 SII: M 00 2m Q + B Q = B Q = 442 MeV Comparable to the orbital angular momentum excitation energy in charmonia B Q (c c) = M(h c ) 1 4 [3M(J/ψ) + M(η c)] = 457 MeV κ cq and a Y for Y states similar to the ones in (X, Z) and Ω c Precise data on the Y-states is needed to confirm or refute the diquark picture Ahmed Ali (DESY, Hamburg) 23 / 45

36 Stable Heavy Tetraquarks T(QQ q q ), (QQ = cc, cb, bb) [See Eichten, Mehen, Quarkonium 2017; S-Q. Luo et al., EPJC 77:709 (2017)] Ahmed Ali (DESY, Hamburg) 24 / 45

37 Doubly Heavy Tetraquarks T(QQ q q ), (QQ = cc, cb, bb) [E. Eichten, C. Quigg, arxiv: ] Ahmed Ali (DESY, Hamburg) 25 / 45

38 Stable Heavy Tetraquarks T(QQ q q ), (QQ = cc, cb, bb) [E. Eichten, C. Quigg, arxiv: ] T(bb[ū d]) and T(bb[ q s]) are stable against strong decay Will decay weakly by charged current interactions Ahmed Ali (DESY, Hamburg) 26 / 45

39 Stable Heavy Tetraquarks T(QQ q q ), (QQ = cc, cb, bb) [T. 2017] Ahmed Ali (DESY, Hamburg) 27 / 45

40 Prospects of Stable Tetraquarks at a Tera-Z Factory LEP : B(Z b b) = (15.12 ± 0.05)% B(Z b bb b) = (3.6 ± 1.3) 10 4 at a Tera-Z factory (CPEC, CERN), anticipate Zs (or more) Great opportunity for a Tera-Z Factory to do precision b-baryon and b b/bb multiquark physics T {bb} [ū d] {bb}[ū d] with J P = 1 + E. Quarkonium-2017 bound by 121 MeV (77 MeV below B B 0 γ threshold) Decay modes of T {bb} [ū d] (10482) T {bb} [ū d] (10482) B D + π ; B 0 D 0 π T {bb} [ū d] (10482) p Ξ 0 b J/ψ T {bb} [ū d] (10482) p Ξ 0 bc ; Λ c Ω 0 bc In two-body hadronic decays, unobserved doubly heavy baryons Ξ 0 bc and Ω0 bc are produced Ahmed Ali (DESY, Hamburg) 28 / 45

41 Prospects of Stable Tetraquarks at a Tera-Z Factory T {bb} {bb}[ū s] and T {bb} {bb}[ d s] with J [ū s] P = 1 + [ d s] bound by 48 MeV (3 MeV below B B s γ threshold) Decay modes of T {bb} [ū s] (10643) T {bb} [ū s] (10643) B D s + π ; B 0 s D 0 π T {bb} [ū s] (10643) Σ Ξ 0 b J/ψ; Λ 0 Ξ b J/ψ T {bb} [ū s] (10643) Σ Ξ 0 bc ; Σ c Ω 0 bc Decay modes of T {bb} (10643) 0 [ d s] T {bb} (10643) 0 B 0 D + [ d s] s π ; B 0 s D + π T {bb} (10643) 0 ( Λ 0, Σ 0) Ξ 0 [ d s] b J/ψ; Σ + Ξ b J/ψ T {bb} (10643) 0 ( Λ 0, Σ 0) Ξ 0 [ d s] bc ; Σ 0 c Ω 0 bc In two-body hadronic decays, unobserved doubly heavy baryons Ξ 0 bc and Ω0 bc are produced Ahmed Ali (DESY, Hamburg) 29 / 45

42 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) 30 / 45

43 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) 31 / 45

44 Summary of the LHCb Pentaquark Measurements (Contd.) Possible J P assignments and the energies of the nearby thresholds Ahmed Ali (DESY, Hamburg) 32 / 45

45 Effective Hamiltonian for Pentaquarks [Ahmed,Rehman,Aslam,AA, arxiv: ] 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) 33 / 45

46 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 } Level spacing for L = 1 in light baryons; Λ(1405) Λ(1116) 290 MeV Light-light diquark mass difference for S = 1: [qq ] s=1 [qq ] s=0 = Σ c (2455) Λ c (2286) 170 MeV Orbital gap P + (3/2 ) P + (5/2 + ) is thereby reduced to 120 MeV, more or less in agreement with data, 70 MeV Ahmed Ali (DESY, Hamburg) 34 / 45

47 Pentaquark production mechanisms in Λ 0 b K J/ψp Two possible mechanisms are proposed by Maiani et al. In the first, 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) 35 / 45

48 Heavy quark symmetry and observed pentaquarks [Ahmed,Rehman,Aslam,AA, arxiv: ] Selection rules from the the data on b c baryonic decays and HQS P + c (4450) = { c[cu] s=1 [ud] s=0 ; L P = 1, J P = 5 2 P + c (4380) = { c[cu] s=1 [ud] s=1 ; L P = 0, J P = } Favored } Disfavored = 3 2 state may require a different interpretation. m[λ c + (2625); J P = 3 2 ] m[λ + c (2286); J P = ] 341 MeV = the mass of J P = 3/2 state to be about 4110 MeV. In diquark-diquark-antiquark spectrum, 2 3 state is favored by HQS, { c[cu] s=1 [ud] s=0 ; L P = 0, J P = 3 }, 2 Third state anticipated in MeV range. A renewed fit of the LHCb data by allowing a third resonance is called for. Ahmed Ali (DESY, Hamburg) 36 / 45

49 Weak decays of the b-baryons into pentaquark states A = PM Heff W B, with Heff W = 4G [ F V cb Vcq(c 1 O (q) c 2 O (q) ] 2 ) H W eff inducing the Cabibbo-allowed I = 0, S = 1 transition b c cs, and the Cabibbo-suppressed S = 0 transition b c cd. O (q) 1 = ( q α c β ) V A ( c α b β ) V A and O (q) 2 = ( q α c α ) V A ( c β b β ) V A B ij ( 3) = Λ 0 b (udb), Ξ0 b (usb), Ξ b (dsb), C ij (6) = Σ b (ddb), Σ0 b (udb), Σ+ b (uub)), Ξ b (dsb), Ξ 0 b (usb), Ω b (ssb) M j i = π η8 6 π + K + π π0 2 + η8 6 K 0 K K 0 2η8 6 ( ), P j i J P = P Σ 0 + P Λ 2 6 P Σ + P p P Σ P Σ 0 + P Λ 2 6 P n P Ξ P Ξ 0 P Λ 6. A decuplet P ijk : P 111 = P P Σ 0 10 / 6, P 223 = P Σ / 3, P 133 = P 10 Ξ 0 10, P 112 = P + / 3, P 122 = P 10 0 / 3, P 222 = P / 3, P 233 = P Ξ 10 / 3 and P 333 = P Ω. 10, P 113 = P Σ + / 3, P 123 = 10 Calculating the decay amplitudes is a formidable challenge. SU(3) F symmetry relations provided useful guide for pentaquark searches, Li et al. [arxiv: ] Ahmed Ali (DESY, Hamburg) 37 / 45

50 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) 38 / 45

51 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) 39 / 45

52 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 (ssb) undergo weak decays b 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) 40 / 45

53 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 At a mega-z factory, such as CPEC, the entire b-baryon multiplet will be measured through the process Z b b; b (Λ b, Ξ b, Ω b,...), allowing to reconstruct a lot of pentaquarks in b-baryon decays Ahmed Ali (DESY, Hamburg) 41 / 45

54 Estimates of the ratio of decay widths for J P = [Ahmed,Rehman,Aslam,AA, arxiv: ] Decay Process Γ/Γ(Λ 0 b P5/2 p K ) Decay Process Γ/Γ(Λ 0 b P5/2 p K ) Λ b P {Y 2} c1 p K 1 Ξ b P{Y 2} c2 K 0 Σ 2.07 Λ b P {(Y 2} c1 n K 0 1 Ξ 0 b P{Y 2} c2 Σ + K 2.07 Λ b P {Y 2} c3 η 0.03 Λ Λ 0 b P {Y 2} c3 η Λ Ξ b P{Y 2} c2 K 1.04 Ξ Σ 0 b P{Y 2} c2 K Λ Ω b P{Y 3} c5 Ξ 10 K Ω b P{Y 3} c5 Ξ 0 10 K 0.14 Decay Process Γ/Γ(Λ 0 b P5/2 p K ) Decay Process Γ/Γ(Λ 0 b P5/2 p K ) Λ b P {Y2}c 1 p π 0.08 Λ b P {Y 2} c1 n π Λ b P {Y 2} c1 n η 0.01 Λ b P {Y 2} c1 n η 0 Ξ b P{Y 2} c4 Ξ K Ξ b P{Y 2} c2 π Σ Ξ b P{Y 2} c2 Σ η 0.02 Ξ b P{Y 2} c2 Σ η 0.01 Ξ b P{Y 2} c2 Σ π Ξ 0 b P{Y 2} c2 π 0 Σ Ξ 0 b P{X 2 (Y 2 )} c2 η 0.01 Ξ 0 Λ 0 b P{Y 2} c2 η Λ Ξ 0 b P{Y 2} c2 π 0 Λ Ω b P{Y 3} c5 π Ω b P{Y 3} c5 π 0.02 Ξ 0 10 We have used the pentaquark masses estimated in this work. S = 0 are suppressed by V cd /V cs 2 compared to S = 1. Ahmed Ali (DESY, Hamburg) 42 / 45 Ξ 10

55 Estimates of the ratio of decay widths for J P = 3 2 Decay Process [Ahmed,Rehman,Aslam,AA, arxiv: ] Γ/Γ(Λ 0 b P{X2} c 1 K p ) Decay Process Γ/Γ(Λ 0 b P{X2} c 1 p K ) Λ b P {X2}c 1 p K 1 Ξ b P{X2}c 2 K 0 Σ 1.38 Λ b P {X2}c 1 n K 0 1 Ξ 0 b P{X2}c 2 Σ + K 1.38 Λ b P {X2}c 3 η 0.17 Λ Λ 0 b P {X2}c 3 η Λ Ξ b P{X2}c 2 K 0.69 Ξ Σ 0 b P{X2}c 2 K Λ Ω b P{X3}c 5 Ξ 10 K Ω b P{X3}c 5 Ξ 0 10 K 0.24 Decay Process Γ/Γ(Λ 0 b P{X2} c 1 K p ) Decay Process Γ/Γ(Λ 0 b P{X2} c 1 p K ) Λ b P {X2}c 1 p π Λ b P {X2}c 1 n π Λ b P {X2}c 1 n η 0.01 Λ b P {X2}c 1 n η 0.01 Ξ b P{X2}c 4 Ξ K Ξ b P{X2}c 2 π Σ Ξ b P{X2}c 2 Σ η 0.02 Ξ b P{X2}c 2 Σ η 0.01 Ξ b P{X2}c 2 Σ π Ξ 0 b P{X2}c 2 π 0 Σ Ξ 0 b P{X2}c 2 η 0 Ξ 0 Λ 0 b P{X2}c 2 η Λ 0 0 Ξ 0 b P{X2}c 2 π 0 Λ Ω b P{X3}c 5 π Ω b P{X3}c 5 π 0.02 Ξ 0 10 Ξ 10 Ahmed Ali (DESY, Hamburg) 43 / 45

56 Summary A new facet of QCD is opened by the discovery of the exotic states X, Y, Z, P(4380), P(4450) Important puzzles remain in the complex: What is the nature of Y c (4260)? A tetraquark? or a c cg hybrid? Is Y c (4260)split? How many P states are there? We do expect a tower of radial and orbital excited states in the diquark picture! A very rich spectrum of tetraquark and pentaquark states is anticipated, including the ones with a single c, or a single b quark, as well as those with multiple heavy quarks CEPC running as a Z factory will advance the multiquark sector of QCD decisively, in particular, the entire pentaquark spectrum with hidden charm discussed here can be measured from the production and decays of the b-baryons Also CEPC has great potential to discover doubly heavy tetraquarks, establishing diquarks as a building block in QCD We look forward to decisive experimental results from BESIII, Belle-II, LHC, and the CEPC Ahmed Ali (DESY, Hamburg) 44 / 45