On the structure of X(3872) and Z(4430)

Transcription

1 First Prev Next Last 2007 Joint BES-Belle-CLEO-Babar Workshop on Charm Physics Beijing, November 26-27, 2007 On the structure of X(3872) and Z(4430) CE MENG Page 1 of 24 Institute of Theoretical Physics, Peking University mengce75@pku.edu.cn

2 First Prev Next Last Outline Experimental Background Before 2007 X(3872) as a charmonium state Coupled-channel effects X(3872) as a virtual state Summary Z(4430): Theory What we have in the market by now Decays of Z(4430) as a resonance Summary Page 2 of 24

3 First Prev Next Last 1. Experimental Background X(3872) Basic information to the threshold of D 0 D 0 : m X = ( ± 0.5) MeV [M(D 0 D 0 ) = ± 0.36 MeV] Narrow: Γ X < 2.3 MeV Quantum number: J P C = 1 ++ (2 +?) Decay modes B(B ± K ± X) B(X ρ(π + π )J/ψ) = (1.14 ± 0.20) 10 5 R ρ/γ = Γ ψρ Γ ψγ = 4-7 R ρ/ω = Γ ψρ Γ ψω = 1.0 ± 0.5 ω π + π π 0 for m 3π > 0.75 MeV [ Belle:hep-ex/ ] Not confirmed by Babar for m 3π > MeV [ Babar: arxiv: ] R ρ/ω 1 shows that there is large isospin violation in decays of X. Page 3 of 24

4 First Prev Next Last X(3872) Production B-production B + = B(B + X(3872)K + ) < Babar: PRL 96(2006) R n/c = B(B0 X(3872)K 0 ) B(B + X(3872)K + ) = 0.50 ± 0.30 ± 0.05 Babar: PRD 73(2006) R n/c = 0.94 ± 0.24 ± 0.10 K. Trabelsi [Belle Collaboration], This Workshop Production at hadron collider Comparison of event-yield fractions for X and ψ in the following regions: a. p T > 15 GeV b. y < 1 c. cos(θ π ) < 0.4 d. dl < 0.01 e. isolation = 1 f. cos(θ µ ) < 0.4 Fraction DØ ψ(2s) X(3872) a b c d e f Comparison Page 4 of 24

5 414 fb -1 II- search for (*) D (*) resonances First Prev Next Last Study of B D(*)D(*)K decays: X(3875)? X(3875) B 0 0 D *0 K 0 + *0 D 0 K 0 BELLE: observation of: B X(3872)K ±, X(3872) D 0 D 0 0 PRL 97, (2006) 414 fb -1 B + 0 D *0 K + + *0 D 0 K + BABAR: B (*) D (*) K fb -1 II- search for (*) D (*) resonances with D *0 D 0 0 and D 0 New Result-Preliminary = ± MeV /c 2 B ± K ± X,X D 0 D 0 0 ) = (1.27 ± )10 4 B + 0 D *0 K + + *0 D 0 K + B 0 0 D *0 K 0 + *0 D 0 K 0 with D *0 D 0 0 and D 0 (X D 0 D 0 0 ) (X J / ) = 9.7 ± fb -1 ass: M = ± MeV /c 2 B(B ± K ± X,X D 0 D 0 0 ) = (1.27 ± )10 4 also in M Babar: = arxiv: v2 ± MeV /c 2 very good B(X agreement D 0 D 0 0 ) btw experiments R(B 0 /B + )=2.23 ± 0.93 ± 0.55 = 9.7 ± 3.4 m X B(X = J / ) ± away from X J/ + MeV m(b : X(3875)? 0 /B ) = ± ± MeV/c 2 also: (3770) D Mass: M = : M= ± MeV ± 3.2 /cmev/c 2 2 oriond QCD B B(X D 0 D0 π 0 ) = very good agreement Grenier (1.02 ± btw Philippe experiments ) 10 4 (1.67 R(B 0 /B ± + )= ± ) ± away from X J/ + m(b : X(3875)? 0 /B + ) = 0.2 ± 1.6 MeV/c 2 R n/c = B(B0 XK 0 ) also: (3770) D : M= ± 3.2 MeV/c B(B + XK + ) = 1.7 ± 0.9 (1.33 ± 0.69 ± 0.43) 2 Moriond QCD 2007 Grenier Philippe 11 R ρ/ddπ = Γ ψρ Γ DDπ = 0.11 ± 0.05 ( ) Page 5 of 24

6 Z + (4430) THE M(π + ψ ) MASS DISTRIBUTION The open histogram in Fig. 3 shows the M(π + ψ ) distribution for events in the M bc - E signal region and with the K veto applied. The bin width is 10 MeV. The shaded histogram shows the scaled distribution from E sidebands ( E ±0.070 < GeV). Here a strong enhancement is evident near M(πψ ) 4.43 GeV. This peak is the subject of this report. 30 Belle (arxiv: ) Events/0.01 GeV/c m Z = 4433 ± 4 ± 1 MeV Γ Z = M(π + ψ ι ) (GeV/c 2 ) FIG. 3: The M(π + ψ ) distribution for events in the M bc - E signal region and with the K veto applied. The shaded histogram show the scaled results from the E sideband. The solid curves show the results of the fit described in the text. The background level in the M(πψ ) = 4.43 GeV region estimated from the scaled E MeV sidebands is relatively small: B/(S + B) = (8.7 ± 1.7)%. This is confirmed by fits to the M bc and E distributions for the same mass interval, which give B/(S +B) = (8.5 ±2.5)% and (7.9 ± 2.4)%, respectively. We fit the M(πψ ) invariant mass distribution with a simple BW function to model the peak plus a smooth phase-space-like function f cont (M), where B(B KZ)B(Z π + ψ ) = (4.1 ± 1.0 ± 1.3) 10 5 [M(D D 1 ) = 4430 ± 4 MeV, M(D D 1) = 4435 ± 26 MeV] Page 6 of 24 R ψ /ψ = Γ Z ψ π Γ Z J/ψπ 1 J/ψ suppression problem f cont (M) = Nq(Q 1/2 + A 1 Q 3/2 + A 2 Q 5/2 ). (1) Here q is the momentum of the π + in the πψ rest frame and Q = M max M, where M max = 4.78 GeV is the maximum M(πψ ) value possible for B Kπψ decay. The normalization N and two shape parameters A 1 and A 2 are left as free parameters in the fit. This form for f cont (M) is chosen because it mimics two-body phase-space behavior at the lower and upper mass boundaries. (Since the M(πψ ) distribution for the non-peaking B-meson and the E sideband events have a similar shape, we represent them both with a single function.) First Prev Next Last

7 First Prev Next Last Before 2007 Highlight ness to the thresholdµm X M(D 0 D 0 ) = 0.6 ± 0.6 MeV Isospin violationµr ρ/ω 1 Small width & Large production rate X(3872) v.s. X(3875) Molecule model Mass J P C R ρ/ω,, B-productionµB < R n/c < 0.1 DecayµR ρ/ddπ > 10 Charmonium modelµχ c1 Large production rate massµpotential models Lattice Coupled channel effects DecaysµIsospin violationº Page 7 of 24 Other interpretationsµ1 ++ cusp, hybrid charmonium, tetraquark state...

8 First Prev Next Last 2.2. X(3872) as a charmonium state χ c1 B-Production (C.M., Y.J. Gao and K.T. Chao, hep-ph/ ) Experimental Data Charmonium Model Molecule Models 10 4 Br d 0.5 ± 0.3 ± 0.05 a < 0.1 d R n/c 1.7 ± 0.9 b e 0.94 ± 0.24 ± 0.10 c a. BaBar, using X J/ψπ + π, PRD b. Belle, using X DDπ, PRL c. K. Trabelsi [Belle Collaboration], using X J/ψπ + π, This Workshop d. E. Braaten and M. Kusunoki, PRD Page 8 of 24 e. E.S. Swanson, Phys. Rept As a by-product: B(X J/ψπ + π ) = (2-4)%

9 First Prev Next Last Large-P T Production at Tevatron Relativistic expansion of Fock state ψ = O(1) c c( 3 S 1 ) 1 + O(v) c c( 3 P J ) 8 + O(v 2 ) c c( 3 S 1 ) σ(p T ) P 8 T P 6 T χ cj = O(1) c c( 3 P J ) 1 + O(v) c c( 3 S 1 ) σ(p T ) P 6 T P 4 T P 4 T The large P T production rate of ψ and χ c1 are both mainly from the matrix elements of operator O 8 ( 3 S 1 ), so that their kinematical distributions should be similar, as we have seen. Provided O 8 ( 3 S 1 ) ψ That can be used to deduce O 8 ( 3 S 1 ) χ c1, the production rates will be equal. B(X J/ψππ) (4-6)% Page 9 of 24

10 Decays of X(3872) as charmonium (C.M. and K.T. Chao, PRD ) th n X (a) R ρ/ddπ R ρ/ω m 2π =2m π m 3π =3m π R ρ/ω m 2π =0.4 GeV 10 R ρ/ddπ m X (MeV) m 3π =0.75GeV th n m X (MeV) (b) th n (a) R ρ/ω th n 10 R ρ/ddπ m 2π =0.4 GeV m 3π 2π =0.75GeV =2m π m 3π =3m π R ρ/ω 100 R ρ/ddπ m X (MeV) m X (MeV) (c) th n (b) R ρ/ω 1 is consistent with experimental data very well. The large isospin violation is due to both the difference between th n = 1.2 m 2π =2m π m 3π =3m π R ρ/ω m D 0 + m D 0 and th c = m D + + m D and the large difference between 0.8 the phase spaces of J/ψρ and J/ψω.(M. Suzuki, PRD ) 0.4 R ρ/ω m 2π =0.4 GeV m 3π =0.75GeV 100 R ρ/ddπ 100 R ρ/ddπ m X (MeV) m X (MeV) (d) (c) The prediction on R ρ/ddπ is roughly consistent with experimental data when m th X < th n, but n about two order smaller when m X > th n. th n Experimental data favor charmonium model if m X < th n. Page 10 of First Prev Next Last

11 First Prev Next Last 2.3. Coupled-channel effects ([1] Yu.S. Kalashnikova, PRD ; [2] B.Q. Li and K.T. Chao, in preparation) Summary of Ref. [2]: The physical state with J P C = 1 ++ has a mass solution near the threshold within 10 MeV. The mass spliting between 1 ++ state and 2 ++ state is about 60 MeV, which is consistent with the measurement of m Z(3930) if the Z(3930) state can be identified with χ c2. In the 1 ++ physical state, the probability of bare χ c1 state Z = (20-70)%, which is very sensitive to the exact value of mass. The influences on our naive charmonium model: The predictions on the production rates and the partial widths should scale as Z. The coupling constant g XDD should scale as Z. The ratios R ρ/ω and R ρ/ddπ are insensitive to Z. No evident contradictions between the coupled-channel improved charmonium model (CCICM) and the experimental data if Z > 30%. Page 11 of 24

12 iny variations of the phase in case B. Tables I and II, we present the sets of the best fitting eters for 2.4. both X(3872) case Aas and a virtual case Bstate and for :3 for[c. thehanhart Belle (Table et al., I) PRD and BABAR ] (Table II) Fit by a virtual state and a 3:98 i0:46 fm; case A Belle; 3:95 i0:55 fm; case B Belle (38) Page 12 of 24. Upper plots: Our fits to the differential rates for the J= channel measured by the Belle [1] and BABAR [25] E = m orations using prescriptions A and B [see Eqs. (31) and (32)]. X th Lower n plots: Corresponding fits for the differential rates in the 0 channel measured by the Belle Collaboration [26]. The distributions integrated over the bins are shown in each panel as solid xperimental data as solid squares with error bars. Scattering length: a 4 fm R ρ/ddπ = 0.1 First Prev Next Last

13 , AND NEFEDIEV Fit by a molecule state PHYSICAL REVIEW D 76, (2007) R; R: (39) l of the fits ginary part tiful cusp in resence of a scenario for mass range virtual D D copic quark the scaling d of scaling light scalar curs if the In the case ere are two charged. energy E in E, then, as 0 0 FIG. 2. The differential rates a for 4 the fm J= (first plot) and D 0 D 0 (second plot) for the fits A Belle (solid curves) and C (dashed curves). R ρ/ddπ = 1.7 quires the coefficient B to be much larger for the virtual state than for the bound state. As a result, the D 0 D 0 rate is Page 13 of 24 First Prev Next Last

14 First Prev Next Last 2.5. Summary of X(3872) Summary: X(3872) behaves like a charmonium state χ c1 in production. Provided X(3872) is a charmonium state, the isospin violation in its decay can be accounted for by the interferences between D 0 D 0 and D ± D intermediate states. The line shapes of X(3872) and X(3875) can be roughly consistent with each other if X(3872) is a virtual state in D 0 D 0 channel. X(3872) is mostly like a state induced by the coupled-channel effects between bare χ c1 and D D channels dynamically. It is produced mainly through its short-sistance c c component, and behaves as a virtual state in long distance (> m 1 π ). Work needs to be done: To replace the Flatte fit by the CCICM one. To improve our calculations by considering the long-distant behaviors of X(3872). To find X ψ γ for experimental physicists. Γ(X ψ γ) = (50-80)Z KeV, for CCICM Γ(X ψ γ) 0.03 KeV, for molecule model (E.S. Swanson, PLB ) Page 14 of 24

15 First Prev Next Last What we have in market by now S-wave threshold effect of DD 1 (2420): J.L. Rosner, S-wave threshold cusp effect of DD 1 (2420): D.V. Bugg, Tetraquark state: L. Maiani et al., ; S.S. Gershtein, First radial excitations of 1 + state with flavor [cu][ c d]. Two-body decay modes should be dominant: DD, D D, ψ ( ) π, ψ ( ) ρ... Bottom partner Z b b with mass about 10.7 GeV: K.M. Cheung, Baryonium: C.F. Qiao, Belong to the series of Y (4260), Y (4361), Z + (4430), Y (4664)... Page 15 of 24

16 First Prev Next Last Resonance of D D 1 (2420)( D D 1(2430)): CM and K.T. Chao, Formed by some attractive interactions (say, π-exchange) between its components Molecule or virtual state, depending on the strength of the attractive force. S-wave coupling to D D 1 ( D D 1): J P (Z) = 0 or 1 Should be in an isospin-triplet: Z (D + D ( )0 Dominant decay mode: Z D D π predicted 1 D 0 D ( )+ 1 ) Dominant production mechanism: B D D ( ) s ZK to be checked 0 molecule in QCD sum rules: m Z = (4.40 ± 0.10) GeV S.H. Lee et al., molecule in EFT: m Zb b = GeV G.J. Ding, Nonet partners and their b-production: Y. Li et al., One-pion exchange between D D ( ) 1 : NOT strong enough to form a molecule X. Liu et al., Page 16 of 24

17 First Prev Next Last 3.2. Decays of Z + (4430) as a resonance (C.M. and K.T. Chao, arxiv: [hep-ph]) Z D D π Γ(Z(0 ) D 1 D D D π) = 25 MeV Γ(Z(0 ) D 1D D D π) = 37 MeV Γ(Z(1 ) D 1 D D D π) = 32 MeV Γ(Z(1 ) D 1D D D π) = 46 MeV g 0 = 5 GeV ZD ( ) 1 D g 1 = 1.5 ZD ( ) 1 D g 0 ZD ( ) 1 D /m D 1 g 1 ZD ( ) 1 D g ψdd 8 Page 17 of 24

18 First Prev Next Last Z + J/ψ(ψ )π + Diagrams for Z + D + D D 0 D 1 + J/ψ(ψ )π + D + 1 π + D 0 1 π + Z + D 0 Z + D D 0 J/ψ(ψ ) (a) D + 1 J/ψ(ψ ) D + J/ψ(ψ ) (b) D 0 1 J/ψ(ψ ) Z + D Z + D 0 Form factor suppressions: For the DDψ ( ) and DDπ vertexes: F(m i, q 2 ) = ( Λ 2 m ) 2 i n Λ 2 q 2 They favor ψ π over J/ψπ We choose Λ = 660 MeV and n ɛ (1, 2) For the ZDD vertex: D 0 (c) Abs i (s) Abs i (s)e β p 2 2 We choose β ɛ (0.4, 1.0) GeV 2 for ZDD system. π + D + (d) π + Page 18 of 24

19 Numerical results: Z + J/ψ(ψ )π + 4 The re-scattering effects of D D 1 are small due to the large width of D 1 TheTABLE contributions II: The arising predictions from diagrams of Γ(Z (a) and + )(b) are ψ ( ) dominant. π + and their dependence on (n, β). Here, we only involve the contributions Provided r = g ψ DD/g ψdd = 2 (g ψ(3770)dd /g ψdd 1.7) arising from Fig. 1(a)-1(b) in D D 1 channel. (n, β GeV 2 ) (1.0, 1.0) (1.5, 0.6) (2.0, 0.4) J P (Z) Γ ψπ +(MeV) Γ ψ π +(MeV) an use e it to timate VMD) (19) (D 1 )D, e esti- D) in The predictions favor 1 : Γ ψ π + = 4.4 MeV, R ψ /ψ 5.2 Can not rule out 0 is implied in the down limit of the integral in (15), consumedly. As a result, the Z(4430) should have little D 1 component. On the other hand, the contributions arising from Fig. 1(c)-1(d) are less than those from Fig. 1(a)-1(b) by a factor of This is probably because the value of coupling constant g ψd1 D, which we choose in Tab. I, is small. We can see it through re-scaling g ψd1 D by m D1 m D and getting the number is 2.3, which is far less than that of g ψd D. The β-dependence of Γ ψ ( ) π Γ ψ ( ) π (MeV) Z + (4430) state is likely to be a resonance in S-wave scattering, and the spin-parity favors 1 but can no out 0. Further studies on its production mechanis needed. Page 19 of 24 In summary, we study both the open-charm an R 5.2, which could be roughly consistent wi out by our calculations. Further studies on the p Γ ψ π hidden-charm decays of Z(4430) based on the as tions that it is a D ( ) 1 D resonance in S-wave. Th tial width of open-charm decay is dominant and c adjusted to be MeV. Then, we find that the S n = 2 threshold effects are significant in D 1 D channel a Γ ψπ suppressed intensively in D 1D channel due to the width of D 1. For the 1 candidate, choosing pa ters aptly, we can get Γ(Z + ψ π + ) 4.4 MeV β(gev 2 ) ψ /ψ perimental data. But the 0 candidate can not be FIG. 3: The β-dependence of Γ(Z + (1 ) First ψ (ψ)π Prev + tion mechanism of Z(4430) are needed. ) with Next Last IV. SUMMARY

20 First Prev Next Last 3.3. Summary for Z + (4430) Summary: Z is most like a resonance of D D 1 in isospin-triplet. The numerical results favor J P = 1, but can not rule out 0. R ψ /ψ 1.4r 2 with Br(Z + ψ π + ) = 0.04r 2. Dominant decay mode should be Z D D π Can decay to ψ(3770)π. Page 20 of 24

21 First Prev Next Last Thank You! Page 21 of 24

22 First Prev Next Last Back Up X J/ψρ(ω) Effective Lagrangian: L X = g X X µ D µ D + h.c. Diagram for the re-scattering D 0 J/ψ X(3872) Imaginary part of the amplitude D 0 ρ(ω) Abs n = p 1 32π 2 m X dωa(x D 0 D 0 )A(D 0 D 0 J/ψρ(ω)) Abs is strongly suppressed by the tiny phase space factor.(x. Liu et al., PLB ) The contribution arising from real part should be dominant in this case. Real part of the amplitude Dis(m 2 X ) = ( 1 π P Abs n (s ) th ds + P 2 n s m 2 X th 2 c P denotes principal integral th n = m D 0 + m D 0, th c = m D + + m D. Naive cut: s max = 2m D Form factor: Abs Abs e β p 1 2 D 0 Abs c (s ) ds ) s m 2 X Page 22 of 24

23 First Prev Next Last Back Up X D 0 D0 π 0 m X > th n Γ(X D 0 D0 π 0 ) = 2Γ(X D 0 D 0 )Br( D 0 D 0 π 0 ) Γ(X D 0 D 0 ) = g2 X p 1 (3 + p 1 2 ) g2 24πm 2 X m 2 X p 1 D 0 8πm 2 X m X < th n X D 0 D 0 (a) π 0 im = i(m a + M b ) = Cascade decay formula: Γ X D 0 D 0 π 0 = 1 π D0 (mx m D 0) 2 X D 0 D 0 (b) π 0 D 0 i 2g X g D [(q k Dπ π)(q ɛ X ) (k q 2 m 2 D 0+im D 0 Γ D 0 m 2 π ɛ X )] D 0 (m π 0+m D 0) 2 ds s 2Γ X D 0 D0(s)Γ D 0 D0 π0(s) (s m 2 D 0 ) 2 + ( s Γ DD 0(s)) 2 Note: all the above formulae will be invalid when m X th n Γ D 0 70 KeV. Page 23 of 24

24 First Prev Next Last Back Up (C. Hanhart et al, PRD ) F (E) = g 2D(E) = 1 γ+κ(e), E = m X th n (g Zg2 X 4πm 2 X ) D(E) = E E f g 2 κ(e) g 2κ(E δ) + iγ(e) 2 κ(e) = 2µE i0 +, µ = m Dm D m D +m D, δ = th c th n The real part of γ can be expanded around E = 0: Reγ = 1/a r s µe +... scattering length: a = ( 2µδ + 2E f /g) 1, 2µδ 125 MeV m π effective range: r s = (1/ 2µδ + 2/µg) 1/m π if g > 0.3 For a 1/m π, there will be a bound state (molecule) just below the threshold with the binding energy E b 1/(µa 2 ), and the line shape of X J/ψππ and X DDπ will exhibit Breit-Wigner distributions very well. For a 1/m π, one get a virtual state. The distribution of X J/ψππ will exhibit a cusp (D.V. Bugg, PLB 598 8) which is peaked exactly at E = 0, and the peak of the distribution of X DDπ will be pushed up to a few MeV above the threshold. Page 24 of 24