X(3872) and Its Production. 2nd workshop on the XYZ particles 11 月 21 日, 安徽黄山

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1 X(3872) and Its Production 孟策 北京大学 2nd workshop on the XYZ particles 11 月 21 日, 安徽黄山 1

2 Outline Experimental information on X(3872) before BESIII Molecular model: a critical review Production rate Decay pattern X as a mixing state of χ c1 and D 0 D 0 + c. c. Spectrum Scattering amplitudes v.s. line shapes Production of X Production in B decays Production in pp /pp collision Production in e + e annihilation Production in the E1 transitions of higher chamonia Summary 2

3 Experimental information 1 st observed by Belle Collaboration in B J/ψπ + π K Mass, width and quantum numbers: Belle 03 m X = ± 0.17 MeV PDG 12 m X m D 0 D 0 = ± MeV Tomaradze et al. 12 Γ < 1.2 MeV CL = 90% PDG 12 J PC = 1 ++ or 2 + J PC = 2 + is favored by the ω π + π π 0 mass spectrum in B X 3872 K J/ψω π + π π 0 K [BaBar 10], but is excluded by the recent analysis on the angular correlations in B X 3872 K J/ψρ π + π K by LHCb [LHCb 13] 3

4 Decay pattern: Experimental information Well-established decay modes: J/ψρ π + π, J/ψω π + π π 0, D 0 D 0 /D 0 D 0 /DDπ, J/ψγ Relative ratios of these 4 modes: 1: 1: 10: 0.3 Large isospin violations R ρ/ω = Br X J/ψρ /Br X J/ψω 1 Br X J/ψρ = Br X J/ψπ + π Br 0 < 9% B-production: PDG < Br B X 3872 K < BaBar 05 Br B X 3872 K Br 0 = 8.6 ± PDG % < Br 0 < 9% 4

5 Experimental informations Hadro-production Large production rate: σ pp X Br 0 ε ψ = 4.8 ± 0.8 % CDF 04 σ pp ψ ε X Similar behaviors to ψ production in p T distribution and D0 PRL 04 CMS arxiv: a. p T > 15 GeV b. Ratio to ψ is not depend on p T 5

6 Molecule models [Tornqvist 04, Voloshin 04, Swanson 04, Braaten 04, ] X(3872) is a loosely bound state of D 0 D 0 /D 0 D 0 The mass, J PC and R ρ/ω can be understood naturally. The large production rate seems to be questionable Naively, σ X k 0 3, k 0 = 2μ DD E b < 40 MeV Explicit calculations [Bignamini et al, PRL 09]: th ex σ CDF X < nb v. s. σ CDF X Br 0 = 3.1 ± 0.7 nb Artoisenet and Braaten [PRD 10] proposed that the rescattering effects of D 0 D 0 may enhance the rate to values consistent with the CDF data if the upper bound of the relative momentum of D 0 D 0 in the rescattering is as large as 3m π 400 MeV Similarly, small B-production rate [Braaten, Lu, Kusunoki 05-06] Br B + K + X 3872 = for k 0 40 MeV 6

7 Molecule models Decay pattern DDπ decay mode [Swanson; Voloshin; Fleming, mehen, ] Γ X D 0 D 0 π 2Γ D 0 D 0 π 100 kev Radiative decays: [Swanson 04] ρ/ω J/ψ γ Γ X J/ψγ 8 kev Γ X ψ γ 0.03 kev Γ X ψ γ Γ X D 0 D 0 π 10 4 v. s ex [BaBar 08] J/ψρ(ω) decay mode [Swanson 04] Γ X J/ψρ(ω) 1-2 MeV D D γ ψ () 7

8 χ c1 D 0 D 0 mixing model Meng, Gao and Chao, PRD_87_ (2013) [hep-ph/ ] X 3872 is a mixing state of χ c1 and D 0 D 0 /D 0 D 0 Both the two components are substantial, and they may play different roles in the dynamics of X The short distance (the b- and hadro-) production and the quark annihilation decays of X 3872 proceed dominantly through the χ c1 component. 2. The D 0 D 0 component is mainly in charge of the hadronic decays of X 3872 into DDπ/DDγ as well as J/ψρ and J/ψω. 3. The long distance coupled-channel effects between the two components could renormalize the short distance dynamics by a product factor Z cc, the equivalent probability of χ c1 in X

9 Mixing state: Decay pattern χ c1 induced decay modes Radiative decay modes Others DD induced decay modes kev 1 MeV Dubynskiy & Voloshin, PRD 08 be relavant to Chengping s talk Γ D 0 D 0 π MeV Γ J/ψρ(ω) kev Meng & Chao 07 Which could not be separated from the LD evolution amplitude, but can be incorporated in fitting the experimental line shapes. 9

10 Quark-level picture Specrum: Charmonium c q c q Quark-pairs creation Screening the linear potential Screened (unquenched) potential model [Chao & Ding & Qin 92] Hadron-level picture H cc D D Coupled-Channel models mixing between H cc and DD Which have been considered even in the Cornell model [E. Eichten et al 78]. 10

11 Specrum: Screened potential model Li & Chao, PRD_79_ (2009) 11

12 Specrum: SPM v.s. CCM Li & Meng & Chao, PRD_80_ (2009) SPM CCM in the global features. CCM is more adept in investigating the open-charmed threshold effects. 12

13 Specrum: S-wave threshold v.s. X(3872) Li & Meng & Chao, PRD_80_ (2009) M M 0 + Π M = 0 Π = d 3 p BC,p H QPC ψ BC, p H QPC ψ 0 Γ ψ BC 2L+1 M M B M C 2 BC E BC p M iε B ψ 0 ψ 0 Π M S-wave threshold effect: L = 0 E = M M B M C 0 Π E E, dπ E /de 1/ E S-wave cusp attracting the mass of the bare state to the threshold M χc1 th DD : M 15 MeV ReΠ 70 MeV M 0 85 MeV C ReΠ χc1 M M M 0 χ c1 13

14 X(3872) in the CCM: Pole Trajectory Near-threshold expansion Π E Π 0 + igk E /2, k E = 2μE + i0 + Solving E E 0 + Π 0 + igk E /2 = 0 k ± = ig 2 μ ± g2 4 μ2 2μ Π 0 E 0 + i0 + Pole trajectory v.s. g Fig. taken from Danilkin & Simonov, PRL 10 (See also Tornqvist, PRD 95) 14

15 X(3872) in the CCM: Pole Trajectory Pole trajectory v.s. g g = 0: bare BW state g is fine tuned: Two near threshold poles mixinginduced virtual state (Pole counting rule Morgan, NPA 92) g is sufficient large: Bound state molecule? Π E = g L E 15

16 Size of χ c1 in the X(3872) For the bound state [Weinberg 65, Baru et al 04] Z = Π E E E= ε 1 1+ g 2 2 μ/ε ε 0 g R = Z g = 2 2 ε μ 1 z see Fengkun s and Qian s talks spectrum density: w E = gk/2π E E 0 +Π E 2 0 spectrum sum rule: Z + w E de Inelastic decay modes: H cc D D Generalized spectrum density: w E = LHs gk+γ 0 2π 0! = 1 [Baru et al 10] Γ 0 1MeV ε + E, Z = w E de E E 0 +Π E +iγ E Γ 0 may make the X spending more time in the short distant c c configuration [Li & Meng & Chao, in progress] 16

17 Coupled-channel amplitude Scattering amplitude F E = g/2 E E 0 + Π 0 + igk E 2 + iγ E 2 + iγ 0 2 Fitting the experimental line-shapes: Vitual state poles are favored [Hanhart et al 07] With nonzero Γ 0, two near threshold poles are favored [Zhang & Meng & Zheng 09] With Γ 0 = 1 2 MeV [Kalashnikova & Nefediev 09] Z = +10 MeV w E de 10 MeV =

18 Scattering amplitude v.s. line shape Meng & Sanz-Cillero & Shi & Yao & Zheng, in preparation Fit I Fit II Fit III Amplitudes C.C. + B.C. Coupled-channel Bubble chain χ 2 d. o. f. 44.1/ / /46 18

19 Production of X(3872) 19

20 General factorization formula Energy scales: p T, m b, m c m c v, m c v 2, Λ QCD ε, Γ X ~1 MeV cc production χ c1 production Binding & Decay LD Factorization I: σ X J/ψπ + π = σ χ c1 k, k = Z cc Br 0 Factorization II: NRQCD Bodwin & Braaten & Lepage 95 n = dσ χ c1 = dσ cc n n O n χ c1 m c 2L n 3 P 1 1 & 3 S 8 1 at leading order in v for χ c1 production 20

21 Production in B decays Theory: [Meng, Gao and Chao, PRD_87_ (2013) [hep-ph/ ]] Input: R 2P 0 2 = R 1P 0 2 = GeV 5 Br B χ c1 K Br B χ c1 K = K = Br B χ c1 Fits: [Kalashnikova & Nefediev PRD 09] Br fit B χ c1 K = Experimental data: Br B X J/ψπ + π K = Br B χ c1 K k = 8.6 ± PDG 12 k = Z cc Br 0 = ± With a modest value Br 0 = 5% 2.6% 9% Z cc = 28% 44 (Z fit = Kalashnikova 09) 21

22 Production in B decays Comparing with exparamental data: Input:Br B χ c1 K = Br PDG B χ c1 K, k = 0.18 Br i Br i = Predictions data B + XK ± ± 0.8 PDG 12 B 0 XK ± ± 1.3 PDG 12 B + XK ± 1.0 B 0 XK + π 6.8 ± ± 1.3 Chenping s talk B 0 XK ± ± 1.0 Chenping s talk Br K 0 K + π = 2/3 22

23 Production at hadron collider NRQCD Factorization: [Bodwin & Braaten & Lepage 95] n = dσ pp χ c1 = n dσ cc n χ O c1 n m c 2Ln χ = i,j,n dx 1 dx 2 G i/p G j/p dσ ij cc n O c1 n 3 P 1 1 & 3 S 8 1 at leading order in v for χ c1 production Molecule model : Artoisenet & Braaten, PRD 09 dσ pp X D 0 D 0 = dσ cc 3 S18 Different long distant matrix elements Different combination of the cc channels D O 0 D S1 One can compare the two models with the help of the CMS data on the pt distribution! 23

24 NLO calculations: Production at hadron collider Meng & Han & Chao, arxiv: Inputs: Ma & Wang & Chao 11 (MWC 11) μ r = μ f = m T = p T 2 + 4m c 2, μ NR = m c = 1.5 ± 0.1 GeV R 2P 0 2 = R 1P 0 2 = GeV 5 To compare our following results with the available ones for χ c1 production [MWC 11], we parameterize the matrix elements as r = m c 2 χ O c1 3 8 S1 χ / O c1 3 1 P1 (r 1P = 0.27 ± 0.06, MWC 11) The cross section in the χ c1 production mechanism is a simple function of r, k and p T 24

25 Fit to the CMS p T distribution χ c1 production mechanism: r = 0.26 ± 0.07, k = ± The central values correspond χ 2 /2 = 0.26 The value of r 2P for χ c1 is almost the same as that for χ c1 1P : r 1P = 0.27 ± 0.06 [MWC 11] which strongly suggests that X(3872) be produced through its χ c1 component at short distance Molecule production mechanism: D O 0 D Br S 0 = (6.0 ± 0.6)10 5 GeV 3 1 χ 2 /3 = 1.03 Meng & Han & Chao, arxiv:

26 Inputs: Predictions v.s. CDF/LHCb data D r = 0.26, k = 0.014; O 0 0 D 3 8 Br0 = GeV 3 S1 Data Meng & Han & Chao, arxiv: χ c1 mechanism molecule σ CMS /nb 1.06 ± ± 0.09 σ CDF /nb 3.1 ± ± ± 0.4 σ LHCb /nb 5.4 ± ± ± 1.3 CMS + CDF data favor the χ c1 production mechanism Same forward rapidity region Almost same gluon energy: s = x 1 x 2 S 2P T Test the universality and the evolution of the gluon PDF CMS + LHCb data favor the molecule production mechanism less meaningful since the predicted pt distribution at CMS is almost inconsistent with the data. 26

27 Fitting k to the CMS data with fixed r Fitting k to B decay data ex 3.1 ± 0.7 nb CDF ex 5.4 ± 1.4 nb LHCb 80% Single parameter fit Kalashnikova & Nefediev PRD 09 k = Z cc Br 0 = ± Window in the table: r = The consistency of the CDF data with our prediction is better, but that for the LHCb data is worse. Similar results were obtained in [Butenschoen & He & Kniehl, arxiv: v2] 27

28 Production in e + e annihilation e + e γx X = η c, χ cj NLO at S = 10.6 GeV: Li & He & Chao 09 σ e + e γχ c1 = 18 fb Search X(3872) at Belle (711 fb 1 data sample) N γx γμ + μ π + π 10 NLO at S = 4 5 GeV: σ 1/S 2 Chao & He & Li & Meng, arxiv: m c = 1.5 GeV Li & Xu &Liu & Zhang, arxiv: (see Guangzhi s talk) m c = M X /2 Relativistic corrections are included 28

29 Production in e + e annihilation LO (pure QED process) σ χ c 1 1 r, r = 2m c 2 /S near-threshold singularity Coulombic g c QCD pollution in the near-threshold region The Coulombic gluons need to be resummed E1 transitions of resonances Soft γ σ m c = 1.5GeV might be viewed as the lower limit of the continuum contribution (without resonance contribution) c 29

30 Production in e + e annihilation Chao & He & Li & Meng, arxiv: σ γx J/ψπ + π = σ γχ c1 k 0.01 pb σ ex 0.3 pb Resonance contributions should be dominant! 30

31 E1 transitions of higher chamonia Li & Meng & Chao, arxiv: Γ ψ n γχ cj m = 4 3 C mne c 2 α χ cj m r ψ n 2 E γ 3 Three potential models are used and they are consistent with each other quite well. (see below for results of SPM) Relativistic corrections are included in the wave functions Γ kev ψ 3S 4040 ψ 2D 4160 ψ 4S 4260 χ c χ c Br ψ 4S γx[j/ψππ] Br ψ 4S γχ c1 k Br Y γx J ψππ Br Y J ψππ Γ ee Br Y J ψππ see Zhiqing s talk 6 ev Need Γ ee 2 kev! Same value is also needed for the molecule model. see Fengkun s talk 31

32 Γ ee 4260 ψ 4S : 970 ev [Li & Chao, PRD 09] Hybrid: 25(20) ev See Ying s talk Fitting the line-shape (e + e Y 4260 J/ψπ + π ): 1. Dai & Shi & Tang & Zheng 12: 211 ev (without Γ 0 ) 2. Cleven et al 13 (see Qian s talk): several tens ev (private communication) Fitting R-value: Mo et al 06 Γ ee < 580 ev Ignoring the dip structure Relative phases between different resonances are important! 32

33 e + e ψ n γx 3872 Li & Meng & Chao, in preparation Amplitude A = BM 1 + BW 2 e iδ 12 + BW 3 e iδ 13 Inputs: BM i s = 12πΓ i ee Γi γx S S m 2 i +im i Γi Γ γx tot i i S = Γ γx 2 m i0 σ e + e γx 3872 [J ψ ππ] = k A 2 i m i /MeV i Γ tot /MeV Γ ee /kev m X 2 S 1 m X 2 m 2 i0 3/2 33

34 e + e ψ n γx 3872 Li & Meng & Chao, in preparation CLEO-c data 13 No inteference δ 12 = δ 13 = 0 δ 12 = π 2, δ 13 = 0 34

35 e + e ψ n e + e 3872 Li & Meng & Chao, in preparation What are indicated? σ > MeV σ e + e γz MeV Contributions from the DD component may also be important especially at 4260 MeV[see Fengkun talk] 35

36 Summary With Z cc = , X(3872) could be understood in the mixing model: Decay pattern (X γψ need to be confirmed) Closeness to the threshold (S-wave threshold effect). Experimental line-shapes Large production rate B-production Hadro-production E1 production (hadron-loop contributions need to be clarified) More efforts (th. & ex.) are needed to study X and BESIII. Resonance parameters and relative phases Line-shapes scanning Continue DD, DDπ, πz c, 36

37 BackUp 37

38 Specrum: SPM v.s. CCM Li & Meng & Chao, PRD_80_ (2009) Two faces of χ c0 : [X. Liu et al, PRL 10, EPJC 12; F.K. Guo et al, PRD 12] Narrow peak (Γ 1 MeV) at 3915 MeV Broad structure (Γ > 100 MeV) around 3850 MeV 38

39 Fit to the CMS p T data S = 7 TeV, y < 1.2, 10 GeV < p T < 30 GeV Molecule production mechanism: D O 0 D Br S 0 = (6.0 ± 0.6)10 5 GeV 3 1 χ 2 /3 =

40 Predictions v.s. CDF data S = 1.96 TeV, y < 0.6, p T > 5 GeV χ c1 production mechanism: Inputs: r = 0.26, k = th σ CDF pp X J/ψπ + π = 2.5 ± 0.7 nb v. s. 3.1 ± 0.7 nb ex The predicted p T distribution of X 3872 is compared with that of ψ [CDF, PRD 09] (see the diagram) Molecule production mechanism: σ molecule CDF = 1.1 ± 0.4 nb 2.6 σ deviation from data Both the CMS and the CDF data favor the χ c1 production mechanism, but a little bit disfavor the molecule production mechanism. 40

41 Comparison with arxiv: Butenschoen & He & Kniehl, arxiv: v1: Set IV: fit two matrix elements to both the CMS and CDF data Input Fit values Predictions R 2P 0 2 /GeV 5 r 10 2 k 10 3 σ th th CDF /nb σ LHCb /nb BHK/set IV ± 4 11 ± ± ±1.5 Ours ± 4 14 ±6 2.5 ± ±2.5 Only stress that the X(3872) could not be a pure χ c1 state 41