Molecular States in QCD Sum Rules

Transcription

1 Hidden Charm Tetraquark States & Molecular States in QCD Sum Rules Cong-Feng Qiao University of Chinese Academy of Sciences (UCAS) nd workshop on the XYZ particles

2 Outline 2 Part I: Exotic States New Exotic States. t Theoretical Interpretations. Part II: Tetraquark States QCD Sum Rules. 1 + Charged Hidden Charm Tetraquark State. C.-F. Qiao & L. Tang, arxiv: &2 + Charged Hidden Charm Tetraquark States. C F Qi & L T Summary of Tetraquark State. Part III: Molecular States C.-F. Qiao & L. Tang, arxiv: Hidden Charm & Strange Molecular States. Discussions and Predictions. C.-F. Qiao & L. Tang, arxiv:

3 3 Part I Exotic States

4 4 Observed by BESIII, this year! New Exotic States List of New Exotic States

5 New Exotic States 5

6 New Charged Charmonium-like Structures 6 Z c+ (3900) observed by BESIII and Belle. BESIII, arxiv: Belle, arxiv: Confirmed with CLEOc data. CLEOc, arxiv:

7 New Charged Charmonium-like Structures 7 Z c+ (4025) observed by BESIII. Z c+ (4020) observed by BESIII. arxiv: , BESIII Colaboration. arxiv: , BESIII Colaboration.

8 New Charged Charmonium-like Structures 8 Z c+ (3885) observed by BESIII. arxiv: , BESIII Colaboration.

9 Theoretical Interpretations 9 Decays to charmonium Contain a pair With electric charge More than 2 quarks! At least four quarks! Exotic state!

10 Theoretical Interpretations 10 Explanations on Z c+ (3900) D*D molecular state: F-K Guo, et al., C. -Y. Cui, et al., Tetraquark state: L. Maiani, et al., PRD87, (R) (2013). J.M. Dias, et al., C.-F. Qiao and L. Tang, Hadron-charmonium: M.B. Voloshin, Heavy quark flavor symmetry QCDSR Dynamic analysis Decay Mass Be argued Initial Single Pion Emission mechanism (ISPE): D.Y. Chen, X. Liu, PRD84 (2011) Predicted

11 Theoretical Interpretations 11 Explanations on Z c+ (4025) D*D* molecular state: F. -K. Guo, et al., Jun He, et al., arxiv: C.-Y. Cui, et al., arxiv: Wei Chen, et al., arxiv: K.P. Khemchandani, et al., arxiv: Tetraquark state: C.-F. Qiao & L Tang, arxiv: Z.-G. Wang, arxiv: Heavy quark flavor symmetry Effective Lagrangian QCDSR-P-wave QCDSR Projected from 2 + current Disfavor 1 -, Favor 2 + Disfavor 1 -

12 Theoretical Interpretations 12 Explanations on Z c+ (4020) : It does not seem to be clear if the states Z c+ (4020) and Z + c+ (4025) are the same or not. Z.-G. Wang, arxiv: Disfavor 1 - Explanations on Z c+ (3885) : It does not seem to be clear if the states Z c+ (3885) and dz + c+ (3900) are the same or not.

13 13 Part II Tetraquark States

14 QCD Sum Rules 14 Review of hidden charm tetraquark states with QCD Sum Rules. I G (J PC )=0 + (1 ++ ) hidden charm tetraquark state was studied to interprete X(3872). RD R.D. Matheus, S. Narison, M. Nielsen, J.M. Richard, PRD 75, (2007). In a systematic way, the vector and axial-vector hidden charm tetraquark states was investigated by W. Chen & S.L. Zhu. They found 1 -- hidden charm tetraquark was consistent with Y(4660). W. Chen, and S.L. Zhu, PRD 83, (2011) and hidden charm tetraquark states have been studied. R.M. Albuquerque, et. al. PLB 715, 129 (2012).

15 QCD Sum Rules 15 A2 - hidden charm tetraquark state was investigated to explore the X(3872). C.Y. Cui, et al., CTP, 57,1033 (2012). Note, these works only refer to the neutral tetraquark states. We estimate the charged hddien charm tetraquark states via QCD Sum Rules. C.-F. Qiao & L. Tang, arxiv: &

16 1 + Charged Hidden Charm Tetraquark State 16 The interpolating current of the 1 + charged hidden charm tetraquark state is used as: Insert this current into the two-point correlation function: This correlation function has the following Lorentz covariance form: where the spin-1 part corresponds to 1 + charged hidden charm tetraquark state.

17 1 + Charged Hidden Charm Tetraquark State 17 On the phenomenological side, the correlation function is expressed as: In the Operator Product Expansion (OPE) side, it is described as: where

18 1 + Charged Hidden Charm Tetraquark State 18 The full propagator of light quark is used as: R.M. Albuquerque, The full propagator of heavy quark is writen as:

19 1 + Charged Hidden Charm Tetraquark State 19 Matching these two sides (quark-hadron dualtiy), and performing the Borel transformation, we obtain the mass function: where M.A. Shifman, et.al., NPB147,385 (1979).

20 1 + Charged Hidden Charm Tetraquark State 20 Generally, two criteria are employed to determine the threshold parameter s 0 and the Borel parameter M B. (A). The OPE convergence. Determine the lower limit constraint of M B2. (B). Pole Contribution dominant. PC> 50% is required here. Determine the upper limit constraint of M B2. These criteria give a reliable window of M B2 with a definite s 0. Additionally, s 2 0 is chosen to ensure the minimum variation of m c 1+with M B2. In the end, with these input parameters, we can obtain the mass of 1 + charged hidden charm tetraquark state.

21 1 + Charged Hidden Charm Tetraquark State 21 OPE convergence of 1 + charged hidden charm tetraquark state: M B2 >1.9 GeV 2

22 1 + Charged Hidden Charm Tetraquark State 22 Pole contribution of 1 + charged hidden charm tetraquark state: M B2 < 2.3 GeV 2 B

23 1 + Charged Hidden Charm Tetraquark State 23 Mass curves of 1 + charged hidden charm tetraquark state:

24 1 - &2 + Charged Hidden Charm Tetraquark States 24 Possible quantum numbers of Z c+ (4025) are 1 +, 1 -, 2 + and so on. We concentrate t on 1 - and 2 +, since our former study favors Z + c+ (3900) as a 1 + tetraquark state. C.-F. Qiao & L. Tang, arxiv: The interpolating i currents of 1 - & 2 + tetraquark states are used as: The mass of 1 - state has been estimated in previous literatures. m 4.6 ~ 4. 7GeV 1 m 4818 MeV 1 W. Chen & S-L Zhu, R.M. Albuquerque, et al., PRD 83, (2011). PLB 715, 129 (2012). We reestimate the mass of 1 - with the aforementioned criteria.

25 1 - Charged Hidden Charm Tetraquark States 25 OPE convergence of 1 - charged hidden charm tetraquark state: M B2 >2.1 GeV 2

26 1 - Charged Hidden Charm Tetraquark States 26 Pole contribution of 1 - charged hidden charm tetraquark state: M B2 < 3.5 GeV 2

27 1 - Charged Hidden Charm Tetraquark States 27 Mass curves of 1 - state where, 2.1 GeV 2 <M B2 <3.5 GeV 2, and we find the optimal threshold parameter is s 0 1/2 =5.0 GeV. Mass of 1 - state t is: m GeV ( ) 1

28 2 + Charged Hidden Charm Tetraquark State 28 OPE Convergence of 2 + state M B2 >2.3 GeV 2

29 2 + Charged Hidden Charm Tetraquark State 29 Pole Contribution of 2 + state M B2 <3.0 GeV 2

30 2 + Charged Hidden Charm Tetraquark State 30 Mass curves of 2 + state Mass of 2 + state is: m G GeV 2

31 Summary of Tetraquark States 31 The mass of 1 + charged hidden charm tetraquark state gives support to the tetraquark picture of Z c+ (3900). Extending to the b-quark sector, we have:, which supports the tetraquark picture of Z b+ (10610). The mass of 1 - charged hidden charm tetraquark state is much higher than Z c+ (4025) or Z c+ (4020), so the possible quantum numbers 1 - of Z c+ (4025)/Z c+ (4020) is ruled out. Maybe it corresponds the charged partner of Y(4360) or Y(4660)! Extending to the b-quark sector, we have:. We suggest that Z c+ (4025) is a 2 + charged hidden charm tetraquark state. Extending to the b-quark sector, we have:.

32 32 Part III Molecular States

33 Hidden Charm and Hidden Strange Molecular States 33 Motivation DD* & D*D* molecular states were used to interpret Z c+ (3900) and Z c+ (4025), so what about D s D s * and D s *D s * in QCD Sum Rules? C-Y Cui, et al., arxiv: ; Wei Chen, et al., arxiv: The interpolating currents of D s D s * & D s *D s * with J pc =1 +- are constructed as:

34 Hidden Charm and Hidden Strange Molecular States 34 OPE convergences:

35 Hidden Charm and Hidden Strange Molecular States 35 Pole contributions:

36 Hidden Charm and Hidden Strange Molecular States 36 Mass curves:

37 Hidden Charm and Hidden Strange Molecular States 37 Results:

38 Hidden Charm and Strange Molecular States 38 Discussion The central value of the D s D s *< (4.08 GeV). The center value of the D s *D s * > (4.22 GeV).

39 Hidden Charm and Hidden Strange Molecular States 39 Predictions Possible decay modes for D s D s * bound state: Possible decay modes for D s *D s * resonance:

40 Thank you! 40