Exotic States in QCD Sum Rules 乔从丰 中国科学院大学 2015.12.17 @2015 BESIII Charm Physics Workshop

Outline Ds Molecular States Background & Motivation Ds Molecular States via QCD Sum Rules Summary of Ds Molecular States Oddballs Background & Motivation Oddballs in QCD Sum Rules Summary of Oddballs

Part I: Ds Molecular States C.-F. Qiao and L. Tang,   EPL107, 31001 (2014).

Background & Motivation Zc(3900) M(+J/) Zc(4020) M(+hc) PRL,111,242001 (2013). PRL, 110, 252001(2013). Zc(3885) M(DD*) Zc(4025) M(D*D*) PRL,112,022001(2014). PRL,112,132001(2014).

Background & Motivation Zc0(4020) M(0hc) Zc0(3900) M(0J/) PRL,115,112003(2015). PRL,113,212002(2014). Zc0(3885) M(DD*) Zc0(4025) M(D*D*) PRL,115,222002(2015). PRL,115,182002(2015).

Background & Motivation Summary of the observed Zc states at BESIII P. Liu [BESIII Collaboration], arXiv:1509.08042 Zc+ Zc0 Zc0

Background & Motivation Possible quark configurations Molecualr states Tetraquark states Q.Wang, C.Hanhart, Q.Zhao, PRL 111, 132003 (2013); H.W.Ke, Z.T.Wei and X.Q.Li, EPJC 73,2561 (2013); J.He, X.Liu, Z.F.Sun and S.L.Zhu,  EPJC 73,2635 (2013); And so on… L.Maiani, et al.,PRD87, 111102(2013); C.F.Qiao and L.Tang,  EPJC74, 3122(2014), EPJC74, 2810(2014); L.Zhao, W.Z.Deng and S.L.Zhu,   PRD 90, 094031 (2014); And so on…

Background & Motivation Interpretation of molecular states via QCDSR Zc(3900) was successfully interpreted as a 𝐷 𝐷 ∗ molecular state. J.R.Zhang, PRD 87, 116004(2013); C.Y.Cui, Y.L.Liu, W.B.Chen and M.Q.Huang,  JPG41, 075003 (2014). Zc(4025) was successfully interpreted as a 𝐷 ∗ 𝐷 ∗ molecular state. C.Y.Cui, Y.L.Liu and M.Q.Huang,  EPJC 73, 2661 (2013); W.Chen, T.G.Steele, M.L.Du and S.L.Zhu,  EPJC 74, 2773 (2014). It is reasonable that there exist Ds molecular states. Our motivation is to explore these states via QCDSR.

Ds Molecular States via QCDSR The calculations of the QCD Sum Rules are based on the correlator constructed by two hadronic currents: As 𝐽 𝜇 (𝑥) is not a conserved current, the two-point correlation function has two independent Lorentz structures: Corresponding to the axial-vector state

Ds Molecular States via QCDSR Phenomenological side 𝜆 𝐻 is defined by 0 𝑗 𝜇 𝑍 𝑐𝑠 = 𝜆 𝐻 𝜖 𝜇 , where 𝑍 𝑐𝑠 is the lowset lying 1 +− 𝐷 𝑠 𝐷 𝑠 ∗ or 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ molecular state. Quark-gluon side where

Ds Molecular States via QCDSR The mass of the Ds molecular state is expressed as where,

Ds Molecular States via QCDSR Input parameters

Ds Molecular States via QCDSR The interpolating currents of 𝐷 𝑠 𝐷 𝑠 ∗ & 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ are constructed as The interpolating currents of 𝐷 𝑠 𝐷 ∗ & 𝐷 𝑠 ∗ 𝐷 ∗ are constructed as

Ds Molecular States via QCDSR OPE convergence in the region 0.30 ≤𝜏≤ 0.65 𝐺𝑒 𝑉 −2 for the 𝐷 𝑠 𝐷 𝑠 ∗ molecular state with √ 𝑠 0 = 4.6 GeV, where 𝜏= 𝑀 𝐵 −2 . The relative pole contribution of 𝐷 𝑠 𝐷 𝑠 ∗ state with √ 𝑠 0 = 4.6 GeV.

Ds Molecular States via QCDSR The mass of the 𝐷 𝑠 𝐷 𝑠 ∗ state as a function of the sum rule parameter 𝜏, for different values of √ 𝑠 0 .

Ds Molecular States via QCDSR OPE convergence in the region 0.25 ≤𝜏≤ 0.50 𝐺𝑒 𝑉 −2 for the 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ molecular state with √ 𝑠 0 = 4.9 GeV, where 𝜏= 𝑀 𝐵 −2 . The relative pole contribution of 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ state with √ 𝑠 0 = 4.9 GeV.

Ds Molecular States via QCDSR The mass of the 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ state as a function of the sum rule paramter 𝜏, for different values of √ 𝑠 0 .

Ds Molecular States via QCDSR The mass of the 𝐷 𝑠 ∗ 𝐷 ∗ state as a function of the sum rule paramter 𝜏, for different values of √ 𝑠 0 .

Ds Molecular States via QCDSR The mass of the 𝐷 𝑠 ∗ 𝐷 ∗ state as a function of the sum rule paramter 𝜏, for different values of √ 𝑠 0 .

Ds Molecular States via QCDSR Numerical Results of Ds Molecular States State Lower MB2 (GeV2) Upper MB2 𝑠 0 (GeV) Mass DsD*s 1.80 3.10 4.60±0.10 3.98±0.15 D*sD*s 2.50 3.60 4.90±0.10 4.38±0.16 DsD* 1.70 2.90 4.50±0.10 3.93±0.15 D*sD* 2.40 3.30 4.80±0.10 4.33±0.15

Ds Molecular States via QCDSR Comparison with their Molecular Thresholds The central value of the 𝐷 𝑠 𝐷 𝑠 ∗ < 𝐸 𝑡ℎ𝑟𝑒 [ 𝐷 𝑠 𝐷 𝑠 ∗ ] (4.08 GeV). Ds and Ds* form a bound state. The center value of the 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ > 𝐸 𝑡ℎ𝑟𝑒 [ 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ ] (4.22 GeV). 𝐷 𝑠 ∗ and 𝐷 𝑠 ∗ form a resonance. The central value of the 𝐷 𝑠 𝐷 ∗ < 𝐸 𝑡ℎ𝑟𝑒 [ 𝐷 𝑠 𝐷 ∗ ] (3.98 GeV). 𝐷 𝑠 and 𝐷 ∗ form a bound state. The center value of the 𝐷 𝑠 ∗ 𝐷 ∗ > 𝐸 𝑡ℎ𝑟𝑒 [ 𝐷 𝑠 ∗ 𝐷 ∗ ] (4.12 GeV). 𝐷 𝑠 ∗ and 𝐷 ∗ form a resonance.

Ds Molecular States via QCDSR Decay Modes of Hidden Charm and Hidden Strange Molecular States Possible decay modes for 𝐷 𝑠 𝐷 𝑠 ∗ bound state: Possible decay modes for 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ resonance:

Ds Molecular States via QCDSR Decay Modes of Hidden Charm and Open Strange Molecular States Possible decay modes for 𝐷 𝑠 𝐷 ∗ bound state: Possible decay modes for 𝐷 𝑠 ∗ 𝐷 ∗ resonance:

Summary of Ds Molecular States Four Ds molecular states, 𝐷 𝑠 𝐷 𝑠 ∗ , 𝐷 𝑠 ∗ 𝐷 𝑠 ∗ , 𝐷 𝑠 𝐷 ∗ , 𝐷 𝑠 𝐷 ∗ , are predicted via QCDSR. The possible decay modes to ascertain these Ds molecular states are suggested. The BESIII and forthcoming BelleII will facilitate searching for such Ds molecular states.

Part II: Oddballs C.-F. Qiao and L. Tang, PRL 113, 221601 (2014) . L. Tang and C.-F. Qiao, arXiv:1509.00305, to appear in NPB.

Background & Motivation Color structure Quark= fundamental representation 3 Gluon= Adjoint representation 8 Observable particles=color singlet 1 Mesons Baryons Glueballs Glueballs are allowed by QCD. No definite observations in the experiment until now. lack knowledge of their production & decay properties mixing with quark states adds difficulty to isolate them.

Background & Motivation Good evidence exists for a scalar glueball ( 0 ++ ) which is mixed with nearby mesons, but a full understanding is still missing. Evidence for tensor (2 ++ ) and pseudoscalar ( 0 − + ) glueballs are weak. The study of the oddballs in experiments is still lacking. Therefore, the glueball has not yet been definitely observed by experiments. V. Crede and C. A. Meyer, Prog.Part.Nucl.Phys. 63 (2009) 74-116, and ref. therein.

Background & Motivation Theoretical Approaches Lattice QCD Flux tube model Constituent Models MIT bag model Coulomb gauge model QCD Sum Rules (QCDSR) V.Mathieu, N.Kochelev&V.Vento, Int.J.Mod.Phys. E18,1(2009)

Background & Motivation Oddballs Oddballs: glueballs with exotic quantum numbers Physics at BESIII, Editors Kuang-Ta Chao & Yifang Wang, Int. JMPA24,1,(2009). Trigluon glueballs V.Mathieu, N.Kochelev&V.Vento, Int.J.Mod.Phys. E18,1(2009). Trigluon glueballs: 𝐶=+ 𝑜𝑟 𝐶=−; Two-gluon glueballs: 𝐶=+. Proofs can be found in 《粒子物理导论》written by 杜东生 杨茂志 Exotic quantum numbers Do not mix with

Oddballs in QCDSR Interpolating currents of 0 −− oddballs Constraints: quantum number, gauge invariance, Lorentz invariance and SUc(3) symmetry where 𝑔 𝛼𝛽 𝑡 = 𝑔 𝛼𝛽 − 𝜕 𝛼 𝜕 𝛽 𝜕 2 , 𝐺 𝜇𝜈 𝑎 = 1 2 𝜖 𝜇𝜈𝜅𝜏 𝐺 𝜅𝜏 𝑎

Oddballs in QCDSR Interpolating currents of 0 +− oddballs

Oddballs in QCDSR Interpolating currents of 2 +− oddballs The two-point correlation function

Oddballs in QCDSR Typical Feynman diagrams of trigluon glueballs Fig-1

Oddballs in QCDSR The QCD side of the correlation function The phenomenological side of the correlation function The dispersion relation

Oddballs in QCDSR The main function The Borel transformation The quark-hadron duality approximation

Oddballs in QCDSR The moments The mass function Ratio to constrain 𝜏 & 𝑠 0 by the pole contribution (PC)

Oddballs in QCDSR Ratio to constrain 𝜏 & 𝑠 0 by convergence of the OPE Input parameters

Oddballs in QCDSR 0 −− -Current A 0 −− -Current B 0 −− -Current A

Oddballs in QCDSR 0 −− -Current D 0 −− -Current C 0 −− -Current C

Oddballs in QCDSR 0 +− -Current A 2 +− -Current B 2 +− -Current B

Oddballs in QCDSR 2 +− -Current C 2 +− -Current D 2 +− -Current C

Oddballs in QCDSR Comparison with other methods, in unit of GeV. [1] N.Isgur and J.E.Paton, PRD 31, 2910 (1985). [2] E.Gregory, et al., JHEP1210, 170 (2012). [3] C.J.Morningstar and M.J.Peardon,PRD60, 034509 (1999). [4] Y.Chen et al.,PRD73, 014516 (2006). [5] K.Ishikawa, et al., PLB120, 387 (1983). [6] L. Bellantuono, et al., JHEP 1510 (2015) 137. [7] Y.-D Chen and Mei Huang, arXiv:1511.07018.

Oddballs in QCDSR Proposed production channels of 0 −− oddball (Taking the lighter 0 −− as an example) Proposed decay channels of 0 −− oddball

Oddballs in QCDSR Proposed production channels of 0 +− and 2 +− oddballs Proposed decay channels of 0 +− and 2 +− oddballs

Summary of Oddballs Four oddballs are predicted via QCDSR. The possible production & decay modes to ascertain these oddballs are suggested. These decay modes are expected to be measured in BESIII, BELLEII, Super-B, PANDA, and LHCb experiments.

谢谢大家！