Hadronic molecules with heavy quarks

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1 Hadronic molecules with heavy quarks Feng-Kun Guo Institute of Theoretical Physics, Chinese Academy of Sciences ICTS, USTC, 17th Nov Feng-Kun Guo (ITP) Hadronic molecules / 30

2 Elementary particles in the Standard Model Feng-Kun Guo (ITP) Hadronic molecules / 30

3 Origin of the mass of the visible universe: strong interaction! M diamond M Catom M Catom 6 (M proton + M neutron + M electron ) M proton }{{} q 938 MeV σ q m q + (900 MeV) lattice QCD results by the BMW Collaboration Feng-Kun Guo (ITP) Hadronic molecules / 30

4 Origin of the mass of the visible universe: strong interaction! photo taken during Z. Fodor s talk at the MENU2016 Conference, Kyoto Feng-Kun Guo (ITP) Hadronic molecules / 30

5 Low-energy QCD is difficult At low energies, nonperturbative lattice QCD, effective field theory (EFT), models color confinement quarks and gluons are confined in color-neutral hadrons Feng-Kun Guo (ITP) Hadronic molecules / 30

Ordinary and exotic hadrons In quark model notation

multiquark states, hybrids and glueballs Hadronic

of asymptotic hadrons (distance hadron size),

the same quantum numbers, always mix source of

6 Ordinary and exotic hadrons In quark model notation + Ordinary mesons and baryons + Exotic hadrons: multiquark states, hybrids and glueballs Hadronic molecules: extended, loosely bound states composed of asymptotic hadrons (distance hadron size), analogues of deuteron and other light nuclei Once the same quantum numbers, always mix source of difficulties/confusions Feng-Kun Guo (ITP) Hadronic molecules / 30

7 Ordinary and exotic hadrons In quark model notation + Ordinary mesons and baryons + Exotic hadrons: multiquark states, hybrids and glueballs Hadronic molecules: extended, loosely bound states composed of asymptotic hadrons (distance hadron size), analogues of deuteron and other light nuclei Once the same quantum numbers, always mix source of difficulties/confusions Feng-Kun Guo (ITP) Hadronic molecules / 30

8 Ordinary and exotic hadrons In quark model notation + Ordinary mesons and baryons + Exotic hadrons: multiquark states, hybrids and glueballs Hadronic molecules: extended, loosely bound states composed of asymptotic hadrons (distance hadron size), analogues of deuteron and other light nuclei Once the same quantum numbers, always mix source of difficulties/confusions Feng-Kun Guo (ITP) Hadronic molecules / 30

9 Hadronic molecules (I) Hadronic molecule: dominant component is a composite state of 2 or more hadrons Concept at large distances, so that can be approximated by system of multi-hadrons at low energies Consider a 2-body bound state with a mass M = m 1 + m 2 E B size: R 1 2µEB r hadron Only narrow hadrons can be considered as components of hadronic molecules, Γ h 1/r, r: range of forces Filin et al., PRL105(2010)019101; FKG, Meißner, PRD84(2011) Feng-Kun Guo (ITP) Hadronic molecules / 30

10 Hadronic molecules (II) Why are hadronic molecules interesting? one realization of color-neutral objects, analogue of light nuclei important information for hadron-hadron interaction understanding the XY Z states model-independent statements can be made for S-wave, compositeness (1 Z) related to measurable quantities Weinberg, PR137(1965); Baru et al., PLB586(2004); Hyodo, IJMPA28(2013) ;... see also, e.g., Weinberg s books: QFT Vol.I, Lectures on QM gnr 2 (1 Z) 2π 2µEB µ 2 2π 2µEB µ 2 2(1 Z) a (2 Z) Z, r e 2µE B (1 Z) 2µE B scale separation: EFT can be applied Feng-Kun Guo (ITP) Hadronic molecules / 30

11 Beginning of the story in 2003: discovery of D s0(2317) Charm-strange c s mesons D s0(2317) and D s1 (2460) D s0(2317): 0 + BaBar (2003) M = ( ± 0.6) MeV, Γ < 3.8 MeV The only hadronic decay: D s π M a s s (M e V ) E x p. d a ta G I q u a rk m o d e l T h re s h o ld 1 3 P 0 (2.4 8 ) 1 3 P 1 (2.5 7 ) 1 1 P 1 (2.5 3 ) D s 1 ( ) D * K D s1 (2460): 1 + CLEO (2003) M = ( ± 0.6) MeV, D * s 0 ( ) D K Γ < 3.5 MeV Notable features: masses are much lower than the quark model predictions for c s mesons M Ds1(2460) M D s0 (2317) M D M D + 1 MeV Feng-Kun Guo (ITP) Hadronic molecules / 30

12 Beginning of the story in 2003: discovery of X(3872) X(3872) Belle, PRL91(2003) Discovered in B ± K ± J/ψππ, mass extremely close to the D 0 D 0 threshold M X = ( ± 0.17) MeV M D 0 + M D 0 M X = (0.12 ± 0.19) MeV Γ < 1.2 MeV J P C = 1 ++ Belle, PRD84(2011) LHCb PRL110(2013) S-wave coupling to D D Observed in the D 0 D 0 mode as well BaBar, PRD77(2008) Large coupling to D 0 D 0 : B(X D 0 D 0 ) > 24% PDG2014 Large isospin breaking: B(X ωj/ψ) B(X π + π = 0.8 ± 0.3 J/ψ) Feng-Kun Guo (ITP) Hadronic molecules / 30

Beginning of the story in 2003: discovery of X(3872) X(3872) Belle, PRL91(2003)262001 Discovered in B ± K ± J/ψππ, mass extremely close to the D 0 D 0 threshold M X = (3871.69 ± 0.

13 Beginning of the story in 2003: discovery of X(3872) X(3872) Belle, PRL91(2003) Discovered in B ± K ± J/ψππ, mass extremely close to the D 0 D 0 threshold M X = ( ± 0.17) MeV M D 0 + M D 0 M X = (0.12 ± 0.19) MeV Γ < 1.2 MeV J P C = 1 ++ Belle, PRD84(2011) LHCb PRL110(2013) S-wave coupling to D D Observed in the D 0 D 0 mode as well BaBar, PRD77(2008) Large coupling to D 0 D 0 : B(X D 0 D 0 ) > 24% PDG2014 Large isospin breaking: B(X ωj/ψ) B(X π + π = 0.8 ± 0.3 J/ψ) Feng-Kun Guo (ITP) Hadronic molecules / 30

14 More exotic structures: Z ± c and Z± b with hidden Q Q Z c ±, Z± b : charged structures in heavy quarkonium mass region, Q Q du, Q Qūd Z c (3900), Z c (4020), Z c (4200), Z c (4430),... Z b (10610) and Z b (10650): Belle, arxiv: ; PRL108(2012) observed in Υ(10860) π [π ± Υ(1S, 2S, 3S)/h b (1P, 2P )] also in Υ(10860) π [B ( ) B ] ± Belle, arxiv: ; PRL116(2016) Feng-Kun Guo (ITP) Hadronic molecules / 30

15 More exotic structures: Z ± c and Z± b with hidden Q Q Z c ±, Z± b : charged structures in heavy quarkonium mass region, Q Q du, Q Qūd Z c (3900), Z c (4020), Z c (4200), Z c (4430),... Z b (10610) and Z b (10650): Belle, arxiv: ; PRL108(2012) observed in Υ(10860) π [π ± Υ(1S, 2S, 3S)/h b (1P, 2P )] also in Υ(10860) π [B ( ) B ] ± Belle, arxiv: ; PRL116(2016) Feng-Kun Guo (ITP) Hadronic molecules / 30

16 Z ± c and Z± b with hidden Q Q (II) Z c (3900/3885) ± : structure around 3.9 GeV seen in J/ψπ by BESIII and Belle in Y (4260) J/ψπ + π, BESIII, PRL110(2013)252001; Belle, PRL110(2013) and in D D by BESIII in Y (4260) π ± (D D ) BESIII, PRD92(2015) can be attributed to the same state Aldaladejo et al., PLB755(2016)337 Feng-Kun Guo (ITP) Hadronic molecules / 30

17 Charmonium spectrum Feng-Kun Guo (ITP) Hadronic molecules / 30

18 Charmonium spectrum Feng-Kun Guo (ITP) Hadronic molecules / 30

19 Charmonium spectrum Note: X(3915) is probably just the χ c2 (2P ) with 2 ++ Z.-Y. Zhou et al., PRL115(2015) Feng-Kun Guo (ITP) Hadronic molecules / 30

20 Charmonium spectrum Note: X(3915) is probably just the χ c2 (2P ) with 2 ++ Z.-Y. Zhou et al., PRL115(2015) Feng-Kun Guo (ITP) Hadronic molecules / 30

: free Hamiltonian, V : interaction potential Compositeness: the probability of finding the physical state B in the 2-body continuum q d

21 Compositeness (I) Weinberg, PR137(1965); Baru et al., PLB586(2004);... see also, e.g., Weinberg s books: QFT Vol.I, Lectures on QM Model-independent result for S-wave loosely bound composite states: Consider a system with Hamiltonian H = H 0 + V H 0 : free Hamiltonian, V : interaction potential Compositeness: the probability of finding the physical state B in the 2-body continuum q d 3 q 1 Z = (2π) 3 q B 2 Z = B 0 B 2, 0 (1 Z) 1 Z = 0: pure composite state Z = 1: pure elementary state Feng-Kun Guo (ITP) Hadronic molecules / 30

Compositeness (II) d 3 q Compositeness : 1 Z = (2π) 3 q B 2 Schrödinger equation (H 0 + V ) B = E B B multiplying by q and using H 0 q = q2 2µ q q V B q B = E B + q 2 /(2µ) S-wave, small binding

22 Compositeness (II) d 3 q Compositeness : 1 Z = (2π) 3 q B 2 Schrödinger equation (H 0 + V ) B = E B B multiplying by q and using H 0 q = q2 2µ q q V B q B = E B + q 2 /(2µ) S-wave, small binding energy so that R = 1/ 2µE B r, r: range of forces Compositeness: 1 Z = d 3 q (2π) 3 q V B = g NR [1 + O(r/R)] gnr 2 [ ( r )] [E B + q 2 /(2µ)] O = µ2 g 2 [ ( NR r )] R 2π 1 + O 2µE B R Feng-Kun Guo (ITP) Hadronic molecules / 30

23 Compositeness (III) Coupling constant measures the compositeness for an S-wave bound state with a small binding energy (model-independent) g 2 NR (1 Z) 2π µ 2 2µEB 2π µ 2 2µEB Z can be measured directly from observables, such as scattering length a and effective range r e Weinberg (1965) 2R(1 Z) [ ( r )] a = 1 + O, r e = RZ [ ( r )] 1 + O 2 Z R 1 Z R Example: deuteron as pn bound state. Exp.: E B = 2.2 MeV, a3 S 1 = 5.4 fm a Z=1 = 0 fm, a Z=0 = ( 4.3 ± 1.4) fm Feng-Kun Guo (ITP) Hadronic molecules / 30

Heavy quark spin symmetry Heavy quark spin symmetry (HQSS): define s l J s Q : total angular momentum of the light quark system J: total angular momentum, s Q :

24 Heavy quark spin symmetry Heavy quark spin symmetry (HQSS): define s l J s Q : total angular momentum of the light quark system J: total angular momentum, s Q : heavy quark spin E.g., for D and D : s P l = 1 2 s l is a good quantum number spin multiplet: (D, D ), (η c, J/ψ) Feng-Kun Guo (ITP) Hadronic molecules / 30

25 HQSS for hadronic molecules FKG, C. Hanhart, U.-G. Meißner, PRL102(2009) Interaction between heavy hadron and light hadron is independent of heavy quark spin for m Q D s0(2317): dominantly DK molecule Barnes, Close, Lipkin (2003); van Beveren, Rupp (2003); Kolomeitsev, Lutz (2004); HQSS spin partner: a D K molecule FKG, Shen, Chiang, Ping, Zou (2006); Gamermann et al. (2007);... natural consequence: M Ds1(2460) M D s0 (2317) M D M D For hadronic molecules of Q Q+light hadron exchange at least two gluons, LO: chromo-electric spin multiplet with approximately the same splitting as that for Q Q Example: if Y (4660) is a ψ f 0 (980) state, then there would be an η cf 0 (980) state the same for hadro-quarkonium Cleven et al., PRD92(2015) Feng-Kun Guo (ITP) Hadronic molecules / 30

26 HQSS for XY Z (I) Consider S-wave interaction between a pair of s P l = 1 2 (anti-)heavy mesons: 0 ++ : D D, D D 1 + : 1 2 ( D D + D D), D D 1 ++ : 1 2 ( D D D D) 2 ++ : D D Heavy quark spin irrelevant interaction matrix elements: s l1, s l2, s L Ĥ s l1, s l2, s L For each isospin, 2 independent terms 1 2, 1 2, 0 Ĥ 1 2, 1 1 2, 0, 2, 1 2, 1 Ĥ 1 2, 1 2, 1 6 pairs grouped in 2 multiplets with s L = 0 and 1, respectively Feng-Kun Guo (ITP) Hadronic molecules / 30

27 HQSS for XY Z (I) Consider S-wave interaction between a pair of s P l = 1 2 (anti-)heavy mesons: 0 ++ : D D, D D 1 + : 1 2 ( D D + D D), D D 1 ++ : 1 2 ( D D D D) 2 ++ : D D Heavy quark spin irrelevant interaction matrix elements: s l1, s l2, s L Ĥ s l1, s l2, s L For each isospin, 2 independent terms 1 2, 1 2, 0 Ĥ 1 2, 1 1 2, 0, 2, 1 2, 1 Ĥ 1 2, 1 2, 1 6 pairs grouped in 2 multiplets with s L = 0 and 1, respectively Feng-Kun Guo (ITP) Hadronic molecules / 30

28 HQSS for XY Z (II) In the limit m c, D and D degenerated, convenient to use the basis of states: s P C L sp C c c S-wave: s P L C, sp c c C multiplet with s L = 0: multiplet with s L = 1: = 0 + or L 0 + c c = 0 ++, 0 + L 1 c c = L 0 + c c = 1 +, 1 L 1 c c = if X(3872) is a 1 ++ D D molecule, then its s L = 1 Multiplets in strict heavy quark limit: X(3872) has three partners with 0 ++, 2 ++ and 1 + Voloshin, PLB604(2004)69 Hidalgo-Duque et al., PLB727(2013)432; Baru et al., arxiv: might be 6 molecules: Z b, Z b and W b0, W b0, W b1 and W b2 (for I = 1) Bondar et al., PRD84(2011)054010; Voloshin, PRD84(2011)031502; Mehen, Powell, PRD84(2011) Feng-Kun Guo (ITP) Hadronic molecules / 30

29 HQSS for XY Z (II) In the limit m c, D and D degenerated, convenient to use the basis of states: s P C L sp C c c S-wave: s P L C, sp c c C multiplet with s L = 0: multiplet with s L = 1: = 0 + or L 0 + c c = 0 ++, 0 + L 1 c c = L 0 + c c = 1 +, 1 L 1 c c = if X(3872) is a 1 ++ D D molecule, then its s L = 1 Multiplets in strict heavy quark limit: X(3872) has three partners with 0 ++, 2 ++ and 1 + Voloshin, PLB604(2004)69 Hidalgo-Duque et al., PLB727(2013)432; Baru et al., arxiv: might be 6 molecules: Z b, Z b and W b0, W b0, W b1 and W b2 (for I = 1) Bondar et al., PRD84(2011)054010; Voloshin, PRD84(2011)031502; Mehen, Powell, PRD84(2011) Feng-Kun Guo (ITP) Hadronic molecules / 30

30 HQSS for XY Z (III) Calculations using physical D and D masses in nonrelativistic EFT the effective Lagrangian for the LO interaction between spin multiplets, L 4H = +C (τ) A [ ] [ H(Q) a H a (Q) γ µ Tr C A Tr [ ] [ Tr H(Q) a τ ab H (Q) b γ µ Tr [ ] +C B Tr H(Q) a H a (Q) γ µ γ 5 Tr +C (τ) B H ( Q) b AlFiky et al., PLB640(2006) H ( Q) b γ µ] H ( Q) c [ H ( Q) b [ [ ] Tr H(Q) a τ ab H (Q) b γ µ γ 5 Tr τ : Pauli matrices in isospin space; Isospin I = 0 or 1 4 independent terms: C 0A, C 0B ; C 1A, C 1B : linear combinations of C (τ) A,B τ cd H( Q) d γ µ] ] H ( Q) b γ µ γ 5 H ( Q) c ] τ cd H( Q) d γ µ γ 5 H a (Q) : D, D ; H ( Q) a C 0φ = C φ + 3C (τ) φ, C 1φ = C φ C (τ) φ, for φ = A, B : D, D Feng-Kun Guo (ITP) Hadronic molecules / 30

31 HQSS for XY Z (IV) Some channels have the same linear combination of contact terms V (D D, 1 ++ ) = V (D D, 2 ++ ) = C IA + C IB V (D D, 1 + ) = V (D D, 1 + ) = C IA C IB D D does not have the same: V (D D, 0 ++ ) = C IA This would suggest spin multiplets. Good candidates: X(3872) and X 2 (4013) (not observed yet!); Z c (3900) and Z c (4020) Nieves, Valderrama, PRD86(2012)056004;... M X2(4013) M X(3872) M Zc(4020) M Zc(3900) M D M D Z b (10610) and Z b (10650) : Bondar et al., PRD84(2011)054010;... M Zb (10650) M Zb (10610) M B M B Feng-Kun Guo (ITP) Hadronic molecules / 30

32 HQSS for XY Z (IV) Some channels have the same linear combination of contact terms V (D D, 1 ++ ) = V (D D, 2 ++ ) = C IA + C IB V (D D, 1 + ) = V (D D, 1 + ) = C IA C IB D D does not have the same: V (D D, 0 ++ ) = C IA This would suggest spin multiplets. Good candidates: X(3872) and X 2 (4013) (not observed yet!); Z c (3900) and Z c (4020) Nieves, Valderrama, PRD86(2012)056004;... M X2(4013) M X(3872) M Zc(4020) M Zc(3900) M D M D Z b (10610) and Z b (10650) : Bondar et al., PRD84(2011)054010;... M Zb (10650) M Zb (10610) M B M B Feng-Kun Guo (ITP) Hadronic molecules / 30

33 Inputs and predictions (I) Solve Lippmann Schwinger equation regularized with a Gaussian form factor, bound states appear as poles in the first Riemann sheet below threshold Inputs: Mass of X(3872) C 0A + C 0B Mass of Z b (10610) C 1A C 1B Predicted many partners of X(3872) and Z b (10610) Partners of X(3872) [1 ++ ]: FKG et al., PRD88(2013) Here V (D D ) = V ( BB [ ( )] ) 1 + O ΛQCD m c,... assumed Feng-Kun Guo (ITP) Hadronic molecules / 30

34 Inputs and predictions (II) Partners of Z b (10610) [1 + ]: Two virtual states in charm sector, could correspond to Z c (3900) and Z c (4020) So far, the assignments of the predicted states to the observed ones only based on masses, decays and productions Feng-Kun Guo (ITP) Hadronic molecules / 30

35 Inputs and predictions (II) Partners of Z b (10610) [1 + ]: Two virtual states in charm sector, could correspond to Z c (3900) and Z c (4020) So far, the assignments of the predicted states to the observed ones only based on masses, decays and productions Feng-Kun Guo (ITP) Hadronic molecules / 30

36 What can we say about decays and productions(i) Essential point of in the spirit of effective field theory: scale separation to include all relevant d.o.f. at the given scale to study near-threshold structures, one has to take into account the corresponding channel, unless the coupling is weak, no matter what structure was used as the starting point for X(3872): has to consider D D Hadronic molecular structure: a long-distance concept not all processes are sensitive to it! Feng-Kun Guo (ITP) Hadronic molecules / 30

37 What can we say about the decays and productions (II) For processes dominated by long-distance physics: calculable with controlled uncertainties using low-energy EFT Examples: X(3872) D 0 D0 π 0, X(3872) D 0 D0 γ Voloshin (2004);... For processes dominated by short-distance physics (unknown in low-energy EFT): order-of-magnitude estimate at best Examples: X(3872) e + e estimate: Γ(X e + e ) 0.03 ev BESIII: Γ(X e + e ) exp < 4.3 ev Denig, FKG, Hanhart, Nefediev, PLB736(2014)221 BESIII: PLB749(2015)414 production of X(3872) in B decays, at hadron colliders with large p T X(3872) J/ψγ Feng-Kun Guo (ITP) Hadronic molecules / 30

38 What can we say about the decays and productions (II) For processes dominated by long-distance physics: calculable with controlled uncertainties using low-energy EFT Examples: X(3872) D 0 D0 π 0, X(3872) D 0 D0 γ Voloshin (2004);... For processes dominated by short-distance physics (unknown in low-energy EFT): order-of-magnitude estimate at best Examples: X(3872) e + e estimate: Γ(X e + e ) 0.03 ev BESIII: Γ(X e + e ) exp < 4.3 ev Denig, FKG, Hanhart, Nefediev, PLB736(2014)221 BESIII: PLB749(2015)414 production of X(3872) in B decays, at hadron colliders with large p T X(3872) J/ψγ Feng-Kun Guo (ITP) Hadronic molecules / 30

39 X(3872), Y (4260) and Z c (3900) (I) Suppose that the X(3872), Y (4260) and Z c (3900) are hadronic molecules: X(3872): J P C = 1 ++, D D Törquist, PLB590(2004)209;... Y (4260): J P C = 1, D 1 (2420) D [two D 1 s, should be the narrow one] Wang, Hanhart, Zhao, PRL111(2013) Z(3900): J P C = 1 +, D D Wang et al. (2013); FKG et al., PRD88(2013)054007;... First lattice result for the X(3872) (L 2 fm), no conclusion on its nature was made, but they gave Prelovsek, Leskovec, PRL111(2013) a D D = ( 1.7 ± 0.4) fm, r D D = (0.5 ± 0.1) fm these values correspond to 1 Z 0.7 lattice evidence for X(3872) being dominantly a D D hadronic molecule So far negative lattice results for Z c (3900) Chen et al., PRD89(2014)094506; Prelovsek et al., PRD91(2015) but Albaladejo et al., EPJC76(2016)576 Feng-Kun Guo (ITP) Hadronic molecules / 30

40 X(3872), Y (4260) and Z c (3900) (I) Suppose that the X(3872), Y (4260) and Z c (3900) are hadronic molecules: X(3872): J P C = 1 ++, D D Törquist, PLB590(2004)209;... Y (4260): J P C = 1, D 1 (2420) D [two D 1 s, should be the narrow one] Wang, Hanhart, Zhao, PRL111(2013) Z(3900): J P C = 1 +, D D Wang et al. (2013); FKG et al., PRD88(2013)054007;... First lattice result for the X(3872) (L 2 fm), no conclusion on its nature was made, but they gave Prelovsek, Leskovec, PRL111(2013) a D D = ( 1.7 ± 0.4) fm, r D D = (0.5 ± 0.1) fm these values correspond to 1 Z 0.7 lattice evidence for X(3872) being dominantly a D D hadronic molecule So far negative lattice results for Z c (3900) Chen et al., PRD89(2014)094506; Prelovsek et al., PRD91(2015) but Albaladejo et al., EPJC76(2016)576 Feng-Kun Guo (ITP) Hadronic molecules / 30

41 X(3872), Y (4260) and Z c (3900) (II) Wang et al., PRL111(2013)132003; Cleven et al., PRD90(2014)074039; FKG et al., PLB725(2013)127 Production of X(3872) and Z c (3900) in Y (4260) decays large couplings Loops are enhanced when the binding energies are small: ( ) ( ) v 5 1 A O (v 2 ) 3 V D1D (q π/γ) = O V D1D v (q π/γ) S-wave vertices for couplings to Y (4260), X(3872) and Z c (3900) intermediate mesons are nonrelativistic. v 0.06: velocity power counting: three-momentum O (v), energy O ( v 2) loop integral measure : v 5, propagator : Feng-Kun Guo (ITP) Hadronic molecules / 30 1 v 2

( ) v 5 1 A O (v 2 ) 3 V D1D (q π/γ) = O V D1D v (q π/γ) S-wave vertices for couplings to Y (4260), X(3872) and Z c (3900) intermediate mesons are

42 X(3872), Y (4260) and Z c (3900) (II) Wang et al., PRL111(2013)132003; Cleven et al., PRD90(2014)074039; FKG et al., PLB725(2013)127 Production of X(3872) and Z c (3900) in Y (4260) decays large couplings Loops are enhanced when the binding energies are small: ( ) ( ) v 5 1 A O (v 2 ) 3 V D1D (q π/γ) = O V D1D v (q π/γ) S-wave vertices for couplings to Y (4260), X(3872) and Z c (3900) intermediate mesons are nonrelativistic. v 0.06: velocity power counting: three-momentum O (v), energy O ( v 2) loop integral measure : v 5, propagator : Feng-Kun Guo (ITP) Hadronic molecules / 30 1 v 2

43 X(3872), Y (4260) and Z c (3900) (III) If these three states are hadronic molecules, then the Z c (3900) can be easily produced in the Y (4260) decays, in line with the BESIII and Belle observations Prediction: FKG et al., PLB725(2013)127 the X(3872) can be easily produced in Y (4260) γx(3872) BESIII observation of e + e γx(3872) γj/ψπ + π at s = 4.26 GeV: 70 Y 4260 ΓX 3872 kev X MeV BESIII, PRL112(2014) Feng-Kun Guo (ITP) Hadronic molecules / 30

44 Decays: X(3872) ψγ FKG, Hanhart, Kalashnikova, Meißner, Nefediev, PLB742(2015)394 B(X(3872) ψ γ) The ratio = 2.46 ± 0.64 ± 0.29 B(X(3872) J/ψγ) is insensitive to the molecular component of the X(3872): LHCb, NPB886(2014)665 loops are sensitive to unknown couplings g ψdd /g ψ DD loops are divergent, needs a counterterm (short-distance physics)! see also Mehen, Springer, PRD83(2011)094009; Molnar et al., arxiv: Feng-Kun Guo (ITP) Hadronic molecules / 30

45 Summary hadronic molecule structure should be detected in processes sensitive to long-distance physics heavy quark symmetry can provide interesting predictions/insights to hadronic molecules should go beyond the mass spectrum because important structure information is contained in the coupling decays and productions Thank you! Feng-Kun Guo (ITP) Hadronic molecules / 30

should go beyond the mass spectrum because important structure information is contained in the

46 Summary hadronic molecule structure should be detected in processes sensitive to long-distance physics heavy quark symmetry can provide interesting predictions/insights to hadronic molecules should go beyond the mass spectrum because important structure information is contained in the coupling decays and productions Thank you! Feng-Kun Guo (ITP) Hadronic molecules / 30

47 Backup slides Feng-Kun Guo (ITP) Hadronic molecules / 6

48 HQSS hadro-charmonia If the Y (4260) and Y (4360) are mixed hadro-charmonia with h c and ψ core, implications of HQSS for hadro-charmonia: Li, Voloshin, MPLA29(2014) Cleven et al., PRD92(2015) Feng-Kun Guo (ITP) Hadronic molecules / 6

Bound state and virtual state (I) Suppose the scattering length is very large, the S- wave scattering amplitude f 0 (k) = 1 k cot δ 0 (k) ik 1 1/a ik bound state pole: 1/a = κ 2µb virtual state pole:

49 Bound state and virtual state (I) Suppose the scattering length is very large, the S- wave scattering amplitude f 0 (k) = 1 k cot δ 0 (k) ik 1 1/a ik bound state pole: 1/a = κ 2µb virtual state pole: 1/a = κ If the same binding energy, cannot be distinguished above threshold (k is real): f 0 (k) 2 1 κ 2 + k 2 Events / 4MeV virtual state bound state m D 0 D *- [GeV] Feng-Kun Guo (ITP) Hadronic molecules / 6

50 Bound state and virtual state (II) Different line shapes below threshold in inelastic channel GZ E GeV E MeV A bound state and virtual state with a 5 MeV binding energy, a width to the inelastic channel is allowed. Cleven et al., EPJA47(2011)120 Feng-Kun Guo (ITP) Hadronic molecules / 6

51 Decays: X(3872) D 0 D 0 π 0 A long-distance process, thus can be studied in nonrelativistic EFT Already studied by many authors Our new insight: Voloshin (2004); Fleming et al (2007); Braaten, Lu (2007); Hanhart et al (2007);... If there is a near-threshold D D hadronic molecule a large impact Problem: one unknown contact term C 0A FKG et al., EPJC74(2014)2885 X 3872 D 0 D 0 Π 0 kev GeV grey band: tree-level result (consistent with Fleming et al., PRD76(2007)) vertical line: a D D bound state at threshold C 0 A fm 2 Feng-Kun Guo (ITP) Hadronic molecules / 6

52 Phenomenology: X 2 (4013) D D/D D X 2 (4013): Albaladejo, FKG, Hidalgo-Duque, Nieves, Pavon Valderrama, EPJC75(2015) , above D D, D D thresholds dominant decay modes: D D and D D + c.c. in D-wave X(4013) D + π 0 D + X(4013) D 0 π D + D D D 0 D Order-of-magnitude estimate: Γ(X 2 ) a few MeV tens of MeV [MeV] without pion-exchange FF with pion-exchange FF Λ = 0.5 GeV Λ = 1 GeV Λ = 0.5 GeV Λ = 1 GeV Γ(D + D ) Γ(D 0 D0 ) Fresh calculation with nonperturbative pion: Γ(X 2 ) 50 MeV Baru et al., arxiv: Feng-Kun Guo (ITP) Hadronic molecules / 6

Decays and productions of hadronic molecules

Decays and productions of hadronic molecules Feng-Kun Guo Institute of Theoretical Physics, Chinese Academy of Sciences The 12th International Workshop on Heavy Quarkonium, PKU, Nov. 06 10, 2017 For more