A composite model for exotic hadrons YongLiang Ma

A composite model for exotic hadrons Yong-Liang Ma Department of Physics, Nagoya University. Talk given @ Crossover Workshop, Jul. 12 – Jul. 13, 2012, Nagoya

Outline I. Introduction II. Field theory foundations of a composite model III. Molecular structures of Ds 0*(2317) and Ds 1(2460) IV. Hidden charm molecular states V. Final remarks 2012/7/12 Composite model @ Crossover 2012 2

I. Introduction Ø Charm physics has played important roles in particle physics and the spectroscopy of charmed mesons has been well predicted in the constituent quark models. Ø But this situation changed since 2003 due to the observation of some ``exotic" states. Ø These states have properties do not consistent with the constituent quark model predictions for mesons made of a quark and an antiquark. Ø Revealing the structures of these states and understanding their decay and production properties are interesting and important problems. Ø In the literature, some of these exotic states have been interpreted as molecules, i. e. , deuteron-like bound states of colorless objects. Ø The purpose of this talk: Explain a molecular model based on the compositeness condition. 2012/7/12 Composite model @ Crossover 2012 3

New charm-strange states. 2012/7/12 A. Valcarce @ Charm 2010 Composite model @ Crossover 2012 4

Hidden charm spectroscopy 2012/7/12 M. Nielsen @ Charm 2010 Composite model @ Crossover 2012 5

Some of them have properties do not fit into quark model calculations Exotic states Possible interpretation: Hadronic Molecule 2012/7/12 Composite model @ Crossover 2012 6

Molecular and tetraquark interpretations differ by the way quarks are organized in the state 2012/7/12 Composite model @ Crossover 2012 7

Field theory foundation of a composite model Ø In quantum field theory we regard a particle as a composite one provided that it is not included in the original Lagrangian. Ø Salam's criterion: The wave function renormalization constant Z 3 for boson (or Z 2 for Fermion) should be equal to zero for a composite particle. A. Salam, Nuovo Cim. 25: 224 -227, 1962; Phys. Rev. 130: 1287, 1963. Ø In the limit of the vanishing of the wave function renormalization constant associated with φ, predictions of theory coincide with those of a theory in whose Lagrangian φ does not appear explicitly and in which the particles associated with φ emerge as bound state. 2012/7/12 Composite model @ Crossover 2012 8

Consider Yukawa interaction and four-Fermion interaction: D. Lurié and A. Macfarlane, Phys. Rev. 136 : B 816, 1964. G 0 : bare coupling constant g 0 : bare coupling constant Yukawa Four-Fermion 2012/7/12 Composite model @ Crossover 2012 9

Yukawa interaction: Fermion-fermion scattering amplitude Dressed Boson propagator Momentum transferred to the Boson propagator Bare mass Physical Fermion mass 2012/7/12 Composite model @ Crossover 2012 10

The residual of the μ 2 pole gives the φ field wave function renormalization constant 2012/7/12 Composite model @ Crossover 2012 11

Define the physical coupling constant: Four Fermion interaction: 2012/7/12 Composite model @ Crossover 2012 12

The condition for: 2012/7/12 Composite model @ Crossover 2012 13

Ø This condition can be proved to all orders of perturbation theory. Ø The method of the derivation is the comparison of the integral equations for the basic Green's functions in the two theories. Ø The boson as a bound state can not arise as external line. Since each external line contributes a factor 2012/7/12 Composite model @ Crossover 2012 14

Ø Write down the effective Lagrangian for the exotic state and its ocnstituents. g Ø Determine the couping constant g using the compositeness conditoin = g^2 Π(q^2) = 1 Ø Calculate the decay and production processes using the determined coupling constant g 2012/7/12 Composite model @ Crossover 2012 15

III. Molecular structures of Ds 0*(2317) and Ds 1(2460) 2012/7/12 Composite model @ Crossover 2012 16

Ø Their spectrum do not fit into potential model and other theoretical approach. 2012/7/12 Composite model @ Crossover 2012 17

Ø Quark model calculation and heavy quark symmetry: j=3/2 j=1/2 Ds 1(2536), Ds. J(2573). Narrow, agree with experiments. missing! Broad, decay into DK and D*K. Ø Observation: Narrow! Isospin-violating decay channel! It’s difficult o identify Ds 0*(2317) and Ds 1(2460) as P-wave quarkantiqiuark states. They are maybe exotic states: The proximity of the DK (D*K) threshold to Ds 0*(2317)(Ds 1(2460)) masses favor a molecular state 2012/7/12 Composite model @ Crossover 2012 18

The Molecular structures of Ds 0*(2317) and Ds 1(2460) A. Faessler, et al. , Phys. Rev. D 76, 014005 (2007), 76, 114008 (2007). Effective Lagrangian 2012/7/12 Composite model @ Crossover 2012 19

Compositeness condition: 2012/7/12 Composite model @ Crossover 2012 20

Strong decay Ds 0* 2012/7/12 D s π0 Composite model @ Crossover 2012 21

Strong decay Ds 1 2012/7/12 Ds * π 0 Composite model @ Crossover 2012 22

Ds 0*→Ds*γ 2012/7/12 Ds 1 →Dsγ Composite model @ Crossover 2012 23

Numerical results for Ds 0* → Dsπ0 at Λ=1. 0 – 2. 0 Ge. V 2012/7/12 Composite model @ Crossover 2012 24

Numerical results for Ds 1 → Ds*π0 at Λ=1. 0 – 2. 0 Ge. V 2012/7/12 Composite model @ Crossover 2012 25

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IV. Hidden charm molecular states ü There is J/ψ or ψ(2 S) in their decay products ➔ they have a pair c c as their quark components ü Their masses do not fit into the quark model predictions for charmonium states. ü Absence of open charm production in their decays ➔ inconsistent with charmonium interpretation. ü Candidates for exotic (not quark-antiquark) states. Some of them have been interpreted as molecular states. 2012/7/12 Composite model @ Crossover 2012 28

X(3872) First observed by the Belle Collaboration: S. K. Choi et al. [Belle Collaboration], Phys. Rev. Lett. 91, 262001 (2003). Confirmed by CDF, D 0 and Ba. Bar. Quantum numbers of X(3872): JP =1++ , 2 - + 2012/7/12 Composite model @ Crossover 2012 29

Because of the mass and presence of c c pair in the decay products one might expect the charmonium nature of X(3872). Measurement of the invariant mass distribution of π+ πindicates that the decay X → J/ψπ+ π- occurs via intermediate process X → J/ψρ0 decay. Since charmonium decay to J/ψρ0 violates isospin symmetry, this observation is a strong argument against charmonium nature of X(3872) state. A Possible Molecular state 2012/7/12 Composite model @ Crossover 2012 30

M. Harada and Y. M. PTP 126 (2011)91. In isospin eigenstate 2012/7/12 Composite model @ Crossover 2012 31

JPC = 2 -+ 2012/7/12 [7] K. Abe et al. (Belle Collaboration), hep-ex/0505037. [8] B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 102 (2009), 132001. Composite model @ Crossover 2012 32

Our result of the small mixing angle implies that the isospin singlet component is dominant. Wave function: 2012/7/12 Composite model @ Crossover 2012 33

Other exotic hadrons studied using this model Ø |X(4350) 〉 = |Ds 0*+ Ds*- 〉+ |Ds 0*- Ds*+ 〉 Ø |Y(3940) 〉 = |D*+ D*- 〉+ |D 0*0 D*0 〉 Ø |X(4350) 〉 = |Ds*+ Ds*- 〉+ |Ds 0*- Ds*+ 〉 Ø Ø Ø 2012/7/12 Composite model @ Crossover 2012 34

V. Conclusion The composite model was applied in the study of some exotic hadrons by regarding them as hadronic molecular states. Advantages: The model is clear and straightforward. Disadvantages: The mediate force is hidden, Although the model is crude, we hope it can give some insight into the structures of some exotic resonances. . To confirm the structure of these exotic mesons, further theoretical an experimental studies are necessary. Thank you ! 2012/7/12 Composite model @ Crossover 2012 35

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