Peng Guo. Physics Department & NTC Indiana University - Bloomington, U.S.A.

Transcription

1 Rescattering effect in decay Peng Guo Physics Department & NTC Indiana University - Bloomington, U.S.A. Collaborators: A.P. Szczepaniak, H. Matevosyan, R. Mitchell and M. Shepherd JLab, Jan.5, 00

2 Outline I. Charmonium Spectroscopy: microscopic approach Hybrid Spectrum in Coulomb Gauge QCD Charmonium in Quark matter II. Charmonium Spectroscopy data analysis How to improve isobar model? Unitarity Analyticity Preliminary result: rho-pi puzzle, effect of inelastic channels Conclusion

3 I. Charmonium Spectroscopy: microscopic approach

4 Charmonium Spectroscopy P = (") L,C = (") L S J PC Missing states from naive quark model: Exotics 0 "",0 ", ", ",!? Hall D at JLab

5 Charmonium Spectroscopy from Lattice QCD q.m. S-waves q.m. D-waves q.m. G-waves this work expt. (PDG) hyb 4 S hyb? D S S ψ(445) 4400±60 48±77 Y(460) ψ(460) ψ(4040) mass / MeV D S D S 864±9 ψ(770) 746±8 ψ(686) exotic exotic S S 06± J/ψ J. Dudek, R.G. Edwards, N. Mathur, D.G. Richards FIG. : spectrum. Black lines are experimental states at various levels of confirmation, blue bars are lattice states with quark model assignments as described in the text. Also shown are quark model predictions and the hybrid prediction of the Coulomb gauge model. Naive quark potential model V (r) = " 4 # s r kr V LS V SS V T T.Barnes, S. Godfrey, E.S. Swanson

6 Charmonium Spectroscopy in Coulomb Gauge QCD J QQ J g

7 J = J g L QQ S QQ J. Dudek, R.G. Edwards, N. Mathur, D.G. Richards S-Wave: Four degenerate states J " # 4 for spin-independent interaction S QQ = 0 S QQ = q.m. S-waves q.m. D-waves q.m. G-waves this work expt. (PDG) J g P g C g : " J PC : "" = 0 " = " = " J g P g C g : "" J PC : " = 0 = = exotic exotic P.Guo, A.P.Szczepaniak, G.Galata, A.Vassallo and E.Santopinto Phys. Rev. D 78, (008), Phys. Rev. D 77, (008)

8 Charmonium at Finite density! "#$%!! Melting Charmonium in quark matter

9 II. Charmonium data analysis(current work)

10 Isobar Model: quasi two-body decays

11 Isobar Model: quasi two-body decays = () () ()

12 Isobar Model: quasi two-body decays = () () () How to extract coupling to resonances How one establishes new resonances Answer? It s important to construct amplitudes which contain all the known physics

13 Isobar Model: quasi two-body decays = () () () How to extract coupling to resonances How one establishes new resonances Answer? It s important to construct amplitudes which contain all the known physics

14 Isobar Model: quasi two-body decays = () () () How to extract coupling to resonances How one establishes new resonances Answer? It s important to construct amplitudes which contain all the known physics

15 Isobar Model: quasi two-body decays = () () () How to extract coupling to resonances How one establishes new resonances Answer? It s important to construct amplitudes which contain all the known physics

16 Current analysis: J/Psi -> pion rho-pi puzzle Experiment PQCD vs What do we learn from Dalitz plot?

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18 Dispersion Relation s s th Subenergy Unitarity Disc () T = ( ) ( ) ( ) (I) Solve double integral equations (II) Parametrize cuts which are associated with rescattering

19 (I) Solving double integral equations Single integral equation: suitable for data fitting ( )* '!" # $%!"& # R.Pasquier & J.Y.Pasquier Phys.Rev.70:94,968!" # $%!"& # * * $%*"& # '( )#

20 J/ " #" $%%&' " #"( J/ " #" $%%&' " #"( Breit-Wigner Rescattering Breit-Wigner Rescattering Re[T! (s,s ij )] 0 Im[T! (s,s ij )] s / ij (GeV) s / ij (GeV) "#S)$ %$ "&&'( $ %$) 0. "S)# $# "%%&' # $#( 0.08 Breit-Wigner Rescattering 0.5 Breit-Wigner Rescattering 0.04 Re[T! (s,s ij )] 0 Im[T! (s,s ij )] s / ij (GeV) s / ij (GeV)

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22 Short distance Long distance

23 Summary Short distance Long distance Long distance final states rescattering cannot be the cause of rho-pi puzzle.

24 Does rescattering effect help explaining the Dalitz plot?. Improve the single Breit-Wigner parametrization.. Not quite the solution. Hist 800! BES Collaboration Phys.Rev.D70:0005, FIG.. The Dalitz plot for J/ 0.

25 (II) Parametrize cuts which are associated with rescattering Inelastic channel Coupled channels: Phase shift Inelasticity Disc = Hist!

26 () (D) () (A) (C) () (B) K K Hist!0 800 K K

27 Hist !0 Hist ! Hist!

28 Summary Long distance final states rescattering cannot be the cause of rho-pi puzzle. Inelastic KK channel contribution is important at.6 GeV region in J/Psi decay channel.