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Resonances and thresholds in charmonium spectra

Resonances and thresholds in charmonium spectra. Yu.S.Kalashnikova, ITEP. Charmonium. Theory: Godfrey-Isgur. M, MeV. ?. 4250. 4000. ?. 3750. DD. 3500. 3250. 3000. 0 -+. 1 --. 0 ++. 1 ++. 2 ++. 1 +-. 2 --. 3 --. 2 -+. 1++(3872). 1--(4260). JPC?(4430). I=1 !?.

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Resonances and thresholds in charmonium spectra

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  1. Resonances and thresholds in charmonium spectra Yu.S.Kalashnikova, ITEP

  2. Charmonium Yu.S.Kalashnikova, ITEP

  3. Theory: Godfrey-Isgur M, MeV ? 4250 4000 ? 3750 DD 3500 3250 3000 0-+ 1-- 0++ 1++ 2++ 1+- 2-- 3-- 2-+ Yu.S.Kalashnikova, ITEP

  4. 1++(3872) 1--(4260) JPC?(4430) I=1 !?

  5. Weird charmoniaand relevant thresholds D0D0*3872 MeV D+D-*3879 MeV • X(3872) • Y(4260) DD14285 MeV • Y(4325) D*D04360 MeV • (4430) D*D14430 MeV Threshold affinity means that the admixture of D-meson pairs in the wavefunction is large Molecular charmonium Yu.S.Kalashnikova, ITEP

  6. 1++(3872)  D Q exch not enough D* uu* vector D* D  exchange drives attraction  D* D Yu.S.Kalashnikova, ITEP

  7. 1--(4260) D D* S-wave 1- - (1-+ !) pi D1 D0  exchange drives attraction D* D1 S-wave 0- (I=0 and I=1) also 1- 2- pi D1 D* JPC?(4460) I=1 !? psi D1 Q exch gives cc* + … final states Verify JPC seek other final states Other places should occur… D* pi

  8. DD  cc (ccg, ccqq) D D = D D D D D D D cc cc + D D D D D Coupling to bare state drives attraction Yu.S.Kalashnikova, ITEP

  9. Doubling of states in DD  cc system bona fide resonance molecule w(M) M Spectral density w(M) of the cc state Yu.S.Kalashnikova, ITEP

  10. Difference between bound states of quarks and hadrons Hadrons can go on-shell -> non-analyticities Quark loop Polynomial in E i(E)1/2 + polynomial, E>0 Hadron loop -(-E)1/2 + polynomial, E<0 Should lead to observable difference Yu.S.Kalashnikova, ITEP

  11. Focus on resonances very close to threshold The case of X Yu.S.Kalashnikova, ITEP

  12. X(3872)  J/ M(X) = 3871.2  0.5 MeV

  13. X(3875)  D0D00 Yu.S.Kalashnikova, ITEP

  14. X(3872)  X(3875) ? Yu.S.Kalashnikova, ITEP

  15. Flattè analysis Assumptions: • 1++ quantum numbers for the X • X -> D0D*0 -> D0D00 decay chain •  J/ and  J/ are the main non – DD* decay modes of the X DD* S-wave Yu.S.Kalashnikova, ITEP

  16. D0*->D00 Differential Rates: B B B->KX Yu.S.Kalashnikova, ITEP

  17. Results (generalities) • +-J/ peak exactly @ D0D0* • peak width 2.3 MeV • D0D0* coupling is large • scaling of Flattè parameters g->g, Ef->Ef, ->, B->B Yu.S.Kalashnikova, ITEP

  18. J/ DD ABelle a(D0D0*) = (-3.98 –i0.46) fm J/ DD BBelle a(D0D*0) = (-3.95 –i0.55) fm

  19. X(3872) as a virtual state: • +-J/ cusp • Large and negative real part of the scattering length (and small imaginary part) • Scaling behaviour of Flattè parameters • Dynamical nature of the X Yu.S.Kalashnikova, ITEP

  20. Why virtual state? Br(X -> D0D00)  9.7  3.4 Br(X -> J/) Yu.S.Kalashnikova, ITEP

  21. Scattering length approximation: re>0

  22. Bound state is below threshold, and decays only because D*0 has finite width. In the limit of infinitely narrow width the bound state is stable. As (D*0->D00)  42 keV, (Xbound -> D0D*00)  In the B-meson decay, together with the bound state contribution to the rate, there is also continuum contribution. The latter is nonzero even in the narrow-width approximation. 2*42 keV naively (2-4)*42 keV with FSI interference Yu.S.Kalashnikova, ITEP

  23. In the B-meson decay, the D0D*0 continuum provides the main contribution to D0D00 rate. In the case of the virtual state it is much larger, than for the bound state. So the large ratio Br(B -> KX) Br(X -> DD) Br(B -> KX) Br(X -> J/) tells that X is a virtual state. It is similar to the virtual state in the 1S0 nucleon-nucleon scattering rather than to the deuteron: the system is almost bound. Yu.S.Kalashnikova, ITEP

  24. Conclusions • The X(3875) can only be related to the X(3872) if we assume the X to be of dynamical origin (molecular charmonium) • However, it is not a bound state, but a virtual one • Only much better resolution on J/ lineshape could confirm or rule out this solution • If the cusp-like lineshape is ruled out, the X(3875) and X(3872) are two different particles Yu.S.Kalashnikova, ITEP

  25. The End Yu.S.Kalashnikova, ITEP

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