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Double charm production in e + e - -annihilation

The conflict between Theory and Experiment in double charmonium production Beyond the -approximation Light-cone results Quark-hadron duality for cccc-sector. Double charm production in e + e - -annihilation. Anatoly Likhoded, IHEP, Protvino. Introduction.

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Double charm production in e + e - -annihilation

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  1. The conflict between Theory and Experiment in double charmonium production • Beyond the -approximation • Light-cone results • Quark-hadron duality for cccc-sector Double charm production in e+e--annihilation Anatoly Likhoded, IHEP, Protvino

  2. Introduction • Bound states are similar to QED positronium • Simple strong-interactive system • Non-relativistic for less for • small component velocity and small are the expansion parameters in NRQCD • The properties of these bound states, their decay and production channels are a good laboratory for QCD both in perturbative and non- perturbative modes • The simplest system clarifying the transitions particles

  3. Double charmonium production One of the most challenging open problems in heavy quarkonium is: the large discrepancy of the double charmonium production cross sections measured in e+e- annihilation at B factories and the theoretical calculations from NRQCD.

  4. Theoretical calculations (LO): (PRD 67 (2003) 054007) E. Braaten, J. Lee: e+ * K.-Y. Liu, Z.-G. He and K.-T Chao: e- NRQCD factorization formalism CS dominant one of 4 diagrams PLB557 (2003) 45 • K. Hagiwara, E. Kou and C.-F.Qiao, • Berezhnoy, A. Likhoded: exclusive double charmonium production via e+e- annihilation to a *. two charmonium states with opposite C parities PLB570 (2003) 39 • The calculated exclusive cross sections are about an order of magnitude smaller than exp. results! • The calculated inclusive cross section of J/ is about a factor of 5 smaller than exp. results!

  5. Experiment • Belle • BaBar • Trends • The Belle cross section has moved down from • BaBar cross section is even lower • NLO in give an enhancement factor 1.8 (Zhang et al) • Discrepancy still remains

  6. NRQCD predictions for double charmonium production Papers where NRQCD was applied for double charmonium production:E.Braaten, J.Lee, Phys. Rev. D67, 054007 (2003)K. Liu, Z. He, K. Chao, Phys.Lett.B557 (2003)G. T. Bodwin, J. Lee, E. Braaten, Phys.Rev.Lett.90, 162001 (2003)G. T. Bodwin, J. Lee, E. Braaten, Phys.Rev.D67, 054023 (2003)Y. Zhang, Y. Gao, K. Chao, Phys.Rev.Lett.96, 092001 (2006)

  7. q e+ * e- x1 x2 g • -approximation (Bethe-Heitler) gluon virtuality for massless quarks • In -approximation

  8. J/ structure function In frame the c-quark distribution over the momentum fraction x is V.G. Kartverishvili, A.K. Likhoded Nucl. Phys. B148 (1979), 400  is the same in fragmentation function

  9. A proposed solution • Bondar and Chernyal have proposed to calculate the cross section in the • framework of light-cone formalism. • BC result • if light-cone distributions (z-1/2) are taken, the cross section reduces to ~3 fb J.P. Ma, Z.G. Si // Phys.ReV. D70 (2004) 074007 A.E. Bondar, V.L. Chernyak // Phys.Lett. B612 (2005) 215 V. Braguta, A. Luchinsky, A. Likhoded // Phys.Rev.D72 (2005) 094018

  10. Light-cone formalism processes where is defined from Leading asymptotic behavior

  11. e+ * e- Light-cone wave functions, that are expressed as the expansion over poorly known wave functions. For example, from the asymptotical Regge behavior x1 y1 In -approximation we have

  12. Light-cone wave functions are unknown. This is a drawback of the light-cone formalism! Can be estimated from the wave-functions obtained in the framework of potential models.

  13. Light cone wave functions.

  14. The model for the light cone wave functions: The property of the wave functions: A.E. Bondar, V.L. Chernyak, Phys.Lett.B612:215, (2005)

  15. e+e-gV(3S1) P(1S0)

  16. e+e-gV(3S1) S(3P0)

  17. Numerical results. Uncertainties: • Poor knowledge of the light cone wave functions • Radiative corrections • 1/s corrections V.V. Braguta, A.K. Likhoded, A.V. Luchinsky Phys.Rev.D72 (2005) 094018 Phys.Lett.B635 (2006) 299 Conclusion: • Formfactor = NRQCD xInternal Motion • WFs of charmonium are wide aNRQCD is not applicable

  18. Observation of X(3940) at Belle. Two possibilities: K.Abe et al., hep-ex/0507019

  19. Hypothesis:X(3940) is one of , , • If is dominant decay mode than X(3940) is • If is seen than must be seen • Decay mode of is We reject this hypothesis

  20. Hypothesis: Our estimation: Experimental result:

  21. Quark-hadron duality Let us consider the process • LO - tot(4c)~O(s)2 depends on s and mc for mc=1.25 GeV and s=0.24 tot(4c)=372 fb • OZI-rule forbids transition to and light quark sectors

  22. It is interesting to compare these results with cccc-final state in hadronic Z-decay, where three experimental values are known (L3, OPAL, ALEPH) A.K. Likhoded, A.I.Onishenko Phys.Atom.Nucl, 60 (1997) 623 Than at we have

  23. Inclusive charmonium production In the peak of Z-boson Numerically at s=0.24 this ratio is E. Braaten and K.Cheung Phys.Rev.D48 (1993) 4230 A.L., V. Kiselev, M. Shevlyagin Phys.Lett.B332 (1995) 351 Good agreement with L3 result.

  24. We can compare the sum of the cross sections of inclusive production of J/, c and P-wave sates calculated in the framework of perturbative QCD (LHS), with the cross section of the singlet cc-production in duality interval (RHS) In the duality interval the RHS cross section The sum is LHS cross section consists of perturbative contributions from J/, c and P-wave states B.K.L // Phys.Lett.B 323 (1994) 411 Liu et al // PR D69 (2004) 094027 There is a reasonable agreement between these two estimates

  25. These cross sections include both and If we restrict the mass of pair in the process by the duality interval, we get It should be compared with Belle and BaBar results: We observe a good agreement with the experiment

  26. Substracting the cross section of exclusive pair production we obtain This value should be compared with the Belle result It should be noticed, that this result is sufficiently larger, than the absolute bound for production cross section

  27. 3c Double charmed baryon production Using final state we can estimate the upper bound on (ccq) baryon production. Let us assume that it is produced through the production of cc-diquark in color-antitriplet state. Cross section of production in duality interval The upper limit for the cross sections of the processes like

  28. First attempt to search doubly charmed baryons and was done in BaBar experiment hep-ex/0605075 Events containing candidates were searched for the processes and Upper limits This is about an order of magnitude higher, than our predictions

  29. Conclusion 1) Light cone partially resolves the discrepancy between theory and experiment The drawback of a light-cone formalism is a large number of unknown wave functions (for critics see G. Bodwin, D. Kang, J. Lee hep-ph/0603185) 2) NRQCD (-approximation) does not work for exclusive processes. In inclusive processes, on the contrary, -approximation gives a quite good accuracy 3) Quark-hadron duality as an independent way to estimate cross section gives good agreement with experiment (20% accuracy) and allows to predict Double Charm Baryon production cross section. A.P. Martynenko , Phys.ReV. D72 (2005) 074022

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