1. Inclusive four charm hadron production at Belle June 16-20, 2005 International Conference on QCD and Hadronic Physics, Beijing JUNGIL LEE

2. 2 JUNGIL LEE, Korea UniversityOutline Brief Review on NRQCD and quarkonium physics Brief Review on NRQCD and quarkonium physics Belle measurement of  [e + e -  J/   c ] Belle measurement of  [e + e -  J/   c ] Previous trials to resolve the large discrepancy between theory and data Previous trials to resolve the large discrepancy between theory and data A test by using four charm hadron final state A test by using four charm hadron final state Discussion Discussion

3. Brief Review on NRQCD

4. 4 JUNGIL LEE, Korea University NRQCD is an Effective Field Theory of QCD that describes Heavy Quarkonium NRQCD[Bodwin,Braaten,Lepage,PRD(‘95)] describes Quarkonium from first principles. NRQCD solved the problem of Infra-Red Divergencies in the Color-Singlet Model [Bodwin,Braaten,Lepage,PRD(‘92)]

5. 5 JUNGIL LEE, Korea University Experimental Verification of NRQCD Factorization Following the theoretical success that solved the Infra-Red Divergence problem, theorists applied NRQCD to issues on quarkonium decays and productions. The first experimental success of NRQCD in quarkonium production was at the Fermilab Tevatron.

6. 6 JUNGIL LEE, Korea University Tevatron Anomaly, resolved by NRQCD As an effective field theory of QCD, NRQCD replaced a 20-year-old phenomenological model at the Fermilab Tevatron. Braaten,Fleming(’95)

7. 7 JUNGIL LEE, Korea University J/  Polarization confronts NRQCD? According to NRQCD, J/  produced at large p T must be transversely polarized. However, CDF measurement seems to contradict the prediction. People have been curious about the reason.

8. 8 JUNGIL LEE, Korea University Lattice NRQCD calculation of Polarized matrix elements Lattice NRQCD calculation to estimate the spin-flip interaction by directly calculating non-perturbative matrix elements from first principles. Bodwin, Lee, Sinclair, hep-lat/0503032 Geoff Bodwin, Plenary Talk Geoff Bodwin, Plenary Talk June 20, 3:50PM June 20, 3:50PM IT’S experimentalists’ (CDF/D0) TURN!  Hopefully with large statistics by a factor 20.

9. 9 JUNGIL LEE, Korea University Chiral perturbation theory and Quarkonium Polarization In Upsilon(3S)  Upsilon(1S), final quarkonium Polarization is not described by QCD multipole expansion, but by chiral perturbation theory. We apply the same idea to gluon fragmenation into spin-triplet quarkonium states. P. Ko, J. Lee, T. Kim,  Pyungwon Ko, Parallel session (Hall B) June 17, 2:30PM June 17, 2:30PM

10. Belle J/  c Anomaly

11. 11 JUNGIL LEE, Korea University B factories at KEK-B & SLAC * Collider : e + e - E C.M. =10.6GeV[  (4S)] * Detectors: KEK-B Belle, SLAC BaBar CP violation in B  J/  K s Main Goal * Measured  J/  c ): Large discrepancy between theory & data Large discrepancy between theory & data * Discoveries:  c (2S), X(3872)[J/  +  -  Remarkable QCD Results from Belle

12. 12 JUNGIL LEE, Korea University Exclusive e + e -  J/   c Precision measurement Precision measurement R=  /   ~ 10 -7 << R hadron ~ 3.6 R=  /   ~ 10 -7 << R hadron ~ 3.6 High-luminosity B factories High-luminosity B factories Theory is clear Theory is clear Exclusive  Color-singlet Only Exclusive  Color-singlet Only Long-distance factors are well determined through Long-distance factors are well determined through J/   e + e -,  c   J/   e + e -,  c  

13. 13 JUNGIL LEE, Korea University Belle Puzzle, Crisis of pQCD??? Braaten, Lee, PRD 67 (2003) Liu, He, Chao, PLB 557 (2003)

14. 14 JUNGIL LEE, Korea University Suggestions & a new Belle analysis  Signals may include J/  J/   exp. ~110MeV M J/  -M  c ~120MeV People thought that J/  J/  is forbidden BUT …

15. 15 JUNGIL LEE, Korea University New Belle Analysis Did NOT see J/  J/  Did NOT see J/  J/  Upper limit compatible with theory Upper limit compatible with theory Puzzle:  [J/   c ] ~  [J/  J/  ]. Puzzle:  [J/   c ] ~  [J/  J/  ]. Why are ONLY J/   c events seen? Why are ONLY J/   c events seen? Failure of pQCD factorization? Failure of pQCD factorization? New Production Mechanism? New Production Mechanism? Or NEW PARTICLES? Or NEW PARTICLES?

16. 16 JUNGIL LEE, Korea University e + e -  J/  G J possibility? e + e -  J/  G J possibility? Glue-rich process   (Q 2 )  J/  gg Glue-rich process   (Q 2 )  J/  gg Safe factorization Q 2 >> M G Safe factorization Q 2 >> M G B-factory can probe wider mass range B-factory can probe wider mass range pQCD factorization[ Brodsky,Lepage ] for G J pQCD factorization[ Brodsky,Lepage ] for G J NRQCD factorization for J/  NRQCD factorization for J/  Same order in  s as   (Q 2 )  J/  c Same order in  s as   (Q 2 )  J/  c

17. 17 JUNGIL LEE, Korea University A scenario Brodsky,Goldhaber,LeePRL91(2003) Signals may include J/  + Glueball. Belle angular distribution is compatible with Spin-2 glueball. Still to be studied

18. What about Four D mesons ?

19. 19 JUNGIL LEE, Korea University Why 4 D final state? Similar parton-level process Similar parton-level process  check if perturbative corrections are large  check if perturbative corrections are large Quark hadron duality Quark hadron duality Inclusive four-charm-hadron production

20. 20 JUNGIL LEE, Korea University Perturbative Calculation

21. 21 JUNGIL LEE, Korea University DD final state study Experimentally, inclusive production of 2 charmed hadrons can be measured with a large number of events. Experimentally, inclusive production of 2 charmed hadrons can be measured with a large number of events. By comparing the measured value with the LO QCD prediction, we can estimate if the NLO correction By comparing the measured value with the LO QCD prediction, we can estimate if the NLO correction is large enough to explain the puzzle.

22. 22 JUNGIL LEE, Korea University Relative rate into charm mesons D + D + : D + D 0 : D 0 D 0 =1 : 6 : 9 D + : D 0 : D + * : D 0 * = 1 : 1 : 3 : 3 D+D+D+D+ D0D0D0D0 11 X 1 D + * → 0.30.7 X 3 D 0 * → 01 X 3 26 Spin singlet : Spin triplet = 1 : 3 Branching fractions spin-triplet states Relative rate into 2 charm mesons

23. 23 JUNGIL LEE, Korea University Predicted 4 charm-hadron envents Events(DD)=X-section(DD)*Br*Eff*Luminosity Br(D + K -  +  + )=9.2% Br(D 0 K -  + )=3.8% Efficiency per hadron = 0.8 Luminosity = 300 fb -1 Xsection(fb)BrEff L(fb -1 ) Events D+D+D+D+D+D+D+D+ 1/16*  0.092 2 0.8 6 30010 D+D0D+D0D+D0D+D0 6/16*  0.038*0.092 0.8 5 30013 D0D0D0D0D0D0D0D0 9/16*  0.038 2 0.8 4 3004 Total Events ≈ 3 0 Belle Analysis is Under way

24. 24 JUNGIL LEE, Korea UniversityDiscussion Belle results of exclusive two-charmonium production is a serious challenge to perturabtive QCD as well as to NRQCD factorization framework. Belle results of exclusive two-charmonium production is a serious challenge to perturabtive QCD as well as to NRQCD factorization framework. BaBar must confirm the Belle results. BaBar must confirm the Belle results. Failure of pQCD factorization? Failure of pQCD factorization? New Particles? New physics? New Particles? New physics? Study of the 4 charm hadrons final state will provide an independent constraint. Study of the 4 charm hadrons final state will provide an independent constraint. Belle analysis of the 4 charm events Belle analysis of the 4 charm events is under way. is under way.

25. 25 JUNGIL LEE, Korea University Large nonperturbative effect? Ma and Si, PRD 70 (2005). Ma and Si, PRD 70 (2005). Bonder and Chernyak, PLB 612 (2005). Bonder and Chernyak, PLB 612 (2005). Braguta, Likhoded, and Luchinsky, Braguta, Likhoded, and Luchinsky, hep-ph/0506009. hep-ph/0506009. Non-zero k T of the quark inside the meson may increase the cross section. Non-zero k T of the quark inside the meson may increase the cross section.

26. 26 JUNGIL LEE, Korea University NLO Corrections are Now Available ! ! ! Zhang, Gao, and Chao, Zhang, Gao, and Chao, hep-ph/0506076. hep-ph/0506076. NLO correction term is as large as NLO correction term is as large as 80% of LO term. 80% of LO term. A large discrepancy between theory and data still exists. A large discrepancy between theory and data still exists. Is the perturbation series convergent? Is the perturbation series convergent?