1. 1 Hadronic decay modes of  b Yu Jia Institute of High Energy Physics, CAS, Beijing (based on hep-ph/0611130) 5 th International Workshop on Heavy Quarkonia, 17-20 October 2007, DESY

2. 2 Outline 1. Current experimental status of the  b 2. Peculiarity about the decay mode  b  J /  + J /  Calculation of the decay rate in the NRQCD factorization framework. Discovery potential of this very clean decay mode at Tevatron Run II and LHC

3. 3 Outline (cont ’ ) 3. Estimates of branching ratios for other hadronic decay modes of  b  b  VV, VP (e.g. , D*D* and D*D )  b  3 P (e.g. K S K    ) 4. Summary

4. 4 What is special about  b ? The missing pseudoscalar ground state of bottomonium family Its existence is a solid prediction of QCD After 30 years extensive searches, still NO conclusive evidence about its existence

5. 5 Mass of  b Various models estimated the mass splitting between  ( 1S ) and  b about 20-140 GeV Latest model-independent estimation (exploiting pNRQCD RG technique) Kniehl et al (PRL 04) M(  b ) = 9.421  0.013 GeV

6. 6 Why it is so difficult to observe  b Because of its heavy mass, many hadronic decay channels of  b partition the branching ratio For a given decay channel, the branching ratio is diluted at least by a factor ( m c / m b ) 4 relative to  c decay. In general, clean modes have rather small branching ratios, overshadowed by copious background events at hadron collider.

7. 7 One candidate event found in  collision at LEP2 ALEPH (PLB 02)

8. 8  b  K S K ¯  ¯  +  + A fit gives: M(  b ) = 9.30  0.03 GeV Lower than most theoretical predictions! Most probably due to background fluctuation or/ probably missing a  0

9. 9  b  J /  + J /  : An ideal searching mode?? Inspired by relatively large branching ratios of  c  , , one may argue the analogous double J /  decay channel  b  J /  + J /   4  may have bright chance to be observed at Tevatron Run II Braaten, Fleming, Leibovich (PRD 01)

10. 10 Estimate based on simple counting From experimental value (PDG 06 edition) : Br[  c   ] = 0.0027  0.0009 Assuming Br ~ 1/ m b 4 scaling, one gets

11. 11 CDF Run I preliminary (Tseng, 02) 7 events are seen, 1.8 expected from background A fit gives M(  b ) = 9.445  0.006 (stat) GeV

12. 12 Potential pitfall of this analogy Reminder:  c  VV is very suppressed in pQCD e.g., light-cone approach generates vanishing amplitude even when light quark mass is kept nonzero Anselmino, Murgia and Caruso (PRD 90) or very small in constituent quark model approach Y. J., Ms thesis (98), Jia & Zhao (HP&NP, 99) Therefore, the large experimental branching ratio seems to arise from nonperturbative mechanism

13. 13 Analogy between  c  VV and  b  J /  J /  may be superficial One should not draw straightforward analogy from  c to  b -- the major mechanism governing exclusive decay can be rather different  b  J /  J /  is not expected to have room to accommodate large nonperturbative effect PQCD is expected to be reliable in this case

14. 14 Some light shed by inclusive 4-charm decay rate of  b  Maltoni’s talk Maltoni and Polosa (PRD, 04) Even the low end of the simple estimate based on Br ~ 1/ m b 4 assumption for Br[  b  J /  J /  ] is larger than the inclusive 4-charm rate 

15. 15 Our goal: calculate the decay rate from NRQCD factorization QCD diagram fragmentation-type QED diagram

16. 16 Angular Momentum Conservation requires: = ̃ The favorable decay is through (, ̃ ) = (0,0) However, the helicity-conserving decay is strictly forbidden in such an “unnatural” process. Chernyak and Zhitnitsky (NPB, 82) Hadron Helicity Selection Rule Brodsky and Lepage (PRD 81)

17. 17 (, ̃ ) = (0,0) helicity state strictly forbidden: a quick proof No enough number of independent Lorentz vectors to contract with anti-symmetric tensor for (0,0) state. Equivalently, because of =0 Y. J., MS thesis (98)  Two J /  must be transversely polarized

18. 18 Keeping transverse momentum of c plays a crucial role LO NRQCD amplitude vanishes Should go to NLO in v expansion Keep transverse momentum of c inside J /  is essential to generate a nonzero amplitude. Helicity selection rule is violated by two units, therefore Br ~ 1/ m b 8 (power correction)

19. 19 NRQCD (color-singlet model) calculation QCD contribution QED contribution

20. 20 Phenomenological Input Using  ee = 5.55  0.14 keV to extract  (0) I borrow the input of J/  from Bodwin et al (PRD 06)

21. 21 Numerical result About 3 orders of magnitude smaller than the estimate based on naive scaling assumption!

22. 22 Consistency check of my prediction The color-singlet model prediction Perfectly compatible with the inclusive bound set by the decay ratio to 4 charm quark

23. 23 Can we find 4  mode of  b at Tevatron? The J/  can be cleanly reconstructed through decay to muon pair. Br[J/   +  - ]  6  We get Br[  b  J/  + J/   4  ]  (0.2-2.4)  10 -10

24. 24 Can we find 4  mode of  b at Tevatron? (cont ’ ) Using  [  b ]  2.5  b @ Tevatron Maltoni and Polosa (PRD, 04)  [  b ]  Br[  b  J /  + J /   4  ]  (0.05  0.6) fb

25. 25 The answer is absolutely no for Tevatron Run I Tevatron Run I:  100 pb -1 data  0.005  0.06 produced events Not yet taking into account the acceptance and efficiency  Will further cut down the number Therefore, the 7 events observed at CDF Run I (Tseng, 02) must not be identified with the true  b signal, merely are statistical fluctuations of continuum background events

26. 26 The answer is still very negative even for Tevatron Run II Tevatron Run II: 8.5 fb -1 data by 2009  0.4  5 produced events Acceptance & efficiency of detecting muons, plus kinematical cuts will decrease these numbers by additional two orders of magnitude The chance for Run II to establish this decay channel seems rather unrealistic

27. 27 Can we find 4  decay mode of  b at LHC? Let us guess  [  b ]  15  b @ LHC LHC design luminosity:  300 fb -1 per year  100  1000 produced events per year  Including acceptance & efficiency for reconstructing muon pairs (  =0.1), we estimate  1  10 observed events per year

28. 28 The answer is perhaps YES for LHC However, one worries about that a few signal events are overwhelmed by rather copious background events. More study on background is welcome. Most important background is through direct double J /  production via gluon fusion: g g  J /  J /  +X Barger, Fleming, Phillips (PLB 96) Qiao (PRD 02)

29. 29 Other exclusive hadronic decay modes of  b Our NRQCD-based method may be superficially applied to  b  VV processes. Equivalent to constitute quark model, hopefully can catch the right order of magnitude. Estimating other decay (e.g.,  b  VP, 3P) by resorting to helicity selection rule

30. 30  b decay into VV The NRQCD-based formula may be superficially applied to  b  VV, hopefully will catch the right order of magnitude. Taking   1 to characterize relativistic nature of strange quark inside 

31. 31  b decay into VP SU(3) F + Helicity selection rule We estimate

32. 32  b decay to two charmed mesons Suggestions are made to search for  b through decay to D * D or D * D * Maltoni and Polosa (PRD, 04) With saturation assumption, they expect

33. 33  b decay into D * D: an estimate Since  b  D * D satisfy helicity conservation, one then expects Br ~ 1/ m b 4 The binding probability between a heavy charm and a light q to form charm meson is ~  QCD /m c Braaten, Jia and Mehen (PRD,02) Therefore I estimate

34. 34  b decay into D * D * : an estimate Since  b  D * D * violates helicity selection rule maximally, we expect that Br ~ 1/ m b 8 Again, q  is the cause of the violation of selection rule Therefore I estimate

35. 35 Discovery potential of  b  D *+ D - at hadron collider Br[  b  D *+ D -  K + K ¯  +  ¯  +  ¯ ]  10 -8 Therefore, one expects ~ O(10 0 ) produced events at Tevatron Run I ~ O(10 2 ) produced events at Tevatron Run II ~ O(10 4 ) produced events at LHC per year

36. 36  b  D*D from perturbative QCD calculation The amplitude vanishes in the exact heavy quark spin symmetry limit. Y.Y.Charng and Y.J. (work in progress) So the actual branching ratio receives an additional  QCD /m c symmetry-breaking suppression, its value might be even smaller than the scaling estimate in previous slide.

37. 37  b decay into 3 pseudoscalar Stimulated by one experimental observation Largest branching ratios of  c come from 3- body decays instead of 2-body decays PDG 06

38. 38  b decay into 3P (cont’) Since these decay modes are most preferred, we assume they exhibit leading-twist scaling Br ~ 1/ m b 4 Therefore I expect

39. 39  b decay into 3P (cont’) A potentially good searching mode is  b  K S K     b  K + K -  0 is not so useful since ubiquitous  0 events in hadronic collision environment. This exclusive mode has the largest branching ratio ~ 10 -4 in what so far we have analyzed for  b decay. However, copious combinatorial background events may make the search rather difficult at hadron collider.

40. 40 Summary Have performed a pQCD calculation for  b  J/  + J/  Find the branching ratio is very suppressed. The LO velocity expansion in NRQCD leads to vanishing amplitude. Must expand the amplitude to the NLO in v 2 Transverse momentum of c inside J/  is the agent to violate the helicity selection rule

41. 41 Summary (cont ’ ) Very suppressed branching ratio implies that Run I CDF results (Tseng, 02) should be attributed to fluctuations of background events It also casts doubt on the experimental efforts of searching for  b through double J/  channel at Tevatron Run II For a different point of view  Santorelli’s talk This decay channel might be worth continuing pursuit at LHC

42. 42 Summary (cont ’ ) It is useful to look for other hadronic decay modes which have clean signature  b  K S K    with a branching ratio of 10 -4 may be worth looking for, but combinatorial background is worrisome  b  K * K, D *+ D - with a branching ratio of 10 -5 may be difficult to search

43. 43 Summary (cont ’ ) Exclusive decay modes with clean signature, not necessarily to be hadronic, should also be studied For example,  b  J/  +  seems much more efficient than  b  J/  +J/   Qiao’s talk

44. 44 Backup Slides

45. 45 A possible Nonperturbative Explanation for large Br[  c  VV ]  c -  -  ’ mixing via anomaly Feldman and Kroll (PRD 00) /or via perturbative box diagram Zhou, Ping & Zou (PRD 05) Light quark pair from vacuum to materialize into VV 3P0 model