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Hadronic decay modes of  b

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. Outline. 1. Current experimental status of the  b 2. Peculiarity about the decay mode

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Hadronic decay modes of  b

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

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

  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. KSK) 4. Summary

  4. What is special about b ? • The missing pseudoscalarground 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. Mass of b Various models estimated the mass splitting between (1S) andbabout 20-140 GeV Latest model-independent estimation (exploiting pNRQCD RG technique) Kniehl et al (PRL 04) M(b) = 9.421  0.013GeV

  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 (mc/mb)4relative to c decay. • In general, clean modes have rather small branching ratios, overshadowed by copious background events at hadron collider.

  7. One candidate event found in collision at LEP2ALEPH (PLB 02)

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

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

  10. Estimate based on simple counting • From experimental value (PDG 06 edition) : Br[c] = 0.0027  0.0009 Assuming Br ~ 1/mb4 scaling, one gets

  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. 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. 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. Some light shed by inclusive 4-charm decay rate of bMaltoni’s talk Even the low end of the simple estimate based on Br ~ 1/mb4 assumption for Br[bJ/ J/]is larger than the inclusive 4-charm rate Maltoni and Polosa (PRD, 04)

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

  16. Hadron Helicity Selection Rule Brodsky and Lepage (PRD 81) 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)

  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<10|10;10>=0 Y. J., MS thesis (98)  Two J/ must be transversely polarized

  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/mb8 (power correction)

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

  20. Phenomenological Input Using ee= 5.55  0.14 keV to extract(0) I borrow the input of <v2>J/ from Bodwin et al (PRD 06)

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

  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. 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. 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. The answer is absolutelynofor Tevatron Run I Tevatron Run I:  100pb-1data • 0.0050.06produced 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. The answer is still very negativeeven for Tevatron Run II Tevatron Run II: 8.5fb-1data by 2009 0.45produced 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. Can we find 4  decay mode of b at LHC? • Let us guess[b] 15 b @ LHC • LHC design luminosity: 300fb-1 per year • 1001000produced events per year • Including acceptance & efficiency for reconstructing muon pairs (=0.1), we estimate • 110observed events per year

  28. The answer isperhaps YESfor 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. Other exclusive hadronic decay modes of b • Our NRQCD-based method may be superficially applied to b VVprocesses. • 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. bdecay into VV • The NRQCD-based formula may be superficially applied to b VV, hopefully will catch the right order of magnitude. • Taking <v2> 1to characterize relativistic nature of strange quark inside 

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

  32. bdecay 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. bdecay into D*D: an estimate • Since bD*D satisfy helicity conservation, one then expects Br ~ 1/mb4 • The binding probability between a heavy charm and a light q to form charm meson is ~ QCD/mc Braaten, Jia and Mehen (PRD,02) • Therefore I estimate

  34. bdecay into D*D*: an estimate • Since bD* D*violates helicity selection rule maximally, we expect that Br ~ 1/mb8 • Again, q is the cause of the violation of selection rule • Therefore I estimate

  35. Discovery potential of b D*+D-at hadron collider • Br[b D*+D-K+K¯+ ¯+ ¯]  10-8 Therefore, one expects ~ O(100) produced events at Tevatron Run I ~ O(102) produced events at Tevatron Run II ~ O(104) produced events at LHC per year

  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/mcsymmetry-breaking suppression, its value might be even smaller than the scaling estimate in previous slide.

  37. bdecay into 3 pseudoscalar • Stimulated by one experimental observation • Largest branching ratios of ccome from 3-body decays instead of 2-body decays PDG 06

  38. bdecay into 3P (cont’) • Since these decay modes are most preferred, we assume they exhibit leading-twist scaling Br ~ 1/mb4 • Therefore I expect

  39. bdecay into 3P (cont’) • A potentially good searching mode is bKSK • bK+ K- 0is 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. 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 v2 Transverse momentum of c inside J/ is the agent to violate the helicity selection rule

  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. Summary (cont’) • It is useful to look for other hadronic decay modes which have clean signature • bKSK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. 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. Backup Slides

  45. A possible Nonperturbative Explanation for large Br[cVV] • c--’ mixing • via anomalyFeldman 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

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