1. Quarkonia spectroscopy at CDF Ulrich Kerzel, University of Karlsruhe for the CDF collaboration Heavy Quarkonia 2006 Content: X(3872) m(  +  - ) mass spectrum quantum numbers J PC search for  b

2. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia2 huge inelastic cross-section: ¼ 5000 times bigger than for ) triggers are essential! events “polluted” by fragmentation tracks, underlying event, pile-up ) need precise tracking and good resolution Heavy quark physics at the Tevatron dedicated trigger for J/  !  +  - : m(  +  - ) around m(J/  ) ) high quality J/  events with large statistics (channel J/  ! e + e - much more challenging in hadronic environment) lepton + track with large IP (semi-leptonic B decay) two tracks with large IP (hadronic B decay)

3. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia3 The X(3872) ) what is the X(3872)? charmonium? exotic? ! determine quantum numbers J PC m(  +  - ) sensitive to J PC use distribution of angles between decay particles to measure J PC  2S) ! J/   +  - known resonance discovered 2003 by Belle in search for charmonium states m(  +  - ) spectrum compatible with  0 CDF PRL 96,102002 (2006) mass: m = 3871.3 § 0.7 § 0.4 MeV/c 2 CDF PRL 93,072001 (2004), width compatible with detector resolution  < 2.3 MeV/c 2 Belle PRL 91,26001 (2003) No X ++ or X – -- CDF PRL 93,072001 (2004) No iso-partner X § BaBar PRD 71, 031501 (2005) Evidence for X ! J/  , J/   Belle hep-ex/0505037

4. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia4 m(  +  - ) mass spectrum for  (2S)  (2S) in same exclusive final state m(  +  - ) spectrum known: s-wave with small d-wave contribution e.g. model by Novikov-Shifman ) high precision data by CDF ) allows to discriminate between models

5. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia5 The m(  +  - ) mass spectrum if (  +  - ) in s-wave state: shape needs to be modelled e.g. multipole expansions for if (  +  - ) in p-wave state: shape follows Breit-Wigner e.g. decay via  0 !  +  - m(  +  - ) favours high end of mass spectrum ) compatible with intermediate  0 !  +  - resonance also 3 S 1 multipole-expansion for charmonium possible no charmonium candidate at that mass 3 S 1 also has J PC = 1 - - ) non-observation by BES (  (e + e - )B(  +  - J/  ) < 10 eV @90% C.L. ) notation: n 2s+1 L J (J PC ) Phys.Lett.B579:74-78 (2004) Mass spectrum sensitive to J PC

6. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia6 The m(  +  - ) mass spectrum Possible  0 -  mixing:  mass contribution far from pole position interference  0 $  possible ) L=0 and L=1 both compatible with m(  +  - ) spectrum ) mixing phase of 95 ± describes data for broad resonances (  0 ): kinematic quantities vary across width introduce form-factor e.g. Blatt-Weisskopf depends on ang. momentum L, effective range R ) affects shape for L=0, L=1

7. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia7 example: J PC assumptions Determination of J PC (1) definition of angular variables:

8. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia8 Determination of J PC (2) Predictions for kinematic decay quantities from helicity formalism: ) decay chain as sequential 2-body decays X(3872) ! J/  (  +  - ) s,p !  +  -  +  - need: one matrix element per decay vertex propagators to connect vertices matrix elements: angular part A and kinetic part T assume state with lowest L dominates, neglect others dedicated simulation for each J PC hypothesis (including detector effects) compare to angular distributions measured in data via  2

9. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia9 Determination of J PC (3) Limitations from helicity formalism: no model-independent description of  +  - in s-wave Breit-Wigner for  0 !  +  - depends on form-factor details ) fix m  distribution to match the data ) analyse angular distributions only N.B.  0 and  have both J PC = 1 - - ) angular distributions not affected by potential interference J PC = 1 -+ and 2 -+ : multiple sub-states with same L contribute ) Can an arbitrary mixture describe the data?

10. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia10 Result for  (2S) obtain expected result: J PC = 1 - - Exploit correlations between angles via 3D fit: 3 bins in  2 bins in  J/  2 bins in  

11. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia11 Result for X(3872) Only J PC = 1 ++ or 2 -+ compatible with data! All other tested hypotheses excluded by > 3 

12. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia12 What is the X(3872) ?? Charmonium ? potential candidates: but: decay via  0 : isospin violating mass predictions from potential models ¼ 50-100 MeV/c 2 off exotic? m(X) ¼ m(D 0 ) + m(D 0 *) ! coincidence? charmed molecule ? ( or or...) hybrid state, i.e. ? (but expected above ¼ 4 GeV/c 2 ) mainly charmonium - but interaction with ? notation: 2s+1 L J (J PC ) e.g. M. Suzuki hep-ph/0508258

13. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia13 X(3872) with neural networks Use sophisticated neural networks for “next generation” X(3872) analyses: exploit correlations between variables ! improved candidate selection train networks for multiple J PC assignments further handle to test hypotheses: “good” hypotheses ! higher significance to be used in likelihood analyses strong suppression of combinatorial BG ! to be used in search for partner of X(3872) in B system:

14. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia14 Search for  b (1) ground state of system test NRQCD: ~30-160 MeV/c 2 lighter than not yet observed, searches: LEP   !  b CLEO 2  evidence from CDF RunI search in exclusive final state:  b ! J/  J/  !  +  -  +  - J PC : 0 -+ ! 1 - - 1 - - BR(  !   ¼ 40%  R  c !   ) ¼ 3¢ 10 -3 expect BR ¼ 7¢ 10 -5 – 7¢ 10 -3 Phys. Rev. D 63, 094006 (2001)

15. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia15 Search for  b (2) use 1.1 fb -1 data from J/  !  +  - trigger candidate selection:  b ! J/  J/   2 of vertex fit < 18.5 |  | < 0.6 p t (  b ) > 3 GeV/c J/  (1): J/  !  +  - trigger |  | < 0.6 p t (J/  ) > 3 GeV/c p t (  § ) > 2.0 GeV/c J/  (2):  + track p t (J/  ) > 3 GeV/c p t (  § ) > 2 GeV/c (|  |<0.6) or > 3.5GeV/c (0.6 < |  | < 1.0) p t (track) > 1.5 GeV/c dE/dx residual < 3.7 (track) p t (J/  ) > 50 GeV/c

16. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia16 Search for  b (3) after cuts: 3 candidates observed in 9.0 – 9.5 GeV/c 2, expect 3.6 background events ) no significant evidence of  b ) upper limit on  b production cross-section

17. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia17 Conclusions & Outlook Tevatron and CDF performing well, rich B physics programme New results on X(3872): 3D angular analysis: J PC = 1 ++ or 2 -+ m(  +  - ): both L=0 or L=1 transition via  0 compatible with data ) cannot exclude J  hypotheses from m(  +  - ) possibly  0 $  interference with  =95 ± ) both charmonium and exotic interpretation still “in the game” further analyses using neural networks started ongoing search for in molecular picture: expect further states similar to X(3872), e.g. Search for  b ! J/  J/  no signal observed, upper limit on production cross section

18. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia18 BACKUP

19. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia19 1 fb -1 delivered June 2005  15-20 pb -1 /week delivered before spring 2006 shutdown Tevatron Run 2 1 fb -1 delivered analyses presented use  0.3 – 1.0 fb -1 (“good data”)

20. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia20 CDF D0 Tevatron Main injector and recycler RunI: 1992 – 1996 data taking period at RunII: 2001 – 2009 major upgrades to collider and detectors The Tevatron

21. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia21 Tevatron performance Running well - both peak luminosity and integrated luminosity before spring 2006 shutdown: ~15-20 pb -1 / week delivered 1 fb -1 delivered in beginning of June 2005. 1 fb -1

22. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia22 precise tracking: silicon vertex detector and drift chamber important for B physics: direct trigger for displaced vertices, J/  !  +  - The CDF detector

23. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia23 Physics at the Tevatron large b production rates: ) 10 3 times bigger than ! spectrum quickly falling with p t Heavy and excited states not produced at B factories: enormous inelastic cross-section: ) triggers are essential events “polluted” by fragmentation tracks, underlying events ) need precise tracking and good resolution!

24. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia24 Dedicated trigger J/  !  +  - trigger events where m(  - ) around m(J/  ) high quality J/  events large statistics available N.B. channel J/  ! e + e - much more challenging in complex hadronic environment! Evaluate muon chamber info on trigger level:

25. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia25 X(3872) with J/  ! e + e - Reconstruction of J/  ! e + e - very difficult in complex hadronic environment dedicated J/  ! e + e - trigger use neural-network based approach to identify soft e § (p t > 2GeV/c) reject e § from conversions based on neural network approach add  at J/  vertex to accommodate Bremsstrahlung X(3872) reconstructions follows J/  !  +  - case ) able to reconstruct X(3872) in this channel! strong radiative tail

26. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia26 ) X(3872) behaves similarly to the  (2S) (with given uncertainties) X(3872) production fraction from B fraction from B decays:  2S): 28.3 § 1.0 (stat.) § 0.7 (syst.) % X(3872): 16.1 § 4.9 (stat.) § 1.0 (syst.)%

27. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia27 The m(  +  - ) mass spectrum Distribution of m(  +  - ) constrains quantum numbers J PC shape depends on: decay of (  +  - ) sub-system: (  +  - ) in s or p wave (i.e. intermediate sub-resonance or not) relative angular momentum between (  +  - ) and (  +  - ) (and detector acceptance, efficiency, etc.) e.g. for decay chain: X ! J/   0 ;  0 !  +  - for broad resonances (kinematic factors vary across width) form-factor spectrum described by Breit – Wigner function

28. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia28 The m(  +  - ) mass spectrum Challenge: Large background, rather low X(3872) yield ) sideband-subtraction difficult, instead: “slicing technique” impose bin borders in m(  +  - ) as additional cuts fit resulting (  +  -  +  - ) mass spectrum obtained yield shows variation with m(  +  - ) need to be careful at kinematic borders

29. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia29 Influence of form-factor on m(  +  - ) use: model from Blatt-Weiskopf: parameter “R” determines effective size, no unique choice

30. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia30 Mixing phase between  and  good fit probability found for relative phase  95  Relatively small influence of  0 form-factor radius, large effect from X(3872) form-factor radius.

31. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia31 Effect of  0 -  mixing ) Neither L=0 nor L=1 can be ruled out from m(  +  - ) alone

32. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia32 Illustration of angular correlation example for J PC = 1 ++

33. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia33 Sample fit for X(3872) angular analysis

34. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia34 Helicity matrix element treat initial and final state in respective rest-frame two body decay: are back-to-back common quantisation axis ) final state helicity = 1 - 2 using Wigner D functions assume lowest angular momentum L is dominant

35. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia35 Transition weight from Helicity matrix element mean over initial state incoherent sum over final states coherent sum over intermediate states in case of several substates: coherent sum contains a priori unknown mixing constant g LS

36. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia36 X(3872) fit results

37. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia37 Systematics for X(3872) systematics: 13 – 17: details of MC 12: use phase-space to describe m(  ) 10, 11: vary  0 form-factor radius 6-9: vary X(3872) mean and width 4,5: vary histogram bin width 2,3: vary X(3872) fit window 1: default result

38. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia38  2S) fit results

39. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia39 Systematics for  (2S) systematics: 13 – 17: details of MC 6,7 : vary  (2S) mean and width 4,5: vary histogram bin width 2,3: vary  (2S) fit window 1: default result

40. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia40 Detector effects Detector acceptance, resolution and cuts affect angular variables:  for J PC = 1 ++  for J PC = 1 -- original after simulation left: 1 ++ right: 1 --

41. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia41 possible formation of “molecules”: decay via: Charmed molecule? e.g. DeRujula, Georgi, Glashow (1977) ? binding by  0 Törnqvist Phys. Lett. B590, 209-215 (2004) Swanson Phys. Lett. B588, 189-195 (2004) 00 similar to deuteron: small attractive force mediated by  0 predict J PC = 1 ++ or 0 -+ isospin breaking via  0 !  +  - allowed Swanson: additional contribution from  0, only J PC = 1 ++

42. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia42 „Deuson“ model (Törnqvist) 00 X(3872) similar to deuteron: composed of two objects bound by  0 exchange Prediction: J PC = 1 ++ or 0 -+ (otherwise potential too weak or repulsive) small binding energy: narrow resonance, big object isospin breaking: X ! J/   0,  0 !  +  - allowed X ! J/   forbidden for any isoscalar  X ! J/   0  0 forbidden

43. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia43 Further properties by B-factories BaBar: search for charged partner X § ! J/   § expect twice the rate if X is part of iso-triplett ) no signal found Belle: 4  evidence for decay X(3872) ! J/   evidence for decay X! J/   +     ) Swanson: 1 ++ has contribution of X ! J/  ,  !  +     search for X!  c1 , X!  c2  ) no signal found C = +1 (hep-ph/0311229) (hep-ex/0505037) (hep-ex/0408083)

44. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia44 Excited B mesons narrow: ~ 10 MeV/c 2 broad : ~ 100 MeV/c 2 similar picture for B s ** Heavy Quark Effective Theory: hydrogen atom like system with heavy + light quark

45. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia45 Exclusive B d ** experimental observable: Q = m(B ** ) – m(B) – m(  ) (free remaining kinetic energy) focus on narrow states: B 1 ! B *  B 2 * ! B  B 2 * ! B *  (  not reconstructed) exclusive analysis ) high resolution

46. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia46 Exclusive B ** observable:Q = m(B ** ) – m(B) – m(  ) (free remaining kinetic energy) focus on narrow states: B 1, B 2 * ! B *  B 2 * ! B  HQET: hydrogen atom like system with heavy + light quark Towards B s ¤¤ : similar to B d ¤¤ : B s ¤¤ ! B § K ¨ situation much less clear: signal so far from DELPHI, OPAL, D0 exclusive B § ! J/  K §, B § ! D  § sophisticated neural networks to suppress background expect result ~summer

47. June 2006U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia47 Towards B s ** Delphi Conf 2005-011 Conf 731 B s ¤ ¤ ! B § K ¨ observed by: DELPHI (inclusive) D0 (exclusive) OPAL (inclusive) D0Note 5027-Conf Rare signal dominated by large background ! deploy sophisticated neural networks B § ! J/  K §, B § ! D  § B s ¤ ¤ resonant signal vs. combinatorial background ) expect CDF result this summer Z. Phys. C66 (1995) 19