Jochen Dingfelder Universität Freiburg

1. B X Semileptonic Decays at the B Factoriesand the CKM Matrix- Probing the Weak and Strong Interactions - Jochen Dingfelder Universität Freiburg Seminar Teilchenphysik, Bonn, December 18, 2008

2. A Brief Outline • Introduction & Motivation: CKM Matrix, B Factories, analysis strategies, and all that … • Inclusive Semileptonic Decays and the Determination of • |Vcb| • |Vub| • Exclusive Semileptonic Decays and the Determination of • |Vcb| • |Vub| • Semileptonic Decays with Tau • Conclusions & Outlook

3. A Good Year for a Talk on the CKM Matrix … The CKM mechanism is now a well-tested theory Experimental proof comes from B-physics experiments by

4. Quarks and the Weak Interaction Vud Vus Vub Vcd VcsVcb VtdVts Vtb 1-c2c A c3(-i) = -c 1- c2/2 A c2 Ac3(1--i) -A c2 1 VCKM = u c t d s b + O(c4) [ c= sinc~ 0.22] Im W Re • Quark mass eigenstates ≠ flavor eigenstates • Mixing matrix: elements  coupling strengths • Unitarity V†V= 1: |Vud|2 + |Vus|2 + |Vub|2 = 1 VudVub* + VcdVcb* + VtdVtb* = 0

5. Constraining the Unitarity Triangle sin2b K0K0 mixing (Kaon experiments) Bd0Bd0 and Bs0Bs0 Mixing (TeVatron) |Vub / Vcb| Best Constraints From B factories Angles : CP violation measurements (time-dependent asymmetries) Sides : Semileptonic decays, B0B0 mixing, …

6. Measuring CKM Elements

7. The Beauty of Semileptonic Decays • Study weak interaction • |Vcb| , |Vub| d • Study strong interaction • Charmed or Charmless decays: BXc ℓnorBXuℓn Analogy to deep-inelast. scattering b Semileptonic decays are an ideal laboratory to study Quark Couplings and B-Meson Structure

8. B-Factory Experimental Tools BXc,uℓn off peak (q=u,d,s,c) - Goode, m ID (p*ℓ> 1 GeV) - Goodhadron ID(e.g. p/K separation) - Angular coverage ≈ 91% of 4p in CMS (challenge fornreconstruction) 2mB BaBar: 531 fb-1 Belle: >840 fb-1 3.1GeV e+ 9GeV e-

9. Analysis Strategies Tagged or untagged: n B+→ r0 m+ n D0 r0 B+ B- p0 Y(4S) n m+ p- signal B tag B p- Hadronic tag: B  D + “ p+, p0, K+, K0”  charge, flavor, p of both B’s (very clean, but e ~ few ‰) p+ r0 m+ pm~2.2 GeV Inclusive: Identify only lepton and “sum over final states” or Exclusive: Reconstruct final-state hadron X (e.g. B+→r0 ℓ +n)

11. Inclusive Semileptonic Decays - Theory Theoretical Tool: Heavy-Quark-Expansion (HQE) • Perturbative corrections are calculable • Anon-pert depends on non-perturbative HQE parameters arising • at each order in 1/mb, they need to be measured

12. HQE Parameters from Moments Lepton energy cut Non-perturbative parameters appearing at order 1/mb2 or 1/mb3 • HQE does not give local quantities such as dG/dE • Calculations exist for moments of inclusive spectra, e.g. • lepton-energy (Eℓ) or hadronic-mass (MX) moments. • Measure over large region of phase space to avoid problem with • quark-hadron duality: • Calculations in two mass schemes: • - Kinetic scheme: Benson, Bigi, Gambino, Mannel, Uraltsev • - 1S scheme : Bauer, Ligeti, Luke, Manohar, Trott • Fit to ~ 60 measured moments from DELPHI, CLEO, BABAR, Belle, CDF • to determine 6 parameters

13. How the Moments are Measured Xc p Btag e- D* e+ n Bsignal Xu l • Fully reconstruct one B • Find lepton with minimum pℓ • Hadron X = rest of event • Improve resolution: kinematic fit • - E, p conservation • - Emiss, pmiss consistent with n • Correct bias of mX moments • due to unmeasured particles D,D* higher-mass states

14. Global Fit to Moments measured moments theory (HQE) <Ee> <(Ee-<Ee>)2> DB <(Ee-<Ee>)3> b → sg b → sg <MX2> <MX4> <Eg> <(Eg-<Eg>)2> lepton momentum cut • Every moment has a different dependence on |Vcb|, mb, mc, HQE par’s • Included in fit: ●, not included: ◦

15. Fit Results: |Vcb| and b-Quark Mass s(|Vcb|) < 2% s(mb) ≈ 1% + results for mc, HQE parameters (e.g. mp2)

17. Charmless Semileptonic Decays We want to measure this ! B → Xu ℓ n Biggest experimental challenge: huge B → Xc ℓ n bkg

18. B → Xu ℓ n Inclusive Rate lepton energy Eℓ q2 = (pℓ+pv)2 hadron mass mX P+ = EX-pX • Suppression of B → Xc ℓ n by restricting phase space (mu < mc) •  measure partial rates: • Big caveat:HQE conversionruined inlimited phase space! • Need to resum non-perturbative contributions •  non-perturbative distribution function (“shape function”)

19. Shape Function – What Is It? B  Xuln E*(lepton) (GeV) B  Xs g E*(photon) (GeV) • Shape function = light-cone momentum distribution of b quark: f(k+) • ≈ Fermi motion of b quark parallel to u-quark velocity • Universal property of B mesons (to leading order) • Consequences: Smearing of kinematic spectra !

20. Shape Function – How to Measure It? • From B → Xc ℓ n (and B → Xsg): HQE Assume functional form of f(k+)

21. Theory Calculations • Measure partial rate in region where S/B good and rate prediction reliable Problem at high q2: Weak Annihilation (WA)

22. Lepton-Energy “Endpoint” Inclusive: events with electron (Ee > 1GeV) on-peak data Continuum Subtract e+e- qq - off-peak data, - on-peak beyond Ee endpoint on-peak data (cont. subtr.) Simulated B Xcln • Subtract B  Xcℓn • fit simulation to data on-peak data (all bkg subtr.) Simulated signal Spectrum needs to be corrected for efficiency predicted partial rate DB(B  Xen) = (0.57 ±0.04stat ±0.07syst) × 10-3 |Vub| = (4.44 ± 0.25exp ± 0.40SF± 0.22theo) ×10-3

23. |Vub| from other Kinematic Spectra 383M BB P+=Ex - |Px| q2 Mx Not efficiency corrected BLNP GDE BLNP GDE BLNP GDE BLL • Hadronic B tags reconstruct kinematic spectra of signal B decay One data set: 3 calculations give 7 values for |Vub|!

24. |Vub| Results BLNP and SF moments from B → Xc ℓ n (and B → Xsg) |Vub|= (4.32 ± 0.16exp ± 0.32th) x 10-3 Error Budget Total Error: 8.9 % Exp. 3.8% Theo. 8.1%

25. |Vub| Average for Various Theories • Many theoretical approaches  many |Vub| values • Results vary from • 3.76 x 10-3 to 4.92 x 10-3 •  not very satisfactory! • Goal for the future: • Try to measure full rate • (or as much as possible) • to avoid shape function •  HQE converges

27. |Vcb| from Exclusive Decays: Theoretical Tools • Form factors (Caprini et al.): From Lattice QCD From Experiment • Differential decay rate: w = 1

28. B → D/D* ℓ n D D* D* M2miss (GeV2) G(1)|Vcb| G(1)|Vcb| slope r2D D D w w • Hadronic B tag • D0→ K-p+ • D*0 → D0p0soft • Determine exclusive • yields in 10 w bins • from fit to M2miss • 2 fit of Caprini et al. • to wspectrum

29. Simultaneous Measurement of D and D* • No psoft reconstruction for D* • Get D/D* rates from binned • 3d fit to pℓ, pD, cosqBY • (pD correlated to w •  sensitivity to rD, rD*,|Vcb|) • Relate BF(B0) to BF(B+) • using lifetime ratio • Fix D** rate (HFAG average)

30. Status of Exclusive |Vcb| B → D ℓ n B → D* ℓ n compare with inclusive: (41.6 ± 0.6) x 10-3  2.3 s difference

31. Anatomy of Semileptonic Decays: D** BaBar preliminary Tagged GeV/c2 Charm states • Use D** as nickname for • D(*) (np) with n ≥ 1 • Narrow states : D1 , D2* • Broad states : D0*, D1’ • Untagged meas. by BaBar (narrow), • tagged meas. by BaBar and Belle • (narrow and broad)

32. Where is the Rest? • Many measurements, but some unsolved puzzles remain: • Inclusive BF ≠ BF(D) + BF(D*) + BF(D**) • > 10% of inclusive rate is missing  non-resonant? • (2) Measured rate for narrow and broad D** states is similar, • but QCD sum rules predict Gnarrow ≈ O(10) Gbroad

34. Exclusive |Vub| r0 p+ h h r+ p0 non-resonant • |Vub| • strong interaction •  form factors = p, h, h’, r, w

35. Overview of Analyses • Many measurements with different tagging techniques  New result (2008) Currently most precise

36. B → pℓnUntagged • Reconstruct neutrino from full event: • Extract signal yield in 12 q2bins from fit toDE vs. mES distributions: BaBar 206 fb-1 • Continuum - low and high q2 • checked with • offres. data Signal • B → Xuℓn • high q2 • -large • uncertainty • B → Xcℓn • medium q2 • overall • largest bkg. Total: Nsig~ 5000

37. q2 Dependence & Form Factor Form-factor calculations Measured q2 spectrum α= 0.52±0.05±0.03 BaBar 206 fb-1 • Use form-factor parametrization to extrapolate LCSR (low q2) • and LQCD(high q2) to all q2: e.g. modified pole approximation (shape parameter a)

38. B → pℓnBranching Fraction and |Vub| untagged Untagged measurement still dominates the average (sstat < ssyst = 5%)

39. Towards a Model-Independent |Vub| f+(q2) q2 (GeV2)

40. Heavier Charmless Resonances 605 fb-1 • Hadronic tagsuseful for measurement of heavier resonances • Pseudoscalar mesons : h → ppp0, h→ hp+p- • Vector mesons :r → p p , w → p+p-p • |Vub| from these modes would be a useful cross-checks of B → pℓ n • LCSR calculations exist; LQCDcalculations aredifficult for these states!

41. |Vub| & CKM Consistency Inclusive • Most probable value of |Vub|from measurements ofother CKM parameters • Standard Model and exclusive result agree well, inclusive results lie • consistently higher • More work on experimental and theoretical side needed

42. Inclusive vs. Exclusive |Vub|: Latest News almost full rate incl. |Vub| higher! • New inclusive (multivariate) analysis from Belle (CKM08) • New Lattice Results FNAL/MILC (2008) excl. |Vub| lower!

43. Tau Final States & New Physics W- or H- • Decay can be mediated by charged Higgs boson • Very clean probe of New Physics • New Physics contributes at tree level • Light-lepton modes well studied •  QCD effects “under control” • Spin-0 Higgs does not couple to all helicity states •  D and D* modes affected differently • No helicity suppression (access to suppress form factor, f0)

44. B → D(*) tn: Signal Fit

45. B → D(*) tn: Lepton-Momentum Projections

46. B → D(*) tn: Results • Standard Model: • Belle: • BaBar: tanb M(H+) Significances: 3.6s (D) , 6.2s (D*) B → D t n already restricts Higgs parameter space in 2HDM, MSSM

47. Conclusions 2004 2008 • An impressive amount of work has been done! • (*) From inclusive measurements, but better agreement with • exclusive measurements required • Progress from theory needed: inclusive rates and form factors (LQCD) • B → D(*)tn can yield powerful new physics/Higgs constraints • with more statistics

48. Outlook – A Super B Factory (*) limited by theory

49. Outlook – A Super B Factory (*) limited by theory “The nightmare”

50. Outlook – A Super B Factory (*) limited by theory “The nightmare” “The dream”