1. Semileptonic B Decays at B A B AR Masahiro Morii Harvard University BNL Particle Physics Seminar, 13 January 2005

2. 13 January 2005M. Morii, Harvard2 Outline Introduction PEP-II and B A B AR Experiment Why semileptonic B decays? Measurements Inclusive b → cℓv  |V cb |, m b, m c Inclusive b → uℓv  |V ub | Exclusive B → D * ℓv  |V cb | Exclusive B →  ℓv  |V ub | Summary

3. 13 January 2005M. Morii, Harvard3 PEP-II Asymmetric B Factory Collides 9 GeV e − against 3.1 GeV e + E CM = 10.58 GeV = mass of  (4S)  Lightest bb resonance that decays into BB meson pair Boost  = 0.56 allows measurement of B decay times Peak luminosity 9.2×10 33 /cm 2 /s  BB production ~10 Hz More than 3× the design luminosity!

4. 13 January 2005M. Morii, Harvard4 PEP-II Luminosity B A B AR has accumulated 244 fb  1 of data Run 4 (Sep’03-Jul’04) was a phenomenal success Run 4

5. 13 January 2005M. Morii, Harvard5 B A B AR Detector Precise vertex with a silicon strip detector Charged particle momentum with a drift chamber in a 1.5 T field Photon energy with a CsI(Tl) crystal calorimeter Particle ID with a Cerenkov detector (DIRC) Muons detected after penetrating iron yoke

6. 13 January 2005M. Morii, Harvard6 B Mesons, CP violation B Factories produce ~2×10 8 B mesons/year B + and B 0 are the most accessible 3rd-generation particles Their decays allow detailed studies of the CKM matrix Unitary matrix V CKM translates mass and weak basis 3 real parameters + 1 complex phase Is this the complete description of the CP violation? Is everything consistent with a single unitary matrix? The only source of CPV in the Minimal SM

7. 13 January 2005M. Morii, Harvard7 Unitarity Triangle Unitarity of V CKM This is neatly represented by the familiar Unitarity Triangle Angles  can be measured with CPV of B decays Measurements of  from B A B AR, by Soeren Prell, 1/20/05 Measurements of  and  from B A B AR, by Malcolm John, 2/20/05 Coming soon:

8. 13 January 2005M. Morii, Harvard8 Consistency Test Compare the measurements (contours) on the ( ,  ) plane If the SM is the whole story, they must all overlap The tells us this is true as of today Still large enough for New Physics to hide Precision of sin2  outstripped the other measurements Must improve the others to make more stringent test

9. 13 January 2005M. Morii, Harvard9 Next Step: |V ub /V cb | Zoom in to see the overlap of “the other” contours It’s obvious: we must make the green ring thinner Left side of the Triangle is Measurement of |V ub /V cb | is complementary to sin2  Goal: Accurate determination of both |V ub /V cb | and sin2 

10. 13 January 2005M. Morii, Harvard10 Semileptonic B Decays Semileptonic decays offer a clear view of the b quark in the B mesons Analogous to deep-inelastic scattering  Good probe for |V cb | and |V ub |  We can also study the structure of the B meson decoupled from hadronic effects More on this as we go

11. 13 January 2005M. Morii, Harvard11 Experimental Approaches Inclusive: B → X c ℓv or X u ℓv Tree-level rates are QCD corrections must be calculated  Operator Product Expansion (OPE) How do we separate X u from X c ?   c = 50 ×  u  Much harder problem for |V ub | Exclusive: B → D * ℓv, Dℓv,  ℓv,  ℓv, etc. Need form factors to relate the rate to |V cb |, |V ub | Focus of this talk

12. 13 January 2005M. Morii, Harvard12 Inclusive |V cb | Operator Product Expansion allows calculation of  Inclusive rate  Lepton energy (E ℓ ) moments  Hadron mass (m X ) moments Expansion in terms of 1/m b and  s (m b ) Separate short- and long-distance effects at  ~ 1 GeV  Perturbative corrections calculable from m b, m c,  s (m b )  Non-perturbative corrections cannot be calculated Ex: 4 parameters up to in the kinetic scheme Strategy: Measure rate + as many moments as possible  Determine all parameters by a global fit  Over-constrain to validate the method

13. 13 January 2005M. Morii, Harvard13 Observables Define 8 moments from inclusive E ℓ and m X spectra  Integrations are done for E ℓ > E cut, with E cut varied in 0.6–1.5 GeV Partial branching fraction Lepton energy moments Hadron mass moments

14. 13 January 2005M. Morii, Harvard14 Electron Energy Moments B A B AR data, 47.4 fb -1 on  (4S) resonance + 9.1 fb -1 off-peak Select events with 2 electrons One (1.4 < p * < 2.3 GeV) to “tag” a BB event The other (p * > 0.5 GeV) to measure the spectrum Use charge correlation Unlike-sign events  dominated by B  X c ev Like-sign events  D  Xev decays, B 0 mixing B A B AR PR D69:111104 Unlike-sign Like-sign B A B AR

15. 13 January 2005M. Morii, Harvard15 Electron Energy Moments Turn the like-/unlike-sign spectra  E ℓ spectrum Divide by the efficiency Account for B 0 mixing Correct for the detector material (Bremsstrahlung) Calculate the moments for E cut = 0.6 … 1.5 GeV Move from  (4S) to B rest frame Correct for the final state radiation using PHOTOS Subtract B  X u ℓv B A B AR Into the OPE fit B A B AR PR D69:111104

16. 13 January 2005M. Morii, Harvard16 Hadron Mass Moments B A B AR data, 81 fb -1 on  (4S) resonance Select events with a fully-reconstructed B meson Use ~1000 hadronic decay chains Rest of the event contains one “recoil” B  Flavor and momentum known Find a lepton with E > E cut in the recoil-B Lepton charge consistent with the B flavor m miss consistent with a neutrino All left-over particles belong to X c Improve m X with a kinematic fit   = 350 MeV  4-momentum conservation; equal m B on both sides; m miss = 0 B A B AR PR D69:111103 Fully reconstructed B  hadrons lepton v XcXc

17. 13 January 2005M. Morii, Harvard17 Hadron Mass Moments Measured m X < true m X Linear relationship  Calibrate using simulation  Depends (weakly) on decay multiplicity and Validate calibration procedure Simulated events in exclusive final states D *±  D 0   ± in real data, tagged by the soft   ± Calculate mass moments with E cut = 0.9 … 1.6 GeV Into the OPE fit B A B AR B A B AR PR D69:111103

18. 13 January 2005M. Morii, Harvard18 Inputs to OPE Fit m X moments E ℓ moments B A B AR B A B AR PRL 93:011803 Error bars are stat. & syst. with comparable sizes

19. 13 January 2005M. Morii, Harvard19 Fit Parameters Calculation by Gambino & Uraltsev (hep-ph/0401063 & 0403166) Kinetic mass scheme to E ℓ moments m X moments 8 parameters to determine 8 moments available with several E cut Sufficient degrees of freedom to determine all parameters without external inputs Fit quality tells us how well OPE works kinetic chromomagnetic Darwin spin-orbit B A B AR PRL 93:011803

20. 13 January 2005M. Morii, Harvard20 Fit Results m X moments E ℓ moments ● = used, ○ = unused in the nominal fit Red line: OPE fit Yellow band: theory errors B A B AR   2 /ndf = 20/15 B A B AR PRL 93:011803

21. 13 January 2005M. Morii, Harvard21 Fit Consistency OPE describes B A B AR data very well   2 /ndf = 20/15 Separate fit of E ℓ and m X moments agree B A B AR B A B AR PRL 93:011803

22. 13 January 2005M. Morii, Harvard22 Fit Results and consistent with B-B * mass splitting and QCD sum rules and the scale of consistent with theoretical expectations Remarkable agreement between data and theory kinetic mass scheme with  = 1 GeV Uncalculated corrections to  B A B AR PRL 93:011803

23. 13 January 2005M. Morii, Harvard23 Heavy Quark Masses Convert m b and m c into MS scheme (N. Uraltsev) theory References in PDG 2002

24. 13 January 2005M. Morii, Harvard24 Inclusive |V cb | in Perspective B A B AR result compares well with previous measurements |V cb | is now measured to ±2%

25. 13 January 2005M. Morii, Harvard25 Inclusive |V ub | |V ub | can be measured from The problem: b → cℓv decay Use m u << m c  difference in kinematics Maximum lepton energy 2.64 vs. 2.31 GeV First observations (CLEO, ARGUS, 1990) used this technique Only 6% of signal accessible  How accurately do we know this fraction? How can we suppress 50× larger background?

26. 13 January 2005M. Morii, Harvard26 b → uℓv Kinematics There are 3 independent variables in B → Xℓv Take E ℓ, q 2 (lepton-neutrino mass 2 ), and m X (hadronic mass) 6% 20% 70% TechniqueEfficiencyTheoretical Error EℓEℓ StraightforwardLowLarge q2q2 ComplicatedModerate mXmX ComplicatedHighLarge Where does it come from?

27. 13 January 2005M. Morii, Harvard27 Theoretical Issues Tree level rate must be corrected for QCD Operator Product Expansion gives us the inclusive rate Expansion in  s (m b ) (perturbative) and 1/m b (non-perturbative) Main uncertainty (±10%) from m b 5  ±5% on |V ub | But we need the accessible fraction (e.g., E ℓ > 2.3 GeV) of the rate known to  (  s 2 ) Suppressed by 1/m b 2

28. 13 January 2005M. Morii, Harvard28 Shape Function OPE doesn’t work everywhere in the phase space OK once integrated Doesn’t converge, e.g., near the E ℓ end point Resumming turns non-perturb. terms into a Shape Function ≈ b quark Fermi motion parallel to the u quark velocity Smears the quark-level distribution  observed spectra Rough features (mean, r.m.s.) are known Details, especially the tail, are unknown

29. 13 January 2005M. Morii, Harvard29 Shape Function – What to Do? Measure: Same SF affects (to the first order) b → s  decays Caveat: whole E  spectrum is needed  Only E  > 1.8 GeV has been measured  Background overwhelms lower energies Compromise: assume functional forms of f(k + )  Example:  Fit b → s  spectrum to determine the parameters  Try different functions to assess the systematics Measure E  spectrum in b → s  Extract f(k + ) Predict E ℓ spectrum in b → uℓv 1.8 2 parameters (  and a) to fit

30. 13 January 2005M. Morii, Harvard30 SF from b → s  CLEO and Belle has measured the b → s  spectrum B A B AR result on the way I use the SF from the Belle data for the rest of the talk CLEO hep-ex/0402009 Belle hep-ex/0407052 Belle Fit 3 models tried

31. 13 January 2005M. Morii, Harvard31 Measurements B A B AR has measured |V ub | using four different approaches Statistical correlations are small Different systematics, different theoretical errors TechniqueReference E ℓ > 2.0 GeV hep-ex/0408075 E ℓ vs. q 2 hep-ex/0408045 m X < 1.55 GeV hep-ex/0408068 m X vs. q 2 Inclusive B → Xev sample. High statistics, low purity. Recoil of fully-reconstructed B. High purity, moderate statistics.

32. 13 January 2005M. Morii, Harvard32 Lepton Endpoint B A B AR data, 80 fb -1 on  (4S) resonance Select electrons in 2.0 < E ℓ < 2.6 GeV Push below the charm threshold  Larger signal acceptance  Smaller theoretical error Accurate subtraction of background is crucial! Data taken below the  4S resonance for light-flavor background Fit the E ℓ spectrum with b → uℓv, B → Dℓv, B → D * ℓv, B → D ** ℓv, etc. to measure Data (eff. corrected) MC Data (continuum sub) MC for BB background B A B AR hep-ex/0408075

33. 13 January 2005M. Morii, Harvard33 Lepton Endpoint Translate   into |V ub | Compare results with different E ℓ cut Theoretical error reduced with lower E ℓ cut E ℓ (GeV)   (10 -4 ) |V ub | (10 -3 ) B A B AR 2.0–2.64.85 ± 0.29 stat ± 0.53 sys 4.40 ± 0.13 stat ± 0.25 sys ± 0.38 theo CLEO2.2–2.62.30 ± 0.15 exp ± 0.35 sys 4.69 ± 0.15 stat ± 0.40 sys ± 0.52 theo Belle2.3–2.61.19 ± 0.11 exp ± 0.10 sys 4.46 ± 0.20 stat ± 0.22 sys ± 0.59 theo B A B AR hep-ex/0408075 CLEO PRL 88:231803 BELLE-CONF-0325

34. 13 January 2005M. Morii, Harvard34 E ℓ vs. q 2 Use p v = p miss in addition to p e  Calculate q 2 Given E e and q 2, maximum hadronic mass squared is gives optimum separation of B → X u ev from X c ev X u ev signalX c ev background  = B boost in the c.m.s. B A B AR hep-ex/0408045

35. 13 January 2005M. Morii, Harvard35 E ℓ vs. q 2 B A B AR data, 80 fb -1 on resonance Subtract off-peak data Subtract BB background normalized by sideband Signal efficiency corrected by B → D (*) ev control samples Inclusive BF measured to be Translate to |V ub | B A B AR hep-ex/0408045

36. 13 January 2005M. Morii, Harvard36 Measuring m X and q 2 Same recoil technique as the b → cℓv m X moment measurement Find a lepton (p ℓ > 1GeV) in recoil B Lepton charge consistent with the B flavor m miss consistent with a neutrino All left-over particles belong to X Improve m X with a kinematic fit Calculate q 2 of lepton-neutrino Sample is mostly b → c ℓ v at this stage Need some charm rejection cuts Fully reconstructed B  hadrons lepton v X B A B AR hep-ex/0408068

37. 13 January 2005M. Morii, Harvard37 Charm Suppression Suppress b → c ℓ v by vetoing against D (*) decays D decays usually produce at least one kaon  Reject events with K ± and K S B 0 → D *+ (→ D 0   + ) ℓ − v has peculiar kinematics    + almost at rest w.r.t. D *+  D *+ momentum can be estimated from   + alone  Calculate for all   +  Reject events consistent with m v = 0 Vetoed events are depleted in b → uℓv Use them to validate simulation of background distributions We’ve got (m X, q 2 ) distribution of a signal-enriched sample B A B AR hep-ex/0408068

38. 13 January 2005M. Morii, Harvard38 Fitting m X B A B AR data, 80 fb -1 on resonance Simple fit in m X shows clear b → uℓv signal Inclusive BF measured to be B A B AR hep-ex/0408068 B A B AR

39. 13 January 2005M. Morii, Harvard39 Fitting m X vs. q 2 2-D fit to measure   in {m X 8} Good resolution allows clean extraction of   Signal event fraction into the “box” calculated by Bauer et al. hep-ph/0111387 G = 0.282 ± 0.053 B A B AR hep-ex/0408068

40. 13 January 2005M. Morii, Harvard40 Inclusive |V ub | Results Summary of B A B AR |V ub | results Statistical correlation between the m X and m X -q 2 results is 72%. Others negligible Theoretical error of the m X -q 2 result is different from the rest  Negligible SF dependence Technique|V ub | × 10 3  (SF) × 10 3 E ℓ > 2.0 GeV4.40 ± 0.13 stat ± 0.25 sys ± 0.38 theo 0.46 E ℓ vs. q 2 4.99 ± 0.23 stat ± 0.42 sys ± 0.32 theo 0.42 m X < 1.55 GeV5.22 ± 0.30 stat ± 0.31 sys ± 0.43 theo 0.45 m X vs. q 2 4.98 ± 0.40 stat ± 0.39 sys ± 0.47 theo 0.06 How much |V ub | moves if the SF is determined by the CLEO data B A B AR hep-ex/0408075 B A B AR hep-ex/0408045 B A B AR hep-ex/0408068

41. 13 January 2005M. Morii, Harvard41 m X vs. q 2 Inclusive |V ub | in Perspective |V ub | is measured to ±9%? E ℓ endpoint m X fit E ℓ vs. q 2 Results have been re-adjusted by the Heavy Flavor Averaging Group

42. 13 January 2005M. Morii, Harvard42 Caveats + Outlook Improved precision of |V ub | require re-evaluation of theoretical uncertainties Poor convergence of OPE calculation in the small m X region  Improved calculations using SCET available now NLO(1/m b ) non-perturbative corrections differ between b → uℓv and b → s   Quantitative estimates in literature more-or-less agree Weak annihilation diagrams may have large (20%?) effect near the lepton energy endpoint  Difference between B 0 and B + needs to be measured Theory and experiment join forces to push the limit

43. 13 January 2005M. Morii, Harvard43 Exclusive |V cb | B  D * ℓv decay rate is given by  (w) is calculable at w = 1, i.e. zero-recoil   (1) = 1 at the heavy-quark limit (m b = m c = ∞)  Lattice calculation gives Shape of  (w) unknown  Parameterized with  2 (slope at w = 1) and R 1, R 2  Use R 1 and R 2 determined by CLEO, PRL 76 (1996) 3898 Measure d  /dw to fit  (1)|V cb | and  2 phase space form factor D * boost  in the B rest frame Hashimoto et al, PRD 66 (2002) 014503

44. 13 January 2005M. Morii, Harvard44 B  D*ℓv Sample B A B AR data, 80 fb -1 on  (4S) Find events with D *+ + lepton with 1.2 < p ℓ < 2.4 GeV/c Background Fake D *  D * – D mass difference True D * but not B  D * ℓv B A B AR hep-ex/0408027

45. 13 January 2005M. Morii, Harvard45 Determination of F(1)|V cb | Correct for efficiency  w distribution Slow pion (from D * decays) efficiency depend on w Fitting dN/dw, we find B A B AR hep-ex/0408027

46. 13 January 2005M. Morii, Harvard46 Determination of |V cb | B A B AR result compares well with existing measurements  Results have been adjusted to use common inputs Using  (1) = 0.91 ± 0.04, the world average is Agrees with the inclusive measurement Accuracy ±5%

47. 13 January 2005M. Morii, Harvard47 Exclusive |V ub | Measure specific final states, e.g., B →  ℓv Good signal-to-background ratio Branching fraction in  (10 -4 )  Statistics limited So far B →  ℓv and  ℓv have been measured Also seen:  (B →  ℓv) = (1.3±0.5)×10 −4 [Belle hep-ex/0402023]  (B →  ℓ v) = (0.84±0.36)×10 −4 [CLEO PRD68:072003] Need Form Factors to extract |V ub | e.g. How are they calculated?

48. 13 January 2005M. Morii, Harvard48 Form Factors Form Factors are calculated using: Lattice QCD (q 2 > 16 GeV 2 )  Existing calculations are “quenched”  ~15% uncertainty Light Cone Sum Rules (q 2 < 16 GeV 2 )  Assumes local quark-hadron duality  ~10% uncertainty All of them have uncontrolled uncertainties LQCD and LCSR valid in different q 2 ranges  No crosscheck Unquenched LQCD starts to appear Preliminary B →  ℓv FF from FNAL+MILC (hep-lat/0409116), HPQCD (hep-lat/0408019) Current technique cannot do B →  ℓv

49. 13 January 2005M. Morii, Harvard49 Measurements Concentrate on B →  ℓv Total rate is measured to ~12% accuracy Need measurement in bins of q 2  LQCD calculation of FF available above 16 GeV 2  Small rate  Large statistical errors New measurements + unquenched LQCD calculations will make |V ub | extraction possible B Sample  (B →  ℓv) × 10 4 q 2 binsReference B A B AR Recoil of B → hadrons1.08 ± 0.28 stat ± 0.16 sys 1 hep-ex/0408068 Recoil of B → D * ℓv1.46 ± 0.27 stat ± 0.35 sys 3 [ICHEP 2004] BelleRecoil of B → D (*) ℓv1.76 ± 0.28 stat ± 0.20 sys 3 hep-ex/0408145 CLEOUntagged1.33 ± 0.18 stat ± 0.13 sys 3 PR D68,072003

50. 13 January 2005M. Morii, Harvard50 Summary Semileptonic decays provide excellent probes for the weak and strong physics of the B mesons |V cb | and |V ub |  Complementary to sin2  from CP violation Heavy quark masses and the non-perturbative parameters |V cb | has been determined to ±2% OPE fit of E ℓ and m X moments by B A B AR gives  Fit quality and consistency support validity of the OPE application Exclusive B  D * ℓv measurements agree World average by HFAG

51. 13 January 2005M. Morii, Harvard51 Summary Significant progress in determination of |V ub | Four (!) B A B AR measurements of |V ub | with inclusive b → uℓv  Overall accuracy of |V ub | around 10% New measurements of B →  ℓv + unquenched LQCD calculations will measure |V ub | soon Technique|V ub | × 10 3 E ℓ > 2.0 GeV4.40 ± 0.13 stat ± 0.25 sys ± 0.38 theo E ℓ vs. q 2 4.99 ± 0.23 stat ± 0.42 sys ± 0.32 theo m X < 1.55 GeV5.22 ± 0.30 stat ± 0.31 sys ± 0.43 theo m X vs. q 2 4.98 ± 0.40 stat ± 0.39 sys ± 0.47 theo