1. B Physics Beyond CP Violation — Semileptonic B Decays — Masahiro Morii Harvard University MIT LNS Colloquium, 2004

2. LNS Colloquium 2004M. Morii, Harvard2 Outline Introduction: Why semileptonic B decays? CP violation — Unitarity Triangle — |V ub | vs. sin2  |V ub | from inclusive b → uℓv decays Measurements: lepton energy, hadron mass, lepton-neutrino mass Theoretical challenge: Shape function |V ub | from exclusive b → uℓv decays Measurements: B →  ℓv Theoretical challenge: Form factors Summary

3. LNS Colloquium 2004M. Morii, Harvard3 History of CP Violation (1) 1964: Cronin & Fitch discover CPV K L (thought to be CP = −1) decayed into   +   − (CP = +1) 1973: Kobayashi-Maskawa mechanism proposed Unitary matrix V CKM translates mass and weak basis 3 real parameters + 1 complex phase 1974: charm quark, 1975:  lepton, 1977: bottom quark The only source of CPV in the Minimal SM

4. LNS Colloquium 2004M. Morii, Harvard4 History of CP Violation (2) 1970s–90s: CPV in K 0 -K 0 mixing (  ) studied in great details ~1999: Direct CPV in K 0 decays (  ') confirmed KM mechanism most likely explanation 1999: B A B AR and Belle start taking data 2001: CPV in B 0 decays (sin2  ) measured Agrees with expectation from the KM mechanism Kobayashi-Maskawa mechanism is likely the dominant source of the CP violation observed in the lab Is it the sole source?

5. LNS Colloquium 2004M. Morii, Harvard5 Quantitative Test CKM matrix has 4 free parameters All but the two smallest elements V ub and V td are well measured In order to test the “KM-only” hypothesis: Interpret measurements assuming the minimal SM is correct Either CPV or non-CPV as long as they are sensitive to V ub and V td Turn them into constraints on ( ,  ) and compare It would be nice to express this graphically… Wolfenstein parameterization

6. LNS Colloquium 2004M. Morii, Harvard6 Unitarity Triangle V CKM is unitary This is neatly represented by the familiar Unitarity Triangle Each measurement constrains the apex position ( ,  ) The only complex phases of  (1) in the minimal SM

7. LNS Colloquium 2004M. Morii, Harvard7 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

8. LNS Colloquium 2004M. Morii, Harvard8 Next Step: |V ub | 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 Uncertainty dominated by ~15% on |V ub | Measurement of |V ub | is complementary to sin2  Goal: Accurate determination of both |V ub | and sin2 

9. LNS Colloquium 2004M. Morii, Harvard9 Measuring |V ub | Best probe: semileptonic b → u decay The problem: b → cℓv decay How can we suppress 50× larger background? Tree level decoupled from hadronic effects

10. LNS Colloquium 2004M. Morii, Harvard10 Detecting b → uℓv Inclusive: 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? Exclusive: Reconstruct final-state hadrons B →  ℓv, B →  ℓv, B →  ℓv, B →  ℓv, … Example: the rate for B →  ℓv is How accurately do we know the FFs? Form Factor (3 FFs for vector mesons)

11. LNS Colloquium 2004M. Morii, Harvard11 Inclusive b → uℓv 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?

12. LNS Colloquium 2004M. Morii, Harvard12 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

13. LNS Colloquium 2004M. Morii, Harvard13 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

14. LNS Colloquium 2004M. Morii, Harvard14 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

15. LNS Colloquium 2004M. Morii, Harvard15 SF from b → s  CLEO and Belle has measured the b → s  spectrum B A B AR result on the way Statistical errors dominate the uncertainty around the peak Model dependence important in the tail CLEO hep-ex/0402009 Belle hep-ex/0407052 Belle Fit 3 models tried

16. LNS Colloquium 2004M. Morii, Harvard16 Predicting b → uℓv Spectra OPE + SF can predict triple-differential rate De Fazio, Neubert (JHEP 9906:017) Every experiment uses DFN for simulating b → uℓv signal Unreliable in the “SF region” where OPE converges poorly Small m X and small q 2  X is jet-like The right tool: Soft Collinear Effective Theory 6% 20% 70%

17. LNS Colloquium 2004M. Morii, Harvard17 Soft Collinear Effective Theory Developed since 2001 by Bauer, Fleming, Luke, Pirjol, Stewart PRD63:014006, PRD63:114020, PRD65:054022 Applied to b → uℓv in the SF region by several groups Bauer, Manohar (PRD70:034024) Bosch, Lange, Neubert, Paz (NPB699:335) Lee, Stewart (hep-ph/0409045) Caveat: Works only in the SF region We tried implementing an event generator with limited success Wanted: Theoretically-sound b → uℓv Monte Carlo generator THAT WORKS

18. LNS Colloquium 2004M. Morii, Harvard18 Lepton Endpoint Select electrons in 2.0 < E ℓ < 2.6 GeV 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 BABAR hep-ex/0408075 CLEO PRL 88:231803 BELLE-CONF-0325 E ℓ (GeV)   (10 -4 ) B A B AR 2.0–2.64.85 ± 0.29 stat ± 0.53 sys CLEO2.2–2.62.30 ± 0.15 stat ± 0.35 sys Belle2.3–2.61.19 ± 0.11 stat ± 0.10 sys

19. LNS Colloquium 2004M. Morii, Harvard19 Lepton Endpoint Translate   into |V ub | using the SF parameters from Belle Lower E ℓ cut-off reduces theoretical uncertainty to ~10% But … theorists raise possibilities of additional uncertainties Sub-leading SFs, 4-quark operators, weak annihilation 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 ± 0.15 exp ± 0.44 th CLEO2.2–2.62.30 ± 0.15 exp ± 0.35 sys 4.69 ± 0.23 exp ± 0.63 th Belle2.3–2.61.19 ± 0.11 exp ± 0.10 sys 4.46 ± 0.23 exp ± 0.61 th Recalculated by the Heavy Flavor Averaging Group BABAR hep-ex/0408075 CLEO PRL 88:231803 BELLE-CONF-0325

20. LNS Colloquium 2004M. Morii, Harvard20 Measuring m X and q 2 Must reconstruct all decay products to measure m X or q 2 E ℓ was much easier B mesons produced in pairs Reconstruct one B in any mode  Rest of the event contains exactly one recoil B Find a lepton in the recoil B  Remaining part must be X in B  Xℓv Calculate m X and q 2 Fully reconstructed B  hadrons lepton v X

21. LNS Colloquium 2004M. Morii, Harvard21 Recoil B Sample Reconstruct B mesons in ~1000 channels used Efficiency ~0.2%/B Yield and purity from m B fit  Recoil B is a clean and unbiased sample of B mesons Charge and 4-momentum known Ideal for measuring branching fractions

22. LNS Colloquium 2004M. Morii, Harvard22 Recoil B → Xℓv Find an ℓ = e ± or  ± (p ℓ > 1GeV) in recoil B and require Total event charge = 0 If it’s a B ±, Q ℓ = Q B Missing 4-momentum consistent with a massless neutrino 2-C kinematical fit to determine p X 4-momentum conservation m v = 0, m B = m B  m X resolution ~ 350 MeV Sample is mostly b → c ℓ v at this stage B  hadrons lepton v X

23. LNS Colloquium 2004M. Morii, Harvard23 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 Used to validate simulation of background distributions We’ve got (m X, q 2 ) distribution of a signal-enriched sample

24. LNS Colloquium 2004M. Morii, Harvard24 Extracting b → uℓv Signal Fit m X to extract  (B → X u ℓv) Best variable for charm rejection  Best statistical error Strong shape-function dependence Fit m X vs. q 2 to extract   (B → X u ℓv) Restrict to, e.g., m X 8 GeV 2 Reduced shape-function dependence Unfold detector effects to get true m X spectrum Limited statistical power Potential for constraining shape function

25. LNS Colloquium 2004M. Morii, Harvard25 Fitting m X Simple fit in m X shows clear b → uℓv signal Signal modeled by DFN with Belle SF Translate to |V ub | Theoretical error ~8%, but strong dependence on the shape function |V ub | moves by 0.45×10 −3 if CLEO SF parameters are used BABAR 80fb -1 hep-ex/0408068 B A B AR

26. LNS Colloquium 2004M. Morii, Harvard26 Unfolding m X Unfold detector efficiency and resolution  true m X spectrum NB: error bars are correlated Matches simulation with different shape functions (curves) Not enough statistics to extract shape function parameters B A B AR has 3× more data Measured m X spectrum Background subtraction Detector unfolding BABAR 80fb -1 hep-ex/0408068

27. LNS Colloquium 2004M. Morii, Harvard27 Fitting m X vs. q 2 – B A B AR Split b → uℓv signal into {m X 8} and elsewhere 2-D fit to measure   in the former region yields BABAR 80fb -1 hep-ex/0408068

28. LNS Colloquium 2004M. Morii, Harvard28 Fitting m X vs. q 2 – Belle Belle has a nearly identical analysis Belle 140fb -1 hep-ex/0408115

29. LNS Colloquium 2004M. Morii, Harvard29 Turning   into |V ub | From Bauer, Ligeti, Luke (hep-ph/0111387) Theoretical error ~10% B A B AR result moves by 0.06×10 −3 with CLEO SF params B A B AR result moves by 0.20×10 −3 with DFN  Results are more stable than the m X fit G = 0.282 ± 0.053 using Belle SF BABAR 80fb -1 hep-ex/0408068 Belle 140fb -1 hep-ex/0408115 |V ub | (10 -3 ) B A B AR 4.98 ± 0.40 stat ± 0.39 syst ± 0.47 theo Belle5.54 ± 0.42 stat ± 0.50 syst ± 0.54 theo

30. LNS Colloquium 2004M. Morii, Harvard30 m X vs. q 2 Status of Inclusive |V ub | E ℓ endpoint m X fit

31. LNS Colloquium 2004M. Morii, Harvard31 Exclusive b → uℓv 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 |

32. LNS Colloquium 2004M. Morii, Harvard32 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 Other approaches 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

33. LNS Colloquium 2004M. Morii, Harvard33 Measuring B →  ℓv Concentrate on B →  ℓv with q 2 binning CLEO [PRD 68:072003] Reconstruct  ℓv using missing 4-momentum as the neutrino Belle [hep-ex/0408145] Tag B → D (*) ℓv and look at m X distribution

34. LNS Colloquium 2004M. Morii, Harvard34 B →  ℓv – CLEO Missing 4-momentum = neutrino CLEO has a better solid-angle coverage than B A B AR /Belle Reconstruct B →  ℓv and calculate m B and  E = E B – E beam /2  Clear signal over background Red:  ℓv,  ℓv,  ℓv Yellow:other X u ℓv Green:continuum (udsc) Black:b → cℓv CLEO PRD 68:072003

35. LNS Colloquium 2004M. Morii, Harvard35 B →  ℓv – Belle Tag B → D (*) ℓv and look at the recoil B Similar to inclusive |V ub | measurements on recoil B D (*) ℓv tag is less pure, but more efficient Hadronic mass distribution shows  ℓv and  ℓv signals Belle hep-ex/0408145  ℓv  ℓv other X u ℓv q 2 < 88 < q 2 < 1616 < q 2

36. LNS Colloquium 2004M. Morii, Harvard36  (B →  ℓv) Small model-dependence due to efficiency estimation  (B →  ℓv) [10 −4 ]   (q 2 > 16 GeV 2 ) [10 −4 ] CLEO1.33 ± 0.18 ± 0.13 0.25 ± 0.09 ± 0.05 Belle1.76 ± 0.28 ± 0.20 0.46 ± 0.17 ± 0.06 CLEO PRD 68:072003 Belle hep-ex/0408145 CLEO Belle

37. LNS Colloquium 2004M. Morii, Harvard37 B →  ℓv to |V ub | FF from LQCD calculations Average of quenched LQCD results: FNAL’01, JLQCD’01, APE’01, UKQCD’00  Unquenched FNAL+MILC Unquenched HPQCD Uncertainty still large Mainly statistical Expect rapid progress in the next year Unquenched LQCD More data from B A B AR, Belle CLEO  ℓv Belle  ℓv CLEO PRD 68:072003 Belle hep-ex/0408145

38. LNS Colloquium 2004M. Morii, Harvard38 ? Exclusive b → uℓv Summary (1) B →  ℓv Inclusive b → uℓv m X -q 2 ?  ℓv,  ℓv ? b → s  Shape Function EE mbmb Inclusive b → cℓv mXmX EℓEℓ HQE Fit mXmX EℓEℓ WA duality LQCD FF quenched unquenched |V ub | SSFs

39. LNS Colloquium 2004M. Morii, Harvard39 Summary (2) Precise determination of |V ub | complements sin2  to test the (in)completeness of the Standard Model <10% accuracy around the corner Close collaboration between theory and experiment is crucial We keep pounding on the Triangle until we make a dent on it |V ub |

40. Backup Slides

41. LNS Colloquium 2004M. Morii, Harvard41 Penguins b → sss decay dominated by the “penguin” diagram In the SM, same CP asymmetry as b → ccs decays: sin2  New Physics may modify the loop  CP asymmetries may not agree Several decay channels are studied B 0 →   K S is pure-penguin Small BF: 7.6  10 -6 B 0 →  ’ K S has larger BF = 5.5  10 -5 Tree diagram affects the asymmetry by <0.1

42. LNS Colloquium 2004M. Morii, Harvard42 Status of Penguins Penguins disagree with sin2  by 2.7  (B A B AR ), 2.4  (Belle) Belle B A B AR

43. LNS Colloquium 2004M. Morii, Harvard43 Sub-leading Shape Functions Shape Function represents non-perturb. effects at  (1/m b 2 ) Next order (1/m b 3 )  4 Sub-leading Shape Functions Bauer, Luke, Mannel calculated their effects on E  (PRD68:094001) and E ℓ (PLB543:261) spectra Neubert (PLB543:269) estimated impact on |V ub | measurement  Errors quoted by HFAG New calculations using SCET appeared recently Lee, Stewart (hep-ph/0409045) Bosch, Neubert, Paz (hep-ph/0409115) Significant impact on |V ub | measured with E ℓ endpoint Re-evaluation of the SSF error is due

44. LNS Colloquium 2004M. Morii, Harvard44 B →  ℓv to |V ub | Average of quenched LQCD results FNAL’01, JLQCD’01, APE’01, UKQCD’00 Two preliminary unquenched LQCD results CLEO Belle Quenched FNAL’04 HPQCD CLEO PRD 68:072003 Belle hep-ex/0408145 LQCD calculation