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B Physics Beyond CP Violation — Semileptonic B Decays —

B Physics Beyond CP Violation — Semileptonic B Decays —. Masahiro Morii Harvard University MIT LNS Colloquium, 2004. Outline. Introduction: Why semileptonic B decays? CP violation — Unitarity Triangle — | V ub | vs. sin2 b | V ub | from inclusive b → uℓv decays

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B Physics Beyond CP Violation — Semileptonic B Decays —

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

  2. Outline • Introduction: Why semileptonic B decays? • CP violation — Unitarity Triangle —|Vub| vs. sin2b • |Vub| from inclusiveb→ uℓv decays • Measurements: lepton energy, hadron mass, lepton-neutrino mass • Theoretical challenge: Shape function • |Vub| from exclusiveb→ uℓv decays • Measurements: B→ pℓv • Theoretical challenge: Form factors • Summary M. Morii, Harvard

  3. History of CP Violation (1) • 1964: Cronin & Fitch discover CPV • KL(thought to be CP = −1) decayed into p+p−(CP = +1) • 1973: Kobayashi-Maskawa mechanism proposed • Unitary matrix VCKM translates mass and weak basis • 3 real parameters + 1 complex phase • 1974: charm quark, 1975: t lepton, 1977: bottom quark The only source of CPV in the Minimal SM M. Morii, Harvard

  4. History of CP Violation (2) • 1970s–90s: CPV in K0-K0 mixing (e) studied in great details • ~1999: Direct CPV in K0 decays (e') confirmed • KM mechanism most likely explanation • 1999: BABAR and Belle start taking data • 2001: CPV in B0 decays (sin2b) 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? M. Morii, Harvard

  5. Quantitative Test • CKM matrix has 4 free parameters • All but the two smallest elements Vub and Vtd 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 Vub and Vtd • Turn them into constraints on (r, h) and compare • It would be nice to express this graphically… Wolfensteinparameterization M. Morii, Harvard

  6. Unitarity Triangle • VCKM is unitary • This is neatly represented by the familiar Unitarity Triangle • Each measurement constrains theapex position (r, h) The only complex phases of O(1) in the minimal SM M. Morii, Harvard

  7. Consistency Test • Compare the measurements (contours) on the (r, h) plane • If the SM is the whole story,they must all overlap • The tells us this is trueas of today • Still large enough for NewPhysics to hide • Precision of sin2b outstrippedthe other measurements • Must improve the others tomake more stringent test M. Morii, Harvard

  8. Next Step: |Vub| • Zoom in to see the overlap of “the other” contours • It’s obvious: we must makethe green ring thinner • Left side of the Triangle is • Uncertainty dominated by~15% on |Vub| Measurement of |Vub| is complementary to sin2b Goal: Accurate determination of both |Vub| and sin2b M. Morii, Harvard

  9. Measuring |Vub| • Best probe: semileptonic b → u decay • The problem: b → cℓv decay • How can we suppress 50× larger background? decoupled from hadronic effects Tree level M. Morii, Harvard

  10. Detecting b → uℓv • Inclusive: Use mu << mc 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 → pℓv, B → rℓv, B → wℓv, B → hℓv, … • Example: the rate for B → pℓv is • How accurately do we know the FFs? Form Factor(3 FFs for vector mesons) M. Morii, Harvard

  11. Inclusive b → uℓv • There are 3 independent variables in B→Xℓv • Take Eℓ, q2 (lepton-neutrino mass2), and mX (hadronic mass) 6% 20% 70% Where does it come from? M. Morii, Harvard

  12. Theoretical Issues • Tree level rate must be corrected for QCD • Operator Product Expansion givesus the inclusive rate • Expansion in as(mb) (perturbative)and 1/mb (non-perturbative) • Main uncertainty (±10%) from mb5 ±5% on |Vub| • But we need the accessible fraction(e.g., Eℓ> 2.3 GeV) of the rate known to O(as2) Suppressed by 1/mb2 M. Morii, Harvard

  13. Shape Function • OPE doesn’t work everywhere in the phase space • OK once integrated • Doesn’t converge, e.g., near the Eℓ 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 M. Morii, Harvard

  14. Shape Function – What to Do? • Measure: Same SF affects (to the first order)b→ sg decays • Caveat: whole Eg spectrum is needed • Only Eg > 1.8 GeV has been measured • Background overwhelms lower energies • Compromise: assume functional forms of f(k+) • Example: • Fit b→ sg spectrum to determine the parameters • Try different functions to assess the systematics Measure Egspectrum inb → sg Predict Eℓspectrum inb → uℓv Extract f(k+) 1.8 2 parameters(L and a) to fit M. Morii, Harvard

  15. CLEO hep-ex/0402009 SF from b→sg Belle hep-ex/0407052 • CLEO and Belle has measured the b→ sg spectrum • BABAR result on the way • Statistical errors dominate the uncertainty around the peak • Model dependence important in the tail Belle 3 models tried Fit M. Morii, Harvard

  16. 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 mX and small q2X is jet-like • The right tool: Soft Collinear Effective Theory 6% 20% 70% M. Morii, Harvard

  17. 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 M. Morii, Harvard

  18. BABARhep-ex/0408075 Lepton Endpoint CLEOPRL 88:231803 BELLE-CONF-0325 • Select electrons in 2.0 < Eℓ < 2.6 GeV • Accurate subtraction of backgroundis crucial! • Data taken below the U4S resonancefor light-flavor background • Fit the Eℓ spectrum with b→ uℓv,B → Dℓv, B → D*ℓv, B → D**ℓv,etc. to measure Data (continuum sub) MC for BB background Data (eff. corrected) MC M. Morii, Harvard

  19. BABARhep-ex/0408075 Lepton Endpoint CLEOPRL 88:231803 BELLE-CONF-0325 • Translate DB into |Vub| using the SF parameters from Belle • Lower Eℓ cut-off reduces theoretical uncertainty to ~10% • But … theorists raise possibilities of additional uncertainties • Sub-leading SFs, 4-quark operators, weak annihilation Recalculated by the Heavy Flavor Averaging Group M. Morii, Harvard

  20. Measuring mX and q2 • Must reconstruct all decay products to measure mX or q2 • Eℓ 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 mX and q2 Fully reconstructedB hadrons v lepton X M. Morii, Harvard

  21. Recoil B Sample • Reconstruct Bmesons in • ~1000 channels used • Efficiency ~0.2%/B • Yield and purity from mB fit  • Recoil B is a clean and unbiasedsample of B mesons • Charge and 4-momentum known • Ideal for measuring branching fractions M. Morii, Harvard

  22. Recoil B → Xℓv • Find an ℓ = e± or m±(pℓ > 1GeV) in recoil B and require • Total event charge = 0 • If it’s a B±, Qℓ = QB • Missing 4-momentum consistentwith a massless neutrino • 2-C kinematical fit to determine pX • 4-momentum conservation • mv = 0, mB = mB  mX resolution ~ 350 MeV • Sample is mostly b → cℓv at this stage B hadrons v lepton X M. Morii, Harvard

  23. Charm Suppression • Suppress b → cℓvby vetoing against D(*) decays • D decays usually produce at least one kaon Reject events with K± and KS • B0→ D*+(→ D0p+)ℓ−vhas peculiar kinematics • p+ almost at rest w.r.t. D*+ D*+ momentum can be estimated from p+ alone • Calculate for all p+  Reject events consistent with mv = 0 • Vetoed events are depleted in b → uℓv • Used to validate simulation of background distributions • We’ve got (mX, q2) distribution of a signal-enriched sample M. Morii, Harvard

  24. Extracting b → uℓv Signal • Fit mX to extract B(B→ Xuℓv) • Best variable for charm rejection  Best statistical error • Strong shape-function dependence • Fit mX vs. q2 to extract DB(B→ Xuℓv) • Restrict to, e.g., mX < 1.7 GeV, q2 > 8 GeV2 • Reduced shape-function dependence • Unfold detector effects to get true mX spectrum • Limited statistical power • Potential for constraining shape function M. Morii, Harvard

  25. BABAR 80fb-1hep-ex/0408068 BABAR BABAR Fitting mX • Simple fit in mX shows clear b→ uℓvsignal • Signal modeled by DFN with Belle SF • Translate to |Vub| • Theoretical error ~8%, but strong dependence on the shape function • |Vub| moves by 0.45×10−3 if CLEO SF parameters are used M. Morii, Harvard

  26. BABAR 80fb-1hep-ex/0408068 Unfolding mX • Unfold detector efficiency andresolution  true mX spectrum • NB: error bars are correlated • Matches simulation with differentshape functions (curves) • Not enough statistics to extract shape function parameters • BABAR has 3× more data Measured mX spectrum Background subtraction Detector unfolding M. Morii, Harvard

  27. BABAR 80fb-1hep-ex/0408068 Fitting mX vs. q2 – BABAR • Split b→ uℓv signal into {mX < 1.7, q2 > 8} and elsewhere • 2-D fit to measure DB in the former region yields M. Morii, Harvard

  28. Belle 140fb-1hep-ex/0408115 Fitting mX vs. q2 – Belle • Belle has a nearly identical analysis M. Morii, Harvard

  29. BABAR 80fb-1hep-ex/0408068 Turning DB into |Vub| Belle 140fb-1hep-ex/0408115 • From Bauer, Ligeti, Luke (hep-ph/0111387) • Theoretical error ~10% • BABAR result moves by 0.06×10−3 with CLEO SF params • BABAR result moves by 0.20×10−3 with DFN Results are more stable than the mX fit G = 0.282 ± 0.053 using Belle SF M. Morii, Harvard

  30. Status of Inclusive |Vub| Eℓ endpoint mXfit mXvs. q2 M. Morii, Harvard

  31. Exclusive b → uℓv • Measure specific final states, e.g., B→pℓv • Good signal-to-background ratio • Branching fraction in O(10-4)  Statistics limited • So far B→pℓv and rℓvhave been measured • Also seen: B(B → wℓv) = (1.3±0.5)×10−4[Belle hep-ex/0402023] B(B → hℓv) = (0.84±0.36)×10−4[CLEO PRD68:072003] • Need Form Factors to extract |Vub| M. Morii, Harvard

  32. Form Factors • Form Factors are calculated using: • Lattice QCD(q2 > 16 GeV2) • Existing calculations are “quenched”  ~15% uncertainty • Light Cone Sum Rules(q2 < 16 GeV2) • Assumes local quark-hadron duality  ~10% uncertainty • Other approaches • All of them have uncontrolled uncertainties • LQCD and LCSR valid in different q2 ranges No crosscheck • Unquenched LQCD starts to appear • Preliminary B→ pℓv FF from FNAL+MILC (hep-lat/0409116), HPQCD (hep-lat/0408019) • Current technique cannot do B→ rℓv M. Morii, Harvard

  33. Measuring B→ pℓv • Concentrate on B→pℓv with q2 binning • CLEO [PRD 68:072003] • Reconstruct pℓv using missing 4-momentum as the neutrino • Belle [hep-ex/0408145] • Tag B→ D(*)ℓv and look at mX distribution M. Morii, Harvard

  34. CLEO PRD 68:072003 B→ pℓv – CLEO • Missing 4-momentum = neutrino • CLEO has a better solid-anglecoverage than BABAR/Belle • Reconstruct B→pℓv and calculatemB and DE = EB–Ebeam/2  • Clear signal over background • Red: rℓv, wℓv, hℓv • Yellow: other Xuℓv • Green: continuum (udsc) • Black: b→ cℓv M. Morii, Harvard

  35. Belle hep-ex/0408145 B→ pℓv – Belle • Tag B→ D(*)ℓv and look at the recoil B • Similar to inclusive |Vub| measurements on recoil B • D(*)ℓv tag is less pure, but more efficient • Hadronic mass distribution shows pℓv and rℓv signals q2 < 8 8 < q2 < 16 16 < q2 rℓv other Xuℓv pℓv M. Morii, Harvard

  36. CLEO PRD 68:072003 DG(B→ pℓv) Belle hep-ex/0408145 • Small model-dependence due to efficiency estimation CLEO Belle M. Morii, Harvard

  37. CLEO PRD 68:072003 B→ pℓv to |Vub| Belle hep-ex/0408145 • 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 BABAR, Belle CLEOpℓv Bellepℓv M. Morii, Harvard

  38. b → sg Inclusive b → cℓv Eg Eℓ mX ShapeFunction HQE Fit ? ? mb FF quenched LQCD Summary (1) SSFs Inclusiveb → uℓv Eℓ Exclusive b → uℓv |Vub| mX B→pℓv wℓv, hℓv? mX-q2 duality unquenched WA M. Morii, Harvard

  39. |Vub| Summary (2) • Precise determination of |Vub| complements sin2b 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 M. Morii, Harvard

  40. Backup Slides

  41. Penguins • b→sss decay dominated by the “penguin” diagram • In the SM, same CP asymmetry asb→ccs decays: sin2b • New Physics may modify the loop CP asymmetries may not agree • Several decay channels are studied • B0→ fKS is pure-penguin • Small BF: 7.610-6 • B0→ h’KS has larger BF = 5.510-5 • Tree diagram affects the asymmetryby <0.1 M. Morii, Harvard

  42. BABAR Status of Penguins • Penguins disagree with sin2bby 2.7s (BABAR), 2.4s (Belle) Belle M. Morii, Harvard

  43. Sub-leading Shape Functions • Shape Function represents non-perturb. effects at O(1/mb2) • Next order (1/mb3) 4 Sub-leading Shape Functions • Bauer, Luke, Mannel calculated their effects on Eg(PRD68:094001)and Eℓ(PLB543:261) spectra • Neubert(PLB543:269) estimated impact on |Vub| 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 |Vub| measured with Eℓ endpoint • Re-evaluation of the SSF error is due M. Morii, Harvard

  44. CLEO PRD 68:072003 B→ pℓv to |Vub| Belle hep-ex/0408145 LQCDcalculation • Average of quenched LQCD results • FNAL’01, JLQCD’01, APE’01, UKQCD’00 • Two preliminary unquenched LQCD results M. Morii, Harvard

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