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B Physics Beyond CP Violation — Semileptonic B Decays —

B Physics Beyond CP Violation — Semileptonic B Decays —. Masahiro Morii Harvard University Columbia University Nuclear/Particle & Astroparticle Physics Seminar 29 March 2006. Outline. Introduction: Why semileptonic B decays? CKM matrix — Unitarity Triangle — CP violation

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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 Columbia University Nuclear/Particle & Astroparticle Physics Seminar 29 March 2006

  2. Outline • Introduction: Why semileptonic B decays? • CKM matrix — Unitarity Triangle — CP violation • |Vub| vs. sin2b • |Vub| from inclusiveb→ uv decays • Measurements: lepton energy, hadron mass, lepton-neutrino mass • Theoretical challenge: Shape Function • Latest from BABAR – Avoiding the Shape Function • |Vub| from exclusiveb→ uv decays • Measurements: G(B→ pv) • Theoretical challenge: Form Factors • Summary M. Morii, Harvard

  3. Particle mass (eV/c2) Mass and the Generations • Fermions come in three generations • They differ only by the masses • The Standard Model has no explanation for the mass spectrum • The masses come from the interaction with the Higgs field • ... whose nature is unknown • We are looking for the Higgs particle at the Tevatron, and at the LHC in the future The origin of mass is one of the most urgent questions in particle physics today Q = 1 0 +2/3 1/3 M. Morii, Harvard

  4. If there were no masses • Nothing would distinguish u from c from t • We could make a mixture of the wavefunctions and pretend it represents a physical particle • Suppose W connects u↔ d, c↔ s, t↔ b • That’s a poor choice of basis vectors M and N are arbitrary33 unitary matrices Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V M. Morii, Harvard

  5. Turn the masses back on • Masses uniquely define the u, c, t, and d, s, b states • We don’t know what creates masses We don’t know how the eigenstates are chosen M and N are arbitrary • V is an arbitrary 33 unitary matrix • The Standard Model does not predict V • ... for the same reason it does not predict the particle masses or CKM for short Cabibbo-Kobayashi-Maskawa matrix M. Morii, Harvard

  6. Structure of the CKM matrix • The CKM matrix looks like this  • It’s not completely diagonal • Off-diagonal components are small • Transition across generations isallowed but suppressed • The “hierarchy” can be best expressed in theWolfenstein parameterization: • One irreducible complex phase  CP violation • The only source of CP violation in the minimal Standard Model Vub M. Morii, Harvard

  7. CP violation and New Physics Are there additional (non-CKM) sources of CP violation? • The CKM mechanism fails to explain the amount of matter-antimatter imbalance in the Universe • ... by several orders of magnitude • New Physics beyond the SM is expected at 1-10 TeV scale • e.g. to keep the Higgs mass < 1 TeV/c2 • Almost all theories of New Physics introduce new sources of CP violation (e.g. 43 of them in supersymmetry) • Precision studies of the CKM matrix may uncover them New sources of CP violation almost certainly exist M. Morii, Harvard

  8. The Unitarity Triangle • V†V = 1 gives us • Measurements of angles and sides constrain the apex (r, h) This one has the 3 terms in the same order of magnitude A triangle on the complex plane M. Morii, Harvard

  9. 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 summer 2004 • Still large enough for NewPhysics to hide • Precision of sin2b outstrippedthe other measurements • Must improve the others tomake more stringent test M. Morii, Harvard

  10. 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

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

  12. Detecting b → un • 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pv, Brv, Bwv, Bhv, … • Example: the rate for Bpv is • How accurately do we know the FFs? 2.31 2.64 Form Factor(3 FFs for vector mesons) M. Morii, Harvard

  13. Inclusive b → un • There are 3 independent variables in B→Xv • Signal events have smaller mX  Larger E and q2 E = lepton energy q2 = lepton-neutrino mass squared u quark turns into 1 or more hardons mX = hadron system mass Not to scale! M. Morii, Harvard

  14. BABARPRD 73:012006Belle PLB 621:28CLEO PRL 88:231803 Lepton Endpoint • Select electrons in 2.0 < E < 2.6 GeV • Push below the charm threshold Larger signal acceptance Smaller theoretical error • Accurate subtraction of backgroundis crucial! • Measure the partial BF BABAR Data MC bkgd.b cv Data – bkgd. MC signalb uv cf. Total BF is ~2103 M. Morii, Harvard

  15. BABAR PRL 95:111801 BABAR E vs. q2 • Use pv = pmiss in addition to pe Calculate q2 • Define shmax = the maximum mX squared • Cutting at shmax < mD2 removes b  cv while keeping most of the signal • S/B = 1/2 achieved for E> 2.0 GeV and shmax < 3.5 GeV2 • cf. ~1/15 for the endpoint E> 2.0 GeV • Measured partial BF q2 (GeV2) b uv b cv E (GeV) Small systematic errors M. Morii, Harvard

  16. BABARhep-ex/0507017Belle PRL 95:241801 Measuring mX and q2 • Must reconstruct all decay products to measure mX or q2 • Select events with a fully-reconstructed B meson • Rest of the event contains one “recoil” B • Flavor and momentum known • Find a lepton in the recoil B • Neutrino = missing momentum • Make sure mmiss ~ 0 • All left-over particles belong to X • We can now calculate mXand q2 • Suppress b → cv by vetoing against D(*) decays • Reject events with K • Reject events with B0→ D*+(→ D0p+)−v Fully reconstructedB hadrons v lepton X M. Morii, Harvard

  17. BABARhep-ex/0507017Belle PRL 95:241801 Measuring Partial BF • Measure the partial BF in regions of (mX, q2) For example:mX < 1.7 GeV and q2 > 8 GeV2 Large DB thanks tothe high efficiency of the mX cut M. Morii, Harvard

  18. 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 (5%) from mb5 2.5% on |Vub| • But we need the accessible fraction(e.g., Eℓ> 2 GeV) of the rate known to O(as2) Suppressed by 1/mb2 M. Morii, Harvard

  19. Shape Function • OPE doesn’t work everywhere in the phase space • OK once integrated • Doesn’t converge, e.g., near the E end point • Resumming turns non-perturb. terms into a Shape Function • b quark Fermi motion parallelto the u quark velocity • Cannot be calculated by theory • Leading term is O(1/mb) insteadof O(1/mb2) We must determine the Shape Function from experimental data M. Morii, Harvard

  20. BABAR PRD 72:052004, hep-ex/0507001Belle hep-ex/0407052CLEO hep-ex/0402009 BABAR Sum of exclusive Partial BF/bin (10-3) Inclusive b→ sg Decays • Measure: Same SF affects (to the first order)b→ sg decays Measure Egspectrum inb → sg Predictpartial BFs inb → uv Extract f(k+) K* Inclusive g measurement. Photon energy in the Y(4S) rest frame Exclusive Xs + g measurement. Photon energy determined from the Xs mass M. Morii, Harvard

  21. Predicting b → un Spectra • Fit the b→ sg spectrum to extract the SF • Must assume functional forms, e.g. • Additional information from b  cv decays • E and mX moments  b-quark mass and kinetic energy • NB: mb is determined to better than 1%  First two moments of the SF • Plug in the SF into the b  uvspectrum calculations • Bosch, Lange, Neubert, Paz, NPB 699:335 • Lange, Neubert, Paz, PRD 72:073006 • Ready to extract |Vub| Buchmüller & Flächerhep-ph/0507253 Lepton-energyspectrum byBLNP M. Morii, Harvard

  22. Turning DB into |Vub| • Using BLNP + the SF parameters from b→ sg, b  cv • Adjusted to mb = (4.60  0.04) GeV, mp2 = (0.20  0.04) GeV2 • Theory errors from Lange, Neubert, Paz, hep-ph/0504071 • Last Belle result(*) used a simulated annealing technique M. Morii, Harvard

  23. Inclusive |Vub| as of 2005 |Vub| world average, Winter 2006 • |Vub| determined to 7.4% • The SF parameters can be improved with b→ sg,b  cv measurements • What’s the theory error? M. Morii, Harvard

  24. Theory Errors • Subleading Shape Function 3.8% error • Higher order non-perturbative corrections • Cannot be constrained with b→ sg • Weak annihilation 1.9% error • Measure G(B0  Xuv)/G(B+  Xuv) orG(D0  Xv)/G(Ds  Xv) to improve the constraint • Also: study q2 spectrum near endpoint (CLEO hep-ex/0601027) • Reduce the effect by rejecting the high-q2 region • Quark-hadron duality is believed to be negligible • b  cv and b→ sg data fit well with the HQE predictions • Ultimate error on inclusive |Vub| may be ~5% M. Morii, Harvard

  25. Avoiding the Shape Function • Possible to combine b  uvand b→ sg so that the SF cancels • Leibovich, Low, Rothstein, PLB 486:86 • Lange, Neubert, Paz, JHEP 0510:084, Lange, JHEP 0601:104 • No need to assume functional forms for the Shape Function • Need b→ sg spectrum in the B rest frame • Only one measurement (BABAR PRD 72:052004) available • Cannot take advantage of precise b  cvdata • How well does this work? Only one way to find out… Weight function M. Morii, Harvard

  26. BABARhep-ex/0601046 1.67 mX cut (GeV) SF-Free |Vub| Measurement • BABAR applied LLR (PLB 486:86) to 80 fb-1 data • G(B Xuv) with varying mX cut • dG(B Xsg)/dEg from PRD 72:052004 • With mX < 1.67 GeV • SF error  Statistical error • Also measured mX < 2.5 GeV • Almost (96%) fully inclusive No SF necessary • Attractive new approaches with increasing statistics Theory error Expt. error stat. syst. theory Theory error ±2.6% M. Morii, Harvard

  27. Exclusive B → pn • Measure specific final states, e.g., B→pv • Can achieve good signal-to-background ratio • Branching fractions in O(10-4)  Statistics limited • Need Form Factors to extract |Vub| • f+(q2) has been calculated using • Lattice QCD(q2 > 15 GeV2) • Existing calculations are “quenched”  ~15% uncertainty • Light Cone Sum Rules(q2 < 14 GeV2) • Assumes local quark-hadron duality  ~10% uncertainty • ... and other approaches One FF for B→pvwith massless lepton M. Morii, Harvard

  28. Form Factor Calculations • Unquenched LQCD calculations started to appear in 2004 • Fermilab (hep-lat/0409116) andHPQCD (hep-lat/0601021) • Uncertainties are ~11% f+(q2) and f0(q2) LCSR*FermilabHPQCDISGW2 q2 (GeV2) • Measure dG(B→ pv)/dq2 as a function of q2 • Compare with differentcalculations *Ball-Zwicky PRD71:014015 M. Morii, Harvard

  29. Measuring B→ pn • Measurements differ in what you do with the “other”B • Total BF is • 8.4% precision B(B0 → p+v) [10-4] M. Morii, Harvard

  30. BABARPRD 72:051102CLEO PRD 68:072003 Untagged B→pn • Missing 4-momentum = neutrino • Reconstruct B→pv and calculate mB and DE = EB–Ebeam/2 BABAR data MC signal signal withwrong p b uv b cv BABAR other bkg. M. Morii, Harvard

  31. BABARhep-ex/0506064, 0506065Belle hep-ex/0508018 soft p p D   v v D(*)n-taggedB→pn • Reconstruct one B and look for Bpv in the recoil • Tag with either B D(*)v or B hadrons • Semileptonic (B D(*)v) tags areefficient but less pure • Two neutrinos in the event • Event kinematics determined assumingknown mB and mv cos2fB 1 for signal data MC signal MC background M. Morii, Harvard

  32. BABARhep-ex/0507085 Hadronic-taggedB→pn • Hadronic tags have high purity, but low efficiency • Event kinematics is known by a 2-C fit • Use mB and mmiss distributions toextract the signal yield soft p p D  p or K v data MC signal b uv b cv other bkg. M. Morii, Harvard

  33. dB(B → pn)/dq2 • Measurements start to constrain the q2 dependence • ISGW2 rejected • Partial BF measured to be Errors on |Vub| dominated by the FF normalization M. Morii, Harvard

  34. Future of B → pn • Form factor normalization dominates the error on |Vub| • Experimental error will soon reach 5% • Significant efforts in both LQCD and LCSR needed • Spread among the calculations still large • Reducing errors below 10% will be a challenge • Combination of LQCD/LCSR with the measured q2 spectrum and dispersive bounds may improve the precision • Fukunaga, Onogi, PRD 71:034506 • Arnesen, Grinstein, Rothstein, StewartPRL 95:071802 • Ball, Zwicky, PLB 625:225 • Becher, Hill, PLB 633:61-69 M. Morii, Harvard

  35. b → sg Inclusive b → cv Eg E mX ShapeFunction HQE Fit mb FF LCSR LQCD How Things Mesh Together SSFs Inclusiveb → uv E Exclusive b → uv |Vub| q2 B→pv wv, hv? mX duality WA unquenching M. Morii, Harvard

  36. The UT 2004  2005 • Dramatic improvement in |Vub|! • sin2b went down slightly  Overlap with |Vub/Vcb| smaller M. Morii, Harvard

  37. |Vub| Summary • Precise determination of |Vub| complements sin2b to test the (in)completeness of the Standard Model • 7.4% accuracy achieved so far  5% possible? • Close collaboration between theory and experiment is crucial • Rapid progress in inclusive |Vub| in the last 2 years • Improvement in B→pn form factor is needed M. Morii, Harvard

  38. Extracting the Shape Function • Data are not (yet) precise enough to extract the SF from scratch • We must assume a few plausible functional forms • Example: • First two moments of the SF are connected with the b-quark mass mb and kinetic energy mp2(Neubert, PLB 612:13) • Can be determined from b→ sgand/or b  cv decays • from b→ sg, and from b  cv • Fit data from BABAR, Belle, CLEO, DELPHI, CDF • NB: mb is determined to better than 1% • We’ve got the Shape Function Buchmüller & Flächerhep-ph/0507253 M. Morii, Harvard

  39. Predicting b → un Spectra • Soft Collinear Effective Theory isused to predict the triple-differential rate: • Developed since 2001 by Bauer,Fleming, Luke, Pirjol, Stewart • A triple-diff. rate calculationavailable since Spring 2005 • Bosch, Lange, Neubert, Paz, NPB 699:335 • Lange, Neubert, Paz, hep-ph/0504071 • We use BLNP to extract |Vub| • New calculations are appearing • Aglietti, Ricciardi, Ferrera, hep-ph/0507285, 0509095, 0509271 • Andersen, Gardi, hep-ph/0509360 • Numerical comparison with BLNP will be done soon Lepton-energyspectrum byBLNP M. Morii, Harvard

  40. |Vub| vs. the Unitarity Triangle • Fitting everything except for|Vub|, CKMfitter Group finds • Inclusive average is • 2.0s off • UTfit Group finds 2.8s • Not a serious conflict (yet) • Careful evaluation of theory errors • Consistency between different calculations Exclusive Inclusive M. Morii, Harvard

  41. SF-free |Vub| errors M. Morii, Harvard

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