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B Physics Beyond CP Violation — Semileptonic B Decays —

B Physics Beyond CP Violation — Semileptonic B Decays —. Masahiro Morii Harvard University KEK Theory Group Seminar 15 November 2005. Outline. Introduction: Why semileptonic B decays? CKM matrix — Unitarity Triangle — CP violation | V ub | vs. sin2 b

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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 KEK Theory Group Seminar 15 November 2005

  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 • |Vub| from exclusiveb→ uv decays • Measurements: G(B→ pv) • Theoretical challenge: Form Factors • Summary M. Morii, Harvard

  3. CKM Matrix • Cabibbo-Kobayashi-Maskawa matrix connects the weak and mass bases of the quarks • We don’t know the origin of the EW symmetry breaking Fermion masses and the CKM matrix are inputs to the SM • We are looking for the Higgs particle at the Tevatron, and at the LHC in the future • Unlike the fermion masses, the CKM matrix contains more measurable quantities than the number of degrees of freedom M. Morii, Harvard

  4. 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 M. Morii, Harvard

  5. 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

  6. 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

  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 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

  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  cv decay • How can we suppress 50× larger background? decoupled from hadronic effects Tree level M. Morii, Harvard

  10. 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? Form Factor(3 FFs for vector mesons) M. Morii, Harvard

  11. 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

  12. BABARhep-ex/0509040Belle 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

  13. 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

  14. BABARhep-ex/0507017Belle hep-ex/0505088 Measuring mX and q2 • Must reconstruct all decay products to measure mX or q2 • E was much easier • 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 in the recoil-B • Lepton charge consistent with the B flavor • mmiss consistent with a neutrino • All left-over particles belong to X • Use a kinematic fit  s(mX) = 350 MeV • 4-momentum conservation; equal mB on both sides; mmiss = 0 Fully reconstructedB hadrons v lepton X M. Morii, Harvard

  15. BABARhep-ex/0507017Belle hep-ex/0505088 Measuring Partial BF • Suppress b → cv by vetoing against D(*) decays • Reject events with K • Reject events with B0→ D*+(→ D0p+)−v • Measure the partial BF in regions of (mX, q2) • For example: mX < 1.7 GeV and q2 > 8 GeV2 M. Morii, Harvard

  16. BABARhep-ex/0507017Belle hep-ex/0505088 Partial BF Results • P+ = EX |PX| is a theoretically clean variable • Bosch, Lange, Neubert, PazPRL 93:221802 • Efficiency high • Signal vs. backgroundseparation is limited Large DB thanks tothe high efficiency of the mX cut Belle M. Morii, Harvard

  17. 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

  18. 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 parallel to the u quark velocity • leading term is O(1/mb) instead of O(1/mb2) Rough features (mean, r.m.s.) are known Details, especially the tail, are unknown M. Morii, Harvard

  19. BABARhep-ex/0507001, 0508004Belle 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

  20. Extracting the Shape Function • We can fit the b→ sg spectrum with theory prediction • Must assume a functional form of f(k+) • Example: • New calculation connect the SF moments with the b-quark mass mb and kinetic energy mp2(Neubert, PLB 612:13) • Determined precisely from b→ sgand 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%  Determine the SF Buchmüller & Flächerhep-ph/0507253 M. Morii, Harvard

  21. Predicting b → un Spectra • OPE + SF can predict triple-differential rate • Unreliable where OPE converges poorly • ... that is where the signal is • Soft Collinear Effective Theory offers the right tool • Developed since 2001 by Bauer, Fleming, Luke, Pirjol, Stewart • Applied to b→ uv by several groups • A triple-diff. rate calculationavailable since Spring 2005 • Bosch, Lange, Neubert, Paz, NPB 699:335 • Lange, Neubert, Paz, hep-ph/0504071 • BABAR and Belle use BLNP toextract |Vub| in the latest results Lepton-energyspectrum byBLNP M. Morii, Harvard

  22. Next in Theory of Inclusive |Vub| • New calculations of partial BFs are appearing • Aglietti, Ricciardi, Ferrera, hep-ph/0507285, 0509095, 0509271 • Andersen, Gardi, hep-ph/0509360 • Numerical comparison with BLNP will be done soon • Combine b  uv and b→ sg without going through the SF • Leibovich, Low, Rothstein, PLB 486:86 • Lange, Neubert, Paz, hep-ph/0508178 • Lange, hep-ph/0511098 • No need to assume functional forms for the Shape Function Weight function M. Morii, Harvard

  23. 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

  24. Status of Inclusive |Vub| |Vub| world average as of Summer 2005 • |Vub| determined to 7.6% • The SF parameters can be improved with b→ sg,b  cv measurements • What’s the theory error? M. Morii, Harvard

  25. Theory Errors • Quark-hadron duality is not considered • b  cv and b→ sg data fit well with the HQE predictions • Weak annihilation 1.9% error • Expected to be <2% of the total rate • Measure G(B0  Xuv)/G(B+  Xuv)to improve the constraint • Reduce the effect by rejecting the high-q2 region • Subleading Shape Function 3.5% error • Higher order non-perturbative corrections • Cannot be constrained with b→ sg • Ultimate error on inclusive |Vub| may be ~5% M. Morii, Harvard

  26. 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 M. Morii, Harvard

  27. Form Factor Calculations • Unquenched LQCD calculations started to appear in 2004 • Preliminary B→ pv FF fromFermilab (hep-lat/0409116) andHPQCD (hep-lat/0408019) • Uncertainties are ~11% • Validity of the techniqueremains controversial • Important to measure dG(B→ pv)/dq2 as afunction of q2 Compare with differentcalculations 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

  28. 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

  29. BABARhep-ex/0507003CLEO 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

  30. 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

  31. 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

  32. 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

  33. 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, hep-ph/0509090 M. Morii, Harvard

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

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

  36. |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) • We keep watch • Careful evaluation of theory errors • Consistency between different methods Exclusive Inclusive M. Morii, Harvard

  37. |Vub| Summary • Precise determination of |Vub| complements sin2b to test the (in)completeness of the Standard Model • 7.6% 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

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