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Semileptonic B Decays

Semileptonic B Decays. Masahiro Morii Harvard University Determination of | V ub | and | V cb | with Inclusive and Exclusive b  u  n and b  c  n Decays APS Meeting, April 22-25, 2006. The Unitary Triangle.

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Semileptonic B Decays

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  1. Semileptonic B Decays Masahiro Morii Harvard University Determination of |Vub| and |Vcb| withInclusive and Exclusiveb  un and b  cn Decays APS Meeting, April 22-25, 2006

  2. The Unitary Triangle • The goal: Over-constrain the apex to test the completeness of the Cabibbo-Kobayashi-Maskawa model •  Let’s measure the opposite side precisely! Right side: Dmd /Dms Left side: |Vub /Vcb| Angles: CP violation M. Morii, Harvard

  3. Hadron level Semileptonic B Decays • Natural probe for |Vub| and |Vcb| • Decay rate GxG(b  xn)  |Vxb|2 • Gc larger than Gu by a factor ~50 • Extracting b  un signal challenging • Sensitive to hadronic effects • Must understand them to extract |Vub|, |Vcb| • Use data to bolster theory Parton level M. Morii, Harvard

  4. Inclusive vs. Exclusive Inclusive B  Xcn Exclusive B  D*n Inclusive B  Xun Exclusive B  pn M. Morii, Harvard

  5. Inclusive Measurements • Operator Product Expansion predicts total rate Gu as • Dominant error from mb5 • mb measured to 1% 2.5% on |Vub| • Total rate can’t be measured due to B  Xcn background • Must enhance S/B with cuts Inclusive B  Xcn Perturbative terms known to O(as2) Non-perturb. terms suppressed by 1/mb2 Inclusive B  Xun M. Morii, Harvard

  6. Kinematical Cuts • Three independent kinematic variables in B→Xv • Measure partial rates in favorable regions of the phase space • Caveat: Spectra more sensitive to non-perturbative effects than the total rate  O(1/mb) instead of O(1/mb2) • Need to know the Shape Function (= what the b-quark is doing inside the B meson) • Solution: Measure B  Xcn spectra  Non-perturb. effects Not to scale! No detector resolution! decay rate E = lepton energy q2 = n mass squared mX = hadron system mass M. Morii, Harvard

  7. Belle, hep-ex/0509013 Belle, hep-ex/0508056 E (GeV) E (GeV) mX2 (GeV2/c4) Inclusive B Xcn Spectra • Observables: E(lepton energy) andmX(hadron system mass) • Measurements by BABAR, Belle, CDF, CLEO, DELPHI • OPE predicts observables integrated over large phase space  Moments: M. Morii, Harvard

  8. PRD 72:052004 BABAR Partial BF (10-3/100 MeV) Eg (GeV) Global OPE Fit • OPE predicts total rate Gcand moments En,mXn as functions of |Vcb|, mb, mc, and several non-perturb. params • Each observable has different dependence Can determine all parameters from a global fit • Egspectrum in B Xsgdecays connected directly to the SF • Small rate and high background makes it tough to measure • Measured by BABAR, Belle, CLEO hep-ex/0507001 BABAR Partial BF (10-4/100 MeV) preliminary M. Morii, Harvard Eg (GeV)

  9. OPE Fit Results • Buchmüller & Flächer (hep-ph/0507253)fit data from 10 measurements with an OPE calculation by Gambino & Uraltsev (Eur. Phys. J. C34 (2004) 181) • Fit parameters: |Vcb|, mb, mc, mp2, mG2, rD3, rLS3, BR(B Xcn) • Goodness of the fit and the consistencybetween Xcn and Xsg add confidenceto the theory 2% Needed for |Vub| 1% b sg b cn combined M. Morii, Harvard

  10. Inclusive B Xun • Measure partial BF DB(B  Xun) in a region where ... • the signal/background is good, and • the partial rate DGu is reliably calculable • Many possibilities – Review a few recent results Large DGu generally good, but not always Eendpoint mXcut q2 (GeV2) q2 (GeV2) mX-q2 cut b uv E-q2 cut b uv b cv b cv mX (GeV) E (GeV) M. Morii, Harvard

  11. BABARPRD 73:012006Belle PLB 621:28CLEO PRL 88:231803 BABAR Data MC bkgd.b cv Data – bkgd. MC signalb uv Lepton Endpoint • Find leptonswith large E • Push below the charm threshold Larger signal acceptance Smaller theoretical error • S/B ~ 1/15 (E > 2 GeV)  Accurate subtraction of backgroundis crucial! Shape Function: determined from the OPE fit Theory errors: Lange et al. PRD72:073006 M. Morii, Harvard

  12. BABARhep-ex/0507017Belle PRL 95:241801 Hadronic B Tag reconstructed B • Fully reconstruct one B in hadronic decays • Use the recoilingBwith known charge and momentum • Access to all kinematic variables 253M BB v lepton X Prelim.

  13. |Vub| from Inclusive B Xun • |Vub| determined to 7.4% • Expt. and SF errors will improve with more data • Theory errors from • Sub-leading SF (3.8%) • Higher-order non-perturbative corrections • Weak annihilation (1.9%) • Can be constrained with future measurements World Average 4.45  0.33 c2/dof = 5.5/6 M. Morii, Harvard

  14. BABARhep-ex/0601046 SF-Free |Vub| Measurement • Possible to combine b  uvand bsg so that the SF cancels • BABARappliedLeibovich, Low, Rothstein(PLB 486:86) to 80 fb-1 data • Trade SF error Stat. error • mX < 2.5 GeV is almost (96%) fullyinclusive  Theory error reduces to2.6% Weight function Fullrate Theory error Expt. error 1.67 mX cut (GeV) M. Morii, Harvard

  15. Inclusive vs. Exclusive Inclusive B  Xcn Exclusive B  D*n Inclusive B  Xun Exclusive B  pn M. Morii, Harvard

  16. Exclusive Measurements • Exclusive rates determined by |Vxb| and Form Factors • Theoretically calculable at kinematical limits • Lattice QCD works if D* or p is ~ at rest relative to B • Empirical extrapolation is necessary to extract |Vxb| from measurements • Measure differential rates to constrain the FF shape • Then use FF normalization from the theory Exclusive B  D*n Exclusive B  pn M. Morii, Harvard

  17. Exclusive B D*n form factor • Decay rate is • F(1) = 1 in the heavy-quark limit; lattice QCD: • F(w) shape expressed by r2 (slope at w = 1) andR1, R2 (form factor ratios) • Curvature constrained by analyticity • Measure decay angles q, qV, c • Fit 3-D distribution in bins of wto extract r2, R1, R2 phase space D* boost in the B rest frame Hashimoto et al,PRD 66 (2002) 014503 Caprini, Lellouch, NeubertNPB530 (1998) 153 M. Morii, Harvard

  18. BABARhep-ex/0602023 B D*n Form Factors Signal MC vs. bkgd.-subtracteddata, 1D projections • BABAR measured FF params. with 79 fb-1 • R1 and R2 improved by a factor 5 over previous CLEO measurement PRL 76 (1996) 3898 • Will improve all measurements of B D*n c w cosqV cosq Using BABAR measurements only M. Morii, Harvard

  19. Average 37.6  0.8 c2/dof = 30.2/14 New BABAR FF |Vcb| from B D*n • HFAG average still uses FF from CLEO |Vcb| = (40.9  0.9  1.5F(1))  10-3 c.f. (42.0  0.7)10-3from inclusive OPE fit M. Morii, Harvard

  20. Exclusive B pn • Bpv rate is given by • Form factor f+(q2) has been calculated using • Lattice QCD • Unquenched calculations by Fermilab (hep-lat/0409116) andHPQCD (PRD73:074502) • 12% for q2 > 16 GeV2 • Light Cone Sum Rules • Ball & Zwicky(PRD71:014015) • 13% for q2< 16 GeV2 One FF for B→pvwith massless lepton Ball-ZwickyFermilabHPQCD ISGW2 Quark model, PRD52 (1995) 2783 M. Morii, Harvard

  21. BABARPRD 72:051102 Untagged Bpn • Missing 4-momentum = neutrino • Reconstruct Bpv and calculate mB and data MC signal BABAR80fb-1 PRD72:051102 signal withwrong p b uv b cv other bkg. BABAR • Measured q2 spectrum starts to constrain the FF shape • LQCD/LCSR favored over ISGW2 M. Morii, Harvard

  22. BABARhep-ex/0506064, 0506065Belle hep-ex/0508018 D(*)n-taggedBpn • Reconstruct one B in D(*)vand look for Bpv in the recoil • BD*nBF large; two neutrinos in the event • Event kinematics determined assumingknown mB and mv = 0 soft p p D   v v p-n r-n 253fb-1 Signal appears in 0 < xB2 < 1 M. Morii, Harvard

  23. |Vub| from B pn • Average BF measurements and apply FF calculations • Consistent within (large)FF errors • Experimental errors already competitive LCSR UnquenchedLQCD Inclusive: 4.45  0.20exp  0.26SF+theo M. Morii, Harvard

  24. Summary • Semileptonic B decays offer exciting physics opportunities • |Vub /Vcb| complements sin2b to test (in)completeness of the SM • Challenge of hadronic physics met by close collaboration between theory and experiment • Inclusive B Xcn & Xsg fit precisely determines |Vcb|, mb, etc. • Dramatic progress in both measurement and interpretation of inclusive B Xun in the last 2 years • Inclusive |Vub| achieved 7.4% accuracy • Room for improvements with additional data statistics • B D*n form factors have improved by a factor 5 • Measurements of Bpn becoming precise • Improved form factor calculation needed M. Morii, Harvard

  25. Backup Slides

  26. Weak Annihilation • WA turns B+ into n + soft hadrons • Size and shape of WA poorly known • Minimize the impact • Measure Xun with v. loose cuts • Cut away large q2 region • Measure WA contribution • Gsl(D+) vs. Gsl(Ds) • CLEO-c • Distortion in q2 • CLEO hep-ex/0601027 • G(B+ Xun) vs. G(B0 Xun) • Work in progress M. Morii, Harvard

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