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

APS April Meeting 2006M. Morii, Harvard2 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! Angles: CP violation Right side:  m d /  m s Left side: |V ub /V cb |

APS April Meeting 2006M. Morii, Harvard3 Hadron level Semileptonic B Decays Natural probe for |V ub | and |V cb | Decay rate  x   (b  x )  |V xb | 2  c larger than  u by a factor ~50 Extracting b  u signal challenging Sensitive to hadronic effects Must understand them to extract |V ub |, |V cb | Use data to bolster theory Parton level

APS April Meeting 2006M. Morii, Harvard4 Inclusive vs. Exclusive Inclusive B  X c Inclusive B  X u Exclusive B  D * Exclusive B  

APS April Meeting 2006M. Morii, Harvard5 Inclusive Measurements Operator Product Expansion predicts total rate  u as Dominant error from m b 5 m b measured to  1%   2.5% on |V ub | Total rate can’t be measured due to B  X c  background Must enhance S/B with cuts Perturbative terms known to  (  s 2 ) Non-perturb. terms suppressed by 1/m b 2 Inclusive B  X c Inclusive B  X u

APS April Meeting 2006M. Morii, Harvard6 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   (1/m b ) instead of  (1/m b 2 ) Need to know the Shape Function (= what the b-quark is doing inside the B meson) Solution: Measure B  X c  spectra  Non-perturb. effects Kinematical Cuts q 2 = mass squared m X = hadron system mass E = lepton energy Not to scale! No detector resolution! Not to scale! No detector resolution! decay rate

APS April Meeting 2006M. Morii, Harvard7 Inclusive B  X c Spectra Observables: E (lepton energy) and m X (hadron system mass) Measurements by B A B AR, Belle, CDF, CLEO, DELPHI OPE predicts observables integrated over large phase space  Moments: Belle, hep-ex/ E (GeV) m X 2 (GeV 2 /c 4 ) Belle, hep-ex/

APS April Meeting 2006M. Morii, Harvard8 Global OPE Fit OPE predicts total rate  c and moments  E n ,  m X n  as functions of |V cb |, m b, m c, and several non-perturb. params Each observable has different dependence  Can determine all parameters from a global fit E  spectrum in B  X s  decays connected directly to the SF Small rate and high background makes it tough to measure Measured by B A B AR, Belle, CLEO B A B AR preliminary E  (GeV) Partial BF (10 -4 /100 MeV) hep-ex/ Partial BF (10 -3 /100 MeV) B A B AR PRD 72: E  (GeV)

APS April Meeting 2006M. Morii, Harvard9 OPE Fit Results Buchmüller & Flächer (hep-ph/ ) fit data from 10 measurements with an OPE calculation by Gambino & Uraltsev (Eur. Phys. J. C34 (2004) 181) Fit parameters: |V cb |, m b, m c,   2,  G 2,  D 3,  LS 3, BR(B  X c  Goodness of the fit and the consistency between X c and X s  add confidence to the theory Needed for |V ub |  2%  1% B A B AR PRD69: PRD69: PRD72: hep-ex/ BellePRL93: hep-ex/ CLEOPRD70: PRL87: CDFPRD71: DELPHIEPJ C45:35 combined b  sb  s b  c

APS April Meeting 2006M. Morii, Harvard10 Inclusive B  X u Measure partial BF   (B  X u  in a region where... the signal/background is good, and the partial rate  u is reliably calculable Many possibilities – Review a few recent results b  c v E (GeV) q 2 (GeV 2 ) b  u v E endpoint E -q 2 cut q 2 (GeV 2 ) m X (GeV) b  c v b  u v m X cut m X -q 2 cut Large  u generally good, but not always

APS April Meeting 2006M. Morii, Harvard11 Lepton Endpoint Find leptons with large E Push below the charm threshold  Larger signal acceptance  Smaller theoretical error S/B ~ 1/15 (E > 2 GeV)  Accurate subtraction of background is crucial! E (GeV)|V ub | (10 -3 ) B A B AR 80fb –  0.29 exp  0.31 SF+theo Belle 27fb –  0.45 exp  0.30 SF+theo CLEO 9fb –  0.48 exp  0.36 SF+theo BABAR PRD 73: Belle PLB 621:28 CLEO PRL 88: B A B AR MC bkgd. b  c v Data Data – bkgd. MC signal b  u v Shape Function:determined from the OPE fit Theory errors: Lange et al. PRD72:073006

Hadronic B Tag Fully reconstruct one B in hadronic decays Use the recoiling B with known charge and momentum Access to all kinematic variables BABAR hep-ex/ Belle PRL 95: lepton v X 253M BB Region|V ub | (10 -3 ) Belle 253M BB m X 8 GeV  0.37 exp  0.31 SF+theo m X < 1.7 GeV 4.09  0.28 exp  0.24 SF+theo P + > 0.66 GeV 4.19  0.36 exp  0.28 SF+theo B A B AR 210M BB m X 8 GeV  0.35 exp  0.32 SF+theo reconstructed B Prelim.

APS April Meeting 2006M. Morii, Harvard13 |V ub | from Inclusive B  X u |V ub | 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 Experimental  4.5% SF params.  4.1% Theory  4.2% World Average 4.45  0.33  2 /dof = 5.5/6

APS April Meeting 2006M. Morii, Harvard14 SF-Free |V ub | Measurement Possible to combine b  u v and b  s  so that the SF cancels B A B AR applied Leibovich, Low, Rothstein (PLB 486:86) to 80 fb -1 data Trade SF error  Stat. error m X < 2.5 GeV is almost (96%) fully inclusive  Theory error reduces to  2.6% Weight function BABAR hep-ex/ m X cut (GeV) 1.67 Theory error Expt. error m X cut|V ub | (10 -3 ) 1.67 GeV 4.43  0.45 exp  0.29 theo 2.5 GeV 3.84  0.76 exp  0.10 theo Full rate

APS April Meeting 2006M. Morii, Harvard15 Inclusive vs. Exclusive Inclusive B  X c Inclusive B  X u Exclusive B  D * Exclusive B  

APS April Meeting 2006M. Morii, Harvard16 Exclusive Measurements Exclusive rates determined by |V xb | and Form Factors Theoretically calculable at kinematical limits Lattice QCD works if D * or  is ~ at rest relative to B Empirical extrapolation is necessary to extract |V xb | from measurements Measure differential rates to constrain the FF shape Then use FF normalization from the theory Exclusive B  D * Exclusive B  

APS April Meeting 2006M. Morii, Harvard17 Exclusive B  D* Decay rate is  (1) = 1 in the heavy-quark limit; lattice QCD:  (w) shape expressed by  2 (slope at w = 1) and R 1, R 2 (form factor ratios) Curvature constrained by analyticity Measure decay angles ,  V,  Fit 3-D distribution in bins of w to extract  2, R 1, R 2 phase space form factor D * boost in the B rest frame Hashimoto et al, PRD 66 (2002) Caprini, Lellouch, Neubert NPB530 (1998) 153

APS April Meeting 2006M. Morii, Harvard18 B  D* Form Factors B A B AR measured FF params. with 79 fb -1 R 1 and R 2 improved by a factor 5 over previous CLEO measurement PRL 76 (1996) 3898 Will improve all measurements of B  D * BABAR hep-ex/ Signal MC vs. bkgd.-subtracted data, 1D projections w cos  cos  V  Using B A B AR measurements only

APS April Meeting 2006M. Morii, Harvard19 |V cb | from B  D* HFAG average still uses FF from CLEO New B A B AR FF c.f. (42.0  0.7)  from inclusive OPE fit Average 37.6  0.8  2 /dof = 30.2/14 |V cb | = (40.9  0.9  1.5  (1) )  10 -3

APS April Meeting 2006M. Morii, Harvard20 Exclusive B   B   v rate is given by Form factor f + (q 2 ) has been calculated using Lattice QCD Unquenched calculations by Fermilab (hep-lat/ ) and HPQCD (PRD73:074502)  12% for q 2 > 16 GeV 2 Light Cone Sum Rules Ball & Zwicky (PRD71:014015)  13% for q 2 < 16 GeV 2 One FF for B →  v with massless lepton Ball-Zwicky Fermilab HPQCD ISGW2 Quark model, PRD52 (1995) 2783

APS April Meeting 2006M. Morii, Harvard21 Untagged B   Missing 4-momentum = neutrino Reconstruct B   v and calculate m B and B A B AR 80fb -1 PRD72: data MC signal signal with wrong  b  u v b  c v other bkg. BABAR PRD 72: Measured q 2 spectrum starts to constrain the FF shape LQCD/LCSR favored over ISGW2 B A B AR

APS April Meeting 2006M. Morii, Harvard22 D (*) -tagged B   Reconstruct one B in D (*) v and look for B   v in the recoil B  D * BF large; two neutrinos in the event Event kinematics determined assuming known m B and m v = 0 vv  D soft  BABAR hep-ex/ , Belle hep-ex/   253fb -1   Signal appears in 0 < x B 2 < 1 ModeBF (10 -4 ) Belle B 0   1.38  0.24 B +   0.77  0.16 B A B AR Prelim. B 0   1.02  0.28 B +   1.86  0.44

APS April Meeting 2006M. Morii, Harvard23 |V ub | from B   Average BF measurements and apply FF calculations Consistent within (large) FF errors Experimental errors already competitive Form Factorq 2 (GeV 2 )|V ub | (10 -3 ) Ball-Zwicky< 16 HPQCD> 16 FNAL> 16 LCSR Unquenched LQCD Inclusive: 4.45  0.20 exp  0.26 SF+theo   (q 2 < 16) (10 -4 )   (q 2 > 16) (10 -4 )Total  (10 -4 ) 0.94  0.06 stat  0.06 syst 0.39  0.04 stat  0.04 syst 1.34  0.08 stat  0.08 syst

APS April Meeting 2006M. Morii, Harvard24 Summary Semileptonic B decays offer exciting physics opportunities |V ub /V cb | complements sin2  to test (in)completeness of the SM Challenge of hadronic physics met by close collaboration between theory and experiment Inclusive B  X c & X s  fit precisely determines |V cb |, m b, etc. Dramatic progress in both measurement and interpretation of inclusive B  X u in the last 2 years Inclusive |V ub | achieved  7.4% accuracy Room for improvements with additional data statistics B  D * form factors have improved by a factor 5 Measurements of B    becoming precise Improved form factor calculation needed

Backup Slides

APS April Meeting 2006M. Morii, Harvard26 Weak Annihilation WA turns B + into  + soft hadrons Size and shape of WA poorly known Minimize the impact Measure X u with v. loose cuts Cut away large q 2 region Measure WA contribution  sl (D + ) vs.  sl (D s ) CLEO-c Distortion in q 2 CLEO hep-ex/  (B +  X u ) vs.  (B 0  X u ) Work in progress