Semileptonic B Decays Masahiro Morii Harvard University Determination
Semileptonic B Decays Masahiro Morii Harvard University Determination of |Vub| and |Vcb| with Inclusive and Exclusive b u n and b c n Decays APS Meeting, April 22 -25, 2006
The Unitary Triangle n The goal: Over-constrain the apex to test the completeness of the Cabibbo-Kobayashi-Maskawa model Rig ht s Left side: |Vub /Vcb| ide: Dm d /Dm s Angles: CP violation n APS April Meeting 2006 Let’s measure the opposite side precisely! M. Morii, Harvard 2
Semileptonic B Decays n Natural probe for |Vub| and |Vcb| Hadron level Parton level n n Gc larger than Gu by a factor ~50 n n Decay rate Gx G(b x n) |Vxb|2 Extracting b u n signal challenging Sensitive to hadronic effects Must understand them to extract |Vub|, |Vcb| n Use data to bolster theory n APS April Meeting 2006 M. Morii, Harvard 3
Inclusive vs. Exclusive Inclusive B Xc n Exclusive B D* n Inclusive B Xu n Exclusive B p n APS April Meeting 2006 M. Morii, Harvard 4
Inclusive Measurements Inclusive B Xc n n Operator Product Expansion predicts total rate Gu as Perturbative terms known to O(as 2) Inclusive B Xu n n Non-perturb. terms suppressed by 1/mb 2 Dominant error from mb 5 n mb measured to 1% 2. 5% on |Vub| n Total rate can’t be measured due to B Xc n background n APS April Meeting 2006 M. Morii, Harvard Must enhance S/B with cuts 5
Kinematical Cuts Three independent kinematic variables in B → X v Not to scale! decay rate n No detector resolution! E = lepton energy n n m. X = hadron system mass 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/mb 2) n n q 2 = n mass squared 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 APS April Meeting 2006 M. Morii, Harvard 6
Inclusive B Xc n Spectra n Observables: n E (lepton energy) and m. X (hadron system mass) Measurements by BABAR, Belle, CDF, CLEO, DELPHI Belle, hep-ex/0508056 E (Ge. V) n OPE Belle, hep-ex/0509013 E (Ge. V) m. X 2 (Ge. V 2/c 4) predicts observables integrated over large phase space Moments: APS April Meeting 2006 M. Morii, Harvard 7
Global OPE Fit predicts total rate Gc and moments E n , m. Xn as functions of |Vcb|, mb, mc, and several non-perturb. params n OPE n n Eg Each observable has different dependence Can determine all parameters from a global fit spectrum in B Xsg decays connected directly to the SF Small rate and high background makes it tough to measure n Measured by BABAR, Belle, CLEO hep-ex/0507001 BABAR APS April Meeting 2006 PRD 72: 052004 Eg (Ge. V) M. Morii, Harvard Partial BF (10 -4/100 Me. V) Partial BF (10 -3/100 Me. V) n BABAR preliminary Eg (Ge. V) 8
OPE Fit Results BABAR PRD 69: 111103 PRD 69: 111104 PRD 72: 052004 hep-ex/0507001 Belle PRL 93: 061803 hep-ex/0508005 CLEO PRD 70: 031002 PRL 87: 251807 CDF PRD 71: 051103 DELPHI EPJ C 45: 35 & Flächer (hep-ph/0507253) fit data from 10 measurements with an OPE calculation by Gambino & Uraltsev (Eur. Phys. J. C 34 (2004) 181) n Buchmüller n Fit parameters: |Vcb|, mb, mc, mp 2, m. G 2, r. D 3, r. LS 3, BR(B Xc n) 2% Needed for |Vub| 1% b sg b c n n Goodness of the fit and the consistency between Xc n and Xsg add confidence to theory APS April Meeting 2006 M. Morii, Harvard combined 9
Inclusive B Xu n n Measure partial BF DB(B Xu n) in a region where. . . the signal/background is good, and n the partial rate DGu is reliably calculable n possibilities – Review a few recent results b c v 2 cut q E b c v m. X (Ge. V) E (Ge. V) APS April Meeting 2006 b u v m. X cut m. X-q 2 cut q 2 (Ge. V 2) E endpoint q 2 (Ge. V 2) n Many Large DGu generally good, but not always M. Morii, Harvard 10
Lepton Endpoint n BABAR PRD 73: 012006 Belle PLB 621: 28 CLEO PRL 88: 231803 Find leptons with large E Push below the charm threshold Larger signal acceptance Smaller theoretical error n S/B ~ 1/15 (E > 2 Ge. V) Accurate subtraction of background is crucial! BABAR n E (Ge. V) |Vub| (10 -3) BABAR 80 fb-1 2. 0– 2. 6 4. 41 0. 29 exp 0. 31 SF+theo Belle 27 fb-1 1. 9– 2. 6 4. 82 0. 45 exp 0. 30 SF+theo CLEO 9 fb-1 2. 2– 2. 6 4. 09 0. 48 exp 0. 36 SF+theo Data MC bkgd. b c v Data – bkgd. MC signal b u v Shape Function: determined from the OPE fit Theory errors: Lange et al. PRD 72: 073006 APS April Meeting 2006 M. Morii, Harvard 11
BABAR hep-ex/0507017 Belle PRL 95: 241801 Hadronic B Tag n reconstructed B Fully reconstruct one B in hadronic decays Use the recoiling B with known charge and momentum n Access to all kinematic variables n 253 M BB v lepton Region X |Vub| (10 -3) m. X < 1. 7 Ge. V, q 2 > 8 Ge. V 2 4. 70 0. 37 exp 0. 31 SF+theo Belle 253 M BB m. X < 1. 7 Ge. V 4. 09 0. 28 exp 0. 24 SF+theo P+ > 0. 66 Ge. V 4. 19 0. 36 exp 0. 28 SF+theo BABAR 210 M BB m. X < 1. 7 Ge. V, q 2 > 8 Ge. V 2 4. 75 0. 35 exp 0. 32 SF+theo Prelim.
|Vub| from Inclusive B Xu n n |Vub| determined to 7. 4% n n Experimental 4. 5% SF params. 4. 1% Theory 4. 2% Expt. and SF errors will improve with more data Theory errors from n World Average 4. 45 0. 33 Sub-leading SF (3. 8%) n c 2/dof = 5. 5/6 n Weak annihilation (1. 9%) n APS April Meeting 2006 M. Morii, Harvard Higher-order nonperturbative corrections Can be constrained with future measurements 13
BABAR hep-ex/0601046 SF-Free |Vub| Measurement n n Possible to combine b u v and b sg so that the SF cancels BABAR applied Leibovich, Low, Rothstein (PLB 486: 86) to 80 fb-1 data m. X cut Weight function Full rate Theory error |Vub| (10 -3) 1. 67 Ge. V 4. 43 0. 45 exp 0. 29 theo Expt. error 2. 5 Ge. V 3. 84 0. 76 exp 0. 10 theo Trade SF error Stat. error 1. 67 n m. X < 2. 5 Ge. V is almost (96%) fully inclusive Theory error reduces to 2. 6% n APS April Meeting 2006 M. Morii, Harvard m. X cut (Ge. V) 14
Inclusive vs. Exclusive Inclusive B Xc n Exclusive B D* n Inclusive B Xu n Exclusive B p n APS April Meeting 2006 M. Morii, Harvard 15
Exclusive Measurements n Exclusive rates determined by |Vxb| and Form Factors n Theoretically calculable at kinematical limits n n Exclusive B D* n Lattice QCD works if D* or p is ~ at rest relative to B Empirical extrapolation is necessary to extract |Vxb| from measurements Exclusive B p n n Measure differential rates to constrain the FF shape n Then use FF normalization from theory APS April Meeting 2006 M. Morii, Harvard 16
Exclusive B D* n n Decay form factor rate is phase space D* boost in the B rest frame F(1) = 1 in the heavy-quark limit; lattice QCD: n F(w) shape expressed by r 2 (slope at w = 1) and R 1, R 2 (form factor ratios) n n Curvature constrained by analyticity n Measure n Hashimoto et al, PRD 66 (2002) 014503 Caprini, Lellouch, Neubert NPB 530 (1998) 153 decay angles q , q. V, c Fit 3 -D distribution in bins of w to extract r 2, R 1, R 2 APS April Meeting 2006 M. Morii, Harvard 17
BABAR hep-ex/0602023 B D* n Form Factors n BABAR measured FF params. with 79 w Signal MC vs. bkgd. -subtracted data, 1 D projections cosq. V cosq n fb-1 c R 1 and R 2 improved by a factor 5 over previous CLEO measurement PRL 76 (1996) 3898 n Using BABAR measurements only APS April Meeting 2006 Will improve all measurements of B D* n M. Morii, Harvard 18
|Vcb| from B D* n n HFAG average still uses FF from CLEO Average 37. 6 0. 8 c 2/dof = 30. 2/14 New BABAR FF |Vcb| = (40. 9 1. 5 F(1)) 10 -3 c. f. (42. 0 0. 7) 10 -3 from inclusive OPE fit APS April Meeting 2006 M. Morii, Harvard 19
Exclusive B p n n B p v rate is given by One FF for B → p v with massless lepton n Form factor f+(q 2) has been calculated using n Lattice QCD n n n Unquenched calculations by Fermilab (hep-lat/0409116) and HPQCD (PRD 73: 074502) 12% for q 2 > 16 Ge. V 2 Light Cone Sum Rules n n Ball & Zwicky (PRD 71: 014015) 13% for q 2 < 16 Ge. V 2 Ball-Zwicky Fermilab HPQCD ISGW 2 Quark model, PRD 52 (1995) 2783 APS April Meeting 2006 M. Morii, Harvard 20
BABAR PRD 72: 051102 Untagged B p n n Missing 4 -momentum = neutrino n Reconstruct B p v and calculate m. B and data MC signal with wrong p b u v b c v BABAR 80 fb-1 PRD 72: 051102 other bkg. BABAR n Measured q 2 spectrum starts to constrain the FF shape n APS April Meeting 2006 LQCD/LCSR favored over ISGW 2 M. Morii, Harvard 21
BABAR hep-ex/0506064, 0506065 Belle hep-ex/0508018 D(*) n-tagged B p n n Reconstruct one B in D(*) v and look for B p v in the recoil n n B D* n BF large; two neutrinos in the event Event kinematics determined assuming known m. B and mv = 0 p- n r- n Belle Signal appears in 0 < x. B 2 < 1 APS April Meeting 2006 p D v 253 fb-1 M. Morii, Harvard soft p v Mode BF (10 -4) B 0 p- n 1. 38 0. 24 B+ p 0 n 0. 77 0. 16 0 BABAR B p n 1. 02 0. 28 Prelim. B+ p 0 n 1. 86 0. 44 22
|Vub| from B p n n Average BF measurements and apply FF calculations DB(q 2 < 16) (10 -4) DB(q 2 > 16) (10 -4) Total B (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 Form Factor q 2 (Ge. V 2) Ball-Zwicky < 16 HPQCD > 16 FNAL > 16 |Vub| (10 -3) LCSR Unquenched LQCD Inclusive: 4. 45 0. 20 exp 0. 26 SF+theo Consistent within (large) FF errors n Experimental errors already competitive n APS April Meeting 2006 M. Morii, Harvard 23
Summary n n Semileptonic B decays offer exciting physics opportunities n |Vub /Vcb| complements sin 2 b to test (in)completeness of the SM Challenge of hadronic physics met by close collaboration between theory and experiment n Inclusive B Xc n & Xsg fit precisely determines |Vcb|, mb, etc. n n Inclusive |Vub| achieved 7. 4% accuracy n n n Dramatic progress in both measurement and interpretation of inclusive B Xu n in the last 2 years 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 n Improved form factor calculation needed APS April Meeting 2006 M. Morii, Harvard 24
Backup Slides
Weak Annihilation n WA turns B+ into n + soft hadrons n Size and shape of WA poorly known Minimize the impact n n n Measure Xu n with v. loose cuts n Cut away large q 2 region Measure WA contribution n Gsl(D+) vs. Gsl(Ds) n n Distortion in q 2 n n CLEO-c CLEO hep-ex/0601027 G(B+ Xu n) vs. G(B 0 Xu n) n Work in progress APS April Meeting 2006 M. Morii, Harvard 26
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