1. Inclusive b → uℓv and b → s  Spectrum Masahiro Morii Harvard University B A B AR Collaboration SLAC/INT Workshop on Flavor Physics and QCD May 11–14, 2005

2. 11 May 2005M. Morii, Harvard2 Experimental Program Inclusive rate  u   (B → X u ℓv)  |V ub | 2 Total rate not measurable due to b → c background Measure partial rate in the “charm-free” regions of phase space Expect theory to calculate Inputs required for the shape function (SF)  E  spectrum in b → s   E ℓ and m X spectra in b → cℓv SF errors considered “experimental” Theoretical errors include:  Perturbative  Sub-leading SF  Weak annihilation (WA) |V ub | Partial  u b → s  b → cℓv Shape Function

3. 11 May 2005M. Morii, Harvard3 Measurements of b → s  E   spectrum depends on the shape function Measure E   moments (1st, 2nd, 3rd)  fit with theory, or Fit the spectrum itself with theory  Is there a preference? Two types of measurements: Inclusive measurement detects only the photon  Poor S/B ratio forces tight selection cuts  Efficiency depends strongly on E  Sum-of-exclusive measurement reconstructs a large number of exclusive decay channels and add them up  Better S/B ratio  Efficiency depends on the s-quark fragmentation model

4. 11 May 2005M. Morii, Harvard4 Inclusive b → s  Inclusive E  spectrum can be measured above ~1.9 GeV Belle, efficiency-corrected DataE  cut<E><E> − 2 Ref. B A B AR 80 fb -1 1.9 GeV2.288 ± 0.033not yet Mommsen, Moriond talk Belle 140 fb - 1 1.8 GeV2.292 ± 0.0430.0305 ± 0.0097 PRL 93:061803,2004 B A B AR, partial BF Belle

5. 11 May 2005M. Morii, Harvard5 Sum of Exclusive B → X s  B A B AR uses 38 channels: (K ± or K S ) plus ≤4 pions, etc. Data sample is 80 fb -1 Measure E  spectrum and the first three truncated moments  Table of values in R. Mommsen’s talk at Moriond Electroweak E  cut (GeV) B A B AR preliminary

6. 11 May 2005M. Morii, Harvard6 Shape Function Parameters Fit the E  spectrum from the B A B AR  (excl.) measurement with Kinetic scheme by Benson, Bigi, Uraltsev (Nucl.Phys.B710:371,2005) Shape-function scheme by Neubert (Eur.Phys.J.C40:165,2004)  b → s  and b → cℓv agree, and have comparable precision  Final results based on the moments in the works |V ub | results in this talk use the SF parameters from b → cℓv Caveat: Error on  is 80 MeV (B A B AR ) vs. 70 MeV (Belle) KineticShape-function b → s  0.63 ± 0.04 b → cℓv0.67 ± 0.070.45 ± 0.060.65 ± 0.080.15 ± 0.07 B A B AR PRL 93:011803,2004 Neubert PLB612:13,2005 Preliminary

7. 11 May 2005M. Morii, Harvard7 Measurements of b → uℓv Three degrees of freedom in B → X u ℓv Lepton energy E ℓ : Easy to measure Hadronic system mass m X : Efficient for b → c rejection Lepton-neutrino mass squared q 2 : Mild dependence on the SF Sample selection technique determines the available variable(s) Inclusive lepton sample  E ℓ Lepton + missing momentum  E ℓ and q 2 Recoil of reconstructed B  E ℓ, m X, and q 2 Experiments measure partial branching fraction   Translation to |V ub | requires  B and B A B AR /Belle use Bosch, Lange, Neubert, Paz (NPB699:335,2004) for the latter Efficiency Purity

8. 11 May 2005M. Morii, Harvard8 Lepton Endpoint Experiments push the E ℓ cut as low as possible  Better efficiency  Weaker SF dependence  Smaller WA error S/B < 1/10  Background modeling! Pushing below 1.9 GeV difficult Hit poorly-understood B → D ** ℓv Data E ℓ (GeV) |V ub | × 10 3 Ref. B A B AR 80 fb - 1 2.0-2.6 3.93 ± 0.34 exp ± 0.38 SF ± 0.18 theo hep-ex/0408075 Belle 27 fb - 1 1.9-2.6 4.49 ± 0.42 exp ± 0.32 SF ± 0.20 theo hep-ex/0504046 Belle on-peak off-peak on – off

9. 11 May 2005M. Morii, Harvard9 Lepton + Neutrino Find lepton with E ℓ > 1.9 GeV and assume p v = p miss of the event Now we have E ℓ and q 2 Define charm-free space by calculating rejects the charm background  Actual cut is s h max < 3.5 GeV 2 Signal/background = 1/2  Final result will have smaller experimental errors Maximum hadronic mass squared + correction for B motion in the c.m.s. Data|V ub | × 10 3 Ref. B A B AR 80 fb - 1 3.89 ± 0.40 exp ± 0.45 SF ± 0.21 theo hep-ex/0408045

10. 11 May 2005M. Morii, Harvard10 Recoil B Analysis Reconstruct one B completely in B → D (*) + hadrons Efficiency ~0.2%/B Recoil gives a clean and unbiased sample of B Charge and 4-momentum known Find a lepton in the recoil B and require Charge conservation Missing mass = 0 Veto against K (likely from D) We get complete event kinematics Leave E ℓ cut loose (>1 GeV) Use m X and/or q 2 to select signal Fully reconstructed B  hadrons lepton v X Recoil B

11. 11 May 2005M. Morii, Harvard11 m X and q 2 Spectra Experiments plan to measure the m X and q 2 spectra in b → uℓv Potential goal: determine the SF parameters with b → uℓv What else can we learn? No q 2 cutm X < 1.7 GeV Belle, background-subtracted distributions B A B AR, corrected for efficiency and resolution

12. 11 May 2005M. Morii, Harvard12 m X vs. q 2 Select m X 8 GeV 2 Proposed by Bauer, Ligeti, Luke (PRD64:113004, 2001)  Reminder: SF errors differ because the error on  is different Data|V ub | × 10 3 Ref. B A B AR 80 fb -1 4.45 ± 0.49 exp ± 0.40 SF ± 0.22 theo hep-ex/0408068 Belle 253 fb - 1 4.34 ± 0.34 exp ± 0.33 SF ± 0.22 theo Bizjak, CKM05 talk signal background b → uℓv outside the signal region

13. 11 May 2005M. Morii, Harvard13 P + Variable Define P + = E X – P X and cut at P + < 0.66 GeV Proposed by Bosch, Lange, Neubert, Paz (PRL93:221801,2004) Belle Data|V ub | × 10 3 Ref. Belle 253 fb - 1 3.87 ± 0.33 exp ± 0.35 SF ± 0.13 theo Bizjak, CKM05 talk Note small theoretical error

14. 11 May 2005M. Morii, Harvard14 Inclusive |V ub | in May 2005 Experimental errors 8–11%  5% if combined Shape-function errors 7–12%  8% on average Theoretical errors 3–5%  4% on average We have determined |V ub | to 5% exp  8% SF  4% theo  10% We said this last summer – Do we believe it now? DataCuts|V ub | × 10 3 B A B AR 80 fb -1 E ℓ > 2.0 GeV 3.93 ± 0.34 exp ± 0.38 SF ± 0.18 theo Belle27 fb -1 E ℓ > 1.9 GeV 4.49 ± 0.42 exp ± 0.32 SF ± 0.20 theo B A B AR 80 fb -1 E ℓ > 1.9 GeV, s h max < 3.5 GeV 2 3.89 ± 0.40 exp ± 0.45 SF ± 0.21 theo B A B AR 80 fb -1 m X 8 GeV 2 4.45 ± 0.49 exp ± 0.40 SF ± 0.22 theo Belle 253 fb - 1 m X 8 GeV 2 4.34 ± 0.34 exp ± 0.33 SF ± 0.22 theo Belle 253 fb - 1 P + < 0.66 GeV 3.87 ± 0.33 exp ± 0.35 SF ± 0.13 theo

15. 11 May 2005M. Morii, Harvard15 Inclusive |V ub | at Moriond 2007 Experimental error (5%) in |V ub | will shrink with the statistics  Even syst. errors improve with larger control samples 500 fb -1 /expt. by summer 2006  2.5%? Largest uncertainty (8%) comes from the shape function  Will improve as soon as we start using the new b → s  results  B A B AR  (excl.) result alone can halve the error on  2 expts. × 2 methods × more data  3%? Theory error (4%) will be the largest error (again) We’d better be darn sure about them We’d better have a strategy to shrink them

16. 11 May 2005M. Morii, Harvard16 Questions + Remark How robust are the current theory errors? B A B AR /Belle rely on calculation by one group  Error estimates come from Lange, Neubert, Paz, hep-ph/0504071  We’d love to have an independent calculation or two Sub-leading SF error small (0.5% for m X -q 2 )  Do we all agree? P + cut has small theo. error (3%)  Will another group confirm? What can we do to shrink the theory errors? Leading error is perturbative  Any hope for improvement? We will pursue B + -B 0 difference  Precision unknown yet Experimental handles on sub-leading SFs? |V ub | will be determined to a 5% precision in 2 years if the theory error becomes 3%, and we believe it