Stato di Vub e Vcb Concezio Bozzi INFN

Stato di Vub e Vcb Concezio Bozzi INFN Ferrara Babar Italia, Trieste 14 Aprile 2005

Sommario • Decadimenti semileptonici inclusivi – con charm (Vcb) – senza charm (Vub) • Decadimenti semileptonici esclusivi – pln, rln (nuovi risultati, Moriond&CKM 05) – D*ln • NB: ho attinto a piene mani da materiale presentato (da altri ma anche da me!) a CKM 2005

Misure inclusive

Inclusive Decays – the Big Picture

Semileptonic B Decays & HQE free-quark rate m= scale which separates effects from long- and short-distance dynamics r = mc/mb; z 0(r), d(r): phase space factors; AEW = EW corrections; Apert = pert. corrections (asj , askb 0) n contains b- and c-quark masses, mb and mc n mp 2 related to kinetic energy of b-quark n m. G 2 related to chromomagnetic operator: B / B* mass splitting n Darwin term (ρD 3) and spin-orbit interaction (ρLS 3) enter at 1/mb 3 No 1/mb term! Several HQE schemes exist; op’s and coeff’s are scheme dependent

Inclusive b cℓν n n n Measure electron momentum spectrum and mass of hadronic system in SL decay Determine moments to allow comparison with partonlevel calculations (duality assumed) Calculations exist for the following: Lepton energy spectrum Mass of hadronic system n Fit for HQE parameters and |Vcb| Gambino & Uraltsev (hep-ph/0401063, 0403166)

BABAR PRL 93: 011803 Fit Results m. X moments ● = used, ○ = unused in the nominal fit BABAR c 2/ndf = 20/15 Eℓ moments Red line: OPE fit Yellow band: theory errors

BABAR PRL 93: 011803 Fit Results precision on |Vcb| = 2% precision on mb = 1. 5% ! y c a r cu c a 2% Uncalculated corrections to G kinetic mass scheme with μ=1 Ge. V Fitted values consistent with external knowledge c 2/ndf = 20/15 n n Impressive agreement between data and theory ≈ identical results obtained in another renorm. scheme: Bauer, Ligeti, Luke, Manohar, Trott in hep-ph/0408002

Inclusive |Vcb| status n Ba. Bar result compared with previous measurements: n Agrees with value coming from exclusive B D* ℓ ν decays (from HFAG):

Inclusive b u n Limiting factor in CKM precision tests; known much less well than |Vcb| n CKM suppressed – therefore harder to measure n Challenge for experiment and theory

Starting point: HQE n Just like b cℓν…, and with similar accuracy m= scale which separates effects from long- and short-distance dynamics AEW = EW corrections; Apert = pert. corrections (asj , askb 0) n …until limited expt’l acceptance is considered n Poor convergence of OPE in region where b cℓν decays are kinematically forbidden n Non-perturbative Shape Function must be used to calculate partial rates

Theory input • Reference (ICHEP 04, HFAG) results based on triple differential decay rate (Ee, m. X, q 2) computed to O(as, mb-2) over the entire phase space by de Fazio and Neubert (DFN, JHEP 06: 17 (1999)) • Use as input the shape function parameters determined by a fit (hep-ex/0407052) to the Belle b→sg spectrum: Λ = 0. 66 Ge. V, λ 1 = -0. 40 Ge. V 2 + covariance δΛ ~ δmb ≈ 80 Me. V Eg spectrum in b → sg • f(k+) Acceptance in b → uℓv q 2 vs m. X analysis: take acceptances from Bauer, Ligeti and Luke (BLL, hep-ph/0111387), OPE calculation in a region of the phase space where SF effects are small.

Inclusive Vub measurements with Ba. Bar method Untagged Electron spectrum endpoint Ee>2. 0 Ge. V Total rate using De. Fazio-Neubert S/B 4. 40 ± 0. 24 exp ± 0. 35 theo ~0. 5 • High statistics • Lower syst. on shape functions • Bkg subtraction 4. 99 ± 0. 48 exp ± 0. 29 theo ~1. 7 • Low background • High resolution • Low statistics • Shape func. syst. 5. 22 ± 0. 43 exp ± 0. 33 theo ~2 • Low background • Very small syst. on SF param. • Small statistics 5. 18 ± 0. 57 exp ± 0. 34 theo Breco Tags m. X analysis (1 -D) m. X<1. 55 Ge. V/c 2 Total rate using De. Fazio-Neubert Breco Tags m. X vs q 2 analysis m. X<1. 7 Ge. V/c 2 and q 2 >8. 0 Ge. V 2/c 4 Vub using Bauer et al. Partial Tags Vub(x 10 -3) • High statistics • Duality valid for 0. 05 0. 2 tight Ee cuts? • Bkg subtraction Untagged Ee vs q 2 and neutrino reconstruction Ee>2. 0 Ge. V and sh<3. 5 Ge. V 2/c 4 Total rate using De. Fazio-Neubert Pros&Cons • Very small bkg Currentexclusive Vub errors: 10 -15% • ~no cut on kinem 1 20 Breco Tags • Small statistics Total experimental syst @250 -500 ifb: 3 -6% Total rate using Form Factors calc.

Vub measurements

A different theory approach • Bosch, Lange, Neubert and Paz (BLNP) Nucl. Phys. B 699, 335 (2004) • Acceptances computed in BLNP using SF parameters from – Belle b→sg hep-ex/0407052 – Ba. Bar b→cℓn moments (hadronic and leptonic) hep-ex/0404017 • Proper translation into shape function scheme of BLNP hep-ph/0412241 Courtesy of Henning Flächer

Results with BLNP and Ba. Bar b→cℓn moments Using mb = 4. 63± 0. 08 Ge. V and μπ2 = 0. 15± 0. 07 Ge. V 2 (SF scheme) with correlation coefficient -0. 4. Errors are: expt ± SF ± theory expt ± (SF+theory) Method Endpoint ∆B × 104 5. 31± 0. 59 q 2 -Ee 4. 46± 0. 93 q 2 -mx 8. 96± 2. 04 Average |Vub| (BLNP) SF params from b cℓν 3. 93 ± 0. 34 ± 0. 38 ± 0. 18 (8. 7 ± 9. 7 ± 4. 6)% 3. 89 ± 0. 40 ± 0. 45 ± 0. 21 (10. 3 ± 11. 5 ± 5. 4)% 4. 45 ± 0. 49 ± 0. 40 ± 0. 22 (11. 1 ± 9. 0 ± 4. 9)% |Vub| (BLNP) (Belle SF) |Vub| ICHEP (DFN, Belle SF) 4. 55 4. 40 ± 0. 24 ± 0. 35 ( ± 6. 4 ± 8. 6) % 4. 53 4. 99 ± 0. 48 ± 0. 29 ( ± 9. 6 ± 5. 8) % 5. 00 5. 18 ± 0. 57 ± 0. 34 ( ± 11. 0 ± 6. 5) % 4. 07 ± 0. 51 b→cℓn moments: significant change in inclusive |Vub| values BLNP: increased sensitivity to SF 4. 61 ± 0. 46

Misure di Vub esclusive

Exclusive B Xuln Decays Breco Tags p+ Y(4 S) n l- Xu = p+, p 0, r+, r 0, w, h, h’, a 00, a 0+ low bkg, low stat. : 27 p, … (ICHEP’ 04) Semilep. Tags Balance between efficiency and purity Untagged High statistics, high hackground (b cln) 3 new pln results ▪ Goal : Measure Branching Fractions and |Vub| ▪ Need FF predictions to describe QCD effects Ø New unquenched LQCD calculations (HPQCD’ 04, FNAL’ 04) Ø Try to measure q 2 dependence of FF with data 03/16/05 Jochen Dingfelder – CKM Workshop 2005

Semileptonic Tag Analyses § Reconstruct B D(*)ln and study semileptonic recoil Ø use both D and D* tags sizable BF Ø Tagging efficiency measured with “Double Tags” (two D(*)ln) D(*)ln decays Correct sl. decay |cosq. BY| < 1 ( tag side: cosq. BY, signal side: cosq. B, pl ) 03/16/05 cos 2 f. B < 1 for signal, bkg flat Jochen Dingfelder – CKM Workshop 2005

p 0 ln with SL Tag : Signal Extraction Ø Cut-and-count analysis in cosq. B, pl and m. D 82 fb-1 Ø Signal region: -1. 1 < cosq. Bpl < 1. 0 Ø Subtract m. D sidebands remove cominatoric background Ø Subtract other background using MC normalized in -10 < cosq. Bpl < -1. 5 45 p 0 03/16/05 Jochen Dingfelder – CKM Workshop 2005

p+ln with SL Tag : Signal Extraction Extract signal yields by binned c 2 fit to cos 2 f. B in 3 bins of q 2: Fit parameters = signal and background normalizations 26 p+ 14 p+ 211 fb-1 Mainly B 0 B 0 bkg ≈ 30% rln X-feed 03/16/05 Jochen Dingfelder – CKM Workshop 2005

p+ln with SL Tag : Branching Fractions and q 2 Ø SL tag analyses statistically limited. Ø Yields not yet large enough to discriminate between FF models. 03/16/05 Jochen Dingfelder – CKM Workshop 2005

Untagged B pln and B rln § Neutrino Reconstruction: Reconstruct n from full event & ensure good reco. quality Ø Cut on missing mass: |M 2 miss / 2 Emiss| < 0. 4 Ge. V § Harsh suppression of b cln bkg (kinem. cuts, mainly for rln) e+e- qq bkg (topological cuts) § Max-LH fit of signal and background in DE, m. ES, and q 2 Ø Fit all 4 signal modes simultaneously (p+, p 0, r+, r 0) Ø Use isospin relations to reduce number of signal parameters: G (B 0 p-l+n) = 2 G (B+ p 0 l+n) G (B 0 r-l+n) = 2 G (B+ r 0 l+n) 03/16/05 Jochen Dingfelder – CKM Workshop 2005

Untagged pln: Fitted DE and m. ES 76 fb-1 427 p+, 147 p 0 03/16/05 Jochen Dingfelder – CKM Workshop 2005 5 bins for pln 3 bins for rln

Untagged pln: Fitted DE and m. ES 76 fb-1 101 r+, 104 r 0 03/16/05 Jochen Dingfelder – CKM Workshop 2005 5 bins for pln 3 bins for rln

Measured q 2 Distributions and Form Factors pln Ø Recent LQCD and LCSR calculations agree well with data Ø ISGW 2 shows marginal agreement for pln Ø Errors for rln still too large to study 3 form factors. 03/16/05 Jochen Dingfelder – CKM Workshop 2005 rln

Systematic Uncertainties (Untagged) Ø Better statistical precision than previous measurements Ø Syst. error dominated by n reconstruction. Will decrease with improved track/neutral reconstruction. Ø Results less dependent on theoretical predictions (own FF measurement) 03/16/05 Jochen Dingfelder – CKM Workshop 2005

Overview: Branching Fraction Measurements pln rln Testing isospin symmetry: Measure p+ln, p 0 ln separately (untagged) 03/16/05 Jochen Dingfelder – CKM Workshop 2005

Extraction of |Vub| Ø Measurement in bins of q 2 allows extraction of |Vub| for various q 2 regimes and FF calculations : LCSR q 2 <15 Ge. V 2, LQCD q 2 > 15 Ge. V 2 or extrapolation to whole q 2 range Quote LQCD 2 as representative 03/16/05 Jochen Dingfelder – CKM Workshop 2005

Misure di Vcb esclusive

Ultimate solution: combined measurement of form factors and Vcb! (work in progress in Trieste)

Other ideas? • D*0 ln (little/undermanned efforts) • Yet another measurement of D*+ln ti t o e dr n A M. thesis Ph. D – D* partial reconstruction – On the recoil of a fully reconstructed hadronic decay Run 1 -4

Conclusioni • Mole impressionante di risultati sperimentali e teorici • Collaborazione virtuosa tra le due comunità • Effetto complessivo: – Vcb inclusivo: ~1. 5% • Accordo impressionante teoria-esperimenti! – Vub inclusivo: 10% → 5% ? • Aggiornare misure con tutta la statistica disponibile • Ampio consenso teorico sulla validità delle relazioni b→cℓν b→sg b→uℓν • Un po’ meno sulle incertezze relative – Vub esclusivo: • Occorre più statistica e migliorare le sistematiche sperimentali • calcolo dei fattori di forma non ancora pienamente maturo – Vcb esclusivo: 4% → ? • Nuove misure (Dln) per limitare incertezze teoriche e per risolvere l’accordo marginale tra le misure esistenti (D*ln)