σ|Vub| at a Super Flavor Factory

σ|Vub| at a Super Flavor Factory
Benoit VIAUD LAL, CNRS-In2p3 March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

B. VIAUD,VIth infn B-physics mting , Ferrara
Super Flavor Factory Generically: similar to BaBar/Belle, with L  100 = 75 ab-1 I focus in this talk on the Italian project: SuperB. Crab waists and Large Piwinski angle to reach L=1036cm-2s-1  =0.28 instead of 0.56. Smaller boost (better hermeticity) and improved vertex detector New Layer 0 at 1.2 cm from the beam) : improved neutrino and background rejection. Start ~ in 2015: theory should be improved by then. CDR : Last Workshop : March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Error on SuperB ?? Today: |Vub| is no longer dominated by stat. SuperB (75ab-1): stat does not count anymore. Predicting what can be achieved at a Super Flavor Factory means predicting how the systematic and theoretical uncertainties will be reduced. Single reliable way: Full MC studies -> not yet possible. Single available way: Educated guesses (science fiction ?) So many experimental and theoretical analyses that it is very hard to consider them all. => Choose a few (promising) ones and extrapolate. March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

|Vub| from inclusive B-> Xu l v decays
March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Inclusive |Vub| Total decay rate precisely known OPE+HQE, expansion in (1/mb)k and (s)k  dominated by 2.5mb/mb : ~3% Not used up to now ulv/ clv ~ 1/50 : harsh cuts necessary OPE convergence spoiled in restricted part of the phase space Must deal with the Fermi motion of the b inside the B March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Many Theoretical Approaches
Have to deal with Shape Functions (SF) to account for the Fermi motion BNLP (PRD71: (2005)) GGOU (JHEP 10(2007)058 ) LNR (JHEP 0510:084 (2005)), LLR (PLB 486:86) Dressed Gluon Exponentiation (DGE) (JHEP 0601:097 (2006)) Analytic Coupling (AC) (PRD74: (2006)) Various ways to treat the SF In a OPE, convoluted with pert. quantities and parameterized with their shape constrained from moments = f( =MB-mb ; 2 ) Take it from B-> Xs  Calculate it Various treatments of the subleading SF (universal only at LO in 1/mb) March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Have to deal with Shape Functions (SF) to account for the Fermi motion Key common points: Consistent results BNLP (PRD71: (2005)) Main source of Uncertainty on |Vub| GGOU (JHEP 10(2007)058 ) LNR (JHEP 0510:084 (2005)), LLR (PLB 486:86) Dressed Gluon Exponentiation (DGE) (JHEP 0601:097 (2006)) Analytic Coupling (AC) (PRD74: (2006)) Dominant source: mb and 2  ~ 4mb/mb Determined from fits to the moments of B-> Xclv and Xs spectra. Various ways to treat the SF In a OPE, convoluted with pert. quantities and parameterized with their shape constrained from moments = f( =MB-mb ; 2 ) Take it from B-> Xs  Calculate it Various treatments of the subleading SF (universal only at LO in 1/mb) March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Many Experimental Approaches
Try several cut variables to find the best trade-off between S/B and th Hadronic Tag No Tag Hadronic Tag Hadronic Tag March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Untagged Semileptonic tag Hadronic tag oFirst find a Btag, then look for B->Xulv in its recoil: - Only one Xu-l pair in the rest of event - No other tracks, small residual energy o tag side: B->D(*)+(π±,K±), full reco. (many modes) o Well defined event: full kinematics, charge, flavor. o Only one neutrino : precise reco of m2miss ,miss ,q2, MX, P+ o tag side: B->D(*)lν o tag-B kinematics incomplete: 2 ν High signal statistics, More sensitive to Background simulation Clean Sample, Better systematics Purity + + Efficiency March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Key common points: Consistent results Leading Uncertainties on |Vub| Detector effects (Tracking and PID efficiency) Fit and Efficiency on the tag side March 19th 2009 Knowledge of the B->Xc l v backgrounds B. VIAUD,VIth infn B-physics mting , Ferrara

Key common points: Consistent results Leading Uncertainties on |Vub| SuperB - Large control samples - Improved detector & bkg rejection Detector effects (Tracking and PID efficiency) Fit and Efficiency on the tag side March 19th 2009 Knowledge of the B->Xc l v backgrounds B. VIAUD,VIth infn B-physics mting , Ferrara

MX Analysis Babar, PRL 100, (2008) First reconstruct the hadronic tag Btag B+tag B0tag Look for the signal in Btag’s recoil One lepton with PBframe > 1 GeV/c Ql consistent with Btag’s flavor, evtQ = 0 mmiss 2 < 0.5 GeV2, miss Good  rejects B -> Xclv Mveto2 = (pB- pD*-pl) < 3GeV2, pD* from slow pion 383 MBB Bsig Kinematic fit: MX~250 MeV Combinatoric background: fit to mES in bins of MX 1.55 GeV Binned X2 fit of B -> Xulv & B -> Xclv MC distrib. to MX data distrib. March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

MX Analysis First reconstruct the hadronic tag Btag B+tag B0tag Look for the signal in Btag’s recoil One lepton with PBframe > 1 GeV/c Ql consistent with Btag’s flavor, evtQ = 0 mmiss 2 < 0.5 GeV2 Good  rejects B -> Xclv Mveto2 = (pB- pD*-pl) < 3GeV2, pD* from slow pion 383 MBB Bsig Kinematic fit: MX~250 MeV Combinatoric background: fit to mES in bins of MX Binned X2 fit of B -> Xulv & B -> Xclv MC distrib. to MX data distrib. |Vub|= /- 0.16stat +/- 0.15syst +/- 0.30th (BNLP) March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

MX Analysis: Error Breakdown
Errors on BF @ SuperB 1 % Data Stat + MC stat: % % Detector Effects : % 1 % Improved with high stat control samples+ better det Signal Model (SF & gluon split.): % 1 % Improved better mb, Xs meas. and th. BF(B->u lv excl.): % 1 % Improved by > SuperB (cf this talk) BF & FF (B->c lv excl.): % 0.3 % Idem (cf this talk) mES fit (parameterization choice): % 1.5 % Better stat + possibility to be more selective for Btag will help. Tot: 12 % % |Vub|exp: 6 % ~1.5 % March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Crucial it we want to use a looser MX cut to reduce th. Improved with a precise measurement of BF(B-c l SuperB (back-up slides). Better detector. Lower  => hermeticity  => better v => better bkg rejection Better Vertexing => B-D separation to veto B->D X l v Hope corresponding  can be divided by ~4. Errors on BF @ SuperB 1 % Data Stat + MC stat: % % Detector Effects : % 1 % Improved with high stat control samples+ better det Signal Model (SF & gluon split.): % 1 % Improved better Xs meas. and th. BF(B->u lv excl.): % 1 % Improved by > SuperB (cf this talk) BF & FF (B->Xc l v excl.): % 0.3 % Idem (cf this talk) mES fit (parameterization choice): % 1.5 % Tot: 12 % % Better stat + possibility to be more selective for Btag will help. |Vub|exp: 6 % ~1.5 % March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Total Error on |Vub| @ SuperB
HFAG, ICHEP 2008, GGOU |Vub| (%) = 3.7  3.9.  1.8  Higher order pert. and non pert. corrections Hadronic param. (mb) q2 tail and Weak Annihil. Exp. SF parame-terization SuperB, > 2015 ?? ?? ?? ?? 1.5 Question to theorists: what can we hope here ? March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

(mb) by SuperB’s time Measured via a fit to the moments of incl. B->Xc l v and B->Xs spectra. Total BF (OPE) = Hadronic, non calculable, parameters. Multiplied by perturbative coefficients. Similar expressions for moments, as a function of a cut lepton energy. Hadr. System Mass Lepton energy Photon energy f( mb, 2,…) => fit to extract these hadronic parameters March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

(mb) by SuperB’s time Example: BaBar (arXiv: v1) March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

(mb) by SuperB’s time HFAG 2008, Kinetic scheme (mb) ~ MeV Theoretical Uncertainties dominate Moment Measurements: syst ~ stat syst dominated by the determination of efficiencies Additional, higher order moments ? At SuperB, > 2015 exp  ½ (?) March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

(mb) by SuperB’s time HFAG 2008, Kinetic scheme (mb) ~ MeV Recent th. progresses to be included in the fit: O(2s) calc. of leading power rate and moments O(s) calc. 1/mb2 power correction LO calc. of 1/mb4 Should remove a large part of th With these improvements + potential still-higher order corrections + B->Xs  puzzle solved + Consistency between 1S and kinetic schemes Can we hope (mb) ~ 20 MeV by 2015 ? March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

HFAG, ICHEP 2008, GGOU |Vub| (%) = 3.7  3.9.  1.8  Higher order pert. and non pert. corrections Hadronic param. (mb) q2 tail and Weak Annihil. Exp. SF parame-terization SuperB, > 2015 ?? ?? ?? 2. 1.5 Include more Terms ? Cut high q2 ? March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

HFAG, ICHEP 2008, GGOU |Vub| (%) = 3.7  3.9.  1.8  Higher order pert. and non pert. corrections Hadronic param. (mb) q2 tail and Weak Annihil. Exp. SF parame-terization SuperB, > 2015 1 1.5 0.5 2 1.5 ½ Realistic ? If not, what can we expect ? March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

HFAG, ICHEP 2008, GGOU |Vub| (%) = 3.7  3.9.  1.8  Higher order pert. and non pert. corrections Hadronic param. (mb) q2 tail and Weak Annihil. Exp. SF parame-terization SuperB, > 2015 If yes: |Vub| ~ 3 % @ SuperB ! March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

SuperB Another option: Use the full decay rate Pioneer Analysis at Babar (88 MBB, hep-ex/ v2) Hadronic Tag Similar to the MX analysis already presented here. Errors on Vub At SuperB -|Vub|exp ~ 2.5 % -|Vub|th ~ 2.5*mb/mb ~ 1% => |Vub| ~3 % 88 fb-1 75 ab-1 18.6% 1% 3.8% 1% Signal Model 5.6% 1.5% 3.8% 1% March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

|Vub| from exclusive B-> Xu l v decays
March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Exclusive |Vub| Harder than the inclusive case: -> need to fully describe specific hadrons Needs Form Factors from theory Unquenched LQCD (q2 > 16 GeV2): HPQCD[1], FNAL[2] LCSR (q2 < 16 GeV2): Ball-Zwicky[3] Th. uncertainties are the main source of |Vub| (~12%) [1] Gulez & al, hep-lat/ [2] Okamoto & al, hep-lat/ [3] Ball & al, hep-ph/ March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Exclusive |Vub| Golden Mode: B-> l v , both for th. and exp. Measured BF(B-> l v ) : -> already syst ~ stat -> better syst will again be the challenge at SuperB -> Hadronic Tag ! HFAG’s Average (FNAL) |Vub|= (3.55± )10-3 th~6% th~12% March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Exclusive |Vub| with an Hadronic Tag @ SuperB
Extrapolation from a recent analysis by Belle (arXiv: v1) 657 MBB Hadron Tag, tight cuts on E and mES (no fit) Signal extraction: -binned fit to the mmiss2 distribution Statistically limited, but low syst : <5% B(B->+lv) =  0.18  0.05 B(q2>16GeV2) = 0.26  0.08  0.01 Leading syst: Detector effects / B->Xulv and Xclv FF & BF / BB initial yield. With : Large Control sample / Improved meas. and th, harsher cuts => Cab hope to reduce syst by ~1/3 at Super B March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Exclusive |Vub| with an Hadronic Tag @ SuperB
Extrapolation from a recent analysis by Belle (arXiv: v1) 657 MBB Hadron Tag, tight cuts on E and mES (no fit) Signal extraction: -binned fit to the mmiss2 distribution Statistically limited, but low syst : <5% B(B->+lv) =  0.18  0.05 B(q2>16GeV2) = 0.26  0.08  0.01 Leading syst: Detector effects / B->Xulv and Xclv FF & BF / BB initial yield. At SuperB, with q2 > 16 GeV2 : - (B)stat ~ 3% and (B)syst~ 3% => (B)exp~ 5% => (|Vub|)exp ~ 2.5 % With : Large Control sample / Improved meas. and th, harsher cuts => Cab hope to reduce syst by ~1/3 at Super B March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

|Vub|th : What improvement from LQCD ?
See Appendix A of the SuperB CDR. Sources of uncertainties: Statistical (number of configurations) Matching to continuum (pert. calculations difficult on the Lattice) Chiral extrapolation (computation  time if mq) Heavy quark treatment All sources would benefit from an improved CPU. With the following evolutions: - Lattice spacing a : 0.1 fm > 0.03 fm - light quark mq : 1/2–1/6 ms -> 1/12 ms - Lattice size L : 3 fm > 4.5 fm f+ ~2-3% March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

See Appendix A of the SuperB CDR. Sources of uncertainties: Statistical (number of configurations) Matching to continuum (pert. calculations difficult on the Lattice) Chiral extrapolation (computation  time if mq) Heavy quark treatment All sources would benefit from an improved CPU. With the following evolutions: - Lattice spacing a : 0.1 fm > 0.03 fm - light quark mq : 1/2–1/6 ms -> 1/12 ms - Lattice size L : 3 fm > 4.5 fm Cost: few PFLOPs-years |Vub|th~2-3% March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

See Appendix A of the SuperB CDR. Evolution law of computers performance with time => Machines available for LQCD could improve from 1-10 TFLops to 1-10 PFlops => |Vub|th~2-3% looks feasible ! March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Exclusive |Vub|: All together
With |Vub|exp~2-3 % and |Vub|th~2-3% => |Vub|tot ~ 4 % seems feasible. March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Conclusion Stat. uncertainty on |Vub|th will be marginal at a Super Flavor Factory To reach |Vub| ~ few percents: big effort to reduce the systematic and theoretical uncertainties. Systematic uncertainties will benefit from the large data sample: Hadronic tag methods not statistically limited any longer Control Samples to reduce detector effects Better knowledge of the B->Xc l v backgrounds Theoretical uncertainties Inclusive: Need to improve mb (~20MeV ?) Exclusive: Large improvement of the computing power should help LQCD |Vub|~3 % (incl.) and |Vub|th ~4% (excl.) seems possible ! March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Back-up March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Improved B->Xc l v BF’s
The control of these backgrounds is essential for any inclusive |Vub| determination. What improvement at SuperB ? Study one example: B->D(*)()lv with a hadronic tag (Babar, arXiv: v1) Hadronic Tag BF measured with respect to the total semileptonic BF. N(Xlv): fit to mES Nsig: fit to the mmiss2 distribution March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

The control of these backgrounds is essential for any inclusive |Vub| determination. What improvement at SuperB ? Study one example: B->D(*)()lv with a hadronic tag (Babar, arXiv: v1) Hadronic Tag BF measured with respect to the total semileptonic BF. N(Xlv): fit to mES Nsig: fit to the mmiss2 distribution Systematic uncertainties Detector Effects Btag efficiency BF(D) Can hope 1/2-1/3 with SuperB statistics March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

PDG 2006 (%) Babar hadr. Tag @ SuperB B- -> D0 l v 2.2 +/- 0.11 2.33 +/ /- 0.09 +/- 0.03 +/- 0.10 B- -> D0* l v 5.7 +/- 0.18 5.83 +/ /- 0.30 B0 -> D+ l v 2.21 +/ /- 0.12 +/- 0.04 2.2 +/- 0.12 +/- 0.08 B0 -> D+* l v 5.49 +/ /- 0.25 5.0 +/- 0.10 B- -> D+ -l v 0.6 +/- 0.05 0.42 +/ /- 0.03 +/- 0.01 B- -> D*+ -l v 0.4 +/- 0.05 0.59 +/ /- 0.04 +/- 0.01 B0 -> D0 -l v +/- 0.01 0.4 +/- 0.06 0.43 +/ /- 0.03 +/- 0.01 B0 -> D0* -l v 0.5 +/- 0.08 0.48 +/ /- 0.04 March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Errors on BF @ SuperB 1 % Data Stat + MC stat: % % Detector Effects : % 1 % Improved with high stat control samples+ better det Signal Model (SF & gluon split.): % 1 % Improved better Xs meas. and th. BF(B->u lv excl.): % 1 % Improved by > SuperB (cf this talk) BF & FF (B->c lv excl.): % 0.3 % Idem (cf this talk) mES fit (parameterization choice): % 1.5 % Better stat + possibility to be more selective for Btag will help. Tot: 12 % % |Vub|exp: 6 % ~1.5 % March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Form Factors [1] Ball & al, hep-ph/ [2] Becirevic & al, Phys. Lett. B478, 417 [3] Ex: Becher&Hill, hep-ph/ [4] P. Ball, hep-ph/ (|Vub|)exp could be further improved using the full measured q2 spectrum. Parameterizations of the FF shape to extend theoretical predictions to the whole q2 spectrum… -Ball-Zwicky (BZ)[1] -Becirevic-Kaidalov (BK)[2] -Boyd/Grinstrin/Lebed+Hill/Becher (BGL)[3] Linear or more ?? BaBar, loose v, 206 fb-1, hep-ex/ Data points not yet precise enough. Fits give the same result whatever the parameterization Using constraints from unitarity and from a fit to data and theoretical points, enough ai’s could be known to yield a precise parameterization. March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

BNLP OPE+HQE, expansion in (1/mb)k and (s)k Fermi motion included via Shape Functions (SF) SF convoluted with perturbative quantities, at each order in 1/mb SF not calculated from first principles, but shape of the leading ones constrained by their (known) 1st , 2nd moments : =MB-mb ; 2 Subleading SF’s showing up at each higher term in (1/mb) accounted for by trying many ad-hoc parameterizations. March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

BNLP OPE+HQE, expansion in (1/mb)k and (s)k Fermi motion included via Shape Functions (SF) SF convoluted with perturbative quantities, at each order in 1/mb SF not calculated from first principles, but shape of the leading ones constrained by their (known) 1st , 2nd moments : Hadronic param. extracted from the moments of B->Xclv and B->Xs  spectra. Dominates |Vub| =MB-mb ; 2 March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Untagged B0->π-l+ν, loose ν-reconstruction
BaBar, 206 fb-1, hep-ex/ No tight ν-reconstruction cuts : Signal Yield ↑ Purity ↓ High statistics allow a precise signal extraction in 12 q2 bins Binned fit to ΔE-mES: renormalize histos from MC. High stat. also allows to control the systematics despite low S/B… -Bkg fitted in q2 bins: reduced σ from B->Xlv FF&BF (leading at high q2) -High stat. in data control samples: continuum bkg correction (leading at low q2) Total Nsig~5000 In q2 bins: Nsig ~ 430 to 500 S/B ~ 1/3 to 1/10 B(B->-lv)= (1.46±0.07stat±0.08syst)10-4 4.8% ΔB(B->-lv; q2>16GeV2)= (0.38±0.04stat±0.03syst)10-4 5.5% |Vub|= ( 3.7±0.2± )10-3 FNAL March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Status of BF’s and |Vub|
Belle, semileptonic tags, B++B0 |Vub|= ( 3.6±0.41± )10-3 FNAL Babar, semileptonic+hadronic , B++B0 |Vub|= ( 4.0±0.5 ± )10-3 FNAL CLEO, untagged |Vub|= (3.6±0.4 ± )10-3 HPQCD Babar Loose-v 1.37±0.15±0.11 |Vub|= (3.7±0.20± )10-3 FNAL Error on the FF determination dominates the most precise results. What improvements with the full B-factories dataset ? March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

few definitions… In the Y(4S) frame: EB, pB= nominal values of the B energy and momentum, from 4-mom. conservation pY = pπ+pl |cosθBY| and |cos2ΦB| <1 if the ν’s are the only undetected particles… March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Results: Relative Errors on ΔBF(q2)
-Dominant syst. errors: Detector effects, Continuum description -Fit of the backgrounds yields in several q2 bins (thanks to high statistics due to loose ν ) => reduced systematic error due backgrounds BF and FF. March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

Form Factors [1] Gulez & al, hep-lat/ [2] Okamoto & al, hep-lat/ [3] Ball & al, hep-ph/ [4] Scora & al, hep-ph/ => Boyd/Grinstrin/Lebed+Hill/Becher (BGL) Babar’s untagged measurement Full dataset ! Most improved points: High / Low z Improved Continuum Improved B->Xul v background) Unitarity: Should obtain a very precise determination of the FF’s shape with a fit to the ΔB(q2) measurements, helped by theoretical constraints (like unitarity). In that case, LCSR and LQCD have to provide only the normalization f+(0). Even closer with the full dataset… March 19th 2009 B. VIAUD,VIth infn B-physics mting , Ferrara

σ|Vub| at a Super Flavor Factory

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