E.Barberio University of Melbourne Daphne04: Frascati 7-11 June 2004 measurements of Vcb E.Barberio University of Melbourne Daphne04: Frascati 7-11 June 2004

precision electroweak tests e.w. process at tree level are computed from 3 parameters , GF , mZ and the CKM matrix elements Vij. aem = 0.004 ppm Gm = 9 ppm mZ = 23 ppm very well measured! Vij are less well known (if at all): extraction limited by theory error CP Violation 8 June 2004 E. Barberio

physics motivation Vcb governs bc transition ultimate goal: precise determination of Vcb ! quarks are inside hadrons bound by soft gluons  both perturbative (mb) and non-perturbative (LQCD) QCD effects Tools: Heavy quark symmetry and lattice QCD 8 June 2004 E. Barberio

heavy quark symmetry u/d b LQCD<<mb asymptotic freedom when the energy of soft gluon LQCD~250 MeV << mb,c heavy quark heavy quark is ‘invisible’ to gluon probes with de Broglie wavelegnth lg>>1/mc,b: heavy quark spin and mass (flavour) are good symmetry as (mQ/LQCD) ∞ - departure from the heavy quark symmetry can be expressed as (LQCD/mQ)n corrections 8 June 2004 E. Barberio

Heavy Quark Effective Theory Heavy Quark Effective Theory (HQET): simplified description of processes involving heavy  heavy quark transitions non-perturbative effects described by form factors all B D(*)ln transitions are described by one form factor  (Isgur-Wise function) as a function of w: the D* boost in B rest frame c q n - w=1 q2  4-momentum transfer l Vcb b c n q2 c q n - w>1 w=1 D* produced at rest in B rest frame in mQ∞ (1)=1 Vcb extraction with little model dependence bonus: BD(*)ln largest branching fraction of B decay modes 8 June 2004 E. Barberio

Vcb from B D*ln F(w): unknown form factor= F(1)•g(w) F(1)Vcb w in HQET F(1)Vcb w DELPHI K(w): is the phase space (known function) F(w): unknown form factor= F(1)•g(w) in the heavy quark limit mQ∞ F(1) =(1)=1 measure dG/dw(w) and extrapolate at w=1  g(w) slope important fit for both intercept F(1)|Vcb| and slope (r2) [Caprini, Lellouch, Neubert, Nucl.Phys.B530(98)] 8 June 2004 E. Barberio

signal and w reconstruction Belle D*  Dp DKp(p) B  D*ln D*  p+slowD0: m(D*)-m(D0)~m(p+): the p+ is almost at rest close to K(w=1) in the B rest frame p+ difficult or impossible to reconstruct if the B is produced at rest or has little boost w  pn and En need good resolution for En+pn: easy if the B is produced at rest of with little boost l Vcb b c n q2 8 June 2004 E. Barberio

B D(*)ln U(4S)  B0 at rest or almost LEP Z bb: B0 large variable momentum ~30 GeV good efficiency at w~1: less extrapolation uncertainty at w=1 U(4S)  B0 at rest or almost large data sample, good w resolution, low D** background poor efficiency at w~1 w CLEO B-D*0- Bd0D*+- poorer w resolution large background from higher D** 8 June 2004 E. Barberio

background from BD**ln BD**ln with D** pD*/pD0 resonant (narrow and wide) and non resonant LEP: resonant D**:different form factors depending on assumption on quark decay dynamics [Leibovich,Ligeti,Stewart,Wise] D** shape from constraints on D** rates: Br(BD*2ln )/ Br(BD1ln) <0.4 U(4S): CLEO cosB,D*l D*l  (73.5%) D**l  (7.5%) fake lep (0.3%) uncorr (6.2%) correlated (1.5%) contin. (3.2%) fake D* (7.75%) BABAR events/01 8 June 2004 E. Barberio

F(1)Vcb CLEO Bd0D*- and B-D*0- OPAL BELLE w w 8 June 2004 E. Barberio

F (1)|Vcb| F (1)|Vcb|=(36.50.3tat0.8syst)x10-3 rA2 =1.470.02stat0.13syst 8 June 2004 E. Barberio

F(1) and Vcb non-perturbative QCD calculations F(1) =0.9070.0070.0250.017 F(1) =0.9000.0150.0250.025 F(1) =0.913 -0.017 -0.030 +0.024 +0.017 future error reduction from unquenched calculations from lattice and sum rule F(1)=0.91  0.04 |Vcb|excl=(40.10.9exp1.8theo) 10-3 8 June 2004 E. Barberio

Vcb from Bd0D+- decays large combinatorial background non-zero 1/mQ corrections to G(1) BELLE consistency check and test of the theory: from Belle D* and D+ results r2D-r2D*=-0.230.29 0.20 G(1)/F(1)=1.160.14 0.12 compatible with expectations G(1)|Vcb|=(41.83.7) x 10-3 rG2 =1.15  0.16 8 June 2004 E. Barberio

Vcb from inclusive semileptonic decays exp. D|Vcb|~1% Gsl described by Heavy Quark Expansion in (1/mb)n and ask non perturbative parameters to be measured and arise at each order expansions depend on mb definition: different expation different non-perturbative terms, but they related pole mass low scale running quark masses L l1 l2 or mp2 mG2 at 1/mb2 rD3,rLS3 or r1,r2,T1-4 at 1/mb3 8 June 2004 E. Barberio

inclusive Vcb W rate |Vcb| shape mb,mc m2G,m2p shape from the shape get non-perturbative parameters though the ‘moments’: 8 June 2004 E. Barberio

moments of kinematic variables how much is there? (area) where is it? (mean) how wide is it? (width) skewness 8 June 2004 E. Barberio

moments in semileptonic decays E : lepton energy spectrum in BXc n (CLEO, DELPHI) MX 2: hadronic mass spectrum in BXc n (CLEO, BaBar, DELPHI) Eg : photon energy spectrum in B Xsg (CLEO,Belle) On=1,2,..: different sensitivities to non-perturbative parameters evaluated on the full spectrum or part of it (p > pmin) OPE predictions can be compared with experiments after smearing  integration over neutrino and lepton phase space provides smearing over the invariant hadronic mass of the final state: test of OPE predictions, quark-hadron duality higher moments used to get sensitivity to 1/mb3 parameters: reduced uncertainty on |Vcb| from inclusive semileptonic decay 8 June 2004 E. Barberio

photon energy spectrum u, c, t photon energy spectrum in B Xsg is not sensitive to new physics and give information on B structure Belle Eg>1.8 GeV Eg>2 GeV without Belle 8 June 2004 E. Barberio

hadronic moments hadronic mass spectra Mx Mx from ln: MX2 = mB2+mn2-2EBEn fit relative contributions of D,D*,D** CLEO 3.2 fb-1 B-meson fully reconstructed MX2 BABAR 51 fb-1 BXn P*min= 1.5 GeV 8 June 2004 E. Barberio

lepton energy spectrum spectra background subtracted ratios of truncated lepton spectra Gremm,Kapustin e m Cleo BABAR Babar, lower momentum cut in the B rest frame: small B boost and larger statistics 8 June 2004 E. Barberio

moments at LEP large momentum of b-hadron ~30 GeV: full lepton energy spectrum in B rest frame  non-truncated spectra lepton spectrum unfolded spectrum background subtracted e+m D**D0+ D**D*+- D**D+- Bd0 D**- decays exclusively reconstructed M=M(D(*))-M(D(*)) fits with resonant and non resonant states 8 June 2004 E. Barberio

parameters extraction CLEO: photon spectrum and hadronic mass spectrum evaluated at 1/mB3 and as2 bo [Ligeti,Luke,Manohar,Wise] [Falk,Luke,Savage] L = 0.350.07  0.1 GeV l1=-0.238 0.0710.078 GeV2 1s theo. photon, hadronic mass and lepton energy spectrum evaluated at 1/mB3and as2 bo L=0.39+0.03stat+0.06sys+0.12th GeV l1=-0.25+0.02stat+0.05sys+0.14th GeV2 from 1/mB3 + as 8 June 2004 E. Barberio

moments at LEP multi-parameter c2 fit to determine relevant 1/mb3 parameters mp2 (GeV2) mb (GeV) rD3 (GeV3) M1(Mx) M2(Mx) M3(Mx) M1(El) M2(El) M3(El) c2/d.o.f.=0.96 input: mG2= 0.35 +0.05 GeV2 rLS3= -0.15 +0.15 GeV3 mc= 1.05  0.30 GeV mb= 4.57  0.10 GeV equivalent to B Xsg mb,kin (1GeV)= 4.59 +0.08fit+0.01sys GeV mc,kin (1GeV)= 1.13 +0.13fit+0.03sys GeV mp2 (1GeV) = 0.31 +0.07fit+0.02sys GeV2 rD3 (1GeV) = 0.05 +0.04fit+0.01sys GeV3 mb(mb)= 4.233 GeV mc(mc)= 1.245 GeV present accuracy: no need of higher order terms L = 0.40 + 0.10fit+ 0.02sys GeV l1=-0.15 + 0.07fit+ 0.03sys GeV2 r1=-0.01 + 0.03fit+ 0.03sys GeV3 r2= 0.03 + 0.03fit + 0.01sys GeV3 pole mass expantion: (compatible with CLEO) similar results with mb1S-l1 formalism Bauer, Ligeti, Luke, Manohar 8 June 2004 E. Barberio

parameters extraction BABAR: up to 1/mb3 fit all parameter and Vcb as function of pcut mb,kin (1GeV) = 4.61 +0.05exp+0.05HQE +0.02as GeV mc,kin (1GeV) = 1.18 +0.07exp+ 0.06HQE +0.02as GeV mp2 (1GeV) = 0. 45 +0.04exp + 0.04HQE +0.01as GeV2 mG2 (1GeV) = 0.27 +0.06exp + 0.03HQE +0.02as GeV2 rD3 (1GeV) = 0.2 + .04exp + 0.02HQE GeV3 rSL3 (1GeV) = -0.09 + .04exp + 0.07HQE +0.01as GeV3 p*min=1.5GeV +  from CLEO bsg: l1=-0.17±0.06±0.07 GeV2 in agreement with CLEO 8 June 2004 E. Barberio

derivation of inclusive Vcb + tB LEP: BR(BXc -) = (10.420.26) 10-2 8 June 2004 E. Barberio

derivation of inclusive Vcb Vcb dependence on non-perturbative parameters in running quark mass scheme: N.Uraltsev hep-ph/0302262 |Vcb| = |Vcb|0 {1 -0.65[ mb(1)-4.6 GeV] + 0.4 [mc(1)-1.15 GeV] + 0.01[ mp2 - 0.4 GeV2] + 0.10 [ rD3 -0.12 GeV3] + 0.05[ mG2- 0.35GeV2] - 0.01 [ rLS3 + 0.15 GeV3] } using sl(world) and Babar: |Vcb| = 41.9 [1±0.009Gsl±0.010fit ±0.005pert]10-3 mb,mc,mp2,mG2,rD3,rLS3 as scale 8 June 2004 E. Barberio

conclusion |Vcb| from exclusive B decays Bd0D(*)- more statistics available and new measurements coming present precision (5%) systematics limited: slow p, D’s BR, D**? need to understand the “exeprimental” spread of F(1)Vcb error on F(1)=1 can be reduced in the future by lattice calculations |Vcb|excl=(40.1 0.9exp 1.8theo) 10-3 |Vcb| from inclusive B decays small error on BR(BXc-) and tB quark-hadron duality violation? no evidence of any effects with the present sensitivity: constraints on non-perturbative parameters reduce the uncertainty on |Vcb| to ~2.% more measurements will consolidate the picture 8 June 2004 E. Barberio

CKM mixing matrix Wolfenstein parameterization: unitarity (A†A = 1) 8 June 2004 E. Barberio

G(bXcln) Word average GBXc-= (0.441 0.008) 10-10 MeV U(4S): BR(BXc -) = (10.830.25) 10-2 tB = (1.5980.01) ps GBXc -= (0.4460.0100.003)10-10 MeV LEP: BR(BXc -) = (10.420.26) 10-2 tb = (1.573  0.01) ps GBXc -= (0.4360.010 0.006)10-10 MeV Word average GBXc-= (0.441 0.008) 10-10 MeV 8 June 2004 E. Barberio

Systematics BELLE CLEO 8 June 2004 E. Barberio

extrapolation: form factor shape · expansion around w=1 up to second order: · use dispersive relations to constraint the shape Relate F (w) to the ratios of HQET form factors R1(w), R2(w) Caprini,Lellouch,Neubert NP B530(98)153 and Boyd,Grinstein,Lebed PRD56(97)6895 R1,R2 calculated using QCD sum rules R1(w)1.27-0.12(w-1)+0.05(w-1)2 R2(w) 0.80+0.11(w-1)-0.06(w-1)2 or measured by CLEO: R1(1)=1.18±0.30±0.12 R2(1)=0.71±0.22±0.07 R1,R2 uncertainty is the major source of systematics on rA2, which should improve with future new measurements 8 June 2004 E. Barberio

Systematics LEP 8 June 2004 E. Barberio