Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
ALEPH | 2.15 +/- 0.18+/- 0.37 | input parameters | Phys.Lett.B395:373-387,1997 [Spires] |
CLEO | 2.07+/- 0.13+/- 0.16 | input parameters | Phys.Rev.Lett.82:3746,1999 [hep-ex/9811042] |
BELLE | 2.13+/- 0.12+/- 0.39 | input parameters | Phys.Lett.B526:258-268,2002 [hep-ex/0111082] |
Average | 2.09+/- 0.18 | chi2/dof = 0.04/2 (CL = 0.98) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
ALEPH (excl) | 5.72 +/- 0.27 +/- 0.35 | input parameters | Phys.Lett.B395:373-387,1997 [Spires] |
OPAL (excl) | 5.24 +/- 0.20 +/- 0.37 | input parameters | Exclusive reco, Phys.Lett.B482:15-30,2000 [hep-ex/0003013] |
OPAL (partial reco) | 6.17 +/- 0.28 +/- 0.58 | input parameters | Partial reco, Phys.Lett.B482:15-30,2000 [hep-ex/0003013] |
DELPHI (partial reco) | 5.00 +/- 0.14 +/- 0.36 | input parameters | Partial reco, Phys.Lett.B510:55-74,2001 [hep-ex/0104026] |
BELLE (excl) | 4.73 +/- 0.24 +/- 0.41 | input parameters | Phys.Lett.B526:247-257,2002 [hep-ex/0111060] |
CLEO (excl) | 6.26 +/- 0.19 +/- 0.38 | input parameters | Phys.Rev.Lett.89:081803,2002[hep-ex/0203032] |
DELPHI (excl) | 5.44 +/- 0.20 +/- 0.43 | input parameters | Eur.Phys.J.C33:213,2004 [hep-ex/0401023] |
BABAR (excl) | 4.77 +/- 0.07 +/- 0.33 | input parameters | Phys.Rev.D71:051502,2004 [hep-ex/0408027] |
Average | 5.28 +/- 0.18 | chi2/dof = 13/7 (CL = 0.068) | eps pdf gif |
All the measurements in the following average had been recalibrated such that R_1=(1.417+/-0.061+/-0.044) and R_2=(0.836+/-0.037+/-0.022) is assumed, as measured by the BABAR collaboration (hep-ex/0607076).
This table and the plots in the last row document the two-dimensional simultaneous fit to |Vcb|*F(1) and rho2.
Experiment | |Vcb| F(1) (rescaled) [10-3] | rho2 (rescaled) | Correlation (stat/syst/total) | Parameters | Remarks |
---|---|---|---|---|---|
ALEPH (excl) | 32.8 +/- 1.8 +/- 1.3 | 0.57+/-0.25+/-0.12 | 0.94/0.60/0.72 | input parameters | Phys.Lett.B395:373-,1997 |
OPAL (excl) | 37.2 +/- 1.6 +/- 1.5 | 1.28+/-0.21+/-0.15 | 0.95/0.42/0.61 | input parameters | Phys.Lett.B482:15-,2000 |
OPAL (partial reco) | 37.9 +/- 1.2 +/- 2.4 | 1.15+/-0.14+/-0.30 | 0.77/0.70/0.71 | input parameters | Phys.Lett.B482:15-,2000 |
DELPHI (partial reco) | 36.2 +/- 1.4 +/- 2.3 | 1.36+/-0.14+/-0.27 | 0.94/0.77/0.79 | input parameters | Phys.Lett.B510:55-,2001 |
BELLE (excl) | 35.2 +/- 1.9 +/- 1.7 | 1.31+/-0.16+/-0.11 | 0.91/0.68/0.78 | input parameters | Phys.Lett.B526:247-,2002 |
CLEO (excl) | 42.7 +/- 1.3 +/- 1.6 | 1.47+/-0.09+/-0.09 | 0.87/0.62/0.67 | input parameters | Phys.Rev.Lett.89:081803,2002 |
DELPHI (excl) | 37.1 +/- 1.8 +/- 1.9 | 1.13+/-0.15+/-0.16 | 0.89/0.50/0.58 | input parameters | Eur.Phys.J.C33:213,2004 |
BABAR (excl) | 34.7 +/- 0.3 +/- 1.1 | 1.18+/-0.05+/-0.03 | 0.27 | input parameters | Preliminary hep-ex/0607076 & Phys.Rev.D74:092004,2006 (supersedes Phys.Rev.D71:051502,2004) |
Average | 36.0 +/- 0.6 | 1.19 +/- 0.05 | 0.69/0.40/0.46 | chi2/dof = 31.1/14 (CL = 0.0054) | eps 1 pdf 1 gif 1 eps 2 pdf 2 gif 2 |
Experiment | |Vcb| G(1) (rescaled) [10-3] | rho2 (rescaled) | Correlation (stat/syst/total) | Parameters | Remarks |
---|---|---|---|---|---|
ALEPH | 39.03+/- 11.80+/- 6.20 | 0.96+/- 0.98+/- 0.36 | 0.98/0.99/0.96 | input parameters | Phys.Lett.B395:373-,1997 |
CLEO | 44.84 +/- 5.90+/- 3.45 | 1.27+/- 0.25+/- 0.14 | 0.95/0.98/0.96 | input parameters | Phys.Rev.Lett.82:3746-,1999 |
BELLE | 41.11+/- 4.40 +/- 5.15 | 1.12+/- 0.22+/- 0.14 | 0.96/0.96/0.92 | input parameters | Phys.Lett.B526:258-268,2002 |
Average | 42.4+/- 4.5 | 1.17+/- 0.18 | 0.95/0.94/0.93 | chi2/dof = 0.3/4 | eps 1 pdf 1 gif 1 eps 2 pdf 2 gif 2 |
Experiment | BF (Rescaled) [%] | Input | Remarks |
---|---|---|---|
p(l) > 0.6 GeV/c | |||
ARGUS (e tag) | 9.17 +/- 0.50 +/- 0.33 | input parameters | Phys.Lett.B318:397-404, 1993 [Spires] |
BELLE (l tag) | 10.32 +/- 0.11 +/- 0.46 | input parameters | Phys.Lett.B547:181-192, 2002 [hep-ex/0208033] |
CLEO (e tag) | 10.24 +/- 0.08 +/- 0.22 | input parameters | Phys.Rev.D70:032003,2004 [hep-ex/0403053] |
BABAR (e tag) | 10.37 +/- 0.06 +/- 0.23 | input parameters | Phys.Rev.D69:111104, 2004 [hep-ex/0403030] |
BABAR (B_{reco} tag) | 10.03 +/- 0.19 +/- 0.33 | input parameters | Phys.Rev.D74:091105,2006 [hep-ex/0607111] |
BELLE (B_{reco} tag) | 10.28 +/- 0.18 +/- 0.24 | input parameters | Phys.Rev.D75:032001,2007 [hep-ex/0610012] |
Average | 10.24 +/- 0.15 | chi2/dof = 4/5 (CL = 0.52) | eps pdf gif |
Experiment | BF (Rescaled) [%] | Input | Remarks |
---|---|---|---|
CLEO (l tag) | 10.25 +/- 0.57 +/- 0.66 | input parameters | Phys.Lett.B399:321,1997 [hep-ex/9702007] |
BABAR (B_{reco} tag) | 10.90 +/- 0.27 +/- 0.39 | input parameters | Phys.Rev.D74:091105,2006 [hep-ex/0607111] |
BELLE (B_{reco} tag) | 11.17 +/- 0.25 +/- 0.28 | input parameters | Phys.Rev.D75:032001,2007 [hep-ex/0610012] |
Average | 10.99 +/- 0.28 | chi2/dof = 1/2 (CL = 0.61) | eps pdf gif |
Experiment | BF(B+->) (Rescaled) [%] | Input | Remarks |
---|---|---|---|
CLEO (partial tag) | 9.9 +/- 3.0 +/- 0.9 | input parameters | Phys.Rev.D45:2212-2231,1992 [Spires] |
ARGUS (partial tag) | 9.3 +/- 1.1 +/- 1.5 | input parameters | Phys.Lett.B324:249-254,1994 [Spires] |
CLEO (partial tag) | 10.78 +/- 0.60 +/- 0.69 | input parameters | Phys.Lett.B399:321-328,1997 [hep-ex/9702007] |
BABAR (B_{reco} tag) | 10.14 +/- 0.28 +/- 0.33 | input parameters | Phys.Rev.D74:091105,2006 [hep-ex/0607111] |
BELLE (B_{reco} tag) | 10.46 +/- 0.30 +/- 0.23 | input parameters | Phys.Rev.D75:032001,2007 [hep-ex/0610012] |
Average | 10.33 +/- 0.28 | chi2/dof = 0.9/4 (CL = 0.92) | eps pdf gif |
Experiment | R+/0(Rescaled) [%] | Input | Remarks |
---|---|---|---|
BABAR | 1.084 +/- 0.041 +/- 0.025 | input | Phys.Rev.D74:091105,2006 [hep-ex/0607111] |
BELLE | 1.069 +/- 0.040 +/- 0.026 | input | Phys.Rev.D75:032001,2007 [hep-ex/0610012] |
Average | 1.076 +/- 0.034 | chi2/dof = 0.05/1 (CL = 0.82) | eps pdf gif |
The latter, BLL, although having been around for quite some time, has
been added to our list of phenomenological frameworks from which one
extract a value of |Vub|. BLL is a local OPE based approach that
first advocated the use of a mX- q2
cut, to not only reduce large b->clnu background, but to reduce
theoretical errors associated with the b-quark light cone distribution
function or shape function, as it more widely known. The extraction is
applied to results of the partial branching fraction of inclusive
charmless semileptonic B decays in the phase space pl>1
GeV/c, mX < 1.7
GeV/c2 & q2
> 8 GeV2/c2.
We perform a total of five averages for the inclusive V_ub:
No attempt is made to average BLNP, DGE or BLL derived |Vub|.
For consistency among all the averages, we use the input parameters from the same global fit to data of B->Xc l nu and B->Xs g decays using the latest measurements from the Collaborations:
Eur. Phys. J C 34 (2004) 181. The global fit is performed in the Kinetic Scheme (Eur. Phys. J C 34 (2004) 181) and then the HQ parameters are translated to the other schemes. A global fit in the 1S scheme is currently under way. Earlier results can be found in Phys. Rev. D 70:094017 (2004).
The procedure for performing the average is documented in a brief note on averaging.
The input files for the average are linked below. To summarize briefly, all theoretical uncertainties are considered to be correlated, as are the uncertainties on the modeling of b -> clnu and b -> ulnu decays. Experimental uncertainties (particle identification, reconstruction efficiencies, etc.) are taken as correlated amongst measurements from the same experiment, but not correlated across experiments. The set of results averaged have negligible statistical correlations.
The errors in the tables are experimental (statistical and systematic) and external (theoretical and HQ parameter uncertainties). The average B lifetime used is 1.584 ps.
V_ub values are obtained using the HQ input parameters (from Phys.Rev.D73,073008(2006)):
BLNP Vub (B->Xc l nu & B->Xs g moments) | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
CLEO (E_{e}) | 4.09 +/- 0.48 +/- 0.37 | input | Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019) | 2.1 < p < 2.6, Vub redetermined from partial BF |
BELLE sim. ann. (m_{X}, q^{2}) | 4.37 +/- 0.46 +/- 0.29 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | mX - Q2, tag with annealing method |
BELLE (E_{e}) | 4.82 +/- 0.45 +/- 0.30 | input | Phys.Lett.B621:28-40 (2005) (hep-ex/0504046) | 1.9 < p < 2.6 |
BABAR (E_{e}) | 4.39 +/- 0.25 +/- 0.32 | input | Phys.Rev.D73:012006,2006 (hep-ex/0509040) | 2.0 < p < 2.6, Vub redetermined from partial BF |
BABAR (E_{e}, s^{max}_{h}) | 4.57 +/- 0.31 +/- 0.42 | input | Phys.Rev.Lett.95:111801,2005 , Erratum-ibid.97:019903,2006 (hep-ex/0506036 (version 3, June 2006)) | (Ee-q2) |
BELLE m_{X} | 4.06 +/- 0.27 +/- 0.24 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088) | mX, BRECO tag; other methods (mX-q2 and P not used) |
BABAR (m_{X}, q^{2}) | 4.75 +/- 0.35 +/- 0.31 | input | preliminary (hep-ex/0507017) | mX-q2, BRECO tag |
Average +/- exp +/- (mb,theory) | 4.52 +/- 0.19 +/- 0.27 | chi2/dof = 6.2/6 (CL = 0.41) | Plots: eps pdf gif | HQ parameter input from b to c l nu and b to s gamma moments |
+-2.1stat +-2.7exp +-2.1b2c model +-1.4b2u model +-4.1HQ param +-0.9sub SF +-3.8matching +-2.1WA = +-7.4tot
where the errors correspond to statistics, experimental systematics, the modeling of b -> c l nu and b -> u l nu decays, the HQ parameters mb and mupi2, subleading shape functions, variation of matching scales, and Weak Annihilation. No uncertainty is assigned for possible duality violations.
Using the average |Vub| along with the calculated full b -> u l nu rate from BLNP \(70.8/ps-1/|Vub|2) results in a total BF
BF(b -> u l nu) = (2.29 +- 0.34)*10-3
V_ub values are obtained using the HQ input parameter (from Phys.Rev.D73,073008(2006)):
DGE Vub (B->Xc l nu & B->Xs g moments) | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
CLEO (E_{e}) | 3.85 +/- 0.45 +/- 0.22 | input | Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019) | 2.1 < p < 2.6, Vub redetermined from partial BF |
BELLE sim. ann. (m_{X}, q^{2}) | 4.42 +/- 0.47 +/- 0.19 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | mX - Q2, tag with annealing method |
BELLE (E_{e}) | 4.80 +/- 0.45 +/- 0.20 | input | Phys.Lett.B621:28-40 (2005) (hep-ex/0504046) | 1.9 < p < 2.6 |
BABAR (E_{e}) | 4.29 +/- 0.29 +/- 0.21 | input | Phys.Rev.D73:012006,2006 (hep-ex/0509040) | 2.0 < p < 2.6, Vub redetermined from partial BF |
BABAR (E_{e}, s^{max}_{h}) | 4.42 +/- 0.30 +/- 0.24 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0506036 (version 3, June 2006)) | (Ee-q2) |
BELLE m_{X} | 4.29 +/- 0.28 +/- 0.22 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088) | mX, BRECO tag; other methods (mX-q2 and P not used) |
BABAR (m_{X}, q^{2}) | 4.80 +/- 0.35 +/- 0.21 | input | preliminary (hep-ex/0507017) | mX-q2, BRECO tag |
Average +/- exp +/- (mb,theory) | 4.46 +/- 0.20 +/- 0.20 | chi2/dof = 10.0/6 (CL = 0.124) | Plots: eps pdf gif | m_b input from b to c l nu and b to s gamma moments |
+-1.8stat +-2.5exp +-2.3b2c model +-2.3b2u model +-1.2mb (R_CUT) +-1.0alpha_s (R_CUT) +-3.0 (TOTAL SL WIDTH) +-2.9DGE theory
=+-6.3totwhere the errors correspond to statistics, experimental systematics,
the
modeling of b -> c l nu and b -> u l nu decays, effect of
uncertainty on mb
on the prediction of the event fraction (R_CUT),
effect of alpha_s uncertainty on R_CUT, uncertainty on total
semileptonic B width, and from the change
and variation of scale of the matching scheme (DGE theory).
Using the average |Vub| along with the calculated full b -> u l nu rate from DGE \(66.5/ps-1/|Vub|2) results in a total BF
BF(b -> u l nu) = (2.10 +- 0.29)*10-3
Vub (B->Xc l nu & B->Xs g moments) | |
Theory framework | Vub [10-3] |
---|---|
BLNP (Phys. Rev. D72:073006 (2005)) | 4.52 +/- 0.19 +/- 0.27 |
DGE (JHEP 0601:097 (2006)) | 4.46 +/- 0.20 +/- 0.20 |
V_ub values are obtained using the b-quark mass (from Phys.Rev.D73,073008(2006))
translated to the 1S scheme using hep-ph/0304132:
BLL Vub (B->Xc l nu & B->Xs g moments) | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
BELLE breco (m_{X}, q^{2}) | 5.04 +/- 0.39 +/- 0.37 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088) | mX-q2, BRECO tag |
BELLE sim. ann. (m_{X}, q^{2}) | 4.72 +/- 0.50 +/- 0.35 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | mX - Q2, tag with annealing method |
BABAR (m_{X}, q^{2}) | 5.12 +/- 0.38 +/- 0.38 | input | preliminary (hep-ex/0507017) | mX-q2, BRECO tag |
Average +/- exp +/- (mb,theory) | 5.02 +/- 0.26 +/- 0.37 | chi2/dof = 0.52/2 (CL = 0.77) | Plots: gif eps pdf | HQ parameter input from b to c l nu and b to s gamma moments |
+-3.2stat +-2.9exp +-1.8b2c model +-2.4b2u model +-3.0Strf +-3.0Pert +-4.5Sf +-4.0H.O. = +-9.1tot
where the errors correspond to statistics, experimental systematics, the modeling of b -> c l nu and b -> u l nu decays, residual shape function effects (Strf), higher order terms in the $\alpha_s$ expansion (Pert), the uncertainty on the b-quark mass (Sf), and third order terms in the OPE expansion(H.O.). No uncertainty is assigned for possible duality violations.
Vub (B->Xc l nu & B->Xs g moments) | |
Theory framework | Vub [10-3] |
---|---|
HFAG Ave. (BLNP) mx-q2 (CL=0.79) | 4.65 +/- 0.25 +/- 0.31 |
HFAG Ave. (DGE) mx-q2 (CL=0.77) | 4.70 +/- 0.26 +/- 0.22 |
HFAG Ave. (BLL) mx-q2 (CL=0.77) | 5.02 +/- 0.26 +/- 0.37 |
Above we have used two theoretical formulations to extract|Vub|from measurements of inclusive charmless B-meson decays in various kinematic regions of phase space. Recently BABAR measured inclusive |Vub|using the prescription of Leibovich, Low, and Rothstein (LLR), Phys.Rev.D62:014010,2000 [hep-ph/0001028], and Phys.Lett.B486:86-91,2000 [hep-ph/0005124], that extracts|Vub|with reduced model dependence by combining data of the hadronic mass spectrum from B->Xulnu decays with that of the photon energy spectrum from B->Xs gamma decays (hep-ex/0601046). The LLR approach reduces the dependence on the shape function because no model for the shape function is assumed, in contrast to the BLNP formulation used above. In hep-ph/0702072, the authors, using the BABAR result on the lepton endpoint, extract|Vub|using three prescriptions proposed by: LLR (Phys.Rev.D61:053006,2000 [hep-ph/9909404]), Neubert (Phys.Lett. B513 (2001) 88-92 [hep-ph/0104280]) and more recent calculations by Lange, Neubert and Paz (JHEP 0510 (2005) 084 [hep-ph/0508178] and JHEP 0601 (2006) 104 [hep-ph/0511098]). Here we provide a comparison among the different|Vub|extractions.
The errors on |Vub| are experimental and theoretical, respectively, for the first three results and experimental on B->Xulnu, experimental on B->Xsgamma, theoretical and due to |Vts| for the last three measurments, .
Description | Vub [10-3] | Reference |
---|---|---|
HFAG Ave. (BLNP) | 4.52 +/- 0.19 +/- 0.27 | |
HFAG Ave. (DGE) | 4.46 +/- 0.20 +/- 0.20 | |
BABAR (LLR) | 4.43 +/- 0.45 +/- 0.29 | Phys.Rev.Lett. 96 (2006) 221801 [hep-ex/0601046] |
BABAR endpoint (LLR) | 4.28 +/- 0.29 +/- 0.29 +/- 0.26 +/- 0.28 | hep-ph/0702072 |
BABAR endpoint (weight) | 4.01 +/- 0.27 +/- 0.29 +/- 0.32 +/- 0.27 | hep-ph/0702072 |
BABAR endpoint (weight BLNP) | 4.40 +/- 0.30 +/- 0.41 +/- 0.23 | hep-ph/0702072 |
A plot of this table is available in three formats: eps pdf gif
Experiment / Mode | BF [10-4] | BF(q2<16 GeV2) [10-4] | BF(q2>16 GeV2) [10-4] | Reference |
---|---|---|---|---|
BABAR SL tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.36 +/- 0.33 +/- 0.15 | 1.17 +/- 0.30 +/- 0.11 | 0.19 +/- 0.22 +/- 0.07 | SL tag, Phys.Rev.Lett.97:211801,2006 [hep-ex/0607089] (input) |
BABAR B_{reco} tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.52 +/- 0.41 +/- 0.20 | 1.04 +/- 0.35 +/- 0.15 | 0.48 +/- 0.22 +/- 0.11 | Breco tag, Phys.Rev.Lett.97:211801,2006 [hep-ex/0607089] (input) |
BELLE SL tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.43 +/- 0.26 +/- 0.16 | 1.06 +/- 0.22 +/- 0.11 | 0.37 +/- 0.15 +/- 0.04 | SL tag, accepted by PLB [hep-ex/0604024] (input) |
BELLE B_{reco} tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.60 +/- 0.32 +/- 0.11 | NA | NA | Preliminary, Breco tag hep-ex/0610054 (input) |
BABAR SL tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.12 +/- 0.25 +/- 0.10 | 0.83 +/- 0.22 +/- 0.08 | 0.29 +/- 0.15 +/- 0.04 | SL tag, Phys.Rev.Lett.97:211801,2006 [hep-ex/0607089] (input) |
BELLE SL tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.38 +/- 0.19 +/- 0.14 | 1.02 +/- 0.16 +/- 0.11 | 0.36 +/- 0.10 +/- 0.04 | SL tag, accepted by PLB [hep-ex/0604024] (input) |
BABAR B_{reco} tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.07 +/- 0.27 +/- 0.15 | 0.42 +/- 0.18 +/- 0.05 | 0.65 +/- 0.20 +/- 0.13 | Breco tag, Phys.Rev.Lett.97:211801,2006 [hep-ex/0607089] (input) |
CLEO untagged: B \rightarrow \pi l^{+} \nu | 1.33 +/- 0.18 +/- 0.11 | 1.08 +/- 0.16 +/- 0.10 | 0.25 +/- 0.09 +/- 0.05 | Untagged, Phys. Rev. D 68, 072003 (2003) ( hep-ex/0304015) (input) |
BABAR untagged: B \rightarrow \pi l^{+} \nu | 1.46 +/- 0.07 +/- 0.08 | 1.09 +/- 0.06 +/- 0.07 | 0.38 +/- 0.04 +/- 0.03 | Untagged loose neutrino, Phys. Rev. Lett. 98, 091801 (2007) [hep-ex/0612020 ] (input) |
BELLE B_{reco} tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.49 +/- 0.26 +/- 0.06 | NA | NA | Preliminary, Breco tag hep-ex/0610054 (input) |
Average: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.39 +/- 0.06 +/- 0.06 | 0.97 +/- 0.05 +/- 0.05 | 0.35 +/- 0.03 +/- 0.03 | Plots: eps pdf gif chi2/dof = 3/9 (CL = 0.95) |
The partial BF quoted above along with theoretical calculations of the form factor normalization can be used to determine Vub; a few recent calculations are shown below. Note that the FNAL04 and HPQCD unquenched LQCD calculations are not entirely independent, we do not use their quenched results as they are superseded by their unquenched results. We also use the quenched LQCD result of the APE collaboration. The Ball-Zwicky calculation is based on light-cone sum rules. At this time we do not attempt to average the Vub results or select a best value. We divide the results into two tables: the first table lists extractions of |V_ub| in q^2 regions where the theory formulation is applicable and the second lists results where these same formulations have relied on a model to extrapolate to the uncovered q^2 region.
A determination of |Vub| making use of the experimental input on the q2 dependence is under study but not yet available.
The errors on |Vub| are experimental and theoretical, respectively.
FF calculation | Vub [10-3] | q2 range | FF norm (ps-1) | Reference |
---|---|---|---|---|
Ball-Zwicky q2 < 16 | 3.41 +/- 0.13 +0.56-0.38 | <16 GeV2 | 5.44 +/- 1.43 | Phys. Rev. D71:014015 (2005) [hep-lat/0406232] |
HPQCD q2 > 16 | 3.97 +/- 0.25 +0.59-0.41 | >16 GeV2 | 1.46 +/- 0.35 | Phys.Rev.D73, 074502 (2006) [hep-lat/0601021] |
FNAL q2 > 16 | 3.55 +/- 0.22 +0.61-0.40 | >16 GeV2 | 1.83 +/- 0.50 | Nucl.Phys.Proc.Suppl.140:464-466,2005 [hep-lat/0408019] |
APE q2 > 16 | 3.58 +/- 0.22 +1.37-0.63 | >16 GeV2 | 1.80 +/- 0.86 | Nucl. Phys. B 619 (2000) 565-587 [hep-lat/0011065] |
A plot of this table is available in three formats: eps pdf gif
FF calculation | Vub [10-3] | q2 range | FF norm (ps-1) | Reference |
---|---|---|---|---|
Ball-Zwicky full q2 | 3.43 +/- 0.10 +0.67-0.42 | full | 7.74 +/- 2.32 | Phys. Rev. D71:014015 (2005) [hep-ph/0406232] |
HPQCD full q2 | 3.89 +/- 0.12 +0.84-0.51 | full | 6.03 +/- 1.94 | Phys.Rev.D73, 074502 (2006) [hep-lat/0601021] |
FNAL full q2 | 3.82 +/- 0.12 +0.88-0.52 | full | 6.24 +/- 2.12 | Nucl.Phys.Proc.Suppl.140:464-466,2005 [hep-lat/0409116] |
APE full q2 | 3.61 +/- 0.11 +1.11-0.57 | full | 7.0 +/- 2.9 | Nucl. Phys. B 619 (2000) 565-587 [hep-lat/0011065] |
A plot of this table is available in three formats: eps pdf gif
Experiment | Mode | BF [10-4] | Reference |
---|---|---|---|
CLEO | B+-> eta l+ nu | 0.84 +/-0.31 +0.16 +/-0.09 | Phys. Rev. D 68, 072003 (2003) [hep-ex/0304019] |
BABAR | B+-> eta l+ nu | 0.84 +/-0.27 +/- 0.21 | Preliminary Breco [hep-ex/0607066] |
BABAR | B+-> eta' l+ nu | 0.33 +/-0.60 +/- 0.30 | Preliminary Breco [hep-ex/0607066] |
CLEO | B0-> rho- l+ nu | 2.69 +/-0.41 +0.35/-0.40 +/-0.50 | Phys. Rev. D 61, 052001 (2000) [hep-ex/9905056] |
BABAR | B0-> rho- l+ nu | 2.57 +/-0.52 +/-0.59 | Preliminary, Breco tag [hep-ex/0408068] |
BABAR | B0-> rho- l+ nu | 3.29 +/-0.42 +/-0.47 +/-0.60 | eConf C0304052:WG117,2003 [hep-ex/0301001] |
CLEO | B0-> rho- l+ nu | 2.17 +/-0.34 +0.47/-0.54 +/-0.41 +/-0.01 | Phys. Rev. D 68, 072003 (2003)[hep-ex/0304019] |
BABAR | B0-> rho- l+ nu | 2.14 +/-0.21 +/-0.51 +/-0.28 | Untagged, Phys .Rev. D72, 051102 (2005) [hep-ex/0507003] |
BELLE | B0-> rho- l+ nu | 2.17 +/-0.54 +/-0.31 +/-0.08 | SL tag, accepted by PLB [hep-ex/0604024] |
BELLE | B+-> rho0 l+ nu | 1.33 +/-0.23 +/-0.17 +/-0.05 | SL tag, accepted by PLB [hep-ex/0604024] |
BELLE | B+-> omega l+ nu | 1.3 +/-0.4 +/-0.2 +/-0.3 | Phys. Rev. Lett. 93:131803 (2004)[hep-ex/0402023] |
Theory framework | Vub [10-3] | References |
---|---|---|
HFAG Ave. (BLNP) | 4.52 +/- 0.19 +/- 0.27 | |
HFAG Ave. (DGE) | 4.46 +/- 0.20 +/- 0.20 | |
HFAG Ave. (BLL) mx-q2 | 5.02 +/- 0.26 +/- 0.37 | |
BABAR (LLR) | 4.43 +/- 0.45 +/- 0.29 | Phys.Rev.Lett. 96 (2006) 221801 [hep-ex/0601046] |
FF calculation | Vub [10-3] | q2 range | FF norm (ps-1) | Reference |
---|---|---|---|---|
Ball-Zwicky q2 < 16 | 3.41 +/- 0.13 +0.56-0.38 | <16 GeV2 | 5.44 +/- 1.43 | Phys. Rev. D71:014015 (2005) [hep-lat/0406232] |
HPQCD q2 > 16 | 3.97 +/- 0.25 +0.59-0.41 | >16 GeV2 | 1.46 +/- 0.35 | Phys.Rev.D73, 074502 (2006) [hep-lat/0601021] |
FNAL q2 > 16 | 3.55 +/- 0.22 +0.61-0.40 | >16 GeV2 | 1.83 +/- 0.50 | Nucl.Phys.Proc.Suppl.140:464-466,2005 [hep-lat/0408019] |
APE q2 > 16 | 3.58 +/- 0.22 +1.37-0.63 | >16 GeV2 | 1.80 +/- 0.86 | Nucl. Phys. B 619 (2000) 565-587 [hep-lat/0011065] |
A plot of this table is available in three formats: eps pdf gif