Experiment | |Vcb| F(1) (rescaled) [10-3] | r2 (rescaled) | Correlation (stat/syst/total) | Parameters | Remarks |
---|---|---|---|---|---|
ALEPH (excl) | 31.6 +/- 1.8 +/- 1.3 | 0.50 +/- 0.20 +/- 0.09 | 0.94/0.54/0.76 | input parameters | Phys.Lett.B395:373-,1997 |
CLEO | 41.3 +/- 1.3 +/- 1.8 |
1.37 +/- 0.08 +/- 0.18 |
0.91/0.85/0.84 |
input
parameters |
Phys.Rev.Lett.89:081803,2002 |
OPAL (excl) | 36.9 +/- 1.6 +/- 1.5 | 1.24 +/- 0.20 +/- 0.14 | 0.95/0.44/0.69 | input parameters | Phys.Lett.B482:15-,2000 |
OPAL (partial reco) | 37.6+/- 1.2 +/- 2.4 | 1.14 +/- 0.13 +/- 0.27 | 0.77/0.73/0.74 | input parameters | Phys.Lett.B482:15-,2000 |
DELPHI (partial reco) | 35.8 +/- 1.4 +/- 2.3 | 1.18 +/- 0.13 +/- 0.25 | 0.94/0.63/0.67 | input parameters | Phys.Lett.B510:55-,2001 |
BELLE (excl) | 34.7 +/- 0.2 +/- 1. | 1.159 +/- 0.040 +/- 0.026 | 0.91/0.87/0.88 | input parameters | Phys.Lett.B526:247-,2002 |
DELPHI (excl) | 36.3 +/- 1.8 +/- 1.9 | 1.04 +/-0.14 +/-0.15 | 0.89/0.76/0.82 | input parameters | Eur.Phys.J.C33:213,2004 |
BABAR (excl) | 33.9 +/- 0.3 +/- 1.1 | 1.18 +/-0.05 +/-0.03 | 0.27/0.09/0.12 | input parameters | Phys.Rev.D77:032002,2008 [arXiv:0705.4008 [hep-ex]] |
BABAR (D*0) | 34.9 +/- 0.8 +/- 1.4 | 1.11 +/-0.06 +/- 0.08 | 0.90/0.07/0.29 | input parameters | Phys.Rev.Lett. 100, 231803, 2008 [arXiv:0712.3493 [hep-ex]] |
BABAR (Global Fit) | 35.7 +/- 0.2 +/- 1.2 | 1.20 +/-0.02 +/- 0.07 | 0.38/0.74/0.73 | input parameters | Phys.Rev.D79:012002, 2009 [arXiv:0809.0828 [hep-ex]] |
Average | 35.41 +/- 0.52 | 1.16 +/- 0.05 | 0.20 |
chi2/dof = 39./21 (CL = 0.01%) | eps 1 pdf 1 gif 1 eps 2 pdf 2 gif 2 eps 2 (zoom) pdf 2 (zoom) gif 2 (zoom) |
Experiment | BF (rescaled) [%] | Remarks |
---|---|---|
ALEPH (excl) | 5.44 +/- 0.25 +/- 0.20 | Phys.Lett.B395:373-387,1997 [Spires] |
OPAL (excl) | 5.17+/- 0.20 +/- 0.38 | Exclusive reco, Phys.Lett.B482:15-30,2000 [hep-ex/0003013] |
CLEO | 6.02 +/- 0.19 +/- 0.20 | Phys.Rev.Lett.89:081803,2002 |
OPAL (partial reco) | 5.63 +/- 0.27 +/- 0.43 | Partial reco, Phys.Lett.B482:15-30,2000 [hep-ex/0003013] |
DELPHI (partial reco) | 5.00 +/- 0.15 +/- 0.18 | Partial reco,Phys.Lett.B510:55-74,2001 [hep-ex/0104026] |
BELLE (excl) | 4.75 +/- 0.25 +/- 0.19 |
Phys.Lett.B526:247-257,2002 [hep-ex/0111060] |
DELPHI (excl) | 5.53 +/- 0.19 +/- 0.34 | Eur.Phys.J.C33:213,2004 [hep-ex/0401023] |
BABAR (excl) | 4.53 +/- 0.04 +/- 0.13 | Phys.Rev.D77:032002,2008 [arXiv:0705.4008 [hep-ex]] |
BABAR (tagged) | 5.40 +/- 0.16 +/- 0.25 | Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
Average | 5.05 +/- 0.10 | chi2/dof = 35.8/9 (CL = 0.00005) eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
ALEPH | 0.45+/- 0.10+/- 0.07 | input parameters | Z.Phys. C 73:601,1997 [Z.Phys.C73] |
OPAL | 0.59 +/- 0.21+/- 0.10 | input parameters | Eur.Phys. J.C 30:467,2003 [hep-ex/0301018] |
CLEO | 0.35 +/- 0.08+/- 0.06 | input parameters | Phys.Rev.Lett.80:4127,1998 [hep-ex/9708035] |
D0 | 0.22 +/- 0.02+/- 0.04 | input parameters | Phys.Rev.Lett.95:171803,1995 [hep-ex/0507046] |
BELLE | 0.44 +/- 0.07+/- 0.06 | input parameters | Phys.Rev.D77:091503, 2008 [arXiv:0711.3252 [hep-ex]] |
BABAR Tagged | 0.28 +/- 0.03+/- 0.03 | input parameters | Phys.Rev.Lett.101:261802,2008 [arXiv:0808.0528 [hep-ex]] |
BABAR Untagged | 0.29 +/- 0.02+/- 0.02 | input parameters | [arXiv:0808.0333 [hep-ex]] |
Average | 0.28 +/- 0.02 | chi2/dof = 13.2/6 (CL = 0.04) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
CLEO | 0.06 +/- 0.07+/- 0.01 | input parameters | Phys.Rev.Lett.80:4127,1998 [hep-ex/9708035] |
D0 | 0.09 +/- 0.02+/- 0.02 | input parameters | Phys.Rev.Lett.95:171803,1995 [hep-ex/0507046] |
BELLE | 0.19 +/- 0.06+/- 0.03 | input parameters | Phys.Rev.D77:091503, 2008 [arXiv:0711.3252 [hep-ex]] |
BABAR Tagged | 0.067 +/- 0.009 +/- 0.016 | input parameters | Phys.Rev.Lett.101:261802,2008 [arXiv:0808.0528 [hep-ex]] |
BABAR Untagged | 0.089 +/- 0.013+/- 0.008 | input parameters | [arXiv:0808.0333 [hep-ex]] |
Average | 0.082 +/- 0.011 | chi2/dof = 3.9/4 (CL = 0.42) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
CLEO | 6.6+/- 0.2+/- 0.4 | input parameters | Phys.Rev.Lett.82:3746,1999 [hep-ex/9811042] |
ARGUS | 6.1 +/- 1.4+/- 1.0 | input parameters | Phys.Lett.B395:373-387,1997 [Spires] |
BABAR Tagged | 5.71 +/- 0.15+/- 0.30 | input parameters | Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
BABAR Untagged | 5.31 +/- 0.08+/- 0.40 | input parameters | Phys.Rev.Lett. 100, 231803 (2008) [arXiv:0712.3493 [hep-ex]] |
BABAR Global Fit | 5.37 +/- 0.02+/- 0.21 | input parameters | Phys.Rev.D79:012002, 2009 [arXiv:0809.0828 [hep-ex]] |
Average | 5.66 +/- 0.18 | chi2/dof = 9.3/5 (CL = 0.05) | eps pdf gif |
Experiment | |Vcb| G(1) (rescaled) [10-3] | rho2 (rescaled) | Correlation (stat/syst/total) | Parameters | Remarks |
---|---|---|---|---|---|
ALEPH | 38.08+/- 11.80+/- 6.09 | 0.91+/- 0.98+/- 0.36 | 0.98/0.99/0.96 | input parameters | Phys.Lett.B395:373-387,1997 [Spires] |
CLEO | 44.53 +/- 5.90+/- 3.42 | 1.27+/- 0.25+/- 0.14 | 0.95/0.98/0.96 | input parameters | Phys.Rev.Lett.82:3746,1999 [hep-ex/9811042] |
BELLE | 40.70+/- 4.40 +/- 5.14 | 1.12+/- 0.22+/- 0.14 | 0.96/0.96/0.92 | input parameters | Phys.Lett.B526:258-268,2002 [hep-ex/0111082] |
BABAR Global Fit | 43.8 +/- 0.8 +/- 2.1 | 1.22+/- 0.04 +/- 0.06 | 0.63/0.63/0.63 | input parameters | Phys.Rev.D79:012002, 2009 [arXiv:0809.0828 [hep-ex]] |
BABAR Tagged | 42.3 +/- 1.90 +/- 1.0 | 1.20+/- 0.09+/- 0.04 | 0.95/0.4/0.7 | input parameters | [arXiv:0807.4978 [hep-ex]] |
Average | 42.4+/- 0.7 +/- 1.4 | 1.19+/- 0.04 +/- 0.04 | 0.96/0.91/0.88 | chi2/dof = 1.2/8 (CL = 0.997) | eps 1 pdf 1 gif 1 eps 2 pdf 2 gif 2 ; eps 2 (zoom) pdf 2 (zoom) gif 2 (zoom) |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
ALEPH | 2.25 +/- 0.18+/- 0.36 | input parameters | Phys.Lett.B395:373-387,1997 [Spires] |
CLEO | 2.10+/- 0.13+/- 0.15 | input parameters | Phys.Rev.Lett.82:3746,1999 [hep-ex/9811042] |
BELLE | 2.09+/- 0.12+/- 0.39 | input parameters | Phys.Lett.B526:258-268,2002 [hep-ex/0111082] |
BABAR | 2.20+/- 0.11+/- 0.12 | input parameters | Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
Average | 2.16+/- 0.12 | chi2/dof = 0.2/3 (CL = 0.97) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
CLEO-2 | 2.20 +/- 0.13+/- 0.17 | input parameters | Phys.Rev.Lett.82:3746,1999 [hep-ex/9811042] |
CLEO | 1.66+/- 0.6+/- 0.21 | input parameters | Phys. Rev. D43:651, 1991 [hep-ex/0111082] |
BABAR | 2.27+/- 0.09+/- 0.09 | input parameters | Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
Average | 2.23+/- 0.11 | chi2/dof = 0.95/2 (CL = 0.62) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
BaBar Global Fit | 2.36+/- 0.03+/- 0.12 | input parameters | Phys.Rev.D79:012002, 2009 [arXiv:0809.0828 [hep-ex]] |
BaBar Tagged | 2.30+/- 0.06+/- 0.08 | input parameters | [arXiv:0807.4978 [hep-ex]] |
Average | 2.32+/- 0.09 | chi2/dof = 0.25/1 (CL = 0.62) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
BELLE | 0.42+/- 0.04+/- 0.05 | input parameters | [Phys.Rev.D77:091503, 2008 [arXiv:0711.3252 [hep-ex]] |
BABAR | 0.42+/- 0.06+/- 0.03 | input parameters | [Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
Average | 0.42+/- 0.05 | chi2/dof = 0.002 (CL = 0.97) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
BELLE | 0.68+/- 0.08+/- 0.07 | input parameters | Phys.Rev.D77:091503, 2008 [arXiv:0711.3252 [hep-ex]] |
BABAR | 0.59+/- 0.05+/- 0.04 | input parameters | Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
Average | 0.61+/- 0.05 | chi2/dof = 0.5 (CL = 0.47) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
BELLE | 0.43+/- 0.07+/- 0.05 | input parameters | Phys.Rev.D77:091503, 2008 [arXiv:0711.3252 [hep-ex]] |
BABAR | 0.42+/- 0.08+/- 0.03 | input parameters | Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
Average | 0.43+/- 0.06 | chi2/dof = 0.002 (CL = 0.96) | eps pdf gif |
Experiment | BF (rescaled) [%] | Parameters | Remarks |
---|---|---|---|
BELLE | 0.57+/- 0.21+/- 0.07 | input parameters | Phys.Rev.D77:091503, 2008 [arXiv:0711.3252 [hep-ex]] |
BABAR | 0.48+/- 0.08+/- 0.04 | input parameters | Phys.Rev.Lett.100:151802, 2008 [arXiv:0712.3503 [hep-ex]] |
Average | 0.49+/- 0.08 | chi2/dof = 0.15 (CL = 0.70) | eps pdf gif |
Global fits to the moments of inclusive distributions in B -> Xc l nu (lepton energy and hadron mass) and B -> Xs gamma (photon energy) transitions are performed in the framework of the Heavy Quark Expansion (HQE), using the calculations in the kinetic mass scheme:
Fits to the B -> Xc l nu & B -> Xs gamma moments and separately to the B -> Xc l nu moments only are performed.
Global fit in the kinetic scheme | ||||
Moments | |Vcb| (10-3) | mb (GeV) | mc (GeV) | mupi2 (GeV2) |
---|---|---|---|---|
B -> Xc l nu & B -> Xs gamma | 41.67 +/- 0.43 +/- 0.08 +/- 0.58 | 4.601 +/- 0.034 | 1.165 +/- 0.050 | 0.440 +/- 0.040 |
B -> Xc l nu | 41.48 +/- 0.47 +/- 0.08 +/- 0.58 | 4.659 +/- 0.049 | 1.285 +/- 0.078 | 0.428 +/- 0.044 |
Reference: | web page | |||
Plots: | (|Vcb|, mb): eps, pdf | (mupi2, mb): eps, pdf |
The errors quoted are the results of the MINUIT fit, where the covariance matrix includes experimental and estimated theoretical uncertainties. On |Vcb| there are additional uncertainties: The second error corresponds to the uncertainty in the B lifetime, and the third error is an additional theoretical uncertainty of 1.4% related to the conversion of the semileptonic branching ratio into |Vcb|. The b quark mass and mupi2 also also translated in other schemes as necessary input parameters for the extraction of |Vub| from inclusive b->ulnu decays.
Translation to other schemes of the parameters from the B -> Xc l nu & B -> Xs gamma fit | ||||
Scheme | mb (GeV) | mupi2 (GeV2) | Comments | |
---|---|---|---|---|
SF | 4.631 +0.041 -0.035 GeV | 0.272 +0.056 -0.076 GeV | Using code from M. Neubert. The total error, for both parameters, is due to the contribution of the error due to the ellipse and the one due to scale variation for alphas. | |
MSbar | 4.243 +- 0.042 GeV | E. Gardi | ||
1S | 4.70 +/- 0.03 GeV |
In the |Vub| averages only measurements for which the correlation is known are considered. They are either independent measurements or correlated measurements for which the correlation among the analyses is available (eg the BaBar B-Reco analyses). If the analyses are correlated but the correlation is not known, the analysis with the smallest error is considered.
No attempt is made to average values for |Vub| from the different theoretical models, but the results are presented independently per each scheme.
The procedure for performing the average is documented in [arXiv:0808.1297]
The input files for the average are linked in the tables with the averages. 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 errors in the tables are experimental (statistical and systematic) and external (theoretical and HQ parameter uncertainties). The average B lifetime used is 1.573 ps. Final state radiation is included in all the measurements.
The input parameters for the different modes are coming from the global fit in the kinetic scheme, translated to the scheme needed per each model. We are aware of ongoing discussions on the best way to determine the b-quark mass. For consistency among all the measurements, we choose the results coming from the fits to the b->clnu and b->sgamma moments.
The |Vub| values are obtained using the HQE input parameter:
|Vub | (BLNP) | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
CLEO (E_{e}) | 3.94 +/-0.46 +0.37 -0.33 | input | Phys.Rev.Lett.88:231803,2002 [arXiv:hep-ex/0202019v1] | 2.1 < p < 2.6 |
BELLE sim. ann. (m_{X}, q^{2}) | 4.33 +/- 0.46 + 0.35 - 0.30 | input | Phys.Rev.Lett.92:101801,2004 [arXiv:hep-ex/0311048v2] | mX - Q2, tag with annealing method |
BELLE (E_{e}) | 4.74 +/- 0.44 + 0.35 - 0.30 | input | Phys.Lett.B621:28-40 (2005) (arXiv:hep-ex/0504046v2 | 1.9 < p < 2.6 |
BABAR (E_{e}) | 4.29 +/- 0.24 + 0.35 - 0.30 | input | Phys.Rev.D73:012006,2006 arXiv:hep-ex/0509040v2 | 2.0 < p < 2.6 |
BABAR (E_{e}, s^{max}_{h}) | 4.41 +/- 0.30 + 0.42 - 0.37 | input | Phys.Rev.Lett.95:111801,2005 , Erratum-ibid.97:019903,2006 [arXiv:hep-ex/0506036v3] | (Ee-q2) |
BELLE (m_{X}) | 3.99 +/- 0.26 + 0.30 - 0.25 | input | Phys.Rev.Lett.95:241801,2005 [arXiv:hep-ex/0505088v2] | mX, BRECO tag; other methods (mX-q2 and P+ not used). Cut on the hadronic mass at 1.7 GeV |
BABAR (m_{X}) | 4.13 +/- 0.20 + 0.32 - 0.27 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | mX, BRECO tag; other methods (mX-q2 and P+ not used). Cut on the hadronic mass at 1.55 GeV |
BABAR (m_{X}-q^{2}) | 4.41 +/- 0.29 + 0.36 - 0.31 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | mX q2, BRECO tag; correlation with mX-q2 and P+ is taken into account |
BABAR (P^{+}) | 3.76 +/- 0.24 + 0.31 - 0.25 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | P+, BRECO tag; correlation with mX-q2 and mX is taken into account |
Average +/- exp + theory - theory | 4.32 +/- 0.16 + 0.32 - 0.27 | chi2/dof = 8.5/8 (CL = 0.39) | Plots: eps pdf gif | mb input from global fit in the kinetic scheme |
positive errors: +2.1stat +2.3exp +1.3b2c model +1.4b2u model +5.7HQE param +2.2SF func +0.9sub SF +3.7matching +1.6WA = +8.2tot
negative errors: -2.1stat -2.3exp -1.3b2c model -1.3b2u model -4.5HQE param -2.1SF func -0.9sub SF -3.4matching -1.6WA = -7.2tot
where the fractions correspond to the statistical error (stat), the experimental systematics (exp), the modeling, e.g. branching fractions for exclusive decays, of b -> c l nu and b -> u l nu decays (b2c model and b2u model, respectively), the HQE parameters mb and mupi2 (HQE param), the functional form of the SF (ie the variation from the exponential to the Gaussian form of the SF, SF func), the subleading shape functions (sub SF), the variation of the matching scales (matching), and the Weak Annihilation (WA). No uncertainty is assigned for possible duality violations. The quoted experimental error in the table above corresponds to the statistical, experimental systematic and the b -> c l nu and b -> u l nu modeling errors. The other uncertainties contribute to the theoretical error.
The |Vub| values are obtained using the HQE input parameter:
|Vub| (DGE) | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
CLEO (E_{e}) | 3.58 +/- 0.42 + 0.26 - 0.20 | input | Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019) | 2.1 < p < 2.6 |
BELLE sim. ann. (m_{X}, q^{2}) | 4.16 +/- 0.44 + 0.24 - 0.14 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | mX - Q2, tag with annealing method |
BELLE (E_{e}) | 4.56 +/- 0.42 + 0.22 - 0.19 | input | Phys.Lett.B621:28-40 (2005) (hep-ex/0504046) | 1.9 < p < 2.6 |
BABAR (E_{e}) | 4.04 +/- 0.27 + 0.24 - 0.21 | input | Phys.Rev.D73:012006,2006 (hep-ex/0509040) | 2.0 < p < 2.6 |
BABAR (E_{e}, s^{max}_{h}) | 4.01 +/- 0.27 + 0.28 - 0.22 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0506036 (version 3, June 2006)) | (Ee-q2) |
BELLE m_{X} | 4.07 +/- 0.27 + 0.22 - 0.19 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088) | mX, BRECO tag; other methods (mX-q2 and P+ not used) |
BABAR m_{X} | 4.25 +/- 0.20 + 0.20 - 0.14 | input | Phys. Rev. Lett. 100, 171802 (2008)[arXiv:0708.3702v1] | mX, BRECO tag; correlation with mX-q2 and P+ analyses is taken into account |
BABAR m_{X}-q^{2} | 4.24 +/- 0.28 + 0.23 - 0.16 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | mX q2, BRECO tag; correlation with mX-q2 and P+ is taken into account |
BABAR P^{+} | 3.73 +/- 0.24 + 0.28 - 0.22 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | P+, BRECO tag; correlation with mX-q2 and mX is taken into account |
Average +/- exp + theory - theory | 4.26 +/- 0.14 + 0.19 - 0.13 | chi2/dof = 7.3/8 (CL = 0.51) | Plots: eps pdf gif | mb input from global fit in the kinetic scheme |
positive errors: +2.2stat +2.1exp +1.2b2c model +1.3b2u model +0.7alpha_s R_CUT +4.0mb +1.5WA +1.2DGE theory =+5.7tot
negative errors: -2.2stat -2.1exp -1.1b2c model -1.3b2u model -0.3alpha_s R_CUT -2.7mb -1.6WA -0.5DGE theory =-4.7tot
where the fractions correspond to the statistical error (stat), the experimental systematics (exp), the modeling, e.g. branching fractions for exclusive decays, of the b -> c l nu and b -> u l nu decays (b2c model and b2u model, respectively), the effect of the alphas uncertainty on R_CUT (alpha_s R_CUT), the effect of the uncertainty on mb on the prediction of the event fraction and the total rate (mb), the Weak Annihilation (WA) and from the change and variation of scale of the matching scheme (DGE theory). The quoted experimental error in the table above corresponds to the statistical, experimental systematic and the b -> c l and b -> u l nu modeling errors. The other uncertainties contribute to the theoretical error.
The |Vub| values are obtained using the HQE input parameters:
The BABAR (E_{e}, s^{max}_{h}) analysis is not included in the average at the moment. The E_{e}, s^{max}_{h} cuts are not yet implemented in the model. Work is under way to include them.
|Vub| (GGOU) | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
CLEO (E_{e}) | 3.77 +/- 0.44 + 0.26 - 0.39 | input | Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019) | 2.1 < p < 2.6 |
BELLE sim. ann. (m_{X}, q^{2}) | 4.23 +/- 0.45 + 0.34 -0.35 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | mX - Q2, tag with annealing method |
BELLE (E_{e}) | 4.61 +/- 0.43 + 0.23 - 0.31 | input | Phys.Lett.B621:28-40 (2005) (hep-ex/0504046) | 1.9 < p < 2.6 |
BABAR (E_{e}) | 4.13 +/- 0.23 + 0.23 - 0.34 | input | Phys.Rev.D73:012006,2006 (hep-ex/0509040) | 2.0 < p < 2.6 |
BELLE m_{X} | 3.93 +/- 0.26 + 0.19 - 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} | 4.07 +/- 0.20 + 0.27 - 0.29 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | mX, BRECO tag; other methods (mX-q2 and P+ not used) |
BABAR m_{X}-q^{2} | 4.29 +/- 0.28 + 0.34 - 0.36 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | mX-q2, BRECO tag; correlation with mX and P+ is taken into account |
BABAR P^{+} | 3.52 +/- 0.23 + 0.30 - 0.31 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | mX, BRECO tag; correlation with mX and mX-q2 is taken into account |
Average +/- exp + theory - theory | 3.96 +/- 0.15 + 0.20 - 0.23 | chi2/dof = 7.0/7 (CL = 0.43) | Plots: eps pdf gif | mb input from global fit in the kinetic scheme |
positive errors: +2.1stat +2.2exp +1.5b2c model +1.4b2u model +3.9par. +1.8pert. +2.5q2* +0.WA +1.3ff =+6.3tot
negative errors: -2.3stat -2.2exp -1.2b2c model -1.5b2u model -3.9par. -1.7pert. -2.6q2* -3.1WA -0.6ff =-7.0tot
where the fractions correspond to the statistical error (stat), the experimental systematics (exp), the modeling, e.g. branching fractions for exclusive decays, of the b -> c l nu and b -> u l nu decays (b2c model and b2u model, respectively), the value of alpha_s, mb and other non-perturbative parameters (par.), higher order perturbative and non-perturbative corrections (pert.), the modelling of the q2 tail and choice of the scale q2* (q2*), the WA matrix element (WA), the functional form of the distribution functions (ff).
The |Vub| values are obtained using the HQE input parameter:
|Vub| (ADFR) | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
CLEO (E_{e}) | 3.49 +/- 0.20 + 0.23 - 0.23 | input | Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019) | 2.3 < p < 2.6, Vub redetermined from partial BF |
BELLE sim. ann. (m_{X}, q^{2}) | 3.95 +/- 0.42 + 0.22 - 0.22 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | mX - Q2, tag with annealing method |
BELLE (E_{e}) | 3.25 +/- 0.17 + 0.22 - 0.21 | input | Phys.Lett.B621:28-40 (2005) (hep-ex/0504046) | 2.3 < p < 2.6 |
BABAR (E_{e}) | 3.46 +/- 0.14 + 0.23 - 0.23 | input | Phys.Rev.D73:012006,2006 (hep-ex/0509040) | 2.3 < p < 2.6, Vub redetermined from partial BF |
BABAR (E_{e}, s^{max}_{h}) | 3.87 +/- 0.26 + 0.23 - 0.24 | input | Phys.Rev.Lett.95:111801,2005 , Erratum-ibid.97:019903,2006 (hep-ex/0506036 (version 3, June 2006)) | (Ee-q2) |
BELLE m_{X} | 3.93 +/- 0.26 + 0.23 - 0.23 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088) | mX, BRECO tag; other methods (mX-q2 and P not used) |
BABAR m_{X} | 4.04 +/- 0.19 + 0.24 - 0.24 | input | Phys. Rev. Lett. 100, 171802 (2008) [hep-ex/0507017] | mX, BRECO tag; correlation with mX-q2 and P+ analyses is taken into account |
BABAR m_{X}-q^{2} | 4.14 +/- 0.26 + 0.23 - 0.23 | input | Phys. Rev. Lett. 100, 171802 (2008) [hep-ex/0507017] | mX q2, BRECO tag; correlation with mX-q2 and P+ is taken into account |
BABAR P^{+} | 3.45 +/- 0.22 + 0.21 - 0.37 | input | Phys. Rev. Lett. 100, 171802 (2008) [hep-ex/0507017] | P+, BRECO tag; correlation with mX-q2 and mX is taken into account |
Average +/- exp + theory - theory | 3.76 +/- 0.13 + 0.22 - 0.22 | chi2/dof = 17.1/8 (CL = 2.9) | Plots: eps pdf gif |
positive errors: +1.8stat +2.4exp +1.2b2c model +1.4b2u model +1.7alpha_s +1.4Vcb +0.6mb +4.4mc +0.9BF +2.9model =+6.8tot
negative errors: -1.8stat -2.3exp -1.3b2c model -1.3b2u model -1.8alpha_s -1.4Vcb -0.6mb -4.2mc -1.0BF -2.9model =-6.8tot
where the fractions correspond to the statistical error (stat), the experimental systematics (exp), the modeling, e.g. branching fractions for exclusive decays, of the b -> c l nu and b -> u l nu decays (b2c model and b2u model, respectively), the effect of the alphas uncertainty (alpha_s), the effect of the uncertainty on Vcb (Vcb), on the b-quark mass in the MS scheme (mb), on the c-quark mass in the MS scheme (mc), on the semileptonic BF (BF) and on the model (model). The quoted experimental error in the table above corresponds to the statistical, experimental systematic and the b -> c l and b -> u l nu modeling errors. The other uncertainties contribute to the theoretical error.
The |Vub| values are obtained using the HQE input parameter:
obtained from the global fit in the kinetic scheme
|Vub| (BLL) using the (mx-q2) analyses | ||||
Experiment | Value [10-3] | Parameters | References | Remarks |
---|---|---|---|---|
BELLE breco (m_{X}, q^{2}) | 4.97 +/- 0.39 + 0.37 - 0.37 | input | Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088) | mX-q2, BRECO tag |
BELLE sim. ann. (m_{X}, q^{2}) | 4.67 +/- 0.49 + 0.34 - 0.34 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | mX - Q2, tag with annealing method |
BABAR (m_{X}, q^{2}) | 4.88 +/- 0.32 + 0.36 - 0.36 | input | Phys. Rev. Lett. 100, 171802 (2008) [arXiv:0708.3702v1] | mX-q2, BRECO tag |
Average +/- exp +/- theory | 4.87 +/- 0.24 + 0.38 - 0.38 | chi2/dof = 0.4/2 (CL = 0.83) | Plots: eps pdf gif | HQE parameter input from b to c l nu and b to s gamma moments |
positive errors: +3.2stat +3.8exp +1.4b2c model +2.1b2u model +3.0Strf +3.0Pert +4.5Sf +4.0H.O. = +9.0tot
negative errors: -3.2stat -3.8exp -1.4b2c model -2.1b2u model -3.0Strf -3.0Pert -4.5Sf -4.0H.O. = -9.0tot
where the fractions correspond to the statistical error (stat), the experimental systematics (exp), the modeling, e.g. branching fractions for exclusive decays, of b -> c l nu and b -> u l nu decays (b2c model and b2u model, respectively), the residual shape function effects (Strf), the higher order terms in the alphas expansion (Pert), the uncertainty on the b-quark mass (Sf), and the third order terms in the OPE expansion(H.O.). No uncertainty is assigned for possible duality violations.
Several years ago, M. Neubert (Phys. Rev. D49, 4623 (1994) ) suggested that |Vub| could be extracted by combining weighted integrals over the photon spectrum in B->Xs gamma decays with integrals over the lepton momentum spectrum near the kinematic endpoint in inclusive B->Xulnu decays decays. The underlying assumption is that the QCD interactions affecting these two processes are the same to leading order, and therefore ratios of decay rates for the two processes have significantly lower sensitivity to the choice of the shape-functions parameterization.
So far, there are two BABAR measurements based on this suggestion to extract |Vub| from charmless B-meson decays from inclusive distributions for different regions of phase space.
BABAR measured |Vub| in inclusive decays using the prescription of Leibovich, Low, and Rothstein (LLR), Phys.Rev.D62:014010,2000 [arXiv:hep-ph/0001028v2], and Phys.Lett.B486:86-91,2000 [arXiv:hep-ph/0005124v1], 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 (Phys.Rev. D72 (2005) 052004 [arXiv:hep-ex/0508004v2]).
Using BABAR measurements of the lepton momentum spectrum near the kinematic endpoint, Phys.Rev. D73 (2006) 012006 [arXiv:hep-ex/0509040v2], two different theoretical prescriptions were tried to extract |Vub|, Phys.Rev.D76:114003,2007 [arXiv:hep-ph/0702072], namely LLR (Phys.Rev. D61 (2000) 053006 [arXiv:hep-ph/9909404v2]]) and LNP, a calculation by Lange, Neubert and Paz (JHEP 0510 (2005) 084 [arXiv:hep-ph/0508178v2] and JHEP 0601 (2006) 104 [arXiv:hep-ph/0511098v1]).
In the following, we provide a comparison of the results of 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 two measurments.
Description | Vub [10-3] | Reference |
---|---|---|
HFAG Ave. (BLNP) | 4.32 +/- 0.16 + 0.32 - 0.27 | |
HFAG Ave. (DGE) | 4.26 +/- 0.14 + 0.19 - 0.13 | |
HFAG Ave. (GGOU) | 3.96 +/- 0.15 + 0.20 - 0.23 | |
HFAG Ave. (ADFR) | 3.76 +/- 0.13 + 0.22 - 0.22 | |
HFAG Ave. (BLL) | 4.87 +/- 0.24 + 0.38 - 0.38 | |
BABAR (LLR) | 4.43 +/- 0.45 +/- 0.29 | Phys.Rev.Lett. 96 (2006) 221801 [arXiv:hep-ex/0601046v2] |
BABAR endpoint (LLR) | 4.28 +/- 0.29 +/- 0.29 +/- 0.26 +/- 0.28 | Phys.Rev.D76:114003,2007 [arXiv:hep-ph/0702072] |
BABAR endpoint (LNP) | 4.40 +/- 0.30 +/- 0.41 +/- 0.23 | Phys.Rev.D76:114003,2007 [arXiv: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_{+} | 1.81 +/- 0.28 +/- 0.13 | 1.37 +/- 0.26 +/- 0.09 | 0.45 +/- 0.17 +/- 0.06 | SL tag, preliminary [arXiv:0805.2408] (input)(param) |
BABAR B_{reco} tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.54 +/- 0.41 +/- 0.21 | 1.05 +/- 0.36 +/- 0.15 | 0.49 +/- 0.23 +/- 0.11 | Breco tag, Phys.Rev.Lett.97:211801,2006 [hep-ex/0607089] (input)(param) |
BELLE SL tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.45 +/- 0.26 +/- 0.15 | 1.07 +/- 0.23 +/- 0.11 | 0.38 +/- 0.15 +/- 0.04 | SL tag, Phys.Lett.B648:139-148,2007 [hep-ex/0604024] (input)(param) |
BELLE B_{reco} tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.24 +/- 0.23 +/- 0.06 | 0.81 +/- 0.19 +/- 0.04 | 0.41 +/- 0.11 +/- 0.02 | Breco tag, preliminary (input) |
BABAR SL tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.38 +/- 0.21 +/- 0.07 | 0.92 +/- 0.16 +/- 0.05 | 0.46 +/- 0.13 +/- 0.03 | SL tag, preliminary [arXiv:0805.2408] (input)(param) |
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, Phys.Lett.B648:139-148,2007 [hep-ex/0604024] (input)(param) |
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)(param) |
CLEO untagged: B \rightarrow \pi l^{+} \nu | 1.37 +/- 0.15 +/- 0.11 | 0.96 +/- 0.13 +/- 0.10 | 0.41 +/- 0.08 +/- 0.04 | Untagged, Phys.Rev.Lett.99:041802,2007 [arXiv:hep-ex/0703041v2] (input)(param) |
BABAR untagged: B \rightarrow \pi l^{+} \nu | 1.46 +/- 0.07 +/- 0.08 | 0.96 +/- 0.13 +/- 0.10 | 0.38 +/- 0.04 +/- 0.03 | Untagged loose neutrino, Phys. Rev. Lett. 98, 091801 (2007) [hep-ex/0612020 ] (input)(param) |
BELLE B_{reco} tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.12 +/- 0.18 +/- 0.05 | 0.85 +/- 0.16 +/- 0.04 | 0.26 +/- 0.08 +/- 0.01 | Preliminary, Breco tag (input) |
Average: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.34 +/- 0.06 +/- 0.05 | 0.93 +/- 0.05 +/- 0.04 | 0.37 +/- 0.03 +/- 0.02 | Plots: eps pdf gif chi2/dof = 3.48/9 (CL = 0.94) |
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, and we do not use their quenched results as they are superseded by their unquenched results. 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.
The errors on |Vub| are experimental and theoretical, respectively.
FF calculation | Vub [10-3] | q2 range | FF norm (ps-1) | Reference |
---|---|---|---|---|
Ball-Zwicky q^{2} < 16 | 3.34 +/- 0.12 +0.55-0.37 | <16 GeV2 | 5.44 +/- 1.43 | Phys. Rev. D71:014015 (2005) [hep-ph/0406232] |
HPQCD q^{2} > 16 | 3.40 +/- 0.20 +0.59-0.39 | >16 GeV2 | 2.07 +/- 0.57 | Phys.Rev.D73, 074502 (2006), Erratum-ibid.D75:119906,2007 [hep-lat/0601021] |
FNAL q^{2} > 16 | 3.62 +/- 0.22 +0.63-0.41 | >16 GeV2 | 1.83 +/- 0.50 | Nucl.Phys.Proc.Suppl.140:461-463,2005 [hep-lat/0409116] |
A plot of this table is available in three formats: eps pdf gif
Consistent results are obtained using quenched Lattice QCD calculations (eg. arXiv:hep-lat/0011065).
Experiment/Mode | BF [10-4] | Reference |
---|---|---|
CLEO untagged: B^{0} \rightarrow \rho^{-} l^{+} \nu | 2.69 +/-0.41 +/- 0.63 | Phys. Rev. D 61, 052001 (2000) [hep-ex/9905056] (input) |
CLEO untagged: B^{0} \rightarrow \rho^{-} l^{+} \nu | 2.93 +/-0.37 +/- 0.37 | PRL 99, 041802 (2007)[arXiv:hep-ex/0703041v2] (input) |
BABAR untagged: B^{0} \rightarrow \rho^{-} l^{+} \nu | 2.14 +/-0.21 +/-0.55 | Untagged, Phys .Rev. D72, 051102 (2005) [hep-ex/0507003] (input) |
BELLE B_{reco} tag:: B^{0} \rightarrow \rho^{-} l^{+} \nu | 2.56 +/-0.46 +/-0.12 | Breco tag, preliminary. Presented at ICHEP08. (input) |
BELLE B_{reco} tag:: B^{+} \rightarrow \rho^{0} l^{+} \nu | 3.39 +/-0.43 +/-0.13 | Breco tag,preliminary. Presented at ICHEP08. (input) |
BELLE SL tag: B^{0} \rightarrow \rho^{-} l^{+} \nu | 2.17 +/-0.54 +/-0.32 | SL tag, Phys.Lett.B648:139-148,2007 [hep-ex/0604024] (input) |
BELLE SL tag: B^{+} \rightarrow \rho^{0} l^{+} \nu | 2.47 +/-0.43 +/-0.33 | SL tag, Phys.Lett.B648:139-148,2007 [hep-ex/0604024] (input) |
Average: B ^{0} \rightarrow \rho^{-} l^{+} \nu | 2.80 +/- 0.18 +/- 0.16 | Plots: eps pdf gif chi2/dof = 3.6/6 (CL = 0.73) |
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 | 0.64 +/-0.20 +/- 0.30 | Preliminary B SL tag [arXiv:0805.2408] |
BABAR | B+-> eta l+ nu | 0.31 +/-0.06 +/- 0.08 | Preliminary Untagged |
BABAR | B+-> eta' l+ nu | 0.33 +/-0.60 +/- 0.30 | Preliminary Breco [hep-ex/0607066] |
BABAR | B+-> eta' l+ nu | <0.47 @ 90% CL | Preliminary B SL tag [arXiv:0805.2408] |
BABAR | B+-> omega l+ nu | 1.14 +/-0.16 +/-0.08 | Preliminary untagged |
BELLE | B+-> omega l+ nu | 1.19 +/-0.32 +/-0.05 | Preliminary Breco |