Updates of Semileptonic Results for Summer 2014

B -> D^*lnu Exclusive

eta_EW F(1) |V_cb| from B -> D^*lnu

In the parameterization of Caprini et al. [Nucl. Phys. B530, 153 (1998)], the decay B -> D^*lnu is described by four quantities: eta_EW F(1) |V_cb|, rho², R₁ and R₂. The following average is the result of a four-dimensional global fit of these four parameters to the measurements listed below. The values reported for each experiment have been rescaled to the most recent values of the external parameters (B lifetimes, D meson branching fractions) and to the values of R₁ and R₂ found by the global fit, R₁(1)=1.406 +/- 0.033 and R₂(1)=0.853 +/- 0.020. The fit assumes isospin symmetry.

Experiment	etaEW F(1) |Vcb| (rescaled) [10-3]	rho2 (rescaled)	Correlation (stat/syst/total)	Parameters	Remarks
ALEPH	31.23 +/- 1.80 +/- 1.30	0.493 +/- 0.228 +/- 0.144	0.94/0.67/0.85	input     parameters	Phys.Lett.B395:373-387,1997
CLEO	39.94 +/- 1.23 +/- 1.62	1.367 +/- 0.085 +/-0.086	0.91/0.83/0.86	input     parameters	Phys.Rev.Lett.89:081803,2002
OPAL excl	36.50 +/- 1.60 +/- 1.49	1.234 +/- 0.212 +/- 0.145	0.95/0.45/0.75	input     parameters	Phys.Lett.B482:15-30,2000
OPAL partial reco	37.14 +/- 1.19 +/- 2.36	1.152 +/- 0.145 +/- 0.294	0.77/0.78/0.78	input     parameters	Phys.Lett.B482:15-30,2000
DELPHI partial reco	35.32 +/- 1.40 +/- 2.33	1.174 +/- 0.126 +/- 0.377	0.94/0.68/0.70	input     parameters	Phys.Lett.B510:55-74,2001
DELPHI excl	36.10 +/- 1.70 +/- 1.97	1.081 +/- 0.142 +/- 0.152	0.89/0.80/0.84	input     parameters	Eur.Phys.J.C33:213-232,2004
BELLE	34.60 +/- 0.17 +/- 1.02	1.212 +/- 0.034 +/- 0.009	0.63/-0.11/0.07	input     parameters	Phys.Rev.D82:112007,2010
BABAR excl	33.94 +/- 0.30 +/- 0.99	1.185 +/- 0.048 +/- 0.029	0.27/0.02/0.08	input     parameters	Phys.Rev.D77:032002,2008
BABAR D*0	35.22 +/- 0.59 +/- 1.33	1.128 +/- 0.058 +/- 0.055	0.90/0.37/0.50	input     parameters	Phys.Rev.Lett.100:231803,2008
BABAR global fit	35.76 +/- 0.20 +/- 1.10	1.193 +/- 0.020 +/- 0.061	0.38/0.85/0.81	input     parameters	Phys.Rev.D79:012002,2009
Average	35.81 +/- 0.11 +/- 0.44	1.207 +/- 0.015 +/- 0.021	0.49/0.32/0.32	chi2/dof = 30.0/23 (CL = 0.150)	eps 1  pdf 1  eps 2  pdf 2

Exclusive Branching Fraction: B⁰ -> D^*-lnu (using both isospin states)

These branching fractions have been calculated from the values of eta_EW F(1) |V_cb|, rho², R₁ and R₂ obtained by the global four-dimensional fit described above.

Experiment	BF (rescaled) [%]	Remarks
ALEPH	5.35 +/- 0.25 +/- 0.31	Phys.Lett.B395:373-387,1997
CLEO	5.62 +/- 0.18 +/- 0.26	Phys.Rev.Lett.89:081803,2002
OPAL excl	5.05 +/- 0.19 +/- 0.42	Phys.Lett.B482:15-30,2000
OPAL partial reco	5.46 +/- 0.25 +/- 0.52	Phys.Lett.B482:15-30,2000
DELPHI partial reco	4.88 +/- 0.13 +/- 0.72	Phys.Lett.B510:55-74,2001
DELPHI excl	5.35 +/- 0.20 +/- 0.37	Eur.Phys.J.C33:213-232,2004
BELLE	4.56 +/- 0.03 +/- 0.26	Phys.Rev.D82:112007,2010
BABAR excl	4.54 +/- 0.04 +/- 0.25	Phys.Rev.D77:032002,2008
BABAR D*0	4.97 +/- 0.07 +/- 0.34	Phys.Rev.Lett.100:231803,2008
BABAR global fit	4.95 +/- 0.02 +/- 0.20	Phys.Rev.D79:012002,2009
Average	4.93 +/- 0.01 +/- 0.11	chi2/dof = 30.0/23 (CL = 0.150)   eps  pdf

Exclusive Branching Fraction: B⁺ -> D^*0bar lnu

The average BF is the result of a one-dimensional fit to the measurements listed.

Experiment	BF (rescaled) [%]	Parameters	Remarks
CLEO	6.60 +/- 0.20 +/- 0.39	input     parameters	Phys.Rev.D67:032001,2003
BABAR tagged	5.74 +/- 0.15 +/- 0.30	input     parameters	Phys.Rev.Lett.100:151802,2008
BABAR untagged	5.36 +/- 0.08 +/- 0.40	input     parameters	Phys.Rev.Lett.100:231803,2008
BABAR global fit	5.42 +/- 0.02 +/- 0.21	input     parameters	Phys.Rev.D79:012002,2009
Average	5.69 +/- 0.02 +/- 0.19	chi2/dof = 9.0/3 (CL = 0.0294)	eps  pdf

B -> Dlnu Exclusive

eta_EW G(1) |V_cb| from B -> Dlnu

In the parameterization of Caprini et al. [Nucl. Phys. B530, 153 (1998)], the decay B -> Dlnu is described by two quantities: eta_EW G(1) |V_cb| and rho². The following average is the result of a two-dimensional global fit of these two parameters to the measurements listed below. The values reported for each experiment have been rescaled to the most recent values of the external parameters (B lifetimes, D meson branching fractions). The fit assumes isospin symmetry.

Experiment	etaEW G(1) |Vcb| (rescaled) [10-3]	rho2 (rescaled)	Correlation (stat/syst/total)	Parameters	Remarks
ALEPH	38.66 +/- 11.80 +/- 5.19	0.942 +/- 0.980 +/- 0.272	0.98/1.00/0.97	input     parameters	Phys.Lett.B395:373-387,1997
CLEO	44.88 +/- 5.96 +/- 3.25	1.270 +/- 0.220 +/- 0.119	0.95/0.40/0.83	input     parameters	Phys.Rev.Lett.82:3746,1999
BELLE	40.96 +/- 4.39 +/- 5.03	1.120 +/- 0.190 +/- 0.111	0.96/0.19/0.62	input     parameters	Phys.Lett.B526:258-268,2002
BABAR global fit	43.25 +/- 0.80 +/- 2.07	1.201 +/- 0.040 +/- 0.057	0.96/0.86/0.85	input     parameters	Phys.Rev.D79:012002,2009
BABAR tagged	42.54 +/- 1.88 +/- 1.02	1.177 +/- 0.088 +/- 0.057	0.95/0.44/0.82	input     parameters	Phys.Rev.Lett.104:011802,2010
Average	42.65 +/- 0.72 +/- 1.35	1.185 +/- 0.035 +/- 0.041	0.96/0.79/0.82	chi2/dof = 0.5/8 (CL = 1.000)	eps 1  pdf 1  eps 2  pdf 2

Exclusive Branching Fraction: B⁰ -> D^-lnu (using both isospin states)

These branching fractions have been calculated from the values of eta_EW G(1) |V_cb| and rho² obtained by the global two-dimensional fit described above.

Experiment	BF (rescaled) [%]	Remarks
ALEPH	2.15 +/- 0.18 +/- 0.45	Phys.Lett.B395:373-387,1997
CLEO	2.19 +/- 0.16 +/- 0.35	Phys.Rev.Lett.82:3746,1999
BELLE	2.08 +/- 0.12 +/- 0.52	Phys.Lett.B526:258-268,2002
BABAR global fit	2.16 +/- 0.03 +/- 0.13	Phys.Rev.D79:012002,2009
BABAR tagged	2.14 +/- 0.11 +/- 0.08	Phys.Rev.Lett.104:011802,2010
Average	2.13 +/- 0.03 +/- 0.09	chi2/dof = 0.5/8 (CL = 1.000)   eps  pdf

Exclusive Branching Fraction: B⁰ -> D^- lnu

The average BF is the result of a one-dimensional fit to the measurements listed.

Experiment	BF (rescaled) [%]	Parameters	Remarks
ALEPH	2.28 +/- 0.18 +/- 0.35	input     parameters	Phys.Lett.B395:373-387,1997
CLEO	2.13 +/- 0.13 +/- 0.15	input     parameters	Phys.Rev.Lett.82:3746,1999
BELLE	2.11 +/- 0.12 +/- 0.39	input     parameters	Phys.Lett.B526:258-268,2002
BABAR	2.22 +/- 0.11 +/- 0.12	input     parameters	Phys.Rev.Lett.100:151802,2008
Average	2.19 +/- 0.06 +/- 0.10	chi2/dof = 0.2/3 (CL = 0.973)	eps  pdf

Exclusive Branching Fraction: B⁺ -> D⁰bar lnu

The average BF is the result of a one-dimensional fit to the measurements listed.

Experiment	BF (rescaled) [%]	Parameters	Remarks
CLEO	2.20 +/- 0.13 +/- 0.17	input     parameters	Phys.Rev.Lett.82:3746,1999
BABAR	2.29 +/- 0.09 +/- 0.09	input     parameters	Phys.Rev.Lett.100:151802,2008
Average	2.27 +/- 0.07 +/- 0.08	chi2/dof = 0.1/1 (CL = 0.721)	eps  pdf

B -> D** lnu Exclusive

Exclusive Branching Fraction: B^- -> D1(D*^-pi^-)lnu

Exclusive Branching Fraction: B^- -> D2(D*^-pi^-)lnu

Exclusive Branching Fraction: B^- -> D1'(D*^-pi^-)lnu

Exclusive Branching Fraction: B^- -> D0*(D^-pi^-)lnu

Exclusive Branching Fraction: B^- -> D⁺ pi^-lnu

Exclusive Branching Fraction: B^- -> D^*+ pi^-lnu

Exclusive Branching Fraction: B⁰ -> D⁰ pi⁺lnu

Exclusive Branching Fraction: B⁰ -> D^*0 pi⁺ lnu

B -> X_clnu Inclusive

Global fit in the kinetic scheme

Theory input

We use the predictions of the semileptonic width, the moments of the lepton energy spectrum and the moments of the hadronic mass spectrum squared in B -> X_clnu for different lepton energy thresholds obtained in JHEP 1109 (2011) 055.

Experimental input

These OPE expressions are fit to these B -> X_clnu moment measurements. The symbol 'n' indicates the order of the moment while 'c' indicates the value of the minimum lepton energy (in GeV). The n=0 lepton moment is the partial branching fraction of B -> X_clnu.

Results

The global fit determines the semileptonic B meson branching fraction, the quark masses m_b and m_c and the OPE parameters mu²_pi, mu²_G, rho³_D and rho³_LS. mu²_G and rho³_LS are constrained to (0.35 +/- 0.07) GeV² and (-0.15 +/- 0.10) GeV³, respectively. The c-quark mass (defined in the MSbar scheme) is fixed to (0.986 +/- 0.013) GeV from Phys.Rev. D80 (2009) 074010. Refer to Phys.Rev. D89 (2014) 014022 for more details on the fit. From these parameters |V_cb| is calculated assuming an average B meson lifetime of (1.579 +/- 0.005) ps. The chi² of the fit is 14.6 for 50-7 degrees of freedom.

The following plots show the result of the fit in terms of the partial branching fraction (e0), the lepton energy (e1, e2, e3) and the hadronic mass squared (h1, h2, h3) moments. In all plots, the grey band is the theory prediction with total theory error. BaBar data are shown by circles, Belle by squares and other experiments (DELPHI, CDF, CLEO) by triangles. Filled symbols mean that the point was used in the fit. Open symbols are measurements that were not used in the fit.

|V_ub| from inclusive semileptonic B decays

• BLNP - B.O. Lange, M. Neubert and G. Paz, Phys. Rev. D72:073006 (2005) [arXiv:hep-ph/0504071v3], and references therein.
• DGE -  J.R. Andersen and E. Gardi, JHEP 0601:097 (2006) [arXiv:hep-ph/0509360v2]. Recent update: [arXiv:0806.4524] which includes the full beta_0*alpha_s^2 correction. Theoretical code in http://www.ph.ed.ac.uk/~egardi/b2uATnnlo.htm
• GGOU - P. Gambino, P. Giordano, G. Ossola, N. Uraltsev, JHEP 0710:058,2007 [arXiv:0707.2493].
• ADFR - U. Aglietti, F. Di Lodovico, G. Ferrera , G. Ricciardi, EPJC, Vol. 59 (2009), [arXiv:0711.0860], U. Aglietti, G. Ferrera and G. Ricciardi, Nucl. Phys. B768, 85 (2007) [arXiv:hep-ph/0608047] and references therein.
• BLL - C.W. Bauer, Z. Ligeti and M.E. Luke, Phys. Rev. D64:113004 (2001) [arXiv:hep-ph/0107074v1] (for measurements that use m_X- q² cut).

In the |V_ub| 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 |V_ub| 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. Statistical correlations are also taken into account, when available.

The errors in the tables are experimental (statistical and systematic) and external (theoretical and HQ parameter uncertainties). The average B lifetime used is 1.582 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. For consistency among all the measurements, we choose the results coming from the fits to the b->clnu moments, with a constraint on the charm quark mass.

Determination of |V_ub| (BLNP)   

The |V_ub| values are obtained using the HQE input parameter:

• m_b (SF) = 4.569 ± 0.023 ± 0.018 GeV
• μ_π² (SF) = 0.145 ± 0.089 -0.040 +0.020 GeV²

|Vub | (BLNP)
Experiment	Value [10-3]	Parameters	References	Remarks
CLEO (Ee)	4.28 ± 0.50 + 0.31 - 0.36	input	Phys.Rev.Lett.88:231803,2002 [arXiv:hep-ex/0202019v1]	2.1 < Ee < 2.6
BELLE sim. ann. (mX, q2)	4.49 ± 0.47 + 0.28 - 0.30	input	Phys.Rev.Lett.92:101801,2004 [arXiv:hep-ex/0311048v2]	Cut on mX<1.7 GeV, q2>8GeV2 tag with annealing method
BELLE (Ee)	4.93 ± 0.46 + 0.27 - 0.29	input	Phys.Lett.B621:28-40 (2005) [arXiv:hep-ex/0504046v2]	1.9 < Ee < 2.6
BABAR (Ee)	4.54 ± 0.26 + 0.27 - 0.33	input	Phys.Rev.D73:012006,2006 [arXiv:hep-ex/0509040v2]	2.0 < Ee < 2.6
BABAR (Ee, shmax)	4.53 ± 0.22 + 0.33 - 0.38	input	preliminary update (EPS2013) of [arXiv:hep-ex/0506036v3]	Ee > 2.0, shmax < 3.5
BELLE multivariate (p*)	4.49 ± 0.27 + 0.20 - 0.22	input	Phys.Rev.Lett.104:021801,2010 [arXiv:0907.0379v1 [hep-ex]]	BRECO tag; multivariate analysis. Cut on lepton energy at 1 GeV
BABAR (mX<1.55)	4.30 ± 0.20 + 0.28 - 0.27	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX< 1.55 GeV
BABAR (mX<1.7)	4.04 ± 0.22 + 0.23 - 0.23	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX<1.7 GeV
BABAR (mX<1.7, q2>8)	4.30 ± 0.23 + 0.26 - 0.28	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at mX<1.7 GeV, q2>8 GeV2
BABAR (P+<0.66)	4.15 ± 0.25 + 0.28 - 0.27	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at P+<0.66 GeV
BABAR (p*>1GeV)	4.32 ± 0.24 + 0.19 - 0.21	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit (mX, q2), cut at p*>1GeV
BABAR (p*>1.3GeV)	4.32 ± 0.27 + 0.20 - 0.21	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit p*, cut at p*>1.3GeV
Average ± exp + th. - th.	4.45 ± 0.16 + 0.21 - 0.22	χ2/dof = 9.00/11 (CL = 0.62)	Plots: eps pdf gif	mb input from global fit in the kinetic scheme

The full breakdown of the uncertainties on the average |V_ub| above is (all errors quoted in percent):

positive errors: +2.0_stat +1.7_exp +1.2_{b2c model} +1.9_{b2u model} +2.6_{HQE param} +0.1_{SF func} +0.6_{sub SF} +0.0_WA +3.8_matching = +5.8_tot

negative errors: -2.1_stat -1.8_exp -1.2_{b2c model} -1.8_{b2u model} -2.7_{HQE param} -0.3_{SF func} -0.6_{sub SF} -1.4_WA -3.8_matching = -5.9_tot

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 m_b and μ_π² (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.

It should be noted that the above results and averages do not include NNLO corrections. A paper By Neubert and collaborators (arxiv:0909.1609 [hep-ph]) suggests that these have non-negligible impact on the determination of V_ub. Unfortunately, the numerical implementation of those corrections is not in a form that would be immediately suitable for public use by HFAG. Moreover, those results only include the NNLO corrections to the leading term in the 1/m_b expansion for the shape-function region. They neglect "kinematic" power corrections that become less and less suppressed as the phase space cuts are less restrictive. Therefore, while this subset of NNLO corrections are presumably dominant and important for restrictive cuts like P⁺<0.66 GeV cut, this should not be the case for less restrictive cuts like p* > 1.0 GeV. Therefore, we continue using the NLO code and we remark that for restrictive cuts one may expect that the NNLO corrections induce order 5.8 % upward shifts in V_ub.

Determination of |V_ub| (DGE)

The |V_ub| values are obtained using the HQE input parameter:

• m_b (MSbar) = 4.177 ± 0.043 GeV

|Vub| (DGE)
Experiment	Value [10-3]	Parameters	References	Remarks
CLEO (Ee)	3.90 ± 0.45 + 0.26 - 0.28	input	Phys.Rev.Lett.88:231803,2002 [arXiv:hep-ex/0202019v1]	2.1 < Ee < 2.6
BELLE sim. ann. (mX, q2)	4.46 ± 0.47 + 0.20 - 0.22	input	Phys.Rev.Lett.92:101801,2004 [arXiv:hep-ex/0311048v2]	Cut on mX<1.7 GeV, q2>8GeV2 tag with annealing method
BELLE (Ee)	4.85 ± 0.45 + 0.21 - 0.25	input	Phys.Lett.B621:28-40 (2005) [arXiv:hep-ex/0504046v2]	1.9 < Ee < 2.6
BABAR (Ee)	4.34 ± 0.25 + 0.23 - 0.25	input	Phys.Rev.D73:012006,2006 [arXiv:hep-ex/0509040v2]	2.0 < Ee < 2.6
BABAR (Ee, shmax)	4.17 ± 0.20 + 0.28 - 0.29	input	preliminary update (EPS2013) of	Ee > 2.0 shmax <3.5
BELLE multivariate (p*)	4.63 ± 0.28 + 0.13 - 0.13	input	Phys.Rev.Lett.104:021801,2010 [arXiv:0907.0379v1 [hep-ex]]	BRECO tag; multivariate analysis. Cut on lepton energy at 1 GeV
BABAR (mX<1.55)	4.53 ± 0.21 + 0.24 - 0.22	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX< 1.55 GeV
BABAR (mX<1.7)	4.26 ± 0.24 + 0.26 - 0.24	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX<1.7 GeV
BABAR (mX<1.7, q2>8)	4.27 ± 0.22 + 0.20 - 0.20	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at mX<1.7 GeV, q2>8 GeV2
BABAR (P+<0.66)	4.24 ± 0.26 + 0.37 - 0.32	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at P+<0.66 GeV
BABAR (mX, q2 fit, p*>1GeV)	4.46 ± 0.24 + 0.13 - 0.13	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit (mX, q2), cut at p*>1GeV
BABAR (p*>1.3GeV)	4.44 ± 0.27 + 0.15 - 0.14	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit p*, cut at p*>1.3GeV
Average ± exp + theory - theory	4.52 ±0.16 + 0.15 - 0.16	χ2/dof = 9.46/11 (CL = 0.58)	Plots: eps pdf gif	mb input from global fit in the kinetic scheme

The full breakdown of the uncertainties on the average |Vub| above is (all errors quoted in percent):

positive errors: +1.8_stat +1.7_exp +1.3_{b2c model} +2.1_{b2u model} +0.5_{alpha_s R_CUT} +3.2_mb +0.0_WA +0.5_{DGE theory} =+4.8_tot

negative errors: -1.8_stat -1.7_exp -1.3_{b2c model} -1.9_{b2u model} -0.5_{alpha_s R_CUT} -3.0_mb -1.9_WA -0.3_{DGE theory} =-5.0_tot

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 alpha_s uncertainty on R_CUT (alpha_s R_CUT), the effect of the uncertainty on m_b 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.

Determination of |V_ub| (GGOU)

The |V_ub| values are obtained using the HQE input parameters:

• m_b(kin) = 4.541 ± 0.023 GeV
  
• μ_π²(kin) = 0.414 ± 0.078 GeV²
  

The BABAR (E_e, s_h^max) analysis is not included in the average, since the E_e, s_h^max cuts are not yet implemented in the model.

|Vub| (GGOU)
Experiment	Value [10-3]	Parameters	References	Remarks
CLEO (Ee)	4.21 ± 0.49 +0.23 -0.33	input	Phys.Rev.Lett.88:231803,2002 [arXiv:hep-ex/0202019v1]	2.1 < Ee < 2.6
BELLE sim. ann. (mX, q2)	4.50 ± 0.47 +0.28 -0.31	input	Phys.Rev.Lett.92:101801,2004 [arXiv:hep-ex/0311048v2]	Cut on mX<1.7 GeV, q2>8GeV2 tag with annealing method
BELLE (Ee)	4.93 ± 0.46 +0.17 -0.22	input	Phys.Lett.B621:28-40 (2005) [arXiv:hep-ex/0504046v2]	1.9 < Ee < 2.6
BABAR (Ee)	4.50 ± 0.26 +0.18 -0.25	input	Phys.Rev.D73:012006,2006 [arXiv:hep-ex/0509040v2]	2.0 < Ee < 2.6
BELLE multivariate (p*)	4.60 ± 0.27 + 0.10 - 0.11	input	Phys.Rev.Lett.104:021801,2010 [arXiv:0907.0379v1 [hep-ex]]	BRECO tag; multivariate analysis. Cut on lepton energy at 1 GeV
BABAR (mX<1.55)	4.29 ± 0.20 + 0.21 - 0.22	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX< 1.55 GeV
BABAR (mX<1.7)	4.09 ± 0.23 + 0.18 - 0.19	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX<1.7 GeV
BABAR (mX<1.7, q2>8)	4.32 ± 0.23 + 0.27 - 0.30	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at mX<1.7 GeV, q2>8 GeV2
BABAR (P+<0.66)	4.24 ± 0.26 + 0.32 - 0.32	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at P+<0.66 GeV
BABAR (mX, q2 fit, p*>1GeV)	4.42 ± 0.24 + 0.09 - 0.11	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit (mX, q2), cut at p*>1GeV
BABAR (p*>1.3GeV)	4.41 ± 0.27 + 0.10 - 0.12	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit p*, cut at p*>1.3GeV
Average ± exp + theory - theory	4.51 ± 0.16 + 0.12 - 0.15	χ2/dof = 8.80/10 (CL=0.55)	Plots: eps pdf gif	mb input from global fit in the kinetic scheme

The full breakdown of the uncertainties on the average |Vub| above is (all errors quoted in percent):

positive errors: +1.9_stat +1.7_exp +1.3_{b2c model} +1.9_{b2u model} +1.6_par. +1.5_pert. +1.4_q2* +0.0_WA +0.2_ff =+4.3_tot

negative errors: -1.9_stat -1.7_exp -1.3_{b2c model} -1.9_{b2u model} -1.6_par. -1.5_pert. -1.4_q2* -2.0_WA -0.2_ff =-4.8_tot

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).

Determination of |V_ub| (ADFR)

The |V_ub| values are obtained using the HQE input parameter:

• m_b (MSbar) = 4.177 ± 0.043 GeV

|Vub| (ADFR)
Experiment	Value [10-3]	Parameters	References	Remarks
CLEO (Ee)	3.44 ± 0.40 + 0.16 - 0.16	input	Phys.Rev.Lett.88:231803,2002 [arXiv:hep-ex/0202019v1]	2.1 < Ee < 2.6
BELLE sim. ann. (mX, q2)	3.94 ± 0.41 + 0.17 - 0.17	input	Phys.Rev.Lett.92:101801,2004 [arXiv:hep-ex/0311048v2]	Cut on mX<1.7 GeV, q2>8GeV2 tag with annealing method
BELLE (Ee)	4.50 ± 0.42 + 0.20 - 0.20	input	Phys.Lett.B621:28-40 (2005) [arXiv:hep-ex/0504046v2]	1.9 < Ee < 2.6
BABAR (Ee)	3.94 ± 0.22 + 0.20 - 0.19	input	Phys.Rev.D73:012006,2006 [arXiv:hep-ex/0509040v2]	2.0 < Ee < 2.6
BABAR (Ee, shmax)	3.64 ± 0.18 + 0.17 - 0.17	input	preliminary update (EPS2013) of [arXiv:hep-ex/0506036v3]	Ee > 2, shmax < 3.5
BELLE multivariate (p*)	4.52 ± 0.30 + 0.19 - 0.19	input	Phys.Rev.Lett.104:021801,2010 [arXiv:0907.0379v1 [hep-ex]]	BRECO tag; multivariate analysis. Cut on lepton energy at 1 GeV
BABAR (mX<1.55)	3.84 ± 0.18 + 0.19 - 0.19	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX< 1.55 GeV
BABAR (mX<1.7)	3.76 ± 0.21 + 0.18 - 0.17	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut on hadronic mass mX<1.7 GeV
BABAR (mX<1.7,q2>8)	3.76 ± 0.20 + 0.17 - 0.16	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at mX<1.7 GeV, q2>8 GeV2
BABAR (P+<0.66)	3.59 ± 0.22 + 0.19 - 0.18	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Cut at P+<0.66 GeV
BABAR ((mX-q2) fit, p*>1)	4.35 ± 0.24 + 0.18 - 0.18	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit (mX, q2), cut at p*>1GeV
BABAR (p*>1.3)	4.30 ± 0.27 + 0.19 - 0.18	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	BRECO tag. Fit p*, cut at p*>1.3GeV
Average ± exp + theory - theory	4.05 ± 0.13 + 0.18 - 0.11	χ2/dof = 31.9/11 (CL = 0.001)	Plots: eps pdf gif

The full breakdown of the uncertainties on the average |Vub| above is (all errors quoted in percent):

positive errors: +1.8_stat +1.8_exp +1.4_{b2c model} +1.3_{b2u model} +1.1_{alpha_s} +2.0_Vcb +0.7_mb +0.4_mc +0.8_BF +3.5_model =+5.4_tot

negative errors: -1.8_stat -2.0_exp -1.4_{b2c model} -1.3_{b2u model} -1.0_{alpha_s} -2.0_Vcb -0.7_mb -0.7_mc -0.7_BF -3.5_model =-5.3_tot

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.

Determination of |V_ub| (BLL) using the (mx-q2) analyses

The |V_ub| values are obtained using the HQE input parameter:

• m_b(1S) = 4.704 ± 0.029 GeV

obtained from a global fit in the 1S scheme

|Vub| (BLL) using the (mx-q2) analyses
Experiment	Value [10-3]	Parameters	References	Remarks
BELLE breco (mX, q2)	5.01 ± 0.39 ± 0.32	input	Phys.Rev.Lett.95:241801,2005 [hep-ex/0505088]	mX-q2, BRECO tag
BELLE sim. ann. (mX, q2)	4.68 ± 0.49 ± 0.30	input	Phys.Rev.Lett.92:101801,2004 [arXiv:hep-ex/0311048v2]	mX - Q2, tag with annealing method
BABAR (mX, q2)	4.50 ± 0.24 ± 0.29	input	arxiv:1112.0702v1 submitted to PRD [arXiv:1112.0702v1]	mX-q2, BRECO tag
Average ± exp ± theory	4.62 ± 0.20 ± 0.29	χ2/dof = 1.4/2 (CL = 0.50)	Plots: eps pdf gif	HQE parameter input from b to c l nu and b to s gamma moments

The full breakdown of the uncertainties on the average |Vub| above is (all errors quoted in percent):

positive errors: +3.3_stat +3.0_exp +1.6_{b2c model} +1.1_{b2u model} +3.0_Strf +3.0_Pert +2.5_Sf +4.0_H.O. = +7.7_tot

negative errors: -3.3_stat -3.0_exp -1.6_{b2c model} -1.1_{b2u model} -3.0_Strf -3.0_Pert -2.5_Sf -4.0_H.O. = -7.7_tot

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 alpha_s 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.

Shape Function Model Independent extraction of |V_ub| from inclusive decays and comparison of results

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 |V_ub| from charmless B-meson decays from inclusive distributions for different regions of phase space.
BABAR measured |V_ub| 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 |V_ub| 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 |V_ub| extractions.

The errors on |V_ub| are experimental and theoretical, respectively, for the first three results and experimental on B->Xulnu, experimental on B->Xsgamma, theoretical and due to |V_ts| for the last two measurments.

Description	Vub [10-3]	Reference
HFAG Ave. (BLNP)	4.40 ± 0.15 +0.19 - 0.21
HFAG Ave. (DGE)	4.45 ± 0.15+ 0.15 - 0.16
HFAG Ave. (GGOU)	4.39 ± 0.15 + 0.12 - 0.20
HFAG Ave. (ADFR)	4.03 ± 0.13 + 0.18 - 0.12
HFAG Ave. (BLL)	4.62 ± 0.20 + 0.29 - 0.29
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

Inclusive Branching Fraction: B --> X_ulnu (P*_lep > 1.0 GeV/c)

|V_ub| from exclusive semileptonic B decays

Branching fractions of B⁰ -> pi^- l⁺ nu

The measurements quoted here include both B⁰ and B⁺ decays. The average assumes equality of the semileptonic decays widths for these isospin-conjugate states, and is quoted for B⁰ decays.

Experiment / Mode	BF [10-4]	BF(q2<12 GeV2) [10-4]	BF(q2<16 GeV2) [10-4]	BF(q2>16 GeV2) [10-4]	Reference
BABAR had. tag: B+ -> pi0 l+ nu × 2 τ0/τ+	1.52 +/- 0.41 +/- 0.30	0.67 +/- 0.30 +/- 0.12	1.04 +/- 0.35 +/- 0.18	0.48 +/- 0.22 +/- 0.12	Breco tag, Phys. Rev. Lett.97, 211801 (2006) [hep-ex/0607089] (input)(param)
Belle had. tag: B+ -> pi0 l+ nu × 2 τ0/τ+	1.48 +/- 0.15 +/- 0.08	0.78 +/- 0.11 +/- 0.04	1.09 +/- 0.12 +/- 0.06	0.36 +/- 0.07 +/- 0.02	Breco tag, Phys. Rev. D88, 032005 (2013) [arXiv:1306.2781 [hep-ex]] (input)(param)
BABAR sl. tag: B+ -> pi0 l+ nu × 2 τ0/τ+	1.78 +/- 0.28 +/- 0.15	1.07 +/- 0.20 +/- 0.09	1.35 +/- 0.22 +/- 0.11	0.44 +/- 0.17 +/- 0.06	SL tag, Phys. Rev. Lett 101, 081801 (2008) [arXiv:0805.2408] (input)(param)
Belle sl. tag: B+ -> pi0 l+ nu × 2 τ0/τ+	1.41 +/- 0.26 +/- 0.15	0.71 +/- 0.17 +/- 0.08	1.05 +/- 0.22 +/- 0.12	0.37 +/- 0.15 +/- 0.04	SL tag, Phys. Lett. B648, 139-148 (2007) [hep-ex/0604024] (input)(param)
BABAR had. tag: B0 -> pi- l+ nu	1.07 +/- 0.27 +/- 0.19	0.26 +/- 0.15 +/- 0.04	0.42 +/- 0.18 +/- 0.06	0.65 +/- 0.20 +/- 0.13	Breco tag, Phys. Rev. Lett.97, 211801 (2006) [hep-ex/0607089] (input)(param)
Belle had. tag: B0 -> pi- l+ nu	1.49 +/- 0.09 +/- 0.07	0.81 +/- 0.06 +/- 0.04	1.06 +/- 0.07 +/- 0.05	0.45 +/- 0.05 +/- 0.02	Breco tag, Phys. Rev. D88, 032005 (2013) [arXiv:1306.2781 [hep-ex]] (input)(param)
BABAR sl. tag: B0 -> pi- l+ nu	1.38 +/- 0.21 +/- 0.08	0.77 +/- 0.14 +/- 0.05	0.92 +/- 0.16 +/- 0.05	0.46 +/- 0.13 +/- 0.03	SL tag, Phys. Rev. Lett 101, 081801 (2008) [arXiv:0805.2408] (input)(param)
Belle sl. tag: B0 -> pi- l+ nu	1.41 +/- 0.19 +/- 0.15	0.80 +/- 0.14 +/- 0.08	1.04 +/- 0.16 +/- 0.11	0.37 +/- 0.10 +/- 0.04	SL tag, Phys. Lett. B648, 139-148 (2007) [hep-ex/0604024] (input)(param)
CLEO untagged: B -> pi l nu	1.38 +/- 0.15 +/- 0.11	0.69 +/- 0.12 +/- 0.07	0.97 +/- 0.13 +/- 0.09	0.41 +/- 0.08 +/- 0.04	Untagged, Phys. Rev. Lett.99, 041802 (2007) [arXiv:hep-ex/0703041v2] (input)(param)
BABAR untagged (6 q2 bins): B -> pi l nu	1.41 +/- 0.05 +/- 0.08	0.88 +/- 0.04 +/- 0.05	1.10 +/- 0.04 +/- 0.06	0.32 +/- 0.02 +/- 0.03	Untagged, Phys. Rev. D83, 032007 (2011) [arXiv:1005.3288v2 [hep/ex] ] (input)(param)
BABAR untagged (12 q2 bins): B -> pi l nu	1.44 +/- 0.04 +/- 0.06	0.83 +/- 0.03 +/- 0.04	1.08 +/- 0.04 +/- 0.05	0.37 +/- 0.02 +/- 0.02	Untagged loose neutrino, Phys. Rev. D86, 092004 (2012) [arXiv:1201.1253 [hep/ex] ] (input)(param)
Belle untagged: B0 -> pi- l+ nu	1.48 +/- 0.04 +/- 0.07	0.82 +/- 0.03 +/- 0.04	1.09 +/- 0.03 +/- 0.05	0.40 +/- 0.02 +/- 0.02	Untagged, Phys. Rev. D83, 071101 (2011) [arXiv:1012.0090 [hep-ex]] (input)(param)
Average: B0 -> pi- l+ nu	1.45 +/- 0.02 +/- 0.04	0.81 +/- 0.02 +/- 0.02	1.06 +/- 0.02 +/- 0.03	0.38 +/- 0.01 +/- 0.01	Plots: eps pdf gif   chi2/dof = 3.4/11 (CL = 0.98)

Exclusive |V_ub| determination

The partial BFs quoted above along with theoretical calculations of the form factor normalization can be used to determine |V_ub|. The |V_ub| results obtained from the HFAG averages for the partial BFs combined with different form factor calculations are shown below. Note that the FNAL/MILC and HPQCD unquenched LQCD calculations are not entirely independent. We also do not use their quenched results as they are superseded by the unquenched results. The calculations by Ball-Zwicky and Khodjamirian et al. are based on light-cone sum rules.  At this time we do not attempt to average the |V_ub| results obtained with different calculations or select a best value.

The errors on |V_ub| are experimental and theoretical.

A plot of this table is available in three formats: eps pdf gif

|V_ub| can also be determined from a simultaneous fit of a B -> pi form factor parameterization to data and LQCD calculations. In contrast to the |V_ub| determinations presented above, this fit makes use of the measured q² spectra over the full q² range. We choose the BCL parameterization (Bourrely, Caprini and Lellouch, Phys. Rev. D79, 013008 (2009) [arXiv:0807.2722v3 [hep-ph]]. A fit of the BCL parameterization with 3+1 parameters (3 parameters for the BCL parameterization: b₀,b₁,b₂ and one parameter for |V_ub| to be determined from the relative normalization of data and LQCD results) to the four most precise measurements of BABAR and Belle (BABAR untagged 6 q² bins B⁰+B⁺, BABAR untagged 12 q² bins B⁰+B⁺, Belle untagged B⁰, Belle had. tag B⁰) and the FNAL/MILC lattice predictions yields the following results:

|V_ub| = (3.28 +- 0.29) × 10^-3
b₁/b₀ = -1.02 +- 0.18
b₂/b₀ = -1.20 +- 0.57

For the product f₊(0)|V_ub| we obtain: f₊(0)|V_ub| = (0.923 +- 0.024) × 10^-3.

The quoted errors are the combined experimental and theoretical errors obtained from the fit. The probability of the fit is 0.053 (χ²/dof = 60.2/44).
Only 4 of the 12 LCQD points were used to avoid the high correlations between neighboring points.

A plot of the fit result is available in three formats: eps pdf gif

|V_ub| = (3.53 +- 0.29) × 10^-3
b₁/b₀ = -0.99 +- 0.20
b₂/b₀ = -1.28 +- 0.61
f₊(0)|V_ub| = (0.922 +- 0.024) × 10^-3
Probability: 0.029 (χ²/dof = 59.8/41)

A plot of the fit result is available in three formats: eps pdf gif

Branching fractions of B⁰ -> rho^- l⁺nu

Experiment/Mode	BF [10-4]	Reference
CLEO untagged: B^{0} - > \rho^{-} l^{+} \nu	2.75 +/-0.41 +/- 0.52	Phys.Rev.D61, 052001 (2000) [hep-ex/9905056] (input)
CLEO untagged: B^{0} -> \rho^{-} l^{+} \nu	2.93 +/-0.37 +/- 0.37	Phys.Rev.Lett.99, 041802 (2007)[arXiv:hep-ex/0703041v2] (input)
BELLE sl.tag: B^{0} -> \rho^{-} l^{+} \nu	2.17 +/-0.54 +/-0.32	Phys.Lett.B648:139-148,2007 [hep-ex/0604024] (input) (param)
BELLE sl.tag: B^{+} -> \rho^{0} l^{+} \nu	2.47 +/-0.43 +/-0.33	Phys.Lett.B648:139-148,2007 [hep-ex/0604024] (input) (param)
BABAR untagged: B^{0} -> \rho^{-} l^{+} \nu	1.98 +/-0.21 +/-0.38	Phys.Rev.D72, 051102 (2011) [arXiv:1005.3288] (input) (param)
BABAR untagged: B^{+} -> \rho^{0} l^{+} \nu	1.87 +/-0.19 +/-0.32	Phys.Rev.D72, 051102 (2011) [arXiv:1005.3288] (input) (param)
BELLE had.tag: B^{0} -> \rho^{-} l^{+} \nu	3.22 +/-0.27 +/-0.24	Phys.Rev.D 88, 032005 (2013)[arXiv:hep-ex/0703041v2] (input)(param)
BELLE had.tag: B^{+} -> \rho^{0} l^{+} \nu	3.39 +/-0.18 +/-0.18	Phys.Rev.D 88, 032005 (2013)[arXiv:hep-ex/0703041v2] (input)(param)
Average: B ^{0} -> \rho^{-} l^{+} \nu	2.94 +/- 0.11 +/- 0.17	Plots: eps pdf gif   chi2/dof = 12.8/7 (CL = 0.08)

Exclusive Branching Fraction: B^- -> Omega l nu

Exclusive Branching Fraction: B^- -> eta l nu

Exclusive Branching Fraction: B^- -> eta' l nu

Experiment/Mode	BF [10-4]	Parameters	Reference
CLEO untagged	2.71+/- 0.80+/- 0.56	input     parameters	Phys.Rev.D76, 012007 (2007) [arXiv:0703042[hep-ex]]
BABAR sl.tag	0.04+/- 0.22+/- 0.04 (<0.47 at 90% C.L.)	input     parameters	Phys.Rev.Lett 101, 081801 (2008) [arXiv:0808.3524 [hep-ex]]
BABAR untagged (loose nu-reco)	0.24 +/- 0.08 +/- 0.03	input     parameters	Phys.Rev.D83, 052011 (2011) [arXiv:1010.0987 [hep-ex]]
Average	0.23 +/- 0.08 +/- 0.03	chi2/dof = 7.2/2. (CL = 0.03)	eps pdf gif