Updates of Semileptonic Results for Lepton Photon 2007

Measurement of |V_cb| F(1) in B⁰ -> D*lnu

Exclusive Branching Fraction: B⁰ -> D*lnu

Measurement of |V_cb|G(1) in B⁰ -> Dlnu

Exclusive Branching Fraction: B⁰ -> Dlnu

Inclusive |V_cb| from global fits

• Kinetic Scheme: using the calculations from P. Gambino, N. Uraltsev, Eur.Phys.J. C34 (2004) 181-189 [arXiv:hep-ph/0401063v1], and D. Benson, I. Bigi, N. Uraltsev, Nucl.Phys. B710 (2005) 371-401 [arXiv:hep-ph/0410080v2]
• 1S: using the calculations from C.W. Bauer, Z. Ligeti and M.E. Luke, Phys.Rev. D64 (2001) 113004 [arXiv:hep-ph/0107074v1]

Fits to the B->Xc l nu & B->Xs g moments and separately to the B->Xc l nu moments only are performed.

Inclusive Semileptonic (Partial) Branching Fraction for B+/B0 Admixture: B -> Xlnu

Inclusive Semileptonic Branching Fraction for B+ -> Xl+nu

Inclusive Semileptonic Branching Fraction for B0 -> X-l+nu

Ratio of Semileptonic Branching Fractions for B+ to B0 -> X-l+nu

|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].
• DGE -  J.R. Andersen and E. Gardi, JHEP 0601:097 (2006) [arXiv:hep-ph/0509360v2].
• 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).

We perform the following |V_ub| averages for:

• all independent measurements (by BaBar and Belle papers "presented at LP" (the hep-ex number will be available soon) and Phys.Rev.Lett. 95 (2005) 241801 [arXiv:hep-ex/0505088v2], respectively, we had to choose one measurement, since the three analyses performed are strongly correlated). We have chosen the m_X analysis.
• all the endpoint analyses
• all the m_Xq² analyes
• all the m_X analyses
• all the P⁺ analyses

No attempt is made to average values for |V_ub| based on BLNP, DGE or BLL derived |V__ub|, but the results are presented independently per each scheme.

The procedure for performing the average is documented in arXiv:0704.3575.

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 1.585 ps.

Determination of |V_ub| (BLNP)

The |V_ub| values are obtained using the HQE input parameters m_b(SF) and mu_pi². Their central values, derived in the kinetic scheme, are taken from Phys.Rev.D73,073008(2006) [arXiv:hep-ph/0507253v3], where they are translated to the Shape Function scheme used by BLNP. The uncertainties are increased to 0.06 GeV and 0.06 GeV², respectively, according to M. Neubert's private communication, to take into account the uncertainty due to higher order corrections not accounted for in the partial rate predictions for B->Xulnu. The values of the HQE parameters used for the determination of |V_ub| are then:

• m_b(SF) = 4.63 +/- 0.06 GeV
  
• mu_pi²(SF) =0.18 +/- 0.06 GeV²
  

+-2.0_stat +-2.6_exp +-1.8_{b2c model} +-1.1_{b2u model} +-6.9_{HQE param} +-1.0_{SF func} +-0.9_{sub SF} +-3.6_matching +-1.7_WA = +-8.9_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 mu_pi² (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.

Averages of the endpoint, mxq2, mx, Pplus analyses are also presented in the corresponding links.

Determination of |V_ub| (BLNP) using only b -> c l nu moments (January 7 2008 update)

• m_b(SF) = 4.707 +0.059/-0.053 GeV
  
• mu_pi² = 0.216 +0.054/-0.076 GeV²
  

+-2.0_stat +-2.5_exp +-1.8_{b2c model} +-1.1_{b2u model} +-6.3_{HQE param} +-0.4_{SF func} +-0.7_{sub SF} +-3.6_matching +-1.4_WA = +-8.3_tot

where the fractions correspond to the statistical error (stat), the experimental systematics (exp), the modeling, e.g. branching fractions for exclusive decays, of b -> c l nu and b -> u l nu decays (b2c model and b2u model, respectively), the HQE parameters m_b and mu_pi² (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.

Using only the m_{X} analyses, the average is: 3.70+/-0.15+/-0.28 10-3.

Determination of |V_ub| (DGE)

The |V_ub| values are obtained using the HQE input parameter (from PDG07):

• m_b (MSbar) = 4.20 +- 0.07 GeV

|Vub| (DGE)
Experiment	Value [10-3]	Parameters	References	Remarks
CLEO (E_{e})	3.84 +/- 0.45 +/- 0.30	input	Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019)	2.1 < p < 2.6
BELLE sim. ann. (m_{X}, q^{2})	4.42 +/- 0.47 +/- 0.26	input	Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048)	mX - Q2, tag with annealing method
BELLE (E_{e})	4.79 +/- 0.45 +/- 0.26	input	Phys.Lett.B621:28-40 (2005) (hep-ex/0504046)	1.9 < p < 2.6
BABAR (E_{e})	4.29 +/- 0.29 +/- 0.28	input	Phys.Rev.D73:012006,2006 (hep-ex/0509040)	2.0 < p < 2.6
BABAR (E_{e}, s^{max}_{h})	4.42 +/- 0.30 +/- 0.38	input	Phys.Rev.Lett.95:241801,2005 (hep-ex/0506036 (version 3, June 2006))	(Ee-q2)
BELLE m_{X}	4.29 +/- 0.28 +/- 0.28	input	Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088)	mX, BRECO tag; other methods (mX-q2 and P+ not used)
BABAR m_{X}	4.56 +/- 0.22 +/- 0.32	input	[arXiv:0708.3702v1]	mX, BRECO tag; other methods (mX-q2 and P+ not used)
Average +/- exp +/- (mb,theory)	4.34 +/- 0.16 +/- 0.25	chi2/dof = 2.3/6 (CL = 0.89)	Plots: eps pdf gif	mb input from PDG07 average

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

+-2.0_stat +-2.4_exp +-1.9_{b2c model} +-1.0_{b2u model} +-0.6_{alpha_s R_CUT} +-3.2_{mb R_CUT} +-3.0_{TOTAL SL WIDTH} +-1.9_WA +-3.1_{DGE theory}

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 (mb R_CUT), the uncertainty on the total semileptonic B width (TOTAL SL WIDTH), 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.

Averages of the endpoint, mxq2, mx, Pplus analyses are also presented in the corresponding links.

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

The |V_ub| values are obtained using the b-quark mass from the 1S Global Fit

• m_b(1S) = 4.70 +/- 0.03 GeV

|Vub| (BLL) using the (mx-q2) analyses
Experiment	Value [10-3]	Parameters	References	Remarks
BELLE breco (m_{X}, q^{2})	5.01 +/- 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})	4.70 +/- 0.49 +/- 0.35	input	Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048)	mX - Q2, tag with annealing method
BABAR (m_{X}, q^{2})	4.81 +/- 0.32 +/- 0.35	input	[arXiv:0708.3702v1]	mX-q2, BRECO tag
Average +/- exp +/- (mb,theory)	4.83 +/- 0.24 +/- 0.37	chi2/dof = 0.48/2 (CL = 0.79)	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):

+-3.2_stat +-3.8_exp +-1.3_{b2c model} +-2.1_{b2u model} +-3.0_Strf +-3.0_Pert +-4.5_Sf +-4.0_H.O. = +-9.0_tot

where the fractions correspond to the statistical error (stat), the experimental systematics (exp), the modeling, e.g. branching fractions for exclusive decays, of 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], three different theoretical prescriptions were tried to extract |Vub|, arXiv:hep-ph/0702072v1, namely LLR (Phys.Rev. D61 (2000) 053006 [arXiv:hep-ph/9909404v2]]), Neubert (Phys.Lett. B513 (2001) 88-92 [arXiv:hep-ph/0104280v3]) and more recent calculations 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 three measurments.

Description	Vub [10-3]	Reference
HFAG Ave. (BLNP)	4.31 +/- 0.17 +/- 0.35
HFAG Ave. (DGE)	4.34 +/- 0.16 +/- 0.25
HFAG Ave. (BLL)	4.83 +/- 0.24 +/- 0.37
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	arXiv:hep-ph/0702072v1
BABAR endpoint (Neubert)	4.01 +/- 0.27 +/- 0.29 +/- 0.32 +/- 0.27	arXiv:hep-ph/0702072v1
BABAR endpoint (LNP)	4.40 +/- 0.30 +/- 0.41 +/- 0.23	arXiv:hep-ph/0702072v1

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

Branching fractions of B -> pi l nu

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, Phys.Lett.B648:139-148,2007 [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, Phys.Lett.B648:139-148,2007 [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/0304019] (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 = 3.23/9 (CL = 0.95)

Exclusive |V_ub| determination

The partial BF quoted above along with theoretical calculations of the form factor normalization can be used to determine |V_ub|; 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. 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 |V_ub| results or select a best value. We divide the results into two tables: the first table lists extractions of |V_ub| in q² 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 q² region.

The errors on |V_ub| are experimental and theoretical, respectively.

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

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

Branching fractions of B -> rho l nu

Experiment/Mode	BF [10-4]	Reference
CLEO: B^{0} \rightarrow \rho^{-} l^{+} \nu	2.69 +/-0.41 +/- 0.65	Phys. Rev. D 61, 052001 (2000) [hep-ex/9905056] (input)
CLEO: B^{0} \rightarrow \rho^{-} l^{+} \nu	2.17 +/-0.34 +/- 0.63	Phys. Rev. D 68, 072003 (2003)[hep-ex/0304019] (input)
BABAR: B^{0} \rightarrow \rho^{-} l^{+} \nu	2.14 +/-0.21 +/-0.56	Untagged, Phys .Rev. D72, 051102 (2005) [hep-ex/0507003] (input)
BELLE: 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: B^{+} \rightarrow \rho^{0} l^{+} \nu\times 2\tau_{0}/\tau_{+}	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	2.38 +/- 0.20 +/- 0.32	Plots: eps pdf gif   chi2/dof = 0.96/4 (CL = 0.92)

Branching fractions of other exclusive charmless semileptonic decays

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]
BELLE	B+-> omega l+ nu	1.3 +/-0.4 +/-0.2 +/-0.3	Phys. Rev. Lett. 93:131803 (2004)[hep-ex/0402023]