A spreadsheet with the breakdown of the errors is available.

For averages not shown here see http://www.slac.stanford.edu/xorg/hfag/semi/winter05/winter05.shtml

The procedure for performing the average is documented in a brief note on averaging. There have been several changes from what was done in previous HFAG semileptonic averages.

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 negligeable statistical correlations. Variations on the assumptions of which experimental errors were taken as correlated were considered; they have no significant impact on the average. If one fails to account for the dependence of the quoted errors on the measured values, the resulting average is biased low by -0.3 sigma.

The errors in the tables are experimental (statistical and systematic) and external (theoretical and HQ parameter uncertainties). The average B lifetime used was 1.604 ps.

These results are similar to those prepared for Lepton-Photon 2005; some minor errors in the input files and typos in the html were fixed, which is why the values are slightly changed.

The following values use HQ parameter input from a global fit to
both b -> c l nu and b -> s g moments in the kinetic
scheme, which gives parameters
m_{b} = 4.60 +- 0.04 GeV and mu_{pi}^{2}=0.20
+- 0.04 GeV^{2} with
correlation coefficient -0.26 (hep-ph/0507253).
The details of the fit are here.

These results are similar to those obtained in the 1S scheme in Phys. Rev. D70:094017, 2004 ( hep-ph/0408002). Work is in progress in HFAG to update the 1S fits using the latest set of moments measurements.

Experiment | Value [10^{-3}] |
Parameters | References | Remarks |
---|---|---|---|---|

CLEO (endpoint) | 4.02 +/- 0.47 +/- 0.35 | input | Phys.Rev.Lett.88:231803,2002 | 2.1 < p < 2.6, Vub redetermined from partial BF |

BELLE (endpoint) | 4.82 +/- 0.45 +/- 0.31 | input | Phys.Lett.B621:28-40 (2005) (hep-ex/0504046) | 1.9 < p < 2.6 |

BABAR (endpoint) | 4.23 +/- 0.27 +/- 0.31 | input | preliminary (hep-ex/0408075) | 2.0 < p < 2.6, Vub redetermined from partial BF |

BABAR (E_{e}, q^{2}) | 4.06 +/- 0.27 +/- 0.36 | input | submitted to PRL (hep-ex/0506036) | (E_{e}-q^{2}) |

BELLE m_{X} | 4.08 +/- 0.27 +/- 0.25 | input | submitted to PRL (hep-ex/0505088) | m_{X}, BRECO tag; other methods (m_{X}-q^{2}
and P_{} not used) |

BELLE sim. ann. (m_{X}, q^{2}) | 4.38 +/- 0.46 +/- 0.30 | input | Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048) | m_{X} - Q^{2}, tag with annealing method |

BABAR (m_{X}, q^{2}) | 4.76 +/- 0.34 +/- 0.32 | input | preliminary (hep-ex/0507017) | m_{X}-q^{2}, BRECO tag |

Average +/- exp +/- (mb,theory) |
4.38 +/- 0.19 +/- 0.27 |
chi2/dof = 5.9/6 (CL = 0.43) |
Plots: eps gif | HQ parameter input from b to c l nu and b to s gamma moments |

+-2.2_{stat}
+-2.5_{exp}
+-1.9_{b2c model}
+-2.2_{b2u model}
+-4.7_{HQ param}
+-3.5_{sub SF}
+-1.9_{WA} = +-7.6_{tot}

where the errors correspond to statistics, experimental systematics,
the
modeling of b -> c l nu and b -> u l nu decays, the HQ parameters
m_{b} and mu_{pi}^{2}, subleading shape
functions
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) = (2.18 +- 0.33)*10^{-3}

Experiment / Mode | BF [10^{-4}] |
BF(q^{2}<16 GeV^{2}) [10^{-4}] |
BF(q^{2}>16 GeV^{2}) [10^{-4}] |
Reference |
---|---|---|---|---|

BABAR SL tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 3.31 +/- 0.68 +/- 0.42 | NA | NA | (1.80+-0.37+-0.23) Preliminary, SL tag (hep-ex/0506065) (input) |

BABAR Breco tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.45 +/- 0.37 +/- 0.12 | 0.99 +/- 0.31 +/- 0.09 | 0.46 +/- 0.20 +/- 0.04 | (0.79+-0.20+-0.11) preliminary Breco tag (hep-ex/0507085) (input) |

BELLE SL tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+} | 1.40 +/- 0.24 +/- 0.16 | 0.99 +/- 0.20 +/- 0.12 | 0.41 +/- 0.15 +/- 0.04 | (0.76+-0.13+-0.09) Preliminary, SL tag, presented at EPS 2005, Lisbon (input) |

BABAR SL tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.02 +/- 0.25 +/- 0.13 | 0.81 +/- 0.22 +/- 0.11 | 0.21 +/- 0.14 +/- 0.05 | Preliminary, SL tag (hep-ex/0506064) (input) |

BELLE SL tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.48 +/- 0.20 +/- 0.16 | 1.08 +/- 0.16 +/- 0.12 | 0.40 +/- 0.12 +/- 0.05 | preliminary, SL tag, presented at EPS 2005, Lisbon (input) |

BABAR Breco tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu | 1.24 +/- 0.29 +/- 0.16 | 0.54 +/- 0.19 +/- 0.06 | 0.70 +/- 0.22 +/- 0.11 | Preliminary, Breco tag, (hep-ex/0507085) (input) |

CLEO untagged: B \rightarrow \pi l^{+} \nu | 1.32 +/- 0.18 +/- 0.13 | 1.07 +/- 0.16 +/- 0.11 | 0.25 +/- 0.09 +/- 0.05 | Phys. Rev. D 68, 072003 (2003) (input) |

BABAR untagged: B \rightarrow \pi l^{+} \nu | 1.38 +/- 0.10 +/- 0.18 | 0.89 +/- 0.09 +/- 0.12 | 0.49 +/- 0.05 +/- 0.06 | Untagged, submitted to PRD-RC (hep-ex/0507003) (input) |

Average: B ^{0} \rightarrow \pi^{-} l^{+} \nu |
1.35 +/- 0.08 +/- 0.08 |
0.89 +/- 0.06 +/- 0.06 |
0.40 +/- 0.04 +/- 0.04 |
Plots: eps gif chi2/dof = 8.0/7 (CL = 0.33) |

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. 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.

A determination of |Vub| making use of the
experimental input on the q^{2} dependence is under study but
not yet available.

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

FF calculation | Vub [10^{-3}] |
q^{2} range |
FF norm (ps^{-1}) |
Reference |
---|---|---|---|---|

Ball-Zwicky full q2 | 3.37 +/- 0.14 +0.66-0.41 | full | 7.74 +/- 2.32 | Phys. Rev. D71:014015 (2005) |

HPQCD full q2 | 3.93 +/- 0.17 +0.77-0.48 | full | 5.70 +/- 1.71 | hep-lat/0408019 |

FNAL full q2 | 3.76 +/- 0.16 +0.87-0.51 | full | 6.24 +/- 2.12 | hep-lat/0409116 |

Ball-Zwicky q2 < 16 | 3.27 +/- 0.16 +0.54-0.36 | <16 GeV^{2} |
5.44 +/- 1.43 | Phys. Rev. D71:014015 (2005) |

HPQCD q2 > 16 | 4.47 +/- 0.30 +0.67-0.46 | >16 GeV^{2} |
1.31 +/- 0.32 | hep-lat/0408019 |

FNAL q2 > 16 | 3.78 +/- 0.25 +0.65-0.43 | >16 GeV^{2} |
1.83 +/- 0.50 | hep-lat/0409116 |

A plot of this table is available in two formats: eps 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) |

CLEO | B^{0}-> rho^{-} l^{+} nu |
2.69 +/-0.41 +0.35/-0.40 +/-0.50 | Phys. Rev. D 61, 052001 (2000) |

BABAR | B^{0}-> rho^{-} l^{+} nu |
2.57 +/-0.52 +/-0.59 | Preliminary, Breco tag (ICHEP conference paper) |

BABAR | B^{0}-> rho^{-} l^{+} nu |
3.29 +/-0.42 +/-0.47 +/-0.60 | Phys. Rev. Lett. 90, 181801 (2003) |

CLEO | B^{0}-> rho^{-} l^{+} nu |
2.17 +/-0.34 +0.47/-0.54 +/-0.41 +/-0.01 | Phys. Rev. D 68, 072003 (2003) |

BABAR | B^{0}-> rho^{-} l^{+} nu |
2.14 +/-0.21 +/-0.51 +/-0.28 | Untagged, submitted to PRD-RC (hep-ex/0507003) |

BELLE | B^{0}-> rho^{-} l^{+} nu |
2.07 +/-0.47 +/-0.25 +/-0.14 | preliminary (Talk presented at EPS 2005, Lisbon) |

BELLE | B^{+}-> rho^{0} l^{+} nu |
1.39 +/-0.23 +/-0.17 +/-0.02 | preliminary (Talk presented at EPS 2005, Lisbon) |

BELLE | B^{+}-> omega l^{+} nu |
1.3 +/-0.4 +/-0.2 +/-0.3 | Phys. Rev. Lett. 93:131803 (2004) |

Last update: 2005/08/24 Bob Kowalewski