Updates of Semileptonic Results for ICHEP 2006

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

Experiment	BF(B0 -> X-l+nu)[%]	Remarks
CLEO	10.78 +/- 0.60 +/- 0.69	Phys.Lett.B399:321,1997
ARGUS	9.3 +/- 1.1 +/- 1.5	Phys.Lett.B324:249,1994
CLEO	9.9 +/- 3.0 +/- 0.9	Phys.Rev.D45:2212,1992
BELLE (breco)	10.32 +/- 0.36 +/- 0.35	Phys.Lett.B614:27-,2005
BABAR (breco)	9.66 +/- 0.27 +/- 0.32	Preliminary (hep-ex/0607111 ) (cut at p>0.6 GeV/c not extrapolated to full region)
BELLE (breco2)	10.30 +/- 0.30 +/- 0.18	Preliminary (BELLE-CONF-667) ICHEP'06 (cut at p*>0.4 GeV/c not extrapolated to full region)

  

Experiment	BF(B+ -> Xl+nu)[%]	Remarks
CLEO	10.25 +/- 0.57 +/- 0.65	Phys.Lett.B399:321,1997
BELLE (breco)	11.15 +/- 0.26 +/- 0.41	Phys.Lett.B614:27-,2005
BABAR (breco)	10.39 +/- 0.26 +/- 0.37	Preliminary (hep-ex/0607111 ) (cut at p>0.6 GeV/c not extrapolated to full region)
BELLE (breco2)	11.00 +/- 0.25 +/- 0.23	Preliminary (BELLE-CONF-667) ICHEP'06 (cut at p*>0.4 GeV/c not extrapolated to full region)

  

Exclusive |V_cb| F(1)

Previously all the measurements in the average assumed (some had to be re-calibrated) form factor ratios of R_1=(1.18+/-0.30+/-0.12) and R_2=(0.71+/-0.22+/-0.07) as measured by the CLEO collaboration (Phys. Rev. Lett. 76, 3898 (1996)). All the measurements in the following average had been recalibrated such that R_1=(1.396+/-0.060+/-0.035+/-0.027) and R_2=(0.885+/-0.040+/-0.022+/-0.013) is assumed, as measured by the BABAR collaboration (hep-ex/0602023: accepted by PRD).

This table and the plots in the last row document the two-dimensional simultaneous fit to |Vcb|*F(1) and rho².

Experiment	|Vcb| F(1) (rescaled) [10-3]	rho2 (rescaled)	Correlation (stat/syst/total)	Parameters	Remarks
ALEPH	32.6 +/- 2.0 +/- 1.3	0.44 +/- 0.25 +/- 0.12	0.94/0.60/0.72	input     parameters	Phys.Lett.B395:373-,1997
OPAL (partial reco)	37.8 +/- 1.2 +/- 2.3	1.09 +/- 0.14 +/- 0.30	0.77/0.70/0.71	input     parameters	Phys.Lett.B482:15-,2000
OPAL (excl)	37.9 +/- 1.6 +/- 1.6	1.17 +/- 0.21 +/- 0.15	0.95/0.42/0.61	input     parameters	Phys.Lett.B482:15-,2000
DELPHI (partial reco)	36.0 +/- 1.4 +/- 2.3	1.27 +/- 0.14 +/- 0.27	0.94/0.77/0.79	input     parameters	Phys.Lett.B510:55-,2001
BELLE	34.9 +/- 1.8 +/- 1.7	1.25 +/- 0.16 +/- 0.11	0.91/0.68/0.78	input     parameters	Phys.Lett.B526:247-,2002
CLEO	42.5 +/- 1.3 +/- 1.6	1.41 +/- 0.09 +/- 0.09	0.87/0.62/0.67	input     parameters	Phys.Rev.Lett.89:081803,2002
BABAR	34.4 +/- 0.3 +/- 1.2	1.09 +/- 0.03 +/- 0.08	0.56/0.73/0.72	input     parameters	Phys.Rev.D71:051502,2004
DELPHI (exclu)	37.6 +/- 1.7 +/- 1.9	1.01 +/- 0.15 +/- 0.16	0.89/0.50/0.58	input     parameters	Eur.Phys.J.C33:213,2004
Average	36.2 +/- 0.8	1.19 +/- 0.06	0.73/0.61/0.63	chi2/dof = 38.7/14	eps 1  pdf 1  gif 1  eps 2  pdf 2  gif 2

|V_ub| in inclusive semileptonic B decays

•   BLNP - B.O. Lange, M. Neubert and G. Paz. Phys. Rev. D72:073006 (2005)
•   DGE. -  J.R. Andersen and E. Gardi. JHEP 0601:097 (2006)
•   BLL -  C.W. Bauer, Z. Ligeti and M.E. Luke. Phys. Rev. D64:113004 (2001) (Only measurements that use m_X- q² cut)
  

The latter, BLL, although having been around for quite some time, has been added to our list of phenomenological frameworks from which one extract a value of |V_ub|. BLL is a local OPE based approach that first advocated the use of a m_X- q² cut, to not only reduce large b->clnu background, but to reduce theoretical errors associated with the b-quark light cone distribution function or shape function, as it more widely known. The extraction is applied to results of  the partial branching fraction of inclusive charmless semileptonic B decays in the phase space  p_l>1 GeV/c, m_X < 1.7 GeV/c² & q² > 8 GeV²/c².

We perform a total of five averages for the inclusive V_ub:

1. BLNP using all the experimental measurements and only the mx-q2 ones
2. DGE using all the experimental measurements and only the mx-q2 ones
3. BLL using only the mx-q2 measurements

No attempt is made to average BLNP, DGE or BLL derived |Vub|.

For consistency among all the averages, we use the input parameters from the same global fit to data of B->Xc l nu  and B->Xs g decays using the latest measurements from the Collaborations: Eur. Phys. J C 34 (2004) 181. The global fit is performed in the Kinetic Scheme (Eur. Phys. J C 34 (2004) 181) and then the HQ parameters are translated to the other schemes. A global fit in the 1S scheme is currently under way. Earlier results can be found in Phys. Rev. D 70:094017 (2004).

The procedure for performing the average is documented in a brief note on averaging. 

The input files for the average are linked below. To summarize briefly, all theoretical uncertainties are considered to be correlated, as are the uncertainties on the modeling of b -> clnu and b -> ulnu decays. Experimental uncertainties (particle identification, reconstruction efficiencies, etc.) are taken as correlated amongst measurements from the same experiment, but not correlated across experiments. The set of results averaged have negligible statistical correlations.

The errors in the tables are experimental (statistical and systematic) and external (theoretical and HQ parameter uncertainties). The average B lifetime used is 1.584 ps.

BLNP : |V_ub| with HQ parameters from b -> c l nu and b -> s g moments

V_ub values are obtained using the HQ input parameters (from Phys.Rev.D73,073008(2006)):

• m_b(SF) = 4.60 +/- 0.04 GeV
  
•  mu_pi²(SF) =0.20 +/- 0.04 GeV²
  

BLNP Vub (B->Xc l nu & B->Xs g moments)
Experiment	Value [10-3]	Parameters	References	Remarks
CLEO (endpoint)	4.09 +/- 0.48 +/- 0.36	input	Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019)	2.1 < p < 2.6, Vub redetermined from partial BF
BELLE (endpoint)	4.82 +/- 0.45 +/- 0.30	input	Phys.Lett.B621:28-40 (2005) (hep-ex/0504046)	1.9 < p < 2.6
BABAR (endpoint)	4.39 +/- 0.25 +/- 0.39	input	Phys.Rev.D73:012006,2006 (hep-ex/0509040)	2.0 < p < 2.6, Vub redetermined from partial BF
BABAR (E_{e}, q^{2})	4.57 +/- 0.31 +/- 0.41	input	Phys.Rev.Lett.95:111801,2005 , Erratum-ibid.97:019903,2006 (hep-ex/0506036 (version 3, June 2006))	(Ee-q2)
BELLE m_{X}	4.06 +/- 0.27 +/- 0.24	input	Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088)	mX, BRECO tag; other methods (mX-q2 and P not used)
BELLE sim. ann. (m_{X}, q^{2})	4.37 +/- 0.46 +/- 0.29	input	Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048)	mX - Q2, tag with annealing method
BABAR (m_{X}, q^{2})	4.75 +/- 0.35 +/- 0.32	input	preliminary (hep-ex/0507017)	mX-q2, BRECO tag
Average +/- exp +/- (mb,theory)	4.49 +/- 0.19 +/- 0.27	chi2/dof = 6.1/6 (CL = 0.407)	Plots: eps pdf gif	HQ 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):

+-2.2_stat +-2.8_exp +-1.9_{b2c model} +-1.6_{b2u model} +-4.2_{HQ param} +-3.8_{sub SF} +-1.9_WA = +-7.3_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_pi², 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) = (2.26 +- 0.33)*10^-3

DGE: |V_ub| with b-quark mass from b -> c l nu and b -> s g moments

V_ub values are obtained using the HQ input parameter (from Phys.Rev.D73,073008(2006)):

• m_b (MSbar) = 4.20 +- 0.04 GeV

DGE Vub (B->Xc l nu & B->Xs g moments)
Experiment	Value [10-3]	Parameters	References	Remarks
CLEO (endpoint)	3.85 +/- 0.45 +/- 0.22	input	Phys.Rev.Lett.88:231803,2002 (hep-ex/0202019)	2.1 < p < 2.6, Vub redetermined from partial BF
BELLE (endpoint)	4.80 +/- 0.45 +/- 0.20	input	Phys.Lett.B621:28-40 (2005) (hep-ex/0504046)	1.9 < p < 2.6
BABAR (endpoint)	4.29 +/- 0.29 +/- 0.21	input	Phys.Rev.D73:012006,2006 (hep-ex/0509040)	2.0 < p < 2.6, Vub redetermined from partial BF
BABAR (E_{e}, q^{2})	4.42 +/- 0.30 +/- 0.24	input	Phys.Rev.Lett.95:241801,2005 (hep-ex/0506036 (version 3, June 2006))	(Ee-q2)
BELLE m_{X}	4.29 +/- 0.28 +/- 0.22	input	Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088)	mX, BRECO tag; other methods (mX-q2 and P not used)
BELLE sim. ann. (m_{X}, q^{2})	4.42 +/- 0.47 +/- 0.19	input	Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048)	mX - Q2, tag with annealing method
BABAR (m_{X}, q^{2})	4.80 +/- 0.35 +/- 0.21	input	preliminary (hep-ex/0507017)	mX-q2, BRECO tag
Average +/- exp +/- (mb,theory)	4.46 +/- 0.20 +/- 0.20	chi2/dof = 10.0/6 (CL = 0.063)	Plots: eps pdf gif	m_b 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):

+-1.8_stat +-2.5_exp +-2.3_{b2c model} +-2.3_{b2u model} +-1.2_{mb (R_CUT)} +-1.0_{alpha_s (R_CUT)} +-3.0 _{(TOTAL SL WIDTH)} +-2.9_{DGE theory}

where the errors correspond to statistics, experimental systematics, the modeling of b -> c l nu and b -> u l nu decays, effect of uncertainty on m_b
on the prediction of  the event fraction (R_CUT),  effect  of alpha_s uncertainty on R_CUT, uncertainty on total semileptonic B width, and from the change
and variation of scale of the matching scheme (DGE theory).

Using the average |Vub| along with the calculated full b -> u l nu rate from DGE \(66.5/ps^-1/|Vub|²) results in a total BF

BF(b -> u l nu) = (2.10 +- 0.29)*10^-3

Inclusive Vub comparison

Vub (B->Xc l nu & B->Xs g moments)
Theory framework	Vub [10-3]
BLNP (Phys. Rev. D72:073006 (2005))	4.49 +/- 0.19 +/- 0.27
DGE (JHEP 0601:097 (2006))	4.46 +/- 0.20 +/- 0.20

BLL : |V_ub| with HQ parameters from b -> c l nu and b -> s g moments (mx-q2)

V_ub values are obtained using the b-quark mass (from Phys.Rev.D73,073008(2006)) translated to the 1S scheme using hep-ph/0304132:

• m_b(1S) = 4.69 +/- 0.04 GeV

BLL Vub (B->Xc l nu & B->Xs g moments)
Experiment	Value [10-3]	Parameters	References	Remarks
BELLE breco (m_{X}, q^{2})	5.04 +/- 0.39 +/- 0.37	input	Phys.Rev.Lett.95:241801,2005 (hep-ex/0505088)	mX-q2, BRECO tag
BELLE sim. ann. (m_{X}, q^{2})	4.72 +/- 0.50 +/- 0.35	input	Phys.Rev.Lett.92:101801,2004 (hep-ex/0311048)	mX - Q2, tag with annealing method
BABAR (m_{X}, q^{2})	5.12 +/- 0.38 +/- 0.38	input	preliminary (hep-ex/0507017)	mX-q2, BRECO tag
Average +/- exp +/- (mb,theory)	5.02 +/- 0.26 +/- 0.37	chi2/dof = 0.52/2 (CL = 0.77)	Plots: gif  eps pdf	HQ parameter input from b to c l nu and b to s gamma moments

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

+-3.2_stat +-2.9_exp +-1.7_{b2c model} +-2.5_{b2u model} +-3.0_Strf +-3.0_Pert +-4.5_Sf +-4.0_H.O. = +-9.0_tot

where the errors correspond to statistics, experimental systematics, the modeling of b -> c l nu and b -> u l nu decays, residual shape function effects (Strf), higher order terms in the $\alpha_s$ expansion (Pert), the uncertainty on the b-quark mass (Sf), and third order terms in the OPE expansion(H.O.). No uncertainty is assigned for possible duality violations.

Comparison of Inclusive Vub using only mX-q2 measurements

Vub (B->Xc l nu & B->Xs g moments)
Theory framework	Vub [10-3]
HFAG Ave. (BLNP) mx-q2 (CL=0.77)	4.65 +/- 0.26 +/- 0.31
HFAG Ave. (DGE) mx-q2 (CL=0.78)	4.70 +/- 0.26 +/- 0.22
HFAG Ave. (BLL) mx-q2 (CL=0.77)	5.02 +/- 0.26 +/- 0.37

Shape Function Model Independent extraction of Inclusive Vub comparison

Above we have used two theoretical formulations to extract Vub from measurements of inclusive charmless B-meson decays in various kinematic regions of phase space. Recently BABAR measured inclusive Vub using the prescription of Leibovich, Low, and Rothstein (LLR) that extracts Vub with reduced model dependence by combining data of the hadronic mass spectrum from B->Xulnu decays with that of the photon energy spectrum from B->Xs gamma decays (hep-ex/0601046). The LLR approach reduces the dependence on the shape function because no model for the shape function is assumed, in contrast to the BLNP formulation used above. Here we provide a comparison.

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

Description	Vub [10-3]	Reference
HFAG Ave. (BLNP)	4.49 +/- 0.19 +/- 0.27
HFAG Ave. (DGE)	4.46 +/- 0.20 +/- 0.20
BABAR (LLR)	4.43 +/- 0.45 +/- 0.29	Phys.Rev.Lett. 96 (2006) 221801 (hep-ex/0601046 )

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_{+}	1.35 +/- 0.33 +/- 0.19	1.17 +/- 0.30 +/- 0.11	0.19 +/- 0.22 +/- 0.07	Preliminary, SL tag (hep-ex/0607089) (input)
BABAR Breco 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	Preliminary, Breco tag (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	Submitted to PLB, SL tag (hep-ex/0604024) (input)
BELLE Breco tag: B ^{+} \rightarrow \pi^{0} l^{+} \nu \times 2\tau_{0}/\tau_{+}	1.60 +/- 0.32 +/- 0.11	NA	NA	Preliminary, Breco tag, (Belle-conf-0666), contribution to ICHEP06 (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	Preliminary, SL tag (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	Submitted to PLB, SL tag (hep-ex/0604024) (input)
BABAR Breco tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu	1.07 +/- 0.27 +/- 0.19	0.42 +/- 0.18 +/- 0.05	0.65 +/- 0.20 +/- 0.13	Preliminary, Breco tag, (hep-ex/0607089) (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	Untagged, Phys. Rev. D 68, 072003 (2003) ) (input)
BABAR untagged: B \rightarrow \pi l^{+} \nu	1.44 +/- 0.08 +/- 0.10	1.07 +/- 0.06 +/- 0.08	0.37 +/- 0.04 +/- 0.03	Preliminary, untagged loose neutrino (hep-ex/0607060 ) (input)
BELLE Breco tag: B ^{0} \rightarrow \pi^{-} l^{+} \nu	1.49 +/- 0.26 +/- 0.06	NA	NA	Preliminary, Breco tag, (Belle-conf-0666), contribution to ICHEP06 (input)
Average: B ^{0} \rightarrow \pi^{-} l^{+} \nu	1.37 +/- 0.06 +/- 0.06	0.95 +/- 0.05 +/- 0.05	0.35 +/- 0.03 +/- 0.03	Plots: eps pdf gif   chi2/dof = 2.9/9 (CL = 0.97)

Exclusive Vub determination

The partial BF quoted above along with theoretical calculations of the form factor normalization can be used to determine Vub; a few recent calculations are shown below. Note that the FNAL04 and HPQCD unquenched LQCD calculations are not entirely independent, we do not use their quenched results as they are superseded by their unquenched results. We also use the quenched LQCD result of the APE collaboration. The Ball-Zwicky calculation is based on light-cone sum rules.  At this time we do not attempt to average the Vub results or select a best value. We divide the results into two tables: the first table lists extractions of |V_ub| in q^2 regions where the theory formulation is applicable and the second lists results where these same formulations have relied on a model to extrapolate to the uncovered q^2 region.

A determination of |Vub| making use of the experimental input on the q² dependence is under study but not yet available.

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

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 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)
BABAR	B+-> eta l+ nu	0.84 +/-0.27 +/- 0.21	Preliminary Breco (hep-ex/0607066)
BABAR	B+-> eta' l+ nu	0.33 +/-0.60 +/- 0.30	Preliminary Breco (hep-ex/0607066)
CLEO	B0-> rho- l+ nu	2.69 +/-0.41 +0.35/-0.40 +/-0.50	Phys. Rev. D 61, 052001 (2000)
BABAR	B0-> rho- l+ nu	2.57 +/-0.52 +/-0.59	Preliminary, Breco tag (ICHEP conference paper)
BABAR	B0-> rho- l+ nu	3.29 +/-0.42 +/-0.47 +/-0.60	Phys. Rev. Lett. 90, 181801 (2003)
CLEO	B0-> rho- l+ nu	2.17 +/-0.34 +0.47/-0.54 +/-0.41 +/-0.01	Phys. Rev. D 68, 072003 (2003)
BABAR	B0-> rho- l+ nu	2.14 +/-0.21 +/-0.51 +/-0.28	Untagged, Phys .Rev. D72, 051102 (2005) (hep-ex/0507003)
BELLE	B0-> rho- l+ nu	2.17 +/-0.54 +/-0.31 +/-0.08	Submitted to PLB, SL tag (hep-ex/0604024)
BELLE	B+-> rho0 l+ nu	1.33 +/-0.23 +/-0.17 +/-0.05	Submitted to PLB, SL tag (hep-ex/0604024)
BELLE	B0-> rho- l+ nu	2.41 +/-0.62 +/-0.24	Preliminary Breco-tag BELLE-CONF-666 ICHEP06 )
BELLE	B+-> rho0 l+ nu	2.00 +/-0.32 +/-0.43	Preliminary Breco-tag BELLE-CONF-666 ICHEP06 )
BELLE	B+-> omega l+ nu	1.17 +/-0.39 +/-0.11	Preliminary Breco-tag BELLE-CONF-666 ICHEP06 )