Results for PDG 2004 review

Only results published (or accepted in a refereed journal) before end November 2003 have been included in the averages computed by the lifetime and oscillations sub-group of the Heavy Flavour Average Group (HFAG) for the 2004 Particle Data Group review. The following material is available publicly:

The most recent (and still up-to-date) description of the combination procedures can be found in chapters 3-5 of cern-ep-2001-050 (although the numerical results in this preprint are as of summer 2000 and include preliminary results as well). Up-to-date lifetime averages are described in an internal note.

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Summary of b-hadron lifetimes, fractions and oscillation averages

The fractions below are for an unbiased sample of weakly decaying b-hadrons produced at high energy. These fractions are assumed to be the same in Z decays or in proton-antiproton collisions at sqrt(s)=1.8 TeV. They have been obtained by combining direct rate measurements from LEP and CDF with all available mixing measurements from ALEPH, CDF, DELPHI, L3, OPAL as well as from ARGUS, CLEO, BABAR and BELLE. The B+ and B0 mesons are assumed to be produced in equal amount, the Bc production is neglected and the sum of the fractions is constrained to unity.

b hadron species	fraction at high energy	correlation with f(Bs)	correlation with f(b-baryon)
Bs	f(Bs) = 0.107 +- 0.011
b baryons	f(b-baryon) = 0.099 +- 0.017	+0.003
B0 or B+	f(Bd) = f(Bu) = 0.397 +- 0.010	-0.540	-0.843

The B+ and B0 fractions below are for an unbiased sample of B-mesons produced in Upsilon(4S) decays. They have been obtained by combining measurements from BABAR, BELLE and CLEO, assuming that the a B+/B0 lifetime ratio of 1.086 +- 0.017 (the current average given below). The sum of these two fractions is constrained to unity.

b hadron species	fraction in Upsilon(4S) decay	ratio
B+ B-	f+- = 0.511 +- 0.012	f+-/f00 = 1.044 +- 0.050
B0 anti-B0	f00 = 0.489 +- 0.012

The lifetimes below have been obtained by combining time-dependent measurements from ALEPH, BABAR, BELLE, CDF, DELPHI, L3, OPAL and SLD. Decay width differences in the B0 and Bs systems have been ignored. The mixtures refer to samples of weakly decaying b-hadrons produced at high energy.

b hadron species	average lifetime	average lifetime relative to B0 average lifetime
B0	1.536 +- 0.014 ps
B+	1.671 +- 0.018 ps	1.086 +- 0.017
Bs	1.461 +- 0.057 ps	0.951 +- 0.038
Bc	0.46 +0.18 -0.16 ps
Lambda_b	1.229 +0.080 -0.080 ps
Xi_b-, Xi_b0 mixture	1.39 +0.34 -0.28 ps
b-baryon mixture	1.208 +- 0.051 ps	0.786 +- 0.034
b-hadron mixture	1.564 +- 0.014 ps

Combined result on B0 mixing, obtained separately from time-dependent measurements of the oscillation frequency dmd (at high energy colliders and asymmetric B factories) and from time-integrated measurements of the mixing probability chid at symmetric Upsilon(4S) machines:

dmd = 0.502 +- 0.007 ps-1	from time-dependent measurements at ALEPH, BABAR, BELLE, CDF, DELPHI, L3, OPAL
chid = 0.182 +- 0.015	from time-integrated measurements at ARGUS and CLEO

Assuming no CP violation in the mixing and no width difference in the B0 system, and assuming a B0 lifetime of 1.536 +- 0.014 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

dmd = 0.502 +- 0.007 ps-1
xd = 0.771 +- 0.012
chid = 0.186 +- 0.004

from all ALEPH, BABAR, BELLE, CDF, DELPHI, L3, OPAL, ARGUS and CLEO measurements

Combined results on Bs oscillations:

dms > 14.4 ps-1 at 95% CL
xs > 20.6 at 95% CL
chis > 0.49883 at 95% CL

from all ALEPH, CDF, DELPHI, OPAL and SLD studies of dms with a combined 95% CL sensitivity on dms of 17.8 ps-1

The above limit on xs is derived from the results of the dms studies assuming a Bs lifetime of 1.461 +- 0.057 ps (the experimental average listed above). The above limit on chis is derived from the limit on xs assuming no CP violation in the mixing and no width difference in the Bs system.

Combined results on the relative decay width differences DGd/Gd and DGs/Gs in the B0 and Bs systems respectively, obtained from time-dependent measurements:

no combined value of DGd/Gd available yet	published results from DELPHI and CLEO (BABAR preprint submitted, not accepted yet)
DGs/Gs = 0.16 +0.15 -0.16 DGs/Gs < 0.54 at 95% CL	from ALEPH, CDF, DELPHI, L3 and OPAL measurements
DGs/Gs = 0.07 +0.09 -0.07 DGs/Gs < 0.29 at 95% CL	same as above but constraining the mean Bs decay width to be equal to 1/tau(B0) where tau(B0) = 1.536 +- 0.014 ps

In the above, Gs and DGs are defined as Gs = (Gamma_short + Gamma_long)/2, DGs = Gamma_short - Gamma_long > 0, and the CP-even eigenstate is assumed to have the largest decay width (Gamma_short), i.e. the smallest lifetime.

Note on the combination procedures

Many B oscillations results depend on the knowledge of certain physics inputs like the lifetimes and production fractions of the various b hadron species. Various analyses have assumed different values for these physics inputs. The combined results quoted on this page have been obtained assuming a common set of physics inputs. To do this, each individual measurement has been adjusted to the common set of physics inputs before averaging. These adjustments have been performed if (and only if) a systematic uncertainty associated to a given physics parameters has been quoted by the experiment. The adjustment procedure affects both the central value of the measurement (by an amount proportionnal to the quoted systematic uncertainty) and the relevant systematic uncertainty. The common set of physics inputs consists mainly of the b hadron fractions and lifetimes given above.

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Plot of dmd measurements and their averages

All individual measurements are listed as quoted by the experiments; they might assume different physics inputs. The averages (which take into account all known correlations) are quoted after adjusting all the individual measurements to the common set of physics inputs. The chid average from ARGUS and CLEO is converted to a dmd measurement assuming no CP violation, no width difference in the B0 system and a B0 lifetime of 1.536 +- 0.014 ps.

colour ps / colour eps / black-and-white ps / black-and-white eps /

Same without average including time-integrated (chid) measurements:
colour ps / colour eps / black-and-white ps / black-and-white eps /

Only measurements and average at high energy colliders:
colour ps / colour eps / black-and-white ps / black-and-white eps /

Only measurements and average at LEP:
colour ps / colour eps / black-and-white ps / black-and-white eps /

Only measurements and average at asymmetric B factories:
colour ps / colour eps / black-and-white ps / black-and-white eps /

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Plot of dmd averages per experiment

All individual experiment averages are listed as quoted by the experiments (or computed by the working group without performing any adjustments); they might assume different physics inputs. The global averages are quoted after adjusting all the individual measurements to the common set of physics inputs. The chid average from ARGUS and CLEO is converted to a dmd measurement assuming no CP violation, no width difference in the B0 system and a B0 lifetime of 1.536 +- 0.014 ps.

colour ps / colour eps / black-and-white ps / black-and-white eps /

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Plot of combined Bs oscillation amplitude vs dms

The combined Bs amplitude is displayed as function of dms. All measurements have been adjusted to the common set of inputs before averaging. Systematic correlations are taken into account. An amplitude consistent with 1 is expected at the true value of dms. An amplitude consistent with 0 is expected far below the true value of dms. All values of dms for which the combined amplitude plus 1.645 times its total uncertainty is smaller than 1 (in this case all values of dms below 14.4 ps-1) are excluded at 95% CL. The combined sensitivity for 95% CL exclusion (equal to 17.8 ps-1 in this case) is defined as the value of dms at which the total uncertainty on the measured amplitude is equal to 1/1.645.

colour ps / colour eps / colour ps (up to 20 ps-1 only) / colour eps (up to 20 ps-1 only) / ASCII file with numerical data /

Same, but using only LEP data:
colour ps / colour eps / colour ps (up to 20 ps-1 only) / colour eps (up to 20 ps-1 only) / ASCII file with numerical data /

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Plot of Bs oscillation amplitude measurements and their average

All individual measurements of the Bs oscillation amplitude at a fixed value of dms are listed as quoted by the experiments (or obtained by a linear interpolation between other dms values at which the experiment did the measurements); they might assume different physics inputs. The sensitivity quoted for each experiment is obtained from the positive amplitude uncertainty, without performing adjustments. The average and combined sensitivity are obtained after adjusting all the individual measurements to the common set of physics inputs. The sensitivites are defined as the value of dms at which the positive uncertainty on the measured amplitude is equal to 1/1.645; they correspond to sensitivites for 95% CL exclusion limits.

colour ps / colour eps / black-and-white ps / black-and-white eps /

Same, but at dms=10 ps-1:
colour ps / colour eps / black-and-white ps / black-and-white eps /

Same, but at dms=19 ps-1:
colour ps / colour eps / black-and-white ps / black-and-white eps /

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Plot of CL contours in the plane DGs/Gs - 1/Gs

This shows the 68%, 95% and 99% CL 2D-contours of the negative log-likelihood in the plane DGs/Gs - 1/Gs, where DGs is the decay width difference and Gs is the mean decay width in the Bs system. Here DGs is defined as DGs = Gamma_short - Gamma_long > 0, and the CP-even eigenstate is assumed to have the largest decay width (Gamma_short), i.e. the smallest lifetime.

2D eps /

Probability density distribution for DGs/Gs:
1D colour eps / 1D black-and-white eps /

Same as above but constraining the mean Bs decay width to be equal to 1/tau(B0) where tau(B0) = 1.536 +- 0.014 ps:
2D eps / 1D colour eps / 1D black-and-white eps /

Author: OS 15-Nov-2003

Latest mod. 06-Dec-2003