Results for the PDG 2002 review


Only results published (or accepted in a refereed journal) before 5 April 2002 have been included in the averages computed by the B oscillations working group for the 2002 edition of the 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 chapter 4 of cern-ep-2001-050 (although the numerical results in this preprint are as of summer 2000 and include preliminary results as well).

Combined results on the b hadron lifetimes are available elsewhere (decay width difference in the Bs system, all other lifetime results).

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Summary of b-hadron 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 correlation with f(Bs) correlation with f(b-baryon)
Bs f(Bs) = 0.106 +- 0.013
b baryons f(b-baryon) = 0.118 +- 0.020 +0.206
B0 or B+ f(Bd) = f(Bu) = 0.388 +- 0.013 -0.652 -0.876


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 = 0.489 +- 0.009 ps-1 from time-dependent measurements at ALEPH, CDF, DELPHI, L3, OPAL, BABAR, BELLE
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 1.542 +- 0.016 ps (an experimental average obtained by the B lifetimes working group), all above measurements can be combined to yield the following world averages:

dmd = 0.489 +- 0.008 ps-1 from all ALEPH, CDF, DELPHI, L3, OPAL, BABAR, BELLE, ARGUS and CLEO measurements
chid = 0.181 +- 0.004 from all ALEPH, CDF, DELPHI, L3, OPAL, BABAR, BELLE, ARGUS and CLEO measurements


Combined results on Bs oscillations:

dms > 13.1 ps-1 at 95% CL from all ALEPH, CDF, DELPHI and OPAL studies with a combined 95% CL sensitivity of 13.3 ps-1


Assuming a Bs lifetime of 1.461 +- 0.057 ps (an average obtained by the B lifetime working group), the above limit corresponds to xs > 19.0 at 95% CL. Assuming no CP violation in the mixing and no width difference in the Bs system, this also corresponds to chis > 0.49862 at 95% CL.


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 systemtic uncertainty) and the relevant systematic uncertainty.

The common set of physics inputs consists mainly of:


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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 1.542 +- 0.016 ps.


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Same without average including time-integrated (chid) measurements:
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Only measurements and average at high energy colliders:
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Only measurements and average at LEP:
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Only measurements and average at asymmetric B factories:
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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 1.542 +- 0.016 ps.


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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 13.1 ps-1) are excluded at 95% CL. The combined sensitivity for 95% CL exclusion (equal to 13.3 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.


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Same, but using only LEP 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.


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Author: OS 05-Apr-2002
Latest mod. 30-Apr-2002