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 subgroup
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 uptodate) description of the combination
procedures can be found in chapters 35 of
cernep2001050 (although the
numerical results in this preprint are as of summer 2000
and include preliminary results as well).
Uptodate lifetime averages are described in an
internal note.
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Summary of bhadron lifetimes, fractions and oscillation averages
The fractions below are for an unbiased sample of weakly decaying bhadrons produced at high energy.
These fractions are assumed to be the same in Z decays or in protonantiproton 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(bbaryon) 
Bs 
f(Bs) =
0.107
+
0.011

b baryons 
f(bbaryon) =
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 Bmesons 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 antiB0 
f00 =
0.489
+
0.012

The lifetimes below
have been obtained by combining timedependent 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 bhadrons
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

bbaryon mixture 
1.208
+
0.051
ps

0.786
+
0.034

bhadron mixture 
1.564
+
0.014
ps

Combined result on B0 mixing, obtained separately from timedependent measurements of the
oscillation frequency dmd (at high energy colliders and asymmetric B factories) and from timeintegrated measurements of the
mixing probability chid at symmetric Upsilon(4S) machines:
dmd =
0.502
+
0.007
ps1

from timedependent measurements at ALEPH, BABAR, BELLE, CDF, DELPHI, L3, OPAL 
chid =
0.182
+
0.015

from timeintegrated 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
ps1
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
ps1 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
ps1

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 timedependent 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 CPeven 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 /
blackandwhite ps /
blackandwhite eps /
Same without average including timeintegrated (chid) measurements:
colour ps /
colour eps /
blackandwhite ps /
blackandwhite eps /
Only measurements and average at high energy colliders:
colour ps /
colour eps /
blackandwhite ps /
blackandwhite eps /
Only measurements and average at LEP:
colour ps /
colour eps /
blackandwhite ps /
blackandwhite eps /
Only measurements and average at asymmetric B factories:
colour ps /
colour eps /
blackandwhite ps /
blackandwhite 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 /
blackandwhite ps /
blackandwhite 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
ps1)
are excluded at 95% CL.
The combined sensitivity for 95% CL exclusion
(equal to
17.8
ps1 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 ps1 only) /
colour eps (up to 20 ps1 only) /
ASCII file with numerical data /
Same, but using only LEP data:
colour ps /
colour eps /
colour ps (up to 20 ps1 only) /
colour eps (up to 20 ps1 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 /
blackandwhite ps /
blackandwhite eps /
Same, but at dms=10 ps1:
colour ps /
colour eps /
blackandwhite ps /
blackandwhite eps /
Same, but at dms=19 ps1:
colour ps /
colour eps /
blackandwhite ps /
blackandwhite eps /
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Plot of CL contours in the plane DGs/Gs  1/Gs
This shows the 68%, 95% and 99% CL 2Dcontours of the negative loglikelihood
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 CPeven 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 blackandwhite 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 blackandwhite eps /
Author: OS 15Nov2003
Latest mod. 06Dec2003