All results available publicly (published and preliminary)
at the time of the Summer 2005 conferences
have been included in the averages computed by the
lifetime and oscillations sub-group
of the Heavy Flavour Average Group (HFAG),
except lifetime results. .
The following material is available publicly:
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b hadron species | average lifetime | average lifetime relative to B0 average lifetime |
B0 | 1.528 +- 0.009 ps | |
B+ | 1.643 +- 0.010 ps | 1.076 +- 0.008 |
Bs | 1.479 +- 0.044 ps | 0.968 +- 0.029 |
Bc | 0.45 +- 0.12 ps | |
Lambda_b | 1.232 +- 0.072 ps | |
Xi_b-, Xi_b0 mixture | 1.39 +0.34 -0.28 ps | |
b-baryon mixture | 1.210 +- 0.048 ps | 0.792 +- 0.032 |
b-hadron mixture | 1.568 +- 0.009 ps |
mixture of the two Bs mass eigenstates | average lifetime |
Bs -> flavour specific | 1.472 +- 0.045 ps |
Bs -> J/psi phi | 1.404 +- 0.066 ps |
These results are used as input to extract the long and short lifetimes
of the Bs system (see next section).
Combined result on the relative decay width difference in the B0 system:
-s*&Delta&Gamma_{d}/&Gamma_{d} = -0.009 +- 0.037 | from BABAR and DELPHI |
The quantity s = sign(Re(&lambda_{CP})), where &lambda_{CP} = (q/p)*Abar_{CP}/A_{CP} refers to a CP-even final state (e.g. J/psi K_long), is predicted to be equal to s= +1 to a high degree of confidence from the Standard Model fits to all available contraints on the unitarity triangle.
Combined results on the decay-width difference in the Bs system are extracted from a global fit including all direct measurements of &Delta&Gamma_{s}/&Gamma_{s}, as well as the lifetime measurements using Bs -> J/psi phi decays and flavour-specific Bs decays (ALEPH, CDF and DELPHI data). The results in the table below are shown both with and without constraining the quantity (1/&Gamma_{s}) * (1 + (&Delta&Gamma_{s}/&Gamma_{s})^{2}/4) / (1 - (&Delta&Gamma_{s}/&Gamma_{s})^{2}/4) to the flavour-specific Bs lifetime average:
Fit results from ALEPH, CDF and DELPHI data |
without constraint from tau(Bs -> flavour specific) |
with constraint from tau(Bs -> flavour specific) |
&Delta&Gamma_{s}/&Gamma_{s} (95% CL range) | [ +0.01 ; +0.59 ] | [ +0.01 ; +0.59 ] |
&Delta&Gamma_{s}/&Gamma_{s} | +0.35 +0.12 -0.16 | +0.33 +0.09 -0.11 |
&Delta&Gamma_{s} | +0.25 +0.09 -0.11 ps-1 | +0.23 +- 0.08 ps-1 |
1/&Gamma_{s} | 1.42 +0.06 -0.07 ps | 1.405 +0.043 -0.047 ps |
tau(short) = 1/&Gamma_{L} | 1.21 +0.08 -0.09 ps | 1.21 +- 0.08 ps |
tau(long) = 1/&Gamma_{H} | 1.72 +- 0.19 ps | 1.68 +0.08 -0.09 ps |
(1/&Gamma_{s}, &Delta&Gamma_{s}/&Gamma_{s})eps /
(1/&Gamma_{L}, 1/&Gamma_{H})eps /
dmd = 0.507 +- 0.005 ps-1 | from time-dependent measurements at ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE |
&chi_{d} = 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 1.528 +- 0.009 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:
dmd =
0.506
+-
0.005
ps-1
xd = 0.774 +- 0.008 &chi_{d} = 0.187 +- 0.002 |
from all ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, ARGUS and CLEO measurements |
In the plot below, 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 &chi_{d} 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 1.528 +- 0.009 ps.
colour eps /
black-and-white eps /
Same without average including time-integrated (&chi_{d}) measurements:
colour eps /
black-and-white eps /
Only measurements and average at LEP and CDF1:
colour eps /
black-and-white eps /
Only measurements and average at LEP:
colour eps /
black-and-white eps /
Only measurements and average at asymmetric B factories:
colour eps /
black-and-white eps /
In the plot below,
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 &chi_{d} 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
1.528
+-
0.009
ps.
colour eps /
black-and-white eps /
dms >
14.4
ps-1 at 95% CL
xs > 19.9 at 95% CL &chi_{s} > 0.49878 at 95% CL |
from all ALEPH, CDF, D0, DELPHI, OPAL and SLD studies of dms with a combined 95% CL sensitivity on dms of 18.9 ps-1 |
In the plot below, 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 18.9 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 eps /
ASCII file with numerical data /
Same, but using an additional unpublished result from SLD:
colour eps /
ASCII file with numerical data /
Same, but using only LEP data:
colour eps /
ASCII file with numerical data /
In the plot below,
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 sensitivities 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 sensitivities for 95% CL exclusion limits.
colour eps /
black-and-white eps /
Same, but at dms=10 ps-1:
colour eps /
black-and-white eps /
Same, but at dms=19 ps-1:
colour eps /
black-and-white eps /
&chi_{d} = 0.182 +- 0.015 | from time-integrated measurements at ARGUS and CLEO |
&chi_{d} = 0.187 +- 0.002 | average including time-dependent measurements of dmd and based on different assumptions, as explained above |
Time-integrated mixing probability for a mixtures of b-hadrons at high-energy decaying semi-leptonically:
chibar = 0.1257 +- 0.0042 | LEP average from LEP EW WG |
chibar = 0.152 +- 0.013 | CDF measurement |
chibar = 0.1281 +- 0.0076 | weighted average of above two, with error rescaled by factor 1.9 according to PDG prescription |
There is CP violation in the mixing if |q/p| is different from 1, i.e. A_SL is different from 0. The averages given below for the B0-B0bar system are all equivalent.
|q/p| =
1.0015
+-
0.0039
A_SL = -0.0030 +- 0.0078 Re(epsB)/(1+|epsB|**2) = -0.0007 +- 0.0020 |
from measurements at LEP, CLEO, BABAR and BELLE |
b hadron species | fraction at high energy | correlation with f(Bs) | correlation with f(b-baryon) |
Bs | f(Bs) = 0.103 +- 0.014 | ||
b baryons | f(b-baryon) = 0.100 +- 0.017 | -0.163 | |
B0 or B+ | f(Bd) = f(Bu) = 0.399 +- 0.010 | -0.563 | -0.724 |
Note: more precise fractions could be obtained by ignoring the Tevatron
data and using only LEP measurements (because one would use a more
precise chibar value, from LEP only). In the future, we will try to
provide two additional sets of fraction averages: one obtained from LEP
data only, and one obtained from Tevatron data only.
The B+ and B0 fractions below are for an unbiased sample of B-mesons
produced in Upsilon(4S) decays.
Most analyses measure the ratio f+-/f00 assuming
isospin invariance in charged and neutral B decays,r
and relying on our knowledge
of the B+/B0 lifetime ratio.
Combining all these analyses from BABAR, BELLE and CLEO
leads to the average
f+-/f00 =
1.021
+-
0.034
after adjusting to a common B+/B0 lifetime ratio of
1.076
+-
0.008
(the current average given above).
On the other hand, BABAR measured directly f00 =
0.487
+-
0.013
without assuming
isospin invariance nor relying on the B+/B0 lifetime ratio.
f+-/f00 = 1.021 +- 0.034 | from ratios of reconstructed B+ and B0 mesons
at BABAR, BELLE and CLEO
(assumptions made, see text above) |
f00 = 0.487 +- 0.013 | from absolute measurement of
B0 mesons at BABAR
(no assumptions) |
Assuming f+- + f00 = 1, the above two independent results
(which are consistent with each other)
can be combined to yield:
b hadron species | fraction in Upsilon(4S) decay | ratio |
B+ B- | f+- = 0.508 +- 0.007 | f+-/f00 = 1.030 +- 0.029 |
B0 anti-B0 | f00 = 0.492 +- 0.007 |