Results for the PDG 2006 review of particle physics
Only results published (or accepted in a refereed journal)
before March 20, 2006
have been included in the averages computed by the
lifetime and oscillations subgroup
of the Heavy Flavour Average Group (HFAG)
for the 2006 Particle Data Group review.
The following material is available publicly:
The combination procedures are described in
Chapter 3 of the following HFAG writeup:
hepex/0603003
(this writeup describes the "end of 2005 averages", which also include
preliminary results).
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bhadron lifetime averages
The lifetimes displayed in the table below
have been obtained by combining timedependent measurements from
ALEPH, BABAR, BELLE, CDF, D0, 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 (mostly in Z decays).
b hadron species 
average lifetime 
average lifetime relative to B0 average lifetime 
B0 
1.530
+
0.009
ps

B+ 
1.638
+
0.011
ps

1.071
+
0.009

Bs 
1.466
+
0.059
ps

0.958
+
0.039

Bc 
0.46
+0.18
0.16
ps

Lambda_b 
1.230
+
0.074
ps

Xi_b, Xi_b0 mixture 
1.39
+0.34
0.28
ps

bbaryon mixture 
1.209
+
0.049
ps

0.790
+
0.032

bhadron mixture 
1.568
+
0.009
ps

The above Bs lifetime average includes all published measurements, except the ones performed
using J/psi phi final states. It is "illdefined" because it includes an unknown proportion of
long and short components. Other (welldefined) averages are provided below:
mixture of the two Bs mass eigenstates 
average lifetime 
Bs > flavour specific 
1.442
+
0.066
ps

Bs > J/psi phi 
1.429
+
0.088
ps

These results are used as input to extract the long and short lifetimes
of the Bs system (see next section).
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Neutral B meson mixing: decay width differences
For both the B0 and Bs systems, the
mean decay width and the decay width difference
are defined here as
&Delta&Gamma = &Gamma_{L}  &Gamma_{H} and
&Gamma = (&Gamma_{L} + &Gamma_{H})/2,
where &Gamma_{L} (&Gamma_{H})
is the decay width of the
light (heavy) mass eigenstate.
In the Standard Model, one expects &Delta&Gamma > 0,
i.e. the light (heavy) mass eigenstate is also the shortlived
(longlived) mass eigenstate.
In the absence of CP violation, the light (heavy) B0 or Bs mass eigenstate is
the CPeven (CPodd) eigenstate. This assumption is made
by several analyses included in the combined results given in this 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 CPeven 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 decaywidth 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 flavourspecific 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 flavourspecific 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
]

[
0.02
;
+0.60
]

&Delta&Gamma_{s}/&Gamma_{s} 
+0.35
+0.12
0.16

+0.31
+0.11
0.13

&Delta&Gamma_{s} 
+0.25
+0.09
0.11
ps1

+0.22
+
0.09
ps1

1/&Gamma_{s} 
1.42
+0.06
0.07
ps

1.398
+0.049
0.050
ps

tau(short) = 1/&Gamma_{L} 
1.21
+0.08
0.09
ps

1.21
+
0.09
ps

tau(long) = 1/&Gamma_{H} 
1.72
+
0.19
ps

1.66
+0.11
0.12
ps

The left plot below shows 1sigma contours in
in the plane (1/&Gamma_{s}, &Delta&Gamma_{s}/&Gamma_{s}) for
the average of all direct measurements (green),
the constraint given by the Bs lifetime using flavourspecific
final states (blue), and their combination (black).
The right plot below shows the 1sigma contour in the plane
(1/&Gamma_{L}, 1/&Gamma_{H}) without (dashed red) and with (plain red) the flavourspecific Bs lifetime constraint (blue).
In both cases, the blue band represents the average
1.450
+
0.075
ps which includes all lifetime measurements with fralvour specific Bs decay,
except those which are not independent of the direct measurements used in the
&Delta&Gamma_{s} averaging.
(1/&Gamma_{s}, &Delta&Gamma_{s}/&Gamma_{s})gif /
(1/&Gamma_{L}, 1/&Gamma_{H})gif /
(1/&Gamma_{s}, &Delta&Gamma_{s}/&Gamma_{s})eps /
(1/&Gamma_{L}, 1/&Gamma_{H})eps /
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B0 mixing: oscillations and mass difference
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 &chi_{d} at symmetric Upsilon(4S) machines:
dmd =
0.507
+
0.005
ps1

from timedependent measurements at
ALEPH, DELPHI, L3, OPAL,
CDF,
BABAR, BELLE

&chi_{d} =
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
1.530
+
0.009
ps (the experimental average listed above),
all above measurements
can be combined to yield the following world averages:
dmd =
0.507
+
0.005
ps1
xd =
0.776
+
0.008
&chi_{d} =
0.188
+
0.003

from all
ALEPH, DELPHI, L3, OPAL,
CDF,
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
1.530
+
0.009
ps.
colour gif /
colour eps /
blackandwhite eps /
Same without average including timeintegrated (&chi_{d}) measurements:
colour eps /
blackandwhite eps /
Only measurements and average at LEP and CDF1:
colour eps /
blackandwhite eps /
Only measurements and average at LEP:
colour eps /
blackandwhite eps /
Only measurements and average at asymmetric B factories:
colour eps /
blackandwhite 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
1.530
+
0.009
ps.
colour gif /
colour eps /
blackandwhite eps /
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2D average of dmd and tau(B0)
BABAR and Belle have performed simultaneous measurements of dmd and tau(B0).
 B. Aubert et al (BABAR), Phys. Rev. D 67, 072002 (2003)
 B. Aubert et al (BABAR), hepex/0507054, to appear in Phys. Rev. D
 K. Abe et al (Belle), hepex/0408111, Phys. Rev. D 71, 072003 (2005)
The Belle analysis is actually a simultaneous measurement of dmd, tau(B0) and tau(B+), and
has been converted, for the purpose of averaging with the BABAR results, into a 2D measurement
of dmd and tau(B0). The plot below displays these measurements (after adjustments to a
common B+ lifetime of
1.638
+
0.011
ps)
together with their 2D average. The result of this 2D combination is
dmd =
0.509
+
0.006
ps1 and tau(B0) =
1.527
+
0.010
ps, with a total (stat+syst) correlation coefficient of
0.23
(note that this result on dmd is already included in the dmd world average
quoted above).
colour gif /
colour eps /
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B0s mixing: oscillations and mass difference
Combined results on Bs oscillations:
dms >
14.4
ps1 at 95% CL
xs >
19.9
at 95% CL
&chi_{s} >
0.49878
at 95% CL

from all ALEPH, CDF, DELPHI, OPAL and SLD studies
of dms with a combined 95% CL sensitivity on dms of
18.2
ps1

The limit on xs is derived from the results of the dms studies
assuming 1/&Gamma_{s} =
1.398
+0.049
0.050
ps (the current experimental average).
The limit on &chi_{s} is derived from the limit on xs
assuming no CP violation in the mixing and
&Delta&Gamma_{s}/&Gamma_{s} =
+0.31
+0.11
0.13
(the current experimental average).
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
ps1)
are excluded at 95% CL.
The combined sensitivity for 95% CL exclusion
(equal to
18.2
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 gif /
colour eps /
ASCII file with numerical data /
Same, but using also unpublished results:
colour gif /
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 gif /
colour eps /
blackandwhite eps /
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B0 mixing: CP violation
Several different parameters can be used to descibe CP violation in B mixing:
q/p, the socalled dilepton asymetry A_SL,
and the real part of epsilon_B (noted here epsB). The
relations between these parameters are as follows
(all are exact except the last one which is an approximation valid for
small CP violation):
A_SL = (p/q**2  q/p**2 ) / (p/q**2 + q/p**2 )
= ( 1  q/p**4 ) / ( 1 + q/p**4 )
q/p = ( (1A_SL)/(1+A_SL) )**0.25
epsilon_B = (pq)/(p+q)
q/p = (1epsilon_B)/(1+epsilon_B)
A_SL ~ 4 Re(epsB)/(1+epsB**2)
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 B0B0bar system are all equivalent.
q/p =
1.0026
+
0.0059
A_SL =
0.0053
+
0.0117
Re(epsB)/(1+epsB**2) =
0.0013
+
0.0029

from measurements at LEP, CLEO and BABAR 
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bhadron fractions in Upsilon(4S) decays
The B+ and B0 fractions below are for an unbiased sample of Bmesons
produced in Upsilon(4S) decays.
Most analyses measure the ratio f+/f00 assuming
isospin invariance in charged and neutral B decays,
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 =
1.029
+
0.035
after adjusting to a common B+/B0 lifetime ratio of
1.071
+
0.009
(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 =
1.029
+
0.035

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+ =
0.509
+
0.007

f+/f00 =
1.037
+
0.029

B0 antiB0 
f00 =
0.491
+
0.007

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bhadron fractions in Z decays
The table below shows the bhadron fractions in
an unbiased sample of weakly decaying bhadrons produced in Z decays.
These fractions have been calculated by combining direct rate measurements
performed at LEP with
the LEP combined measurement the timeintegrated mixing probability
averaged over an unbiased sample of semileptonic bhadron decays, chibar =
0.1259
+
0.0042
.
This combination relies on the world average of &chi_{d},
on the assumption &chi_{s} = 1/2,
as well as on the world averages of
the lifetimes of the individual bhadrons species.
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 in Z decays 
correlation with f(Bs) 
correlation with f(bbaryon) 
Bs 
f(Bs) =
0.102
+
0.009

b baryons 
f(bbaryon) =
0.100
+
0.017

+0.027

B0 or B+ 
f(Bd) = f(Bu) =
0.399
+
0.010

0.511

0.873

This is based on the following average of chibar in Z decays:
chibar(LEP) =
0.1259
+
0.0042

LEP average from LEP EW WG 
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bhadron fractions at high energy
The table below shows the bhadron fractions in
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 calculated by combining direct rate measurements
performed at LEP and CDF with
the world average of the timeintegrated mixing probability
averaged over an unbiased sample of semileptonic bhadron decays, chibar =
0.1283
+
0.0076
.
This combination relies on the world average of &chi_{d},
on the assumption &chi_{s} = 1/2,
as well as on the world averages of
the lifetimes of the individual bhadrons species.
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) =
0.103
+
0.014

b baryons 
f(bbaryon) =
0.100
+
0.020

0.104

B0 or B+ 
f(Bd) = f(Bu) =
0.398
+
0.012

0.489

0.816

This is based on the following average of chibar at high energy:
chibar =
0.1259
+
0.0042

LEP average from LEP EW WG 
chibar =
0.152
+
0.013

CDF measurement 
chibar =
0.1283
+
0.0076

weighted average of above two,
with error rescaled by factor
1.9
according to PDG prescription 
Note:
 The above fractions at high energy are less precise than the fractions
in Z decays, although they are obtained using more measurements.
This is because
the data from LEP and CDF are not entirely consistent with each other,
and we apply the PDG prescription by rescaling errors based on a chi2.
Two such scaling factors need to be applied independently in
our procedure: a scaling factor of
1.9
when computing the world average of chibar and another
scaling factor of
1.2
when combining the direct rate measurements at LEP and CDF.
 This may be an indication that the fractions in high energy hadronic
collisions may not be identical to those in Z decays.
 We hope that, in the future, we can produce a set of fractions
obtained only from measurements at the Tevatron.
 For the time being, we recommend that our fractions at high energy
(rather than our fractions
in Z decays) be used by anyone who needs these fractions in the context
of high energy hadronic collisions (Tevatron or LHC).
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Notes 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 includes
the b hadron fractions and lifetimes given above.
Author: OS 27Avr2006
Latest mod.
Mon May 1 01:20:19 CEST 2006