Results for the PDG 2008
Only results published (or accepted in a refereed journal)
by March 31, 2008
have been included in the averages computed by the
lifetime and oscillations subgroup
of the Heavy Flavour Average Group (HFAG)
for the 2008 update of the Particle Data Group review.
The following material is available publicly:
The combination procedures are described in
chapter 3 of the following HFAG writeup:
arXiv:0704.3575v1 [hepex]
(this writeup describes the "end 2006" averages, which also include
preliminary results, and are not identical to the ones presented here).
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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 
1.470
+0.026
0.027
ps

0.961
+
0.018

Bc 
0.463
+
0.071
ps

Lambda_b 
1.383
+0.049
0.048
ps

0.904
+
0.032

Xi_b, Xi_b0 mixture 
1.42
+0.28
0.24
ps

bbaryon mixture 
1.319
+0.039
0.038
ps

0.862
+
0.026

bhadron mixture 
1.568
+
0.009
ps

The above B0 lifetime average is obtained assuming there is no decay width difference in the B0 system.
The above Bs lifetime is defined as 1/Gamma_s, where Gamma_s = (Gamma_Light + Gamma_Heavy)/2 is the mean
mean decay width of the Bs system.
The Lambda_b lifetime average has increased significantltly since PDG 2006,
due to a new CDF measurement
which was 3.2 sigma above the previous average;
no scale factor was applied on the new combined error,
although the Lambda_b lifetime measurements are slightly discrepant
(see plot).
The Xi_b, bbaryon and bhadron mixtures are illdefined, i.e. the
proportion of the different species is these mixtures is not perfectly known.
The table below gives other Bs lifetime averages, consisting of different
mixtures of the two Bs mass eigenstates. The "Bs > flavour specific" lifetime is measured mainly
with Bs > Ds lepton X decays; it is used as input to extract the long and short lifetimes of
the Bs system (see next section). The "Bs > Ds X" lifetime is illdefined becauses it includes an
unknown proportion of short and long components.
mixture of the two Bs mass eigenstates 
average lifetime 
Bs > flavour specific 
1.417
+
0.042
ps

Bs > Ds X 
1.425
+
0.041
ps

Bs > J/psi phi 
1.429
+
0.088
ps

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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 (CDF, D0, ALEPH and DELPHI data).
This combination is performed under the assumption of no CP violation in Bs mixing.
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 CDF, D0, ALEPH and DELPHI data 
without constraint from tau(Bs > flavour specific) 
with constraint from tau(Bs > flavour specific) 
1/&Gamma_{s} 
1.514
+0.034
0.037
ps

1.470
+0.026
0.027
ps

tau(short) = 1/&Gamma_{L} 
1.420
+0.040
0.040
ps

1.419
+0.039
0.038
ps

tau(long) = 1/&Gamma_{H} 
1.622
+0.097
+0.090
ps

1.525
+0.062
0.063
ps

&Delta&Gamma_{s} (95% CL range) 
[
0.009
;
+0.179
] ps1

[
0.038
;
+0.125
] ps1

&Delta&Gamma_{s} 
+0.088
+0.047
0.048
ps1

0.049
+0.040
0.043
ps1

&rho(&Delta&Gamma_{s},1/&Gamma_{s}) 
+0.56

+0.37

&Delta&Gamma_{s}/&Gamma_{s} (95% CL range) 
[
0.011
;
+0.278
]

[
0.052
;
+0.180
]

&Delta&Gamma_{s}/&Gamma_{s} 
+0.133
+0.074
0.074

+0.069
+0.058
0.062

&rho(&Delta&Gamma_{s}/&Gamma_{s},1/&Gamma_{s}) 
+0.57

+0.38

The left plot below shows
contours of Delta(log(L)) = 0.5
(39% CL for the enclosed 2dim regions, 68% CL for the bands)
in the plane (1/&Gamma_{s}, &Delta&Gamma_{s}) for
the average of all direct measurements (red),
the constraint given by the Bs lifetime using flavourspecific
final states (blue),
and their combination (black).
The yellow band is a recent theory prediction &Delta&Gamma_{s} = 0.088 +0.017 ps1
which assumes no new physics in Bs mixing
[A. Lenz and U. Nierste, JHEP 06 (2007) 072].
The right plot below shows the same contours in the plane
(1/&Gamma_{L}, 1/&Gamma_{H}).
In both cases, the blue band represents the average
1.417
+
0.044
ps which includes all lifetime measurements with flavourspecific Bs decays,
except those which are not independent of the direct measurements used in the
&Delta&Gamma_{s} averaging.
Above plots: (1/&Gamma_{s}, &Delta&Gamma_{s}) gif /
(1/&Gamma_{L}, 1/&Gamma_{H}) gif /
(1/&Gamma_{s}, &Delta&Gamma_{s}) eps /
(1/&Gamma_{L}, 1/&Gamma_{H}) eps /
Another (1/&Gamma_{s}, &Delta&Gamma_{s}) plot
showing only the direct measurements and their average:
gif / 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, D0,
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} =
0.1878
+
0.0024

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
1.530
+
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), Phys. Rev. D 73, 012004 (2006)
 K. Abe et al (Belle), 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
In 2006, CDF has obtained the first direct evidence for
and then the first observation of Bs oscillations. The measured
value of dms is (A. Abulencia et al., Phys. Rev. Lett. 97, 242003 (2006)):
dms =
17.77
+
0.10
(stat) +
0.07
(syst) ps1

CDF (Run II)

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Neutral B meson mixing: CP violation
Several different parameters can be used to describe 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
epsB = (pq)/(p+q)
q/p = (1epsB)/(1+epsB)
A_SL ~ 4 Re(epsB)/(1+epsB**2)
The parameters q/p, A_SL and Re(epsB)/(1+epsB**2) are thuis equivalent.
There is CP violation in the mixing
if q/p is different from 1, i.e. A_SL is different from 0.
Averages are given below separately for the Bd and the Bs systems.
Two sets of averages are given for the Bd system in the first table:
a first set using only measurements performed at Upsilon(4S) machines,
and a second set using all measurements
(including those performed at high energy, but under the assumption of
no CP violation in Bs mixing). The second table presents an average for the
Bs system, based on measurements performed at the Tevatron, where some analyses
measure a mixture of the Bd and Bs parameters: the effect from the Bs is
then isolated by using the value and error of the Bd parameter
obtained at the B factories.
CP violation parameter in Bd mixing 
q/p =
1.0002
+
0.0028
A_SL =
0.0005
+
0.0056
Re(epsB)/(1+epsB**2) =
0.0001
+
0.0014

from measurements at CLEO, BABAR and BELLE 
q/p =
1.0025
+
0.0019
A_SL =
0.0049
+
0.0038
Re(epsB)/(1+epsB**2) =
0.0012
+
0.0010

same but adding measurements from ALEPH, OPAL and D0 (and assuming A_SL(Bs) = 0) 
CP violation parameter in Bs mixing 
q/p =
1.0015
+
0.0051
A_SL =
0.0030
+
0.0101

from measurements at CDF and D0
(and assuming
A_SL(Bd) =
0.0005
+
0.0056
)

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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 =
1.068
+
0.029
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 =
1.068
+
0.029

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+ =
0.516
+
0.006

f+/f00 =
1.065
+
0.026

B0 antiB0 
f00 =
0.484
+
0.006

Note that the ratio f+/f00 differs from unity by
2.5
sigmas.
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bhadron fractions in Upsilon(5S) decays
The table and plot below show the fraction fs(*)(*) of Bs(*) antiBs(*) events over all events with a pair of
bflavored mesons produced in e+e collisions at a centreofmass energy equal to the Upsilon(5S) mass.
Since all Bs* mesons decay to a Bs meson (by photon emission), this fraction is equal to the probability
fs(Ups(5S)) that a weakly decaying bhadron produced in such collisions be a Bs meson.
The average for this fraction has been obtained by combining modeldependent estimates of CLEO3 and Belle based
on the measurements of several inclusive Upsilon(5S) branching fractions, after performing adjustements
to common external inputs. Most of this Bs production proceeds
in the Bs* antiBs* channel, with the ratio of Bs* antiBs* events
over Bs(*) antiBs(*) events (from Belle only) indicated in the table.
b hadron species 
fraction in Upsilon(5S) decay 
ratio 
Bs(*) antiBs(*) 
fs(*)(*) = fs(Ups(5S)) =
0.193
+
0.029

Bs* antiBs* 
fs**
 fs**/fs(*)(*) = 0.94 +0.060.09

colour gif /
colour eps /
blackandwhite eps /
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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) =
0.104
+
0.009

b baryons 
f(bbaryon) =
0.091
+
0.015

+0.021

B0 or B+ 
f(Bd) = f(Bu) =
0.402
+
0.009

0.521

0.864

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 =
0.1284
+
0.0069
.
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) =
0.110
+
0.012

b baryons 
f(bbaryon) =
0.092
+
0.019

0.096

B0 or B+ 
f(Bd) = f(Bu) =
0.399
+
0.011

0.477

0.829

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

LEP average from LEP EW WG 
chibar =
0.147
+
0.011

Tevatron average 
chibar =
0.1284
+
0.0069

weighted average of above two,
with error rescaled by factor
1.8
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
1.8
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 23May2008
Latest mod.
Tue May 13 20:25:52 CEST 2008