Results for the PDG 2010 review
Only results published (or accepted in a refereed journal)
by March 15, 2010
have been included in the averages computed by the
lifetime and oscillations subgroup
of the Heavy Flavour Averaging Group (HFAG)
for the 2010 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:0808.1297v3 [hepex]
(this writeup describes the "end 2007" averages, which also include
preliminary results as well as some results released in the first half of
2008; these averages do not include results published after that; hence they
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 B^{0} and B_{s} 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 B^{0} average lifetime 
B^{0} 
1.525
±
0.009
ps

B^{+} 
1.638
±
0.011
ps

1.071
±
0.009

B_{s} 
1.472
+0.024
−0.026
ps

0.965
±
0.017

B_{c} 
0.453
±
0.041
ps

Λ_{b} 
1.391
+0.038
−0.037
ps

0.912
±
0.025

Ξ_{b}^{−} 
1.56
+0.27
−0.25
ps

Ω_{b}^{−} 
1.13
+0.53
−0.40
ps

Ξ_{b}^{−}, Ξ_{b}^{0} mixture 
1.49
+0.19
−0.18
ps

bbaryon mixture 
1.345
±
0.032
ps

0.882
±
0.022

bhadron mixture 
1.568
±
0.009
ps

The above B^{0} lifetime average is obtained assuming there is no decay width difference in the B^{0} system.
The above B_{s} lifetime is defined as 1/Γ_{s},
where Γ_{s} = (Γ_{Light} + Γ_{Heavy})/2 is the mean
mean decay width of the B_{s} system.
The Λ_{b} lifetime average include a measurement which is
2.8
sigma away from the average recomputed without this measurement;
no scale factor was applied on the new combined error,
although the Λ_{b} lifetime measurements are slightly discrepant
(see plot).
The Ξ_{b}, bbaryon and bhadron mixtures are ill defined, i.e. the
proportion of the different species is these mixtures is not perfectly known.
The table below gives other B_{s} lifetime averages, consisting of different
mixtures of the two B_{s} mass eigenstates. The "B_{s} → flavour specific" lifetime is measured mainly
with B_{s} → D_{s} lepton X decays; it is used as input to extract the long and short lifetimes of
the B_{s} system (see next section). The "B_{s} → D_{s} X" lifetime is illdefined becauses it includes an
unknown proportion of short and long components.
mixture of the two B_{s} mass eigenstates 
average lifetime 
B_{s} → flavour specific 
1.417
±
0.042
ps

B_{s} → D_{s} X 
1.425
±
0.041
ps

B_{s} → J/ψ φ 
1.429
±
0.088
ps

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Neutral B meson mixing: decay width differences
For both the B^{0} and B_{s} systems, the
mean decay width and the decay width difference
are defined here as
ΔΓ = Γ_{L}  Γ_{H} and
Γ = (Γ_{L} + Γ_{H})/2,
where Γ_{L} (Γ_{H})
is the decay width of the
light (heavy) mass eigenstate.
In the Standard Model, one expects ΔΓ > 0,
i.e. the light (heavy) mass eigenstate is also the shortlived
(longlived) mass eigenstate.
In the absence of CP violation, the light (heavy) B^{0} or B_{s} 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 B^{0} system:
s*ΔΓ_{d}/Γ_{d} =
0.010
±
0.037

from BABAR and DELPHI 
The quantity s = sign(Re(λ_{CP})), where
λ_{CP} = (q/p)*Abar_{CP}/A_{CP}
refers to a CPeven final state (e.g. J/ψK_{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 B_{s} system are extracted from
a global fit including all direct measurements of
ΔΓ_{s}/Γ_{s}, as well as
the lifetime measurements using B_{s} → J/ψ φ decays
and flavourspecific B_{s} decaysi, and the measurements of the
B_{s} → D_{s}^{(*)}D_{s}^{(*)}
branching fraction (CDF, D0, ALEPH and DELPHI data).
This extraction is done under the assumption of no CP violation
(see elsewhere for an extraction in presence of CP violation).
The results in the table below are shown both with and without
constraining
the quantity
(1/Γ_{s})
× (1 + (ΔΓ_{s}/Γ_{s})^{2}/4)
/ (1 − (ΔΓ_{s}/Γ_{s})^{2}/4)
to the flavourspecific B_{s} lifetime average, and the
quantity 1/(2Γ_{s}/ΔΓ_{s}+1) to BR((B_{s} → D_{s}^{(*)}D_{s}^{(*)}) =
0.044
±
0.015
. In the application of the latter constraint as a Gaussian penalty function,
the theoretical uncertainty is dealt with in two ways: the PDF of the
CPodd fraction of B_{s} → D_{s}^{(*)}D_{s}^{(*)} is taken to be a uniform
distribution ranging from 0 to 0.05 and convoluted in the Gaussian;
alternatively, the fractional uncertainty on the measured value
of the branching fraction is increased in quadrature by 30%,
and the more conservative result is taken.
The default set of results (recommended for the 2010 Review of Particle Physics)
is the one where only the constraint from τ(B_{s} → flavour specific)
is applied.
Fit results from CDF, D0, ALEPH and DELPHI data 
without constraint from τ(B_{s} → flavour specific) nor BR(B_{s} → D_{s}^{(*)}D_{s}^{(*)}) 
with constraint from τ(B_{s} → flavour specific) only 
with constraint from τ(B_{s} → flavour specific) and BR(B_{s} → D_{s}^{(*)}D_{s}^{(*)}) 
1/Γ_{s} 
1.515
+0.034
−0.034
ps

1.472
+0.024
−0.026
ps

1.472
±
0.024
ps

τ_{Short} = 1/Γ_{L} 
1.407
+0.035
−0.034
ps

1.408
+0.033
−0.030
ps

1.408
+0.028
−0.027
ps

τ_{Long} = 1/Γ_{H} 
1.642
+0.091
+0.083
ps

1.543
+0.058
+0.060
ps

1.544
±
0.041
ps

ΔΓ_{s} (95% CL range) 
[
+0.016
;
+0.192
] ps^{−1}

[
−0.013
;
+0.130
] ps^{−1}

[
+0.018
;
+0.102
] ps^{−1}

ΔΓ_{s} 
+0.102
+0.043
−0.043
ps^{−1}

+0.062
+0.034
−0.037
ps^{−1}

+0.063
±
0.022
ps^{−1}

ΔΓ_{s}/Γ_{s} (95% CL range) 
[
+0.024
;
+0.290
]

[
−0.020
;
+0.193
]

[
+0.027
;
+0.155
]

ΔΓ_{s}/Γ_{s} 
+0.154
+0.067
−0.065

+0.092
+0.051
−0.054

+0.092
+0.032
−0.033

The left plot below shows
contours of Δ(log(L)) = 0.5
(39% CL for the enclosed 2dim regions, 68% CL for the bands)
in the plane (1/Γ_{s}, ΔΓ_{s}) for
the average of all direct measurements (red),
the constraint given by the B_{s} lifetime using flavourspecific
final states (blue),
and their combination (black).
The yellow band is a theory prediction ΔΓ_{s} = 0.088 ±0.017 ps^{−1}
which assumes no new physics in B_{s} mixing
[A. Lenz and U. Nierste, JHEP 06 (2007) 072].
The right plot below shows the same contours in the plane
(1/Γ_{L}, 1/Γ_{H}).
In both cases, the blue band represents the average
1.417
±
0.044
ps which includes all lifetime measurements with flavourspecific B_{s} decays,
except those which are not independent of the direct measurements used in the
ΔΓ_{s} averaging.
Above plots: (1/Γ_{s}, ΔΓ_{s}) gif /
(1/Γ_{L}, 1/Γ_{H}) gif /
(1/Γ_{s}, ΔΓ_{s}) eps /
(1/Γ_{L}, 1/Γ_{H}) eps /
Another (1/Γ_{s}, ΔΓ_{s}) plot
showing only the direct measurements and their average:
gif / eps /
The two plots below are similar to the plots above, but represent the combined results when including the additional
contraint from
BR((B_{s} → D_{s}^{(*)}D_{s}^{(*)}) = (
0.044
±
0.015
) × (1 ± 0.3(theory)), shown as a green band.
Above plots: (1/Γ_{s}, ΔΓ_{s}) gif /
(1/Γ_{L}, 1/Γ_{H}) gif /
(1/Γ_{s}, ΔΓ_{s}) eps /
(1/Γ_{L}, 1/Γ_{H}) eps /
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B^{0} mixing: oscillations and mass difference
Combined result on B^{0} mixing, obtained separately from timedependent measurements of the
oscillation frequency Δm_{d} (at high energy colliders and asymmetric B factories) and from timeintegrated measurements of the
mixing probability χ_{d} at symmetric Υ(4S) machines:
Δm_{d} =
0.508
±
0.005
ps^{−1}

from timedependent measurements at
ALEPH, DELPHI, L3, OPAL,
CDF, D0,
BABAR, BELLE

χ_{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
B^{0} system, and assuming a B^{0} lifetime of
1.525
±
0.009
ps (the experimental average listed above),
all above measurements
can be combined to yield the following world averages:
Δm_{d} =
0.507
±
0.005
ps^{−1}
x_{d} =
0.774
±
0.008
χ_{d} =
0.1873
±
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 χ_{d} average from ARGUS and CLEO is converted to a Δm_{d} measurement
assuming no CP violation, no width difference in the B^{0} system and a
B^{0} lifetime of
1.525
±
0.009
ps.
colour gif /
colour eps /
blackandwhite eps /
Same without average including timeintegrated (χ_{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 χ_{d} average from ARGUS and CLEO is converted to a Δm_{d} measurement
assuming no CP violation, no width difference in the B^{0} system and a
B^{0} lifetime of
1.525
±
0.009
ps.
colour gif /
colour eps /
blackandwhite eps /
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2D average of Δm_{d} and τ(B^{0})
BABAR and Belle have performed simultaneous measurements of Δm_{d} and τ(B^{0}).
 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 Δm_{d}, τ(B^{0}) and τ(B^{+}), and
has been converted, for the purpose of averaging with the BABAR results, into a 2D measurement
of Δm_{d} and τ(B^{0}). 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
Δm_{d} =
0.509
±
0.006
ps^{−1} and τ(B^{0}) =
1.527
±
0.010
ps, with a total (stat+syst) correlation coefficient of
−0.23
(note that this result on Δm_{d} is already included in the Δm_{d} world average
quoted above).
colour gif /
colour eps /
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B_{s} mixing: oscillations and mass difference
In 2006, CDF has obtained the first direct evidence for
and then the first observation of B_{s} oscillations. The measured
value of Δm_{s} is (A. Abulencia et al., Phys. Rev. Lett. 97, 242003 (2006)):
Δm_{s} =
17.77
±
0.10
(stat) ±
0.07
(syst) ps^{−1}

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 ε_{B}. 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 = [(1−A_{SL})/(1+A_{SL})]**0.25
ε_{B} = (p−q)/(p+q)
q/p = (1−ε_{B})/(1+ε_{B})
A_{SL} ~ 4 Re(ε_{B})/(1+ε_{B}^{2})
The parameters q/p, A_{SL} and Re(ε_{B})/(1+ε_{B}^{2}) are thus 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 B^{0} and the B_{s} systems.
Two sets of averages are given for the B^{0} system in the first table:
a first set using only measurements performed at Υ(4S) machines,
and a second set using all measurements
(including those performed at high energy, but under the assumption of
no CP violation in B_{s} mixing). The second table presents an average for the
B_{s} system, based on measurements performed at the Tevatron, where some analyses
measure a mixture of the B^{0} and B_{s} parameters: the effect from the B_{s} is
then isolated by using the value and error of the B^{0} parameter
obtained at the B factories.
CP violation parameter in B^{0} mixing 
q/p =
1.0002
±
0.0028
A_{SL} =
−0.0005
±
0.0056
Re(ε_{B})/(1+ε_{B}^{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(ε_{B})/(1+ε_{B}^{2}) =
−0.0012
±
0.0010

same but adding measurements from ALEPH, OPAL and D0 (and assuming A_{SL}(B_{s}) = 0) 
CP violation parameter in B_{s} mixing 
q/p =
1.0018
±
0.0047
A_{SL} =
−0.0036
±
0.0094

from measurements at CDF and D0
(and assuming
A_{SL}(B^{0}) =
−0.0005
±
0.0056
)

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Phase difference between B_{s}mixing and b→ccs amplitudes
The phase difference φ_{s} = −2β_{s} between the B_{s} mixing amplitude and
the b→ccs decay amplitude of the B_{s} meson (for example in B_{s} → J/ψφ)
is the equivalent of 2β for the B^{0} meson.
In the Standard Model β_{s} =
arg(−(V_{ts} V_{tb}^{*})/(V_{cs} V_{cb}^{*})) ~ 1 degree.
CDF and D0 have published results on this CPviolating parameter. Combined
2D fits of β_{s} and DGs, without external assumption,
yield two symmetric solutions
related through β_{s} ↔ π/2−β_{s} (or φ_{s} ↔ π−φ_{s})
and ΔΓ_{s} ↔ −ΔΓ_{s}. Alternatively, the 2D fit is repeated, but using
external constraints provided by the flavourspecific B_{s} lifetime,
τ(B_{s} → flavourspecific) =
(1/Γ_{s})[1+((ΔΓ_{s}/(2Γ_{s}))^{2}]/
[1−((ΔΓ_{s}/(2Γ_{s}))^{2}] =
1.417
±
0.042
ps
and by the semileptonic asymmetry,
A_{SL}(B_{s}) = Im(Γ_{12}/M_{12}) =
−0.0036
±
0.0094
.
The latter is sensitive to the angle arg(−Γ_{12}/M_{12}),
which is predicted to be very small in the Standard Model.
A new physics phase in B_{s} mixing would affect
arg(−Γ_{12}/M_{12}) and −2β_{s}
in the same manner. The constrained fit is performed under
the assumption that this new physics contribution is much larger than
both the Standard Model values of arg(−Γ_{12}/M_{12})
and β_{s}.
Fit results from CDF and D0 data 
without external constraints 
with constraint from τ(B_{s} → flavour specific) and A_{SL}(B_{s}) 
β_{s} 
+0.39
+0.18
−0.14
or
+1.18
+0.14
−0.18

+0.47
+0.13
−0.21
or
+1.09
+0.21
−0.13

β_{s} (90% CL range) 
[
+0.14
;
+0.73
]
∪
[
+0.82
;
+1.43
]

[
+0.10
;
+0.68
]
∪
[
+0.89
;
+1.47
]

φ_{s} = −2 β_{s} 
−0.77
+0.29
−0.37
or
−2.36
+0.37
−0.29

−0.94
+0.43
−0.25
or
−2.19
+0.25
−0.43

φ_{s} = −2 β_{s} (90% CL range) 
[
−1.47
;
−0.29
]
∪
[
−2.85
;
−1.65
]

[
−1.35
;
−0.20
]
∪
[
−2.94
;
−1.77
]

ΔΓ_{s} 
+0.154
+0.054
−0.070
or
−0.154
+0.070
−0.054
ps^{−1}

+0.098
+0.075
−0.026
or
−0.098
+0.026
−0.075
ps^{−1}

ΔΓ_{s} (90% CL range) 
[
+0.036
;
+0.264
] ∪
[
−0.264
;
−0.036
] ps^{−1}

[
−0.163
;
+0.163
] ps^{−1}

The two plot below shows different confidencelevel contours in the (φ_{s}=−2β_{s}, ΔΓ_{s}) plane,
with and without the two external constraints.
Above combined plots:
without constraint (gif,pdf,eps) /
with both contraints (gif,pdf,eps)
Individual plots (without external constraint):
CDF (gif,pdf,eps) /
D0 (gif,pdf,eps)
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bhadron fractions in Υ(4S) decays
The B^{+} and B^{0} fractions below are for an unbiased sample of Bmesons
produced in Υ(4S) decays.
Most analyses measure the ratio f^{+−}/f^{00} assuming
isospin invariance in charged and neutral B decays,
and relying on our knowledge
of the B^{+}/B^{0} lifetime ratio.
Combining all these analyses from BABAR, BELLE and CLEO
leads to the average
f^{+−}/f^{00} =
1.068
±
0.029
after adjusting to a common B^{+}/B^{0} lifetime ratio of
1.071
±
0.009
(the current average given above).
On the other hand, BABAR measured directly f^{00} =
0.487
±
0.013
without assuming
isospin invariance nor relying on the B^{+}/B^{0} lifetime ratio.
f^{+−}/f^{00} =
1.068
±
0.029

from ratios of reconstructed B^{+} and B^{0} mesons
at BABAR, BELLE and CLEO
(assumptions made, see text above) 
f^{00} =
0.487
±
0.013

from absolute measurement of
B^{0} mesons at BABAR
(no assumptions) 
Assuming f^{+−} + f^{00} = 1, the above two independent results
(which are consistent with each other)
can be combined to yield:
b hadron species 
fraction in Υ(4S) decay 
ratio 
B^{+} B^{−} 
f^{+−} =
0.516
±
0.006

f^{+−}/f^{00} =
1.065
±
0.026

B^{0} antiB^{0} 
f^{00} =
0.484
±
0.006

Note that the ratio f+/f00 differs from unity by
2.5
sigmas.
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bhadron fractions in Υ(5S) decays
The table and plot below show the fraction f_{s}^{(*)(*)} of B_{s}^{(*)} antiB_{s}^{(*)} events over all events with a pair of
bflavored mesons produced in e+e collisions at a centreofmass energy equal to the Υ(5S) mass.
Since all B_{s}^{*} mesons decay to a B_{s} meson (by photon emission), this fraction is equal to the probability
f_{s}(Υ(5S)) that a weakly decaying bhadron produced in such collisions be a B_{s} meson.
The average for this fraction has been obtained by combining modeldependent estimates of CLEO3 and Belle based
on the measurements of several inclusive Υ(5S) branching fractions, after performing adjustements
to common external inputs. Most of this B_{s} production proceeds
in the B_{s}^{*} antiB_{s}^{*} channel, with the ratio of B_{s}^{*} antiB_{s}^{*} events
over B_{s}^{(*)} antiB_{s}^{(*)} events (from Belle, R. Louvot et al, PRL 102, 021801 (2009))
indicated in the table.
b hadron species 
fraction in Υ(5S) decay 
ratio 
B_{s}^{(*)} antiB_{s}^{(*)} 
f_{s}^{(*)(*)} = f_{s}(Υ(5S)) =
0.194
±
0.029

B_{s}* antiB_{s}^{*} 
f_{s}^{**}
 f_{s}**/f_{s}^{(*)(*)} = 0.901 +0.038−0.040

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 of the timeintegrated mixing probability
averaged over an unbiased sample of semileptonic bhadron decays, χbar =
f'(B_{d})χ_{d}+f'(B_{s})χ_{s} =
0.1259
±
0.0042
.
This combination relies on the world average of χ_{d},
on the assumption χ_{s} = 1/2,
as well as on the world averages of
the lifetimes of the individual bhadrons species.
The B^{+} and B^{0} mesons are assumed to be produced in equal amount,
the B_{c} production is neglected and the sum of the fractions is constrained to unity.
b hadron species 
fraction in Z decays 
correlation with f(B_{s}) 
correlation with f(bbaryon) 
B_{s} 
f(B_{s}) =
0.104
±
0.009

b baryons 
f(bbaryon) =
0.091
±
0.015

+0.017

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.403
±
0.009

−0.522

−0.862

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

LEP average from LEP EW WG 
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bhadron fractions in ppbar collisions at 1.8−2 TeV
The table below shows the bhadron fractions in
an unbiased sample of weakly decaying bhadrons produced in ppbar collisions at √s = 1.8−2 TeV.
These fractions have been calculated by combining direct rate measurements
performed at Tevatron with
the Tevatron combined measurement of the timeintegrated mixing probability
averaged over an unbiased sample of semileptonic bhadron decays, χbar =
0.147
±
0.011
.
This combination relies on the world average of χ_{d},
on the assumption χ_{s} = 1/2,
as well as on the world averages of
the lifetimes of the individual bhadrons species.
The B^{+} and B^{0} mesons are assumed to be produced in equal amount,
the B_{c} production is neglected and the sum of the fractions is constrained to unity.
b hadron species 
fraction in ppbar collisions at 1.8−2 TeV 
correlation with f(B_{s}) 
correlation with f(bbaryon) 
B_{s} 
f(B_{s}) =
0.121
±
0.015

b baryons 
f(bbaryon) =
0.214
±
0.068

−0.603

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.333
±
0.030

+0.439

−0.981

This is based on the following average of χbar in ppbar collisions at 1.8−2 TeV:
χbar(Tevatron) =
0.147
±
0.011

average of CDF and D0 measurements 
(home , top , next, previous)
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 the Tevatron (√s=1.8−2 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, χbar =
0.1284
±
0.0069
.
This combination relies on the world average of χ_{d},
on the assumption χ_{s} = 1/2,
as well as on the world averages of
the lifetimes of the individual bhadrons species.
The B^{+} and B^{0} mesons are assumed to be produced in equal amount,
the B_{c} production is neglected and the sum of the fractions is constrained to unity.
b hadron species 
fraction at high energy 
correlation with f(B_{s}) 
correlation with f(bbaryon) 
B_{s} 
f(B_{s}) =
0.113
±
0.013

b baryons 
f(bbaryon) =
0.085
±
0.022

−0.041

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.401
±
0.013

−0.483

−0.855

This is based on the following average of χbar at high energy:
χbar =
0.1259
±
0.0042

LEP average from LEP EW WG 
χbar =
0.147
±
0.011

Tevatron average 
χbar =
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 Tevatron 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 χbar and another
scaling factor of
1.5
when combining the direct rate measurements at LEP and Tevatron.
 This may be an indication that the fractions in high energy hadronic
collisions may not be identical to those in Z decays.
(home , top , previous)
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 13Apr2010
Latest mod.
Wed Apr 14 09:18:27 CEST 2010