Spring 2010 results
All results available publicly (published and preliminary)
before the summer 2010 conferences
have been included in the averages computed by the
lifetime and oscillations subgroup
of the Heavy Flavour Averaging Group (HFAG).
The following material is available publicly:
These "end of 2009" averages include in fact all presummer 2010 results.
They are described (together with the combination procedures used to obtain them)
in Chapter 3 of the following HFAG writeup:
arXiv:1010.1589 [hepex]
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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} 
1.518
±
0.007
ps

B^{+} 
1.641
±
0.008
ps

1.081
±
0.006

B_{s} 
1.477
+0.021
−0.022
ps

0.973
±
0.015

B_{c} 
0.461
±
0.036
ps

Λ_{b} 
1.425
±
0.032
ps

0.939
±
0.022

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 
1.382
±
0.029
ps

0.910
±
0.020

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
3.3
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 
1.455
±
0.030
ps

B_{s} → D_{s} X 
1.458
±
0.030
ps

B_{s} → J/ψ φ 
1.477
±
0.046
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} =
0.011
±
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}
performed at Tevatron Run II (earlier measurements would not affect the results),
as well as
the lifetime measurements using B_{s} → J/ψ φ decays,
flavourspecific B_{s} decays,
B_{s} decays to CP eigenstates,
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 obtained both without and with
some or all of the following external constraints:
 the quantity
(1/Γ_{s})
× (1 + (ΔΓ_{s}/Γ_{s})^{2}/4)
/ (1 − (ΔΓ_{s}/Γ_{s})^{2}/4)
is constrained to τ(B_{s} → flavour specific) =
1.455
±
0.030
ps, which is the average of all lifetime measurements with flavourspecific B_{s} decays;
 the quantity
Γ_{L} = Γ_{s} (1+ΔΓ_{s}/(2Γ_{s}))
is constrained to
τ(B_{s} → CPeven) =
1.47
±
0.16
ps, which is the average of the lifetime measurements with
B_{s} → K^{+}K^{−} and
B_{s} → D_{s}^{(*)}D_{s}^{(*)} decays;
these two decays are assumed to be 100% CP even, with a 5% theoretical uncertainty;
 the quantity
1/(2Γ_{s}/ΔΓ_{s}+1)
is constrained to
BR((B_{s} → D_{s}^{(*)}D_{s}^{(*)}) =
0.049
±
0.014
. 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 (recommended) set of results
is the one where only the constraint I from τ(B_{s} → flavour specific)
is applied; it is free of theoretical uncertainties.
Fit results from CDF, D0, ALEPH and DELPHI data 
without any external constraint 
with constraint I above 
with constraints I, II and III above 
1/Γ_{s} 
1.506
±
0.032
ps

1.477
+0.021
−0.022
ps

1.479
±
0.021
ps

τ_{Short} = 1/Γ_{L} 
1.431
+0.038
−0.037
ps

1.425
+0.037
−0.035
ps

1.416
±
0.027
ps

τ_{Long} = 1/Γ_{H} 
1.590
+0.075
+0.071
ps

1.532
±
0.049
ps

1.548
+0.036
−0.037
ps

ΔΓ_{s} (95% CL range) 
[
−0.006
;
+0.146
] ps^{−1}

[
−0.019
;
+0.112
] ps^{−1}

[
+0.017
;
+0.101
] ps^{−1}

ΔΓ_{s} 
+0.070
±
0.039
ps^{−1}

+0.049
+0.033
−0.034
ps^{−1}

+0.060
±
0.021
ps^{−1}

ΔΓ_{s}/Γ_{s} (95% CL range) 
[
−0.011
;
+0.224
]

[
−0.028
;
+0.167
]

[
+0.025
;
+0.150
]

ΔΓ_{s}/Γ_{s} 
+0.105
±
+0.060

+0.072
+0.049
−0.051

+0.089
±
0.032

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 ellipse),
the constraint I given by the B_{s} lifetime using flavourspecific
final states (blue band),
and their combination (large solid black ellipse).
The combination including in addition constraint II from the B_{s} lifetime using CPeven final states (not represented)
and constraint III from the B_{s} → D_{s}^{(*)}D_{s}^{(*)} branching fraction (green band)
is also shown (small dashed black ellipse).
The yellow band is a recent 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}).
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 /
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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
±
0.004
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
1.518
±
0.007
ps (the experimental average listed above),
all above measurements
can be combined to yield the following world averages:
Δm_{d} =
0.508
±
0.004
ps^{−1}
x_{d} =
0.771
±
0.007
χ_{d} =
0.1864
±
0.0022

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
1.518
±
0.007
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
1.518
±
0.007
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
1.641
±
0.008
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,
published in A. Abulencia et al., Phys. Rev. Lett. 97, 242003 (2006), and measured
Δm_{s} = 17.77 ±0.010 (stat) ± 0.07 (syst) ps^{−1}.
In 2007, D0 obtained a preliminary evidence of B_{s} oscillations and measured Δm_{s} = 18.53 ± 0.97 ps^{−1} (D0 note 5474).
The world average is:
Δm_{s} =
17.78
±
0.12
ps^{−1}

CDF+D0 (Run II)

The plots below shows the B_{s} oscillation amplitude
as a function of Δm_{s}.
An amplitude consistent with 1 is expected
at the true value of Δm_{s}. An amplitude consistent with 0 is expected far
below the true value of Δm_{s}.
The top plot shows the CDF results from Tevatron Run II data.
A signal is clearly visible close to 17.75 ps^{−1}. The significance of this
signal (computed as the measured amplitude divided by its total error at
17.75 ps^{−1}) is 4.7 sigma. A more sophisticated analysis performed by CDF
concludes that such a signallike feature could be produce by a statistical
fluctuation with a probability of 8×10^{−8}, corresponding to a 5.4 sigma
significance. The middle plot shows the preliminary results of D0, with evidence
of a signal in the region 16−20 ps^{−1}, with a maximal significance
(computed as the measured amplitude divided by its total error) of 3.1 sigma
around ∼ 18 ps^{−1}. The bottom plot shows the combined amplitude spectrum
from all previous published results obtained until 2004
by the ALEPH, DELPHI, OPAL, SLD and CDF (Run I) experiments,
which shows no significant signal (maximal significance of 1.9 sigma at 17 ps^{−1}),
but is compatible with the D0 and CDF (Run II) results.
Above plot:
gif /
eps /
ASCII files (of above plots):
CDF Run II /
D0 /
average of ALEPH, DELPHI, OPAL, SLD and CDF Run I
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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 =
1.0024
±
0.0023
A_{SL} =
−0.0047
±
0.0046
Re(ε_{B})/(1+ε_{B}^{2}) =
−0.0012
±
0.0011

from measurements at CLEO, BABAR and BELLE 
q/p =
1.0030
±
0.0017
A_{SL} =
−0.0058
±
0.0034
Re(ε_{B})/(1+ε_{B}^{2}) =
−0.0015
±
0.0008

same but adding measurements from ALEPH, OPAL, CDF2 and D0 (and assuming A_{SL}(B_{s}) = 0) 
CP violation parameter in B_{s} mixing 
q/p =
1.0044
±
0.0029
A_{SL} =
−0.0088
±
0.0058

from measurements at CDF and D0
(and assuming
A_{SL}(B^{0}) =
−0.0047
±
0.0046
)

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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 ΔΓ_{s}, 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 semileptonic asymmetry,
A_{SL}(B_{s}) = Im(Γ_{12}/M_{12}) =
−0.0088
±
0.0058
;
 the flavourspecific B_{s} lifetime,
τ(B_{s} → flavourspecific) =
(1/Γ_{s})
× (1 + (ΔΓ_{s}/Γ_{s})^{2}/4)
/ (1 − (ΔΓ_{s}/Γ_{s})^{2}/4) =
1.455
±
0.030
ps;
 the short B_{s} lifetime,
τ(B_{s} → CPeven) =
Γ_{L} = Γ_{s} (1+ΔΓ_{s}/(2Γ_{s})) =
1.47
±
0.16
ps, which is the average of the lifetime measurements with
B_{s} → K^{+}K^{−} and
B_{s} → D_{s}^{(*)}D_{s}^{(*)} decays;
these two decays are assumed to be 100% CP even, with a 5% theoretical uncertainty;

the branching fraction BR((B_{s} → D_{s}^{(*)}D_{s}^{(*)}) =
1/(2Γ_{s}/ΔΓ_{s}+1) =
0.049
±
0.014
. 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 A_{SL}(B_{s}) observable 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 fits involving A_{SL}(B_{s}) are 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 A_{SL}(B_{s}) only 
with all 4 constraints mentioned above 
β_{s} 
+0.41
+0.18
−0.15
or
+1.16
+0.15
−0.18

+0.41
+0.10
−0.08
or
+1.18
+0.07
−0.10

+0.37
+0.11
−0.16
or
+1.19
+0.17
−0.13

β_{s} (90% CL range) 
[
+0.16
;
+0.75
]
∪
[
+0.82
;
+1.41
]

[
+0.22
;
+0.60
]
∪
[
+1.00
;
+1.36
]

[
+0.10
;
+0.59
]
∪
[
+0.97
;
+1.47
]

φ_{s} = −2 β_{s} 
−0.83
+0.30
−0.36
or
−2.31
+0.36
−0.30

−0.82
+0.16
−0.21
or
−2.36
+0.20
−0.14

−0.75
+0.32
−0.21
or
−2.38
+0.25
−0.34

φ_{s} = −2 β_{s} (90% CL range) 
[
−1.50
;
−0.32
]
∪
[
−2.82
;
−1.64
]

[
−1.20
;
−0.45
]
∪
[
−2.72
;
−1.99
]

[
−1.19
;
−0.21
]
∪
[
−2.94
;
−1.93
]

ΔΓ_{s} 
+0.150
+0.055
−0.056
or
−0.150
+0.056
−0.055
ps^{−1}

+0.150
+0.045
−0.049
or
−0.150
+0.042
−0.049
ps^{−1}

+0.054
+0.026
−0.015
or
−0.054
+0.016
−0.026
ps^{−1}

ΔΓ_{s} (90% CL range) 
[
+0.060
;
+0.297
] ∪
[
−0.297
;
−0.060
] ps^{−1}

[
+0.075
;
+0.228
] ∪
[
−0.220
;
−0.071
] ps^{−1}

[
+0.025
;
+0.097
] ∪
[
−0.099
;
−0.024
] ps^{−1}

Deviation from Standard Model 
2.3
σ

2.8
σ

2.7
σ

Plot showing confidencelevel contours in (φ_{s}=−2β_{s}, ΔΓ_{s}) plane 
Combined:
gif / eps
Combined + A_{SL}(B_{s}):
gif / eps
CDF only:
gif / eps
D0 only: gif / eps

Combined:
gif / eps

Combined:
gif / eps

The three plot below show different combined confidencelevel contours in the (φ_{s}=−2β_{s}, ΔΓ_{s}) plane,
without external constraint, with A_{SL}(B_{s}) constraint only, and with all constraints.
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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} =
1.052
±
0.028
after adjusting to a common B^{+}/B^{0} lifetime ratio of
1.081
±
0.006
(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} =
1.052
±
0.028

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^{+−} =
0.513
±
0.006

f^{+−}/f^{00} =
1.052
±
0.025

B^{0} antiB^{0} 
f^{00} =
0.487
±
0.006

Note that the ratio f+/f00 differs from unity by
2.1
sigmas.
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bhadron fractions in Υ(5S) decays
The table below show the fraction of events containingr
nonstrange B mesons (f_{ud}),
strange B mesons (f_{s}),
or no B mesons at all (f_{noB})
in a sample of Υ(5S) decays, or more precisely in a sample of
bb events produced in e^{+}e^{−} collisions at a
centreofmass energy equal to the Υ(5S) mass. The sum of the
three fractions is contrained to unity:
f_{ud}+f_{s}+f_{noB}=1.
Their combined values have 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.
final states 
fraction in Υ(5S) decay 
B_{u,d}^{(*)} antiB_{u,d}^{(*)}(π(π)) 
f_{u,d}(Υ(5S)) =
0.763
±
0.046

B_{s}^{(*)} antiB_{s}^{(*)} 
f_{s}(Υ(5S)) =
0.202
±
0.036

no open bottomness 
f_{noB}(Υ(5S)) =
0.035
±
0.057

The plot below shows the published measurements of f_{s}.
All values have been obtained assuming f_{noB}=0.
They are quoted as in the original publication,
except for the most recent measurement of Belle which
is quoted as f_{s} = 1f_{ud}. The average value of
all these measurements is quoted with or without the assumption that
f_{noB}=0,
after performing adjustements
to common external inputs.
The fraction f_{noB} is known to be nonzero,
from direct measurements of Υ(5S) decays to final states
without bottom mesons.
colour gif /
colour eps /
blackandwhite eps /
(home , top , next, previous)
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}) =
0.103
±
0.009

b baryons 
f(bbaryon) =
0.090
±
0.015

+0.035

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

−0.523

−0.870

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

LEP average from LEP EW WG 
(home , top , next, previous)
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}) =
0.111
±
0.014

b baryons 
f(bbaryon) =
0.211
±
0.069

−0.582

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.339
±
0.031

+0.426

−0.984

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}) =
0.109
±
0.012

b baryons 
f(bbaryon) =
0.083
±
0.020

−0.053

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.404
±
0.012

−0.475

−0.854

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
1.4
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 Feb 2 00:51:27 CET 2011