Results for the PDG 2013 web update
Only results published (or accepted in a refereed journal)
by March 31, 2013
have been included in the averages computed by the
lifetime and oscillations subgroup
of the Heavy Flavour Averaging Group (HFAG)
for the 2013 web 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:1207.1158 [hepex]
(this writeup describes the "Spring 2012" averages, which also include
preliminary results;
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, LHCb, OPAL and SLD.
The mixtures refer to samples of weakly decaying bhadrons
produced at high energy.
b hadron species 
average lifetime 
average lifetime relative to B^{0} average lifetime 
B^{0} 
1.519
±
0.007
ps

B^{+} 
1.641
±
0.008
ps

1.079
±
0.007

B_{s} 
1.516
±
0.011
ps

0.998
±
0.009

B_{c} 
0.452
±
0.033
ps

Λ_{b} 
1.429
±
0.024
ps

0.941
±
0.016

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 
1.402
±
0.023
ps

0.923
±
0.016

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_{L} + Γ_{H})/2 is the
mean decay width of the B_{s} system, i.e. the average of the decay widths of the light and heavy states
(Γ_{L} and Γ_{H}).
The Λ_{b} lifetime average include a measurement which is
2.7
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 illdefined, 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 because it includes an
unknown proportion of short and long components. The "B_{s} → J/ψ φ" lifetime is an average of the
results from single exponential fits. Nowadays, the time dependence and the angular dependence
of the B_{s} → J/ψ φ decays is analysed
in a more sophisticated way in order to extract separately the long and short lifetimes (see further below).
mixture of the two B_{s} mass eigenstates 
average lifetime 
B_{s} → flavour specific 
1.463
±
0.032
ps

B_{s} → D_{s} X 
1.466
±
0.031
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. This expectation has been observed to be correct for the B_{s} system.
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 some 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} =
0.015
±
0.018

from Belle, BABAR and DELPHI 
The quantity s = sign(Re(λ_{CP})), where
λ_{CP} = (q/p)×A_{CP}/A_{CP}
refers to a CPeven final state (e.g. J/ψK_{L}),
is predicted to be equal to s= +1
to a high degree of confidence from the Standard Model fits
to all available constraints on the unitarity triangle.
The ATLAS, CDF, D0 and LHCb analyses of the B_{s} → J/ψ φ decay
provide information on Γ_{s}, ΔΓ_{s}
and the weak phase φ_{s}^{ccs},
defined as the phase difference between the mixing amplitude and
the b→ccs decay amplitude
of the B_{s} meson.
Combined values of the average decay width Γ_{s} and the decay width difference
ΔΓ_{s} are obtained from of a twodimensional fit of the experimental results.
In this fit, the CPviolating phase
φ_{s}^{ccs}
is fixed to
+0.04
, which is the central value of the
φ_{s}^{ccs}average described below.
The correlation between Γ_{s} and
ΔΓ_{s} in each analysis is
taken into account (but correlations with other parameters are ignored).
The following additional constraints are applied, using effective lifetime measurements:
 B_{s} → J/ψf_{0}(980) lifetime measurements from CDF and LHCb (pure CPodd final state), which average to τ(B_{s}→ J/ψf_{0}(980)) =
1.700
±
0.044
ps,
taken to be equal to (1/Γ_{H})×[1−(φ_{s}^{ccs})^{2}×ΔΓ_{s}/4];
 B_{s} → K^{+}K^{−} lifetime measurements from LHCb (pure CPeven final state), which average to τ(B_{s}→ K^{+}K^{−}) =
1.452
±
0.042
ps,
taken to be equal to (1/Γ_{L})×[1+(φ_{s}^{ccs})^{2}×ΔΓ_{s}/4];
 flavourspecific B_{s} lifetime average
τ(B_{s} → flavour specific) =
1.463
±
0.032
ps, taken to be equal to (1/Γ_{s})
× (1 + (ΔΓ_{s}/Γ_{s})^{2}/4)
/ (1 − (ΔΓ_{s}/Γ_{s})^{2}/4).
The implementation of contraints I and II, described in full in the literature [R. Fleischer and R. Knegjens, Eur. Phys. J. C (2011) 1789], neglects here possible subleading Penguin contributions and possible direct CP violation.
The table below shows the results with and without these additional constraints.
The default (i.e. recommended) set of results is the one with all the constraints applied.
Fit results from ATLAS, CDF, D0 and LHCb data 
without constraint from effective lifetime measurements 
with constraints I and II 
with constraints I, II and III 
Γ_{s} 
0.6600
±
0.0054
ps

0.6557
±
0.0049
ps

0.6596
±
0.0046
ps

1/Γ_{s} 
1.515
±
0.012
ps

1.525
±
0.011
ps

1.516
±
0.011
ps

τ_{Short} = 1/Γ_{L} 
1.432
±
0.015
ps

1.432
±
0.014
ps

1.428
±
0.013
ps

τ_{Long} = 1/Γ_{H} 
1.609
±
0.025
ps

1.622
±
0.023
ps

1.615
±
0.021
ps

ΔΓ_{s} 
+0.077
±
0.013
ps^{−1}

+0.086
±
0.012
ps^{−1}

+0.081
±
0.011
ps^{−1}

ΔΓ_{s}/Γ_{s} 
+0.116
±
0.020

+0.131
±
0.018

+0.123
±
0.017

correlation ρ(Γ_{s}, ΔΓ_{s}) 
−0.324

−0.245

−0.195

The two plots below show
contours of Δ(ln(L)) = 0.5
(39% CL for the enclosed 2D regions, 68% CL for the bands),
in the plane (Γ_{s}, ΔΓ_{s}) on the left and
in the plane (1/Γ_{L}, 1/Γ_{H}) on the right.
The average of all B_{s} → J/ψ φ measurements is shown as
the red contour, and the constraints given by the effective lifetime measurements of
B_{s} → J/ψf_{0}(980),
B_{s} → K^{+}K^{−} and
B_{s} to flavourspecific
final states (
1.463
±
0.032
ps)
are shown as the green, purple and blue bands, respectively.
The average taking all constraints into account is shown as the gray filled contour.
The yellow band is a theory prediction ΔΓ_{s} = 0.087 ±0.021 ps^{−1}
which assumes no new physics in B_{s} mixing
[A. Lenz and U. Nierste, arXiv:1102.4274 [hepph]].
Above plots: gif /
eps /
pdf /
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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} =
0.510
±
0.004
ps^{−1}

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

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
1.519
±
0.007
ps (the experimental average listed above),
all above measurements
can be combined to yield the following world averages:
Δm_{d} =
0.510
±
0.004
ps^{−1}
x_{d} =
0.775
±
0.006
χ_{d} =
0.1875
±
0.0020

from all
ALEPH, DELPHI, L3, OPAL,
CDF, D0,
BABAR, BELLE, LHCb,
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
1.519
±
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
1.519
±
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
Combined result on B^{0}_{s} mixing, obtained from timedependent measurements of the
oscillation frequency Δm_{s} at highenergy hadron colliders:
Δm_{s} =
17.69
±
0.08
ps^{−1}

CDF, LHCb

With a mean B^{0}_{s} lifetime of 1/Γ_{s} =
1.516
±
0.011
ps, a decay width difference of ΔΓ_{s} =
+0.081
±
0.011
ps^{−1}
and the assumption of no CP violation in B^{0}_{s} mixing, this leads to
x_{s} =
26.82
±
0.23

χ_{s} =
0.499309
±
0.000012

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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 asymmetry 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
(excluding those that assume no CP violation in B_{s} mixing).
The second table presents an average for the
B_{s} system. Measurements performed at high energy that do not separate the B^{0} and B_{s} contributions are
no longer used to obtain the final averages (at this time, the only measurements at high energy used in the averages are from D0).
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 the Υ(4S) 
q/p =
0.9997
±
0.0013
A_{SL} =
+0.0007
±
0.0027
Re(ε_{B})/(1+ε_{B}^{2}) =
+0.0002
±
0.0007

world average 
CP violation parameter in B_{s} mixing 
q/p =
1.0086
±
0.0028
A_{SL} =
−0.0171
±
0.0055

world average

The above world averages
A_{SL}(B^{0}) =
+0.0007
±
0.0027
and A_{SL}(B_{s}) =
−0.0171
±
0.0055
are obtained from a twodimensional fit of the CLEO, BABAR, Belle and D0 results: the correlation coefficient between them is found to be
−0.462
.
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Phase difference between B_{s}mixing and b→ccs amplitudes
The weak phase difference
φ_{s}^{ccs}
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 predicted by the Standard Model to be approximately equal to −2β_{s}, where
β_{s} =
arg(−(V_{ts} V_{tb}^{*})/(V_{cs} V_{cb}^{*})) ~ 1 degree.
The phase −2β_{s} is the equivalent of 2β for the B^{0} meson.
The phase
φ_{s}^{ccs}
has been measured in five analyses: four
B_{s} → J/ψφ analyses from CDF, D0, ATLAS and LHCb,
and one B_{s} → J/ψπ^{+}π^{−} analysis from LHCb. A combined
2D fit of
φ_{s}^{ccs}
and ΔΓ_{s}, without external assumption,
yields two symmetric solutions
related through
φ_{s}^{ccs}
↔ π−
φ_{s}^{ccs}
and ΔΓ_{s} ↔ −ΔΓ_{s}. Only the solution with positive ΔΓ_{s} is
shown in the table below, as detailed analysis of the strong phases in B_{s} → J/ψK^{+}K^{−} by LHCb
(arXiv:1202.4717 [hepex])
has shown that this is the physical solution.
Only the correlations between the measurements of
φ_{s}^{ccs}
and
ΔΓ_{s} are taken into account (possible correlations with other parameters are ignored).

Combined result from CDF, D0, ATLAS and LHCb data 
φ_{s}^{ccs}

+0.04
^{
+0.10
}_{
−0.13
}

The recommended final average of ΔΓ_{s} is the one given
in the section on decay width differences
where additional constraints from effective lifetime measurements are applied.
The two plots below show different 68% confidencelevel contours in the
(φ_{s}^{ccs}, ΔΓ_{s}) plane.
The left plot shows the individual contours of CDF, D0 and LHCb,
their combined contour (solid line and shaded area), as well as the Standard Model predictions. The prediction for
φ_{s}^{ccs} is taken as the
indirect determination of −2β_{s} via a global fit to experimental data within the Standard Model,
−2β_{s} = −0.0363^{+0.0016}_{−0.0015}
[CKMfitter, Phys. Rev. D84, 033005 (2011)] , while the Standard Model prediction for ΔΓ_{s} is
0.087 ±0.021 ps^{−1}
[A. Lenz and U. Nierste, arXiv:1102.4274 [hepph]].
The combined result is consistent with these predictions at the
0.56
σ level.
The right plot shows the same combined contour and SM predictions together with the regions
allowed at 68% and 95% CL
by the average measurements A_{SL}(B_{s}) =
−0.0171
±
0.0055
and Δm_{s} =
17.69
±
0.08
ps^{−1},
through the relation tanφ_{12} = A_{SL}(B_{s}) × Δm_{s} / ΔΓ_{s},
where φ_{12} = arg(−M_{12}/Γ_{12}) is the phase mismatch between the offdiagonal
elements of the mass and decay matrices of the B_{s}−B_{s} system.
This region is drawn under the
assumption that possible new physics will not affect the phase difference φ_{s}^{ccs}−φ_{12}, i.e. that
this phase difference is equal to its Standard Model prediction
[A. Lenz and U. Nierste, arXiv:1102.4274 [hepph]].
ATLAS, CDF, D0, LHCb, and their average: colour gif /
colour eps /
colour pdf /
average and region allowed by A_{SL}(B_{s}): colour gif /
colour eps /
colour pdf /
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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} =
1.056
±
0.028
after adjusting to a common B^{+}/B^{0} lifetime ratio of
1.079
±
0.007
(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} =
1.056
±
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} =
1.055
±
0.025

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

Note that the ratio f+/f00 differs from unity by
2.2
sigmas.
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bhadron fractions in Υ(5S) decays
The table below show the fraction of events containing
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
centerofmass energy equal to the Υ(5S) mass. The sum of the
three fractions is constrained 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 adjustments
to common external inputs. A onesided constraint on f_{noB}
from the direct measurements of Υ(5S) decays to final states
without bottom mesons has been used, caused the strongly asymmetric
uncertainty on the final value of f_{noB}.
final states 
fraction in Υ(5S) decay 
ratio of fractions 
B_{u,d}^{(*)} antiB_{u,d}^{(*)}(π(π)) 
f_{u,d}(Υ(5S)) =
0.759
+0.027
−0.040

B_{s}^{(*)} antiB_{s}^{(*)} 
f_{s}(Υ(5S)) =
0.199
±
0.030

f_{s}(Υ(5S))/f_{u,d}(Υ(5S)) =
0.262
+0.051
−0.043

no open bottomness 
f_{noB}(Υ(5S)) =
0.042
+0.046
−0.006

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 adjustments
to common external inputs.
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}) =
0.103
±
0.009

b baryons 
f(bbaryon) =
0.090
±
0.015

+0.043

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.404
±
0.009

−0.527

−0.872

B_{s} / (B^{0} or B^{+}) ratio 
f(B_{s})/f(B_{d}) =
0.254
±
0.025

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}) =
0.111
±
0.014

b baryons 
f(bbaryon) =
0.212
±
0.069

−0.581

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.338
±
0.031

+0.425

−0.984

B_{s} / (B^{0} or B^{+}) ratio 
f(B_{s})/f(B_{d}) =
0.328
±
0.039

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 
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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 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}) =
0.104
±
0.006

b baryons 
f(bbaryon) =
0.093
±
0.015

−0.277

B^{0} or B^{+} 
f(B_{d}) = f(B_{u}) =
0.402
±
0.007

−0.112

−0.924

B_{s} / (B^{0} or B^{+}) ratio 
f(B_{s})/f(B_{d}) =
0.258
±
0.016

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:

This set of averages assumes that the fractions are the
same at LEP, Tevatron and LHCb. However, this is known to be
a bad approximation, since the ratio Λ_{b}/(B_{u}+B_{d}) has been
observed to depend on p_{T}, and the mean p_{T} is not the same at
LEP, Tevatron or the LHC. No additional uncertainty has been
included in these averages to take into account these differences.

The value of chibar is based on both LEP data and Tevatron data;
the LEP and Tevatron values show a
1.8
σ discrepancy;
therefore the error on the combined chibar value has been rescaled
by a factor
1.8
.
Author: OS 17Apr2013
Latest mod.
dim jui 14 14:58:03 CEST 2013