Results for the PDG 2012 review

Only results published (or accepted in a refereed journal) by March 31, 2012 have been included in the averages computed by the lifetime and oscillations sub-group of the Heavy Flavour Averaging Group (HFAG) for the 2012 edition 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:1010.1589 [hep-ex] (this writeup describes the "end 2009" averages, which also include preliminary results as well as some results released in the first ~3/4 of 2010; these averages do not include results published after that; hence they are not identical to the ones presented here).

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b-hadron lifetime averages

The lifetimes displayed in the table below have been obtained by combining time-dependent measurements from ALEPH, BABAR, BELLE, CDF, D0, DELPHI, L3, LHCb, OPAL and SLD. The mixtures refer to samples of weakly decaying b-hadrons produced at high energy.

b hadron species average lifetime average lifetime relative to B0 average lifetime
B0 1.519 ± 0.007 ps
B+ 1.641 ± 0.008 ps 1.079 ± 0.007
Bs 1.495 ± 0.015 ps 0.984 ± 0.011
Bc 0.453 ± 0.041 ps
Λb 1.425 ± 0.032 ps 0.938 ± 0.022
Ξb− 1.56 +0.27 −0.25 ps
Ωb− 1.13 +0.53 −0.40 ps
Ξb−, Ξb0 mixture 1.49 +0.19 −0.18 ps
b-baryon mixture 1.382 ± 0.029 ps 0.910 ± 0.020
b-hadron 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/Γs, where Γs = (ΓL + ΓH)/2 is the mean decay width of the Bs system, i.e. the average of the decay widths of the light and heavy states (ΓL and ΓH). The Λb lifetime average include a measurement which is 3.3 sigma away from the average re-computed without this measurement; no scale factor was applied on the new combined error, although the Λb lifetime measurements are slightly discrepant (see plot). The Ξb, b-baryon and b-hadron mixtures are ill-defined, 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 ill-defined because it includes an unknown proportion of short and long components. The "Bs → J/ψ φ" lifetime is an average of the results from single exponential fits. Nowadays, the time dependence and the angular dependence of the Bs → 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 Bs mass eigenstates average lifetime
Bs → flavour specific 1.463 ± 0.032 ps
Bs → Ds X 1.466 ± 0.031 ps
Bs → J/ψ φ 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 ΔΓ = ΓL - ΓH and Γ = (ΓL + ΓH)/2, where ΓL (ΓH) 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 short-lived (long-lived) mass eigenstate. This expectation has been observed to be correct for the Bs system. In the absence of CP violation, the light (heavy) B0 or Bs mass eigenstate is the CP-even (CP-odd) 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*ΔΓd/Γd = 0.015 ± 0.018 from Belle, BABAR and DELPHI

The quantity s = sign(Re(λCP)), where λCP = (q/p)*AbarCP/ACP refers to a CP-even final state (e.g. J/ψKL), 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 CDF, D0 and LHCb and analyses of the Bs → J/ψ φ decay provide information on 1/Γs, ΔΓs and the weak phase φs, defined as the phase difference between the mixing amplitude and the b→ccs decay amplitude of the Bs meson. A combined value of the average decay width 1/Γs is obtained as a weighted average of the quoted results, assuming no correlations. Using the likelihood scans from the different analyses, a combined value of ΔΓs is obtained from a 2D fit of ΔΓs and φs, under a Gaussian constraint of φs to its Standard Model value of −2βs=−0.0363+0.0016−0.0015 [CKMfitter, Phys. Rev. D84, 033005 (2011)]. These two averages are then used as input to a fit where the following additional three constraints are applied, using effective lifetime measurements:

The table below shows the results with and without the additional constraints. The default set of results (recommended for the 2012 Review of Particle Physics) is the one with all the constraints applied.

Fit results from
CDF, D0 and LHCb data 		without constraint
from effective
lifetime measurements 		with constraints
from effective
lifetime measurements
1/Γs 1.509 ± 0.017 ps    1.497 ± 0.015 ps   
τShort = 1/ΓL 1.400 ± 0.021 ps    1.393 ± 0.019 ps   
τLong = 1/ΓH 1.637 ± 0.028 ps    1.618 ± 0.024 ps   
ΔΓs +0.103 ± 0.014 ps−1 +0.100 ± 0.013 ps−1
ΔΓs/Γs +0.155 ± 0.021         +0.150 ± 0.020        

The two plots below show contours of Δ(log(L)) = 0.5 (39% CL for the enclosed 2D regions, 68% CL for the bands), in the plane (1/Γs, ΔΓs) on the left and in the plane (1/ΓL, 1/ΓH) on the right. The average of all Bs → J/ψ φ measurements is shown as the red contour, and the constraints given by the effective lifetime measurements of Bs to flavour-specific final states ( 1.463 ± 0.032 ps), Bs → J/ψf0(980) and Bs → K+K− are shown as the blue, green and purple bands, respectively. The average taking all constraints into account is shown as the gray filled contour. The yellow band is a theory prediction ΔΓs = 0.087 ±0.021 ps−1 which assumes no new physics in Bs mixing [A. Lenz and U. Nierste, arXiv:1102.4274 [hep-ph]].


Above plots: (1/Γs, ΔΓs) gif / (1/Γs, ΔΓs) eps / (1/Γs, ΔΓs) pdf /

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B0 mixing: oscillations and mass difference

Combined result on B0 mixing, obtained separately from time-dependent measurements of the oscillation frequency Δmd (at high energy colliders and asymmetric B factories) and from time-integrated measurements of the mixing probability χd at symmetric Υ(4S) machines:

Δmd = 0.507 ± 0.004 ps−1 from time-dependent measurements at ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, LHCb
χd = 0.182 ± 0.015 from time-integrated 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 1.519 ± 0.007 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

Δmd = 0.507 ± 0.004 ps−1
   xd = 0.770 ± 0.008
χd = 0.1862 ± 0.0023 		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 χd average from ARGUS and CLEO is converted to a Δmd measurement assuming no CP violation, no width difference in the B0 system and a B0 lifetime of 1.519 ± 0.007 ps.


colour gif / colour eps / black-and-white eps /

Same without average including time-integrated (χd) measurements:
colour eps / black-and-white eps /

Only measurements and average at LEP and CDF1:
colour eps / black-and-white eps /

Only measurements and average at LEP:
colour eps / black-and-white eps /

Only measurements and average at asymmetric B factories:
colour eps / black-and-white 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 χd average from ARGUS and CLEO is converted to a Δmd measurement assuming no CP violation, no width difference in the B0 system and a B0 lifetime of 1.519 ± 0.007 ps.


colour gif / colour eps / black-and-white eps /

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2D average of Δmd and τ(B0)

BABAR and Belle have performed simultaneous measurements of Δmd and τ(B0). The Belle analysis is actually a simultaneous measurement of Δmd, τ(B0) and τ(B+), and has been converted, for the purpose of averaging with the BABAR results, into a 2D measurement of Δmd and τ(B0). 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 Δmd = 0.509 ± 0.006 ps−1 and τ(B0) = 1.527 ± 0.010 ps, with a total (stat+syst) correlation coefficient of −0.23 (note that this result on Δmd is already included in the Δmd world average quoted above).


colour gif / colour eps /

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Bs mixing: oscillations and mass difference

Combined result on B0s mixing, obtained from time-dependent measurements of the oscillation frequency Δms at high-energy hadron colliders:

Δms = 17.69 ± 0.08 ps−1 CDF, LHCb

With a mean B0s lifetime of 1/Γs = 1.495 ± 0.015 ps, a decay width difference of ΔΓs = +0.100 ± 0.013 ps−1 and the assumption of no CP violation in B0s mixing, this leads to

xs = 26.49 ± 0.29
χs = 0.499292 ± 0.000016

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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 so-called dilepton asymmetry ASL, and the real part of εB. The relations between these parameters are as follows (all are exact except the last one which is an approximation valid for small CP violation):
   ASL = (|p/q|2−|q/p|2)/(|p/q|2+|q/p|2) = (1 − |q/p|4)/(1+|q/p|4)
   |q/p| = [(1−ASL)/(1+ASL)]**0.25
   εB = (p−q)/(p+q)
   q/p = (1−εB)/(1+εB)
   ASL ~ 4 Re(εB)/(1+|εB|2)

The parameters |q/p|, ASL and Re(εB)/(1+|εB|2) are thus equivalent. There is CP violation in the mixing if |q/p| is different from 1, i.e. ASL is different from 0.

Averages are given below separately for the B0 and the Bs systems. Two sets of averages are given for the B0 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 Bs mixing). The second table presents an average for the Bs system. Measurements performed at high energy that do not separate the B0 and Bs 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 B0 mixing
|q/p| = 1.0002 ± 0.0028
ASL = −0.0005 ± 0.0056
Re(εB)/(1+|εB|2) = −0.0001 ± 0.0014
from measurements at the Υ(4S)
|q/p| = 1.0017 ± 0.0017
ASL = −0.0033 ± 0.0033
Re(εB)/(1+|εB|2) = −0.0008 ± 0.0008
world average

CP violation parameter in Bs mixing
|q/p| = 1.0052 ± 0.0032
ASL = −0.0105 ± 0.0064
world average

The above world averages ASL(B0) = −0.0033 ± 0.0033 and ASL(Bs) = −0.0105 ± 0.0064 are obtained from a two-dimensional fit of the CLEO, BABAR, Belle and D0 results: the correlation coefficient between them is found to be −0.574 .

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Phase difference between Bs-mixing and b→ccs amplitudes

The weak phase difference φs between the Bs mixing amplitude and the b→ccs decay amplitude of the Bs meson (for example in Bs → J/ψφ) is predicted by the Standard Model to be (approximately) equal to −2βs, where βs = arg(−(Vts Vtb*)/(Vcs Vcb*)) ~ 1 degree. The phase φs = −2βs is the equivalent of 2β for the B0 meson. CDF, D0 and LHCb have published results on this CP-violating parameter. The phase φs has been measured in 4 published analyses: three Bs → J/ψφ analyses from CDF, D0 and LHCb, and one Bs → J/ψf0(980) analysis from LHCb. A combined 2D fit of φs and ΔΓs, without external assumption, yields two symmetric solutions related through φs ↔ π−φs (or βs ↔ π/2−βs) and ΔΓs ↔ −ΔΓs. Only the solution with positive ΔΓs is considered here, as detailed analysis of the strong phases in Bs → J/ψKK by LHCb (arXiv:1202.4717 [hep-ex]) has shown that this is the physical solution. Alternatively, the 2D fit is repeated, but using the external constraint provided by the measured semileptonic asymmetry, ASL(Bs) = Im(Γ12/M12) = −0.0105 ± 0.0064 . The semileptonic asymmetry depends on the phase arg(−Γ12/M12) and on ΔΓs. Since New Physics is expected to affect arg(−Γ12/M12) and φs in the same way, the constraint is implemented under the assumption that a new physics phase in Bs mixing would not change the difference arg(−Γ12/M12)−φs from its Standard Model value.

The table below shows the results with and without ASL(Bs) constraint. The default value of φs (recommended for the 2012 Review of Particle Physics) is the one with the constraint applied, while the recommended value of ΔΓs is the one given above (where φs is constrained to the SM and additional constraints from effective lifetime measurements are applied).

Fit results from
CDF, D0 and LHCb data 		without external constraint
 with constraint from ASL(Bs)
βs +0.07 +0.06 −0.08 +0.08 +0.05 −0.07
φs = −2 βs −0.14 +0.16 −0.11 −0.17 +0.14 −0.11
ΔΓs +0.104 +0.024 −0.013 ps−1 +0.107 +0.021 −0.016 ps−1
Deviation from
Standard Model 		0.8 σ 0.9 σ

The two plots below show different 68% confidence-level contours in the (φs=−2βs, ΔΓs) plane. The left plot shows the individual contours of CDF, D0 and LHCb, together with the combined contour, without the ASL(Bs) constraint. The right plot shows the ASL(Bs) constraint, as well as its effect on the combined contour. The Standard Model predictions shown in these plots are φs = −0.0363+0.0016−0.0015 [CKMfitter, Phys. Rev. D84, 033005 (2011)] and ΔΓs = 0.087 ±0.021 ps−1 [A. Lenz and U. Nierste, arXiv:1102.4274 [hep-ph]].


without ASL(Bs) constraint: colour gif / colour eps / colour pdf /
with ASL(Bs) constraint: colour gif / colour eps / colour pdf /

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b-hadron fractions in Υ(4S) decays

The B+ and B0 fractions below are for an unbiased sample of B-mesons produced in Υ(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 = 1.056 ± 0.028 after adjusting to a common B+/B0 lifetime ratio of 1.079 ± 0.007 (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 = 1.056 ± 0.028 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 Υ(4S) decay ratio
B+ B− f+− = 0.513 ± 0.006 f+−/f00 = 1.055 ± 0.025
B0 anti-B0 f00 = 0.487 ± 0.006
Note that the ratio f+-/f00 differs from unity by 2.2 sigmas.

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b-hadron fractions in Υ(5S) decays

The table below show the fraction of events containing non-strange B mesons (fud), strange B mesons (fs), or no B mesons at all (fnoB) in a sample of Υ(5S) decays, or more precisely in a sample of bb events produced in e+e− collisions at a center-of-mass energy equal to the Υ(5S) mass. The sum of the three fractions is constrained to unity: fud+fs+fnoB=1. Their combined values have been obtained by combining model-dependent estimates of CLEO3 and Belle based on the measurements of several inclusive Υ(5S) branching fractions, after performing adjustments to common external inputs. A one-sided constraint on fnoB 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 fnoB.

final states fraction in Υ(5S) decay ratio of fractions
Bu,d(*) anti-Bu,d(*)(π(π)) fu,d(Υ(5S)) = 0.759 +0.027 −0.040
Bs(*) anti-Bs(*) fs(Υ(5S)) = 0.199 ± 0.030 fs(Υ(5S))/fu,d(Υ(5S)) = 0.262 +0.051 −0.043
no open bottomness fnoB(Υ(5S)) = 0.042 +0.046 −0.006


The plot below shows the published measurements of fs. All values have been obtained assuming fnoB=0. They are quoted as in the original publication, except for the most recent measurement of Belle which is quoted as fs = 1-fud. The average value of all these measurements is quoted with or without the assumption that fnoB=0, after performing adjustments to common external inputs.


colour gif / colour eps / black-and-white eps /

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b-hadron fractions in Z decays

The table below shows the b-hadron fractions in an unbiased sample of weakly decaying b-hadrons produced in Z decays. These fractions have been calculated by combining direct rate measurements performed at LEP with the LEP combined measurement of the time-integrated mixing probability averaged over an unbiased sample of semi-leptonic b-hadron decays, χbar = f'(Bd)χd+f'(Bs)χs = 0.1259 ± 0.0042 . This combination relies on the world average of χd, on the assumption χs = 1/2, as well as on the world averages of the lifetimes of the individual b-hadrons 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(b-baryon)
Bs f(Bs) = 0.103 ± 0.009
b baryons f(b-baryon) = 0.090 ± 0.015 +0.036
B0 or B+ f(Bd) = f(Bu) = 0.403 ± 0.009 −0.522 −0.871
Bs / (B0 or B+) ratio f(Bs)/f(Bd) = 0.256 ± 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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b-hadron fractions in p-pbar collisions at 1.8−2 TeV

The table below shows the b-hadron fractions in an unbiased sample of weakly decaying b-hadrons produced in p-pbar 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 time-integrated mixing probability averaged over an unbiased sample of semi-leptonic b-hadron decays, χbar = 0.147 ± 0.011 . This combination relies on the world average of χd, on the assumption χs = 1/2, as well as on the world averages of the lifetimes of the individual b-hadrons 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 p-pbar collisions at 1.8−2 TeV correlation with f(Bs) correlation with f(b-baryon)
Bs f(Bs) = 0.111 ± 0.014
b baryons f(b-baryon) = 0.212 ± 0.069 −0.581
B0 or B+ f(Bd) = f(Bu) = 0.339 ± 0.031 +0.425 −0.984
Bs / (B0 or B+) ratio f(Bs)/f(Bd) = 0.328 ± 0.039

This is based on the following average of χbar in p-pbar collisions at 1.8−2 TeV:

χbar(Tevatron) = 0.147 ± 0.011 average of CDF and D0 measurements


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b-hadron fractions at high energy

The table below shows the b-hadron fractions in an unbiased sample of weakly decaying b-hadrons produced at high energy. These fractions are assumed to be the same in Z decays or in proton-antiproton 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 time-integrated mixing probability averaged over an unbiased sample of semi-leptonic b-hadron decays, χbar = 0.1284 ± 0.0069 . This combination relies on the world average of χd, on the assumption χs = 1/2, as well as on the world averages of the lifetimes of the individual b-hadrons 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(b-baryon)
Bs f(Bs) = 0.105 ± 0.006
b baryons f(b-baryon) = 0.093 ± 0.016 −0.277
B0 or B+ f(Bd) = f(Bu) = 0.401 ± 0.008 −0.119 −0.921
Bs / (B0 or B+) ratio f(Bs)/f(Bd) = 0.263 ± 0.017

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:




Author: OS 22-Apr-2012
Latest mod. mer avr 18 11:23:41 CEST 2012