PDG 2021 averages

All results published before March 1, 2021 have been included in the averages computed by the lifetime and oscillations sub-group of the Heavy Flavour Averaging Group (HFLAV) for the 2021 web updatweb update of the Particle Data Group. The following material is available: The combination procedures are described in Chapter 4 of the HFLAV publication quoted just below. Averages or plots obtained from this web page should be quoted as

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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, ATLAS, BABAR, BELLE, CDF, CMS, D0, DELPHI, L3, LHCb, OPAL and SLD.

b-hadron species average lifetime lifetime ratio
B0 1.519 ± 0.004 ps
B+ 1.638 ± 0.004 ps B+/B0 = 1.076 ± 0.004
Bs0 1.516 ± 0.006 ps Bs0/B0 = 0.998 ± 0.005
BsL 1.427 ± 0.007 ps
BsH 1.616 ± 0.010 ps
Bc+ 0.510 ± 0.009 ps
Λb 1.471 ± 0.009 ps Λb/B0 = 0.969 ± 0.006
Ξb− 1.572 ± 0.040 ps
Ξb0 1.480 ± 0.030 ps Ξb0/Ξb− = 0.929 ± 0.028
Ωb− 1.64 +0.18 −0.17 ps
b-hadron average
(weighted by fractions
in Z decays) 		1.5667 ± 0.0029 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 (BsL and BsH). The Λb lifetime average is computed using only measurements with fully reconstructed hadronic decays; the measurements are slighlty discrepant (see plot), but no scale factor is applied on the combined error. The b-hadron average ignores the rare species (Bc and b baryons other than Λb).

The tables below give a number of effective Bs lifetime averages, measured from single exponential fits of the proper time distributions of Bs decays to a number of interesting final states. In general each final state may be a different mixture of the two Bs mass eigenstates, and hence the effective lifetime falls somewhere between 1/ΓL and 1/ΓH. 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 → 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). The Bs → μ+μ- effective lifetime is expected to be equal to the long lifetime in the Standard Model, but could be a mixture.

mixture of the two
Bs mass eigenstates 		effective lifetime from
single exponential fits
Bs → flavour specific 1.527 ± 0.011 ps
Bs → J/ψφ 1.480 ± 0.007 ps
Bs → μ+μ- 1.91 +0.37 −0.35 ps

The two tables below report effective Bs lifetime averages for final states that are either pure CP-even or pure CP-odd eigenstates. If the corresponding Bs decays are dominated by a single weak phase and if CP violation can be neglected, then the effective lifetime for decays to CP-even (CP-odd) eigenstates corresponds to 1/ΓL (1/ΓH). These averages are used as constraints in the fit to determine Γs and ΔΓs (see further below).

CP-even final states effective lifetime from
single exponential fits
Bs →  J/ψη,   Ds+Ds− 1.422 ± 0.023 ps

CP-odd final states effective lifetime from
single exponential fits
Bs →  J/ψf0(980),   J/ψπ+π− 1.666 ± 0.024 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 some 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 = 0.001 ± 0.010 from DELPHI, BABAR, Belle, ATLAS, CMS and LHCb

The quantity s = sign(Re(λCP)), where λCP = (q/p)×ACP/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 time-dependent and tagged angular analyses of the Bs → J/ψ φ decay by ATLAS, CMS, CDF and D0, as well as those of the Bs → J/ψKK and Bs → ψ(2S)φ decays by LHCb, provide information on Γs, ΔΓs and the weak phase φsccs, defined as the phase difference between the mixing amplitude and the b→ccs decay amplitude of the Bs meson. Combined values of the average decay width Γs and the decay width difference ΔΓs are obtained from of a multi-dimensional fit of the experimental results, extracting several other physics parameters in addition to Γs, ΔΓs and φsccs. The φsccsaverage is given further below. The correlation matrix between all physics parameters in each analysis is taken into account. Due to tensions between analyses for some of the measured parameters, scale factors are applied on their errors. The scale factors are calculated per parameter, in one dimension, using the PDG prescription. For example the scale factors of the errors of Γs, ΔΓs and φsccs are 2.5, 1.77 and 1, respectively. The scale factors are applied in a way that preserves the total correlation matrix of each analysis. The following additional constraints are then applied, using effective lifetime measurements:

  1. Bs → J/ψf0(980) lifetime measurements from CDF and D0, and Bs → J/ψπ+π− lifetime measurement from LHCb (Run 1 only) and CMS (pure CP-odd final states), which average to τ(Bs→ CP-odd) = 1.666 ± 0.024 ps, taken to be equal to (1/ΓH)×[1−(φsccs)2×ΔΓs/4];
  2. Bs → J/ψη and Bs → Ds+Ds− lifetime measurement from LHCb (pure CP-even final states), which average to τ(Bs→ CP-even) = 1.422 ± 0.023 ps, taken to be equal to (1/ΓL)×[1+(φsccs)2×ΔΓs/4];
  3. flavour-specific Bs lifetime average τ(Bs → flavour specific) = 1.527 ± 0.011 ps, taken to be equal to (1/Γs) × (1 + (ΔΓs/Γs)2/4) / (1 − (ΔΓs/Γs)2/4).
The implementation of constraints I and II, described in full in the literature [R. Fleischer and R. Knegjens, Eur. Phys. J. C (2011) 1789], neglects here possible sub-leading 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, CMS,
D0 and LHCb data 		without constraint
from effective
lifetime measurements 		with constraints
I and II 		with constraints
I, II and III
Γs 0.6628 ± 0.0035 ps−1 0.6596 ± 0.0031 ps−1 0.6597 ± 0.0026 ps−1
1/Γs 1.509 ± 0.008 ps    1.516 ± 0.007 ps    1.516 ± 0.006 ps   
τShort = 1/ΓL 1.426 ± 0.008 ps    1.427 ± 0.008 ps    1.427 ± 0.007 ps   
τLong = 1/ΓH 1.601 ± 0.013 ps    1.616 ± 0.012 ps    1.616 ± 0.010 ps   
ΔΓs +0.077 ± 0.006 ps−1 +0.082 ± 0.005 ps−1 +0.082 ± 0.005 ps−1
ΔΓs/Γs +0.115 ± 0.009         +0.124 ± 0.008         +0.124 ± 0.008        
correlation ρ(Γs, ΔΓs) −0.240 −0.170 −0.070



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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 = 0.5065 ± 0.0019 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 using the B0 lifetime average of 1.519 ± 0.004 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

Δmd = 0.5065 ± 0.0019 ps−1
   xd = 0.769 ± 0.004
χd = 0.1858 ± 0.0011 		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 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 ± 0.004 ps.


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Same without average including time-integrated (χd) measurements:
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Only measurements and average at LEP:
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Only measurements and average at Tevatron:
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Only measurements and average at asymmetric B factories:
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In the plot below, the 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 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 ± 0.004 ps.


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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 = 17.741 ± 0.020 ps−1 CDF, LHCb, CMS
(see plot)

With a mean B0s lifetime of 1/Γs = 1.516 ± 0.006 ps, a decay width difference of ΔΓs = +0.082 ± 0.005 ps−1 and the assumption of no CP violation in B0s mixing, this leads to

xs = 26.89 ± 0.11
χs = 0.499312 ± 0.000006

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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 and LHCb).

CP violation parameter in B0 mixing
|q/p| = 1.0009 ± 0.0013
ASL = −0.0019 ± 0.0027
Re(εB)/(1+|εB|2) = −0.0005 ± 0.0007
from measurements at the Υ(4S)
|q/p| = 1.0010 ± 0.0008
ASL = −0.0021 ± 0.0017
Re(εB)/(1+|εB|2) = −0.0005 ± 0.0004
world average

CP violation parameter in Bs mixing
|q/p| = 1.0003 ± 0.0014
ASL = −0.0006 ± 0.0028
world average

The above world averages ASL(B0) = −0.0021 ± 0.0017 and ASL(Bs) = −0.0006 ± 0.0028 are obtained from a two-dimensional fit of the CLEO, BABAR, Belle, D0 and LHCb results: the correlation coefficient between them is found to be −0.054 . This is illustrated in the plot below, where the vertical band shows the B-factory average of ASL(B0) (measurements performed by CLEO, BABAR and Belle at the Υ(4S)), the green ellipses the D0 measurements, the blue ellipse the LHCb measurements, and the red ellipse the result of the two-dimensional averaging of all measurements. The red point close to (0,0) is the Standard Model prediction [M. Artuso, G. Borissov and A. Lenz, arXiv:1511.09466 [hep-ph]] with errors bars multiplied by 10. The prediction and experimental average deviate from each other by 0.5 σ.


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CP violation in Bs mixing is caused by the weak phase difference φ12=arg[−M12/Γ12], where M12 and Γ12 are the off-diagonal elements of the mass and decay matrices. The tangent of this phase difference can be estimated (approximately) as ASL(Bs) Δms/ΔΓs= −0.1 ± 0.6 using the above averages of ASL(Bs), Δms and ΔΓs.

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Phase difference between Bs-mixing and b→ccs amplitudes

The weak phase difference φsccs 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 −2βs is the equivalent of 2β for the B0 meson. The phase φsccs has been measured in several analyses: Bs → J/ψφ analyses from CDF, D0, ATLAS and CMS, and analyses from LHCb of the decay modes Bs → J/ψK+K− (including Bs → J/ψφ), Bs → ψ(2S)φ, Bs → J/ψπ+π− and Bs → DsDs. A combined multi-dimentional fit of φsccs, ΔΓs, Γs and other physics parameters is performed. The correlation matrix between all physics parameters in each analysis is taken into account. Due to tensions between analyses for some of the measured parameters, scale factors are applied on their errors. The scale factors are calculated per parameter, in one dimension, using the PDG prescription. For example the scale factors of the errors of Γs, ΔΓs and φsccs are 2.5, 1.77 and 1, respectively. The scale factors are applied in a way that preserves the total correlation matrix of each analysis.

Combined result from
CDF, D0, ATLAS, CMS and LHCb data
(complete list of inputs and references)
φsccs −0.050 ± 0.019

The two plots below show some of the results of the multi-dimentional fit. The plot on the left shows, in the (φsccs, ΔΓs) plane, the individual 68% confidence-level contours of ATLAS, CMS, CDF, D0 and LHCb, their combined contour (black solid line and shaded area), as well as the Standard Model predictions (very thin white rectangle). The prediction for φsccs is taken as the indirect determination of −2βs via a global fit to experimental data within the Standard Model, −2βs = −0.0370 +0.0007 −0.0008 [CKMfitter, Phys. Rev. D84, 033005 (2011), updated with Summer 2019 results], while the Standard Model prediction for ΔΓs is 0.091 ±0.013 ps−1 [A. Lenz and G. Tetlalmatzi-Xolocotzi, JHEP 07 (2020) 177]. The combined result is consistent with these predictions. The plot on the right shows, in the (Γs, ΔΓs) plane, the individual 68% confidence-level contours of ATLAS, CMS, CDF, D0 and LHCb, their combined contour (black solid line and shaded area), as well as the Standard Model prediction for ΔΓs (horizontal gray band). Because of tensions between the measurements, the errors on Γs and ΔΓs have been scaled by 2.5 and 1.77, respectively (the ellipses representing the results of each experiment are shown before scaling, while the combined ellipses include the scale factors).


Left plot in several formats: jpg / png / eps / pdf /
Right plot in several formats: jpg / png / eps / pdf /

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b-hadron fractions in Υ(4S) decays

[This section is no longer updated. The averages computed for PDG 2020 are reported.]

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 = 1.059 ± 0.027 after adjusting to a common B+/B0 lifetime ratio of 1.076 ± 0.004 (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 = 1.059 ± 0.027 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+− = 0.514 ± 0.006 f+−/f00 = 1.058 ± 0.024
B0 B0 f00 = 0.486 ± 0.006
Note that the ratio f+-/f00 differs from unity by 2.4 σ.

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b-hadron fractions in Υ(5S) decays

[This section is no longer updated. The averages computed for PDG 2020 are reported.]

The table below show the fraction of events containing non-strange B mesons (fu,d), 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 centre-of-mass energy equal to the Υ(5S) mass. The sum of the three fractions is constrained to unity: fu,d+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, causing the strongly asymmetric uncertainty on the final value of fnoB.

final states fraction in Υ(5S) decays ratio of fractions
Bu,d(*) Bu,d(*)(π(π)) fu,d  = 0.757 +0.027 −0.039
Bs(*) Bs(*) fs     = 0.199 +0.030 −0.029 fs / fu,d = 0.262 +0.052 −0.043
no open bottomness fnoB = 0.045 +0.045 −0.005


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.


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b-hadron fractions in Z decays

[This section is no longer updated. The averages computed for PDG 2020 are reported.]

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, χ = 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) = 0.100 ± 0.008
b baryons f(b-baryon) = 0.084 ± 0.011 +0.064
B0 or B+ f(Bd) = f(Bu) = 0.408 ± 0.007 −0.633 −0.813
Bs / (B0 or B+) ratio f(Bs)/f(Bd) = 0.246 ± 0.023

This is based on the following average of χ in Z decays:

  χ(LEP) = 0.1259 ± 0.0042     LEP average from LEP EW WG


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b-hadron fractions in pp collisions at 1.8−2 TeV

[This section is no longer updated. The averages computed for PDG 2020 are reported.]

The table below shows the b-hadron fractions in an unbiased sample of weakly decaying b-hadrons produced in pp 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, χ = 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 pp collisions
at 1.8−2 TeV		 correlation with f(Bs) correlation with f(b-baryon)
Bs f(Bs) = 0.115 ± 0.013
b baryons f(b-baryon) = 0.198 ± 0.046 −0.429
B0 or B+ f(Bd) = f(Bu) = 0.344 ± 0.021 +0.159 −0.960
Bs / (B0 or B+) ratio f(Bs)/f(Bd) = 0.333 ± 0.040

This is based on the following average of χ in pp collisions at 1.8−2 TeV:

  χ(Tevatron) = 0.147 ± 0.011     Average of CDF and D0 measurements


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b-hadron fractions at high energy

This section used to present, but now no longer presents, averages for the b-hadron fractions in an unbiased sample of weakly decaying b-hadrons produced at high energy, computed under the assumption that they are the same in Z decays, in pp collisions at the Tevatron (√s=1.8−2 TeV) or in proton-proton collisions at the LHC (√s=7−13 TeV). While this assumption was plausible in the past, it is now known since quite a few years that it is incorrect. The available data show that the fractions depend on the kinematics of the produced b hadron. Both CDF and LHCb reported a transverse-momentum (pT ) dependence of the fractions, with the fraction of Λb baryons observed at low pT being enhanced with respect to that seen at LEP at higher pT.


Author: OS 04-apr-2021
Latest mod. Sat Apr 3 18:36:41 CEST 2021