Results for the PDG 2010 review

Only results published (or accepted in a refereed journal) by March 15, 2010 have been included in the averages computed by the lifetime and oscillations sub-group of the Heavy Flavour Averaging Group (HFAG) for the 2010 update of the Particle Data Group review. The following material is available publicly: The combination procedures are described in Chapter 3 of the following HFAG writeup: arXiv:0808.1297v3 [hep-ex] (this writeup describes the "end 2007" averages, which also include preliminary results as well as some results released in the first half of 2008; these averages do not include results published after that; hence they are not identical to the ones presented here).

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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, OPAL and SLD. Decay width differences in the B0 and Bs systems have been ignored. The mixtures refer to samples of weakly decaying b-hadrons produced at high energy (mostly in Z decays).

b hadron species average lifetime average lifetime relative to B0 average lifetime
B0 1.525 ± 0.009 ps
B+ 1.638 ± 0.011 ps 1.071 ± 0.009
Bs 1.472 +0.024 −0.026 ps 0.965 ± 0.017
Bc 0.453 ± 0.041 ps
Λb 1.391 +0.038 −0.037 ps 0.912 ± 0.025
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 1.345 ± 0.032 ps 0.882 ± 0.022
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 = (ΓLight + ΓHeavy)/2 is the mean mean decay width of the Bs system. The Λb lifetime average include a measurement which is 2.8 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 becauses it includes an unknown proportion of short and long components.

mixture of the two Bs mass eigenstates average lifetime
Bs → flavour specific 1.417 ± 0.042 ps
Bs → Ds X 1.425 ± 0.041 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. 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 = 0.010 ± 0.037 from 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/ψKLong), 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 decay-width difference in the Bs system are extracted from a global fit including all direct measurements of ΔΓs/Γs, as well as the lifetime measurements using Bs → J/ψ φ decays and flavour-specific Bs decaysi, and the measurements of the Bs → Ds(*)Ds(*) branching fraction (CDF, D0, ALEPH and DELPHI data). This extraction is done under the assumption of no CP violation (see elsewhere for an extraction in presence of CP violation). The results in the table below are shown both with and without constraining the quantity (1/Γs) × (1 + (ΔΓs/Γs)2/4) / (1 − (ΔΓs/Γs)2/4) to the flavour-specific Bs lifetime average, and the quantity 1/(2Γs/ΔΓs+1) to BR((Bs → Ds(*)Ds(*)) = 0.044 ± 0.015 . In the application of the latter constraint as a Gaussian penalty function, the theoretical uncertainty is dealt with in two ways: the PDF of the CP-odd fraction of Bs → Ds(*)Ds(*) is taken to be a uniform distribution ranging from 0 to 0.05 and convoluted in the Gaussian; alternatively, the fractional uncertainty on the measured value of the branching fraction is increased in quadrature by 30%, and the more conservative result is taken. The default set of results (recommended for the 2010 Review of Particle Physics) is the one where only the constraint from τ(Bs → flavour specific) is applied.

Fit results from CDF, D0,
ALEPH and DELPHI data 		without constraint from
τ(Bs → flavour specific)
nor BR(Bs → Ds(*)Ds(*))		 with constraint from
τ(Bs → flavour specific)
only		 with constraint from
τ(Bs → flavour specific)
and BR(Bs → Ds(*)Ds(*))
1/Γs 1.515 +0.034 −0.034 ps    1.472 +0.024 −0.026 ps    1.472 ± 0.024 ps   
τShort = 1/ΓL 1.407 +0.035 −0.034 ps    1.408 +0.033 −0.030 ps    1.408 +0.028 −0.027 ps   
τLong = 1/ΓH 1.642 +0.091 +0.083 ps    1.543 +0.058 +0.060 ps    1.544 ± 0.041 ps   
ΔΓs (95% CL range) [ +0.016 ; +0.192 ] ps−1 [ −0.013 ; +0.130 ] ps−1 [ +0.018 ; +0.102 ] ps−1
ΔΓs +0.102 +0.043 −0.043 ps−1 +0.062 +0.034 −0.037 ps−1 +0.063 ± 0.022 ps−1
ΔΓs/Γs (95% CL range) [ +0.024 ; +0.290 ]         [ −0.020 ; +0.193 ]         [ +0.027 ; +0.155 ]        
ΔΓs/Γs +0.154 +0.067 −0.065         +0.092 +0.051 −0.054         +0.092 +0.032 −0.033        

The left plot below shows contours of Δ(log(L)) = 0.5 (39% CL for the enclosed 2-dim regions, 68% CL for the bands) in the plane (1/Γs, ΔΓs) for the average of all direct measurements (red), the constraint given by the Bs lifetime using flavour-specific final states (blue), and their combination (black). The yellow band is a theory prediction ΔΓs = 0.088 ±0.017 ps−1 which assumes no new physics in Bs mixing [A. Lenz and U. Nierste, JHEP 06 (2007) 072]. The right plot below shows the same contours in the plane (1/ΓL, 1/ΓH). In both cases, the blue band represents the average 1.417 ± 0.044 ps which includes all lifetime measurements with flavour-specific Bs decays, except those which are not independent of the direct measurements used in the ΔΓs averaging.


Above plots: (1/Γs, ΔΓs) gif / (1/ΓL, 1/ΓH) gif / (1/Γs, ΔΓs) eps / (1/ΓL, 1/ΓH) eps /
Another (1/Γs, ΔΓs) plot showing only the direct measurements and their average: gif / eps /
The two plots below are similar to the plots above, but represent the combined results when including the additional contraint from BR((Bs → Ds(*)Ds(*)) = ( 0.044 ± 0.015 ) × (1 ± 0.3(theory)), shown as a green band.


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

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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 = 0.508 ± 0.005 ps−1 from time-dependent measurements at ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE
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 1.525 ± 0.009 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

Δmd = 0.507 ± 0.005 ps−1
   xd = 0.774 ± 0.008
χd = 0.1873 ± 0.0024 		from all ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, ARGUS and CLEO measurements

In the plot below, all individual measurements are listed as quoted by the experiments; they might assume different physics inputs. The averages (which take into account all known correlations) are quoted after adjusting all the individual measurements to the common set of physics inputs. The 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 1.525 ± 0.009 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 1.525 ± 0.009 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 1.638 ± 0.011 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

In 2006, CDF has obtained the first direct evidence for and then the first observation of Bs oscillations. The measured value of Δms is (A. Abulencia et al., Phys. Rev. Lett. 97, 242003 (2006)):

Δms = 17.77 ± 0.10 (stat) ± 0.07 (syst) ps−1 CDF (Run II)

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Neutral B meson mixing: CP violation

Several different parameters can be used to describe CP violation in B mixing: |q/p|, the so-called dilepton asymetry 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 (including those performed at high energy, but under the assumption of no CP violation in Bs mixing). The second table presents an average for the Bs system, based on measurements performed at the Tevatron, where some analyses measure a mixture of the B0 and Bs parameters: the effect from the Bs is then isolated by using the value and error of the B0 parameter obtained at the B factories.

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 CLEO, BABAR and BELLE
|q/p| = 1.0025 ± 0.0019
ASL = −0.0049 ± 0.0038
Re(εB)/(1+|εB|2) = −0.0012 ± 0.0010
same but adding measurements from ALEPH, OPAL and D0 (and assuming ASL(Bs) = 0)

CP violation parameter in Bs mixing
|q/p| = 1.0018 ± 0.0047
ASL = −0.0036 ± 0.0094
from measurements at CDF and D0
(and assuming ASL(B0) = −0.0005 ± 0.0056 )

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Phase difference between Bs-mixing and b→ccs amplitudes

The phase difference φs = −2βs between the Bs mixing amplitude and the b→ccs decay amplitude of the Bs meson (for example in Bs → J/ψφ) is the equivalent of 2β for the B0 meson. In the Standard Model βs = arg(−(Vts Vtb*)/(Vcs Vcb*)) ~ 1 degree. CDF and D0 have published results on this CP-violating parameter. Combined 2D fits of βs and DGs, without external assumption, yield two symmetric solutions related through βs ↔ π/2−βs (or φs ↔ π−φs) and ΔΓs ↔ −ΔΓs. Alternatively, the 2D fit is repeated, but using external constraints provided by the flavour-specific Bs lifetime, τ(Bs → flavour-specific) = (1/Γs)[1+((ΔΓs/(2Γs))2]/ [1−((ΔΓs/(2Γs))2] = 1.417 ± 0.042 ps and by the semileptonic asymmetry, ASL(Bs) = Im(Γ12/M12) = −0.0036 ± 0.0094 . The latter is sensitive to the angle arg(−Γ12/M12), which is predicted to be very small in the Standard Model. A new physics phase in Bs mixing would affect arg(−Γ12/M12) and −2βs in the same manner. The constrained fit is performed under the assumption that this new physics contribution is much larger than both the Standard Model values of arg(−Γ12/M12) and βs.

Fit results from
CDF and D0 data 		without external
constraints
 with constraint from
τ(Bs → flavour specific)
and ASL(Bs)
βs +0.39 +0.18 −0.14 or +1.18 +0.14 −0.18 +0.47 +0.13 −0.21 or +1.09 +0.21 −0.13
βs (90% CL range) [ +0.14 ; +0.73 ] ∪ [ +0.82 ; +1.43 ] [ +0.10 ; +0.68 ] ∪ [ +0.89 ; +1.47 ]
φs = −2 βs −0.77 +0.29 −0.37 or −2.36 +0.37 −0.29 −0.94 +0.43 −0.25 or −2.19 +0.25 −0.43
φs = −2 βs (90% CL range) [ −1.47 ; −0.29 ] ∪ [ −2.85 ; −1.65 ] [ −1.35 ; −0.20 ] ∪ [ −2.94 ; −1.77 ]
ΔΓs +0.154 +0.054 −0.070 or −0.154 +0.070 −0.054 ps−1 +0.098 +0.075 −0.026 or −0.098 +0.026 −0.075 ps−1
ΔΓs (90% CL range) [ +0.036 ; +0.264 ] ∪ [ −0.264 ; −0.036 ] ps−1 [ −0.163 ; +0.163 ] ps−1

The two plot below shows different confidence-level contours in the (φs=−2βs, ΔΓs) plane, with and without the two external constraints.


Above combined plots: without constraint (gif,pdf,eps) / with both contraints (gif,pdf,eps)
Individual plots (without external constraint): CDF (gif,pdf,eps) / D0 (gif,pdf,eps)

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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 = 1.068 ± 0.029 after adjusting to a common B+/B0 lifetime ratio of 1.071 ± 0.009 (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 = 1.068 ± 0.029 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+− = 0.516 ± 0.006 f+−/f00 = 1.065 ± 0.026
B0 anti-B0 f00 = 0.484 ± 0.006
Note that the ratio f+-/f00 differs from unity by 2.5 sigmas.

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b-hadron fractions in Υ(5S) decays

The table and plot below show the fraction fs(*)(*) of Bs(*) anti-Bs(*) events over all events with a pair of b-flavored mesons produced in e+e- collisions at a centre-of-mass energy equal to the Υ(5S) mass. Since all Bs* mesons decay to a Bs meson (by photon emission), this fraction is equal to the probability fs(Υ(5S)) that a weakly decaying b-hadron produced in such collisions be a Bs meson. The average for this fraction has been obtained by combining model-dependent estimates of CLEO3 and Belle based on the measurements of several inclusive Υ(5S) branching fractions, after performing adjustements to common external inputs. Most of this Bs production proceeds in the Bs* anti-Bs* channel, with the ratio of Bs* anti-Bs* events over Bs(*) anti-Bs(*) events (from Belle, R. Louvot et al, PRL 102, 021801 (2009)) indicated in the table.

b hadron species fraction in Υ(5S) decay ratio
Bs(*) anti-Bs(*) fs(*)(*) = fs(Υ(5S)) = 0.194 ± 0.029
Bs* anti-Bs* fs** fs**/fs(*)(*) = 0.901 +0.038−0.040



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) = 0.104 ± 0.009
b baryons f(b-baryon) = 0.091 ± 0.015 +0.017
B0 or B+ f(Bd) = f(Bu) = 0.403 ± 0.009 −0.522 −0.862

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

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


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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) = 0.121 ± 0.015
b baryons f(b-baryon) = 0.214 ± 0.068 −0.603
B0 or B+ f(Bd) = f(Bu) = 0.333 ± 0.030 +0.439 −0.981

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) = 0.113 ± 0.013
b baryons f(b-baryon) = 0.085 ± 0.022 −0.041
B0 or B+ f(Bd) = f(Bu) = 0.401 ± 0.013 −0.483 −0.855

This is based on the following average of χbar at high energy:

χbar = 0.1259 ± 0.0042 LEP average from LEP EW WG
χbar = 0.147 ± 0.011 Tevatron average
χbar = 0.1284 ± 0.0069 weighted average of above two, with error rescaled by factor 1.8 according to PDG prescription

Note:



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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 13-Apr-2010
Latest mod. Wed Apr 14 09:18:27 CEST 2010