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 sub-group of the Heavy Flavour Averaging Group (HFAG). The following material is available publicly: These "end of 2009" averages include in fact all pre-summer 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 [hep-ex]

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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 1.518 ± 0.007 ps
B+ 1.641 ± 0.008 ps 1.081 ± 0.006
Bs 1.477 +0.021 −0.022 ps 0.973 ± 0.015
Bc 0.461 ± 0.036 ps
Λb 1.425 ± 0.032 ps 0.939 ± 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 = (ΓLight + ΓHeavy)/2 is the mean mean decay width of the Bs system. 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 becauses it includes an unknown proportion of short and long components.

mixture of the two Bs mass eigenstates average lifetime
Bs → flavour specific 1.455 ± 0.030 ps
Bs → Ds X 1.458 ± 0.030 ps
Bs → J/ψ φ 1.477 ± 0.046 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 = 0.011 ± 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 performed at Tevatron Run II (earlier measurements would not affect the results), as well as the lifetime measurements using Bs → J/ψ φ decays, flavour-specific Bs decays, Bs decays to CP eigenstates, 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 obtained both without and with some or all of the following external constraints:

  1. the quantity (1/Γs) × (1 + (ΔΓs/Γs)2/4) / (1 − (ΔΓs/Γs)2/4) is constrained to τ(Bs → flavour specific) = 1.455 ± 0.030 ps, which is the average of all lifetime measurements with flavour-specific Bs decays;
  2. the quantity ΓL = Γs (1+ΔΓs/(2Γs)) is constrained to τ(Bs → CP-even) = 1.47 ± 0.16 ps, which is the average of the lifetime measurements with Bs → K+K− and Bs → Ds(*)Ds(*) decays; these two decays are assumed to be 100% CP even, with a 5% theoretical uncertainty;
  3. the quantity 1/(2Γs/ΔΓs+1) is constrained to BR((Bs → Ds(*)Ds(*)) = 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 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 (recommended) set of results is the one where only the constraint I from τ(Bs → 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/Γs 1.506 ± 0.032 ps    1.477 +0.021 −0.022 ps    1.479 ± 0.021 ps   
τShort = 1/ΓL 1.431 +0.038 −0.037 ps    1.425 +0.037 −0.035 ps    1.416 ± 0.027 ps   
τLong = 1/ΓH 1.590 +0.075 +0.071 ps    1.532 ± 0.049 ps    1.548 +0.036 −0.037 ps   
ΔΓs (95% CL range) [ −0.006 ; +0.146 ] ps−1 [ −0.019 ; +0.112 ] ps−1 [ +0.017 ; +0.101 ] ps−1
ΔΓs +0.070 ± 0.039 ps−1 +0.049 +0.033 −0.034 ps−1 +0.060 ± 0.021 ps−1
ΔΓs/Γs (95% CL range) [ −0.011 ; +0.224 ]         [ −0.028 ; +0.167 ]         [ +0.025 ; +0.150 ]        
ΔΓs/Γs +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 2-dim regions, 68% CL for the bands) in the plane (1/Γs, ΔΓs) for the average of all direct measurements (red ellipse), the constraint I given by the Bs lifetime using flavour-specific final states (blue band), and their combination (large solid black ellipse). The combination including in addition constraint II from the Bs lifetime using CP-even final states (not represented) and constraint III from the Bs → Ds(*)Ds(*) branching fraction (green band) is also shown (small dashed black ellipse). The yellow band is a recent 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).


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 /

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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 ± 0.004 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 1.518 ± 0.007 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

Δmd = 0.508 ± 0.004 ps−1
   xd = 0.771 ± 0.007
χd = 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 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 1.518 ± 0.007 ps.


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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 1.518 ± 0.007 ps.


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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).


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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, published in A. Abulencia et al., Phys. Rev. Lett. 97, 242003 (2006), and measured Δms = 17.77 ±0.010 (stat) ± 0.07 (syst) ps−1. In 2007, D0 obtained a preliminary evidence of Bs oscillations and measured Δms = 18.53 ± 0.97 ps−1 (D0 note 5474). The world average is:

Δms = 17.78 ± 0.12 ps−1 CDF+D0 (Run II)

The plots below shows the Bs oscillation amplitude as a function of Δms. An amplitude consistent with 1 is expected at the true value of Δms. An amplitude consistent with 0 is expected far below the true value of Δms. 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 signal-like 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 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| = 1.0024 ± 0.0023
ASL = −0.0047 ± 0.0046
Re(εB)/(1+|εB|2) = −0.0012 ± 0.0011
from measurements at CLEO, BABAR and BELLE
|q/p| = 1.0030 ± 0.0017
ASL = −0.0058 ± 0.0034
Re(εB)/(1+|εB|2) = −0.0015 ± 0.0008
same but adding measurements from ALEPH, OPAL, CDF2 and D0 (and assuming ASL(Bs) = 0)

CP violation parameter in Bs mixing
|q/p| = 1.0044 ± 0.0029
ASL = −0.0088 ± 0.0058
from measurements at CDF and D0
(and assuming ASL(B0) = −0.0047 ± 0.0046 )

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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 ΔΓs, 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 ASL(Bs) observable 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 fits involving ASL(Bs) are 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
ASL(Bs) only		 with all 4 constraints
mentioned above
βs +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
βs (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 ]
φs = −2 βs −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
φs = −2 βs (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 ]
ΔΓs +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
ΔΓs (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 confidence-level
contours in (φs=−2βs, ΔΓs) plane 		Combined: gif / eps
Combined + ASL(Bs): gif / eps
CDF only: gif / eps
D0 only: gif / eps  		Combined: gif / eps Combined: gif / eps

The three plot below show different combined confidence-level contours in the (φs=−2βs, ΔΓs) plane, without external constraint, with ASL(Bs) constraint only, and with all constraints.



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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 = 1.052 ± 0.028 after adjusting to a common B+/B0 lifetime ratio of 1.081 ± 0.006 (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 = 1.052 ± 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 = 1.052 ± 0.025
B0 anti-B0 f00 = 0.487 ± 0.006
Note that the ratio f+-/f00 differs from unity by 2.1 sigmas.

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b-hadron fractions in Υ(5S) decays

The table below show the fraction of events containingr 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 centre-of-mass energy equal to the Υ(5S) mass. The sum of the three fractions is contrained 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 adjustements to common external inputs.

final states fraction in Υ(5S) decay
Bu,d(*) anti-Bu,d(*)(π(π)) fu,d(Υ(5S)) = 0.763 ± 0.046
Bs(*) anti-Bs(*) fs(Υ(5S)) = 0.202 ± 0.036
no open bottomness fnoB(Υ(5S)) = 0.035 ± 0.057


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 adjustements to common external inputs. The fraction fnoB is known to be non-zero, from direct measurements of Υ(5S) decays to final states without bottom mesons.


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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 +0.035
B0 or B+ f(Bd) = f(Bu) = 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


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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) = 0.211 ± 0.069 −0.582
B0 or B+ f(Bd) = f(Bu) = 0.339 ± 0.031 +0.426 −0.984

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) = 0.109 ± 0.012
b baryons f(b-baryon) = 0.083 ± 0.020 −0.053
B0 or B+ f(Bd) = f(Bu) = 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:



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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 Feb 2 00:51:27 CET 2011