Results after the summer and fall 2005 conferences

All results available publicly (published and preliminary) have been included in the averages computed by the lifetime and oscillations sub-group of the Heavy Flavour Average Group (HFAG). The following material is available publicly:

• b-hadron lifetimes
• Neutral B meson mixing: decay width differences
• B0 mixing: oscillations and mass difference
• 2D average of dmd and tau(B0)
• B0s mixing: oscillations and mass difference
• Neutral B meson mixing: time-integrated results
• B0 mixing: CP violation
• b-hadron fractions
• Notes on combination procedures

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b-hadron lifetime averages

These results are used as input to extract the long and short lifetimes of the Bs system (see next section).

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Neutral B meson mixing: decay width differences

Combined result on the relative decay width difference in the B0 system:

The quantity s = sign(Re(&lambda_CP)), where &lambda_CP = (q/p)*Abar_CP/A_CP refers to a CP-even final state (e.g. J/psi K_long), 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 &Delta&Gamma_s/&Gamma_s, as well as the lifetime measurements using Bs -> J/psi phi decays and flavour-specific Bs decays (ALEPH, CDF and DELPHI data). The results in the table below are shown both with and without constraining the quantity (1/&Gamma_s) * (1 + (&Delta&Gamma_s/&Gamma_s)²/4) / (1 - (&Delta&Gamma_s/&Gamma_s)²/4) to the flavour-specific Bs lifetime average:

(1/&Gamma_s, &Delta&Gamma_s/&Gamma_s)eps / (1/&Gamma_L, 1/&Gamma_H)eps /

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B0 mixing: oscillations and mass difference

Assuming no CP violation in the mixing and no width difference in the B0 system, and assuming a B0 lifetime of 1.527 +- 0.008 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

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 &chi_d average from ARGUS and CLEO is converted to a dmd measurement assuming no CP violation, no width difference in the B0 system and a B0 lifetime of 1.527 +- 0.008 ps.

colour eps / black-and-white eps /

Same without average including time-integrated (&chi_d) measurements:
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Only measurements and average at LEP and CDF1:
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Only measurements and average at LEP:
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Only measurements and average at asymmetric B factories:
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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 &chi_d average from ARGUS and CLEO is converted to a dmd measurement assuming no CP violation, no width difference in the B0 system and a B0 lifetime of 1.527 +- 0.008 ps.

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2D average of dmd and tau(B0)

• 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)

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B0s mixing: oscillations and mass difference

In the plot below, the combined Bs amplitude is displayed as function of dms. All measurements have been adjusted to the common set of inputs before averaging. Systematic correlations are taken into account. An amplitude consistent with 1 is expected at the true value of dms. An amplitude consistent with 0 is expected far below the true value of dms. All values of dms for which the combined amplitude plus 1.645 times its total uncertainty is smaller than 1 (in this case all values of dms below 16.6 ps-1) are excluded at 95% CL. The combined sensitivity for 95% CL exclusion (equal to 20.0 ps-1 in this case) is defined as the value of dms at which the total uncertainty on the measured amplitude is equal to 1/1.645.

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Same, but using an additional unpublished result from SLD:
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Same, but using only LEP data:
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In the plot below, all individual measurements of the Bs oscillation amplitude at a fixed value of dms are listed as quoted by the experiments (or obtained by a linear interpolation between other dms values at which the experiment did the measurements); they might assume different physics inputs. The sensitivity quoted for each experiment is obtained from the positive amplitude uncertainty, without performing adjustments. The average and combined sensitivity are obtained after adjusting all the individual measurements to the common set of physics inputs. The sensitivities are defined as the value of dms at which the positive uncertainty on the measured amplitude is equal to 1/1.645; they correspond to sensitivities for 95% CL exclusion limits.

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Same, but at dms=10 ps-1:
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Same, but at dms=20 ps-1:
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Neutral B meson mixing: time-integrated results

Time-integrated mixing probability for a mixtures of b-hadrons at high-energy decaying semi-leptonically:

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B0 mixing: CP violation

There is CP violation in the mixing if |q/p| is different from 1, i.e. A_SL is different from 0. The averages given below for the B0-B0bar system are all equivalent.

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b-hadron fractions

Note: more precise fractions could be obtained by ignoring the Tevatron data and using only LEP measurements (because one would use a more precise chibar value, from LEP only). In the future, we will try to provide two additional sets of fraction averages: one obtained from LEP data only, and one obtained from Tevatron data only.

The B+ and B0 fractions below are for an unbiased sample of B-mesons produced in Upsilon(4S) decays. Most analyses measure the ratio f+-/f00 assuming isospin invariance in charged and neutral B decays,r 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 = 1.020 +- 0.034 after adjusting to a common B+/B0 lifetime ratio of 1.076 +- 0.008 (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.

Assuming f+- + f00 = 1, the above two independent results (which are consistent with each other) can be combined to yield:

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Notes on the combination procedures