Results for the summer 2004 conferences and HFAG paper hep-ex/0412073

32nd International Conference on High Energy Physics, ICHEP04, Beijing (China), August 16-22, 2004

HFAG writeup hep-ex/0412073


Apart from the results listed here, 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:

These combination procedures and averages are described in chapter 3 of the HFAG writeup: hep-ex/0412073


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b-hadron lifetime averages

The lifetimes 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.

b hadron species average lifetime average lifetime relative to B0 average lifetime
B0 1.534 +- 0.013 ps
B+ 1.653 +- 0.014 ps 1.081 +- 0.015
Bs 1.469 +- 0.059 ps 0.958 +- 0.039
Bc 0.45 +- 0.12 ps
Lambda_b 1.232 +- 0.072 ps
Xi_b-, Xi_b0 mixture 1.39 +0.34 -0.28 ps
b-baryon mixture 1.210 +- 0.048 ps 0.789 +- 0.032
b-hadron mixture 1.574 +- 0.008 ps



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Neutral B meson mixing: decay width differences

Combined results on the relative decay width differences DGd/Gd and DGs/Gs in the B0 and Bs systems respectively, obtained from time-dependent measurements:

no combined value of DGd/Gd available yet published results from DELPHI and CLEO
(BABAR preprint submitted, not accepted yet)
DGs/Gs = 0.16 +0.15 -0.16
DGs/Gs < 0.54 at 95% CL
from ALEPH, CDF, DELPHI, L3 and OPAL measurements
DGs/Gs = 0.07 +0.09 -0.07
DGs/Gs < 0.29 at 95% CL
same as above but constraining the mean Bs decay width to be equal to 1/tau(B0) where tau(B0) = 1.534 +- 0.013 ps

In the above, Gs and DGs are defined as Gs = (Gamma_short + Gamma_long)/2, DGs = Gamma_short - Gamma_long > 0, and the CP-even eigenstate is assumed to have the largest decay width (Gamma_short), i.e. the smallest lifetime.

The plot below shows the 68%, 95% and 99% CL 2D-contours of the negative log-likelihood in the plane DGs/Gs - 1/Gs, where DGs is the decay width difference and Gs is the mean decay width in the Bs system. Here DGs is defined as DGs = Gamma_short - Gamma_long > 0, and the CP-even eigenstate is assumed to have the largest decay width (Gamma_short), i.e. the smallest lifetime.


2D eps /

Probability density distribution for DGs/Gs:
1D colour eps / 1D black-and-white eps /

Same as above but constraining the mean Bs decay width to be equal to 1/tau(B0) where tau(B0) = 1.534 +- 0.013 ps:
2D eps / 1D colour eps / 1D black-and-white 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 dmd (at high energy colliders and asymmetric B factories) and from time-integrated measurements of the mixing probability chid at symmetric Upsilon(4S) machines:

dmd = 0.502 +- 0.006 ps-1 from time-dependent measurements at ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE
chid = 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 1.534 +- 0.013 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

dmd = 0.502 +- 0.006 ps-1
   xd = 0.770 +- 0.011
chid = 0.186 +- 0.003
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 chid 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 1.534 +- 0.013 ps.


colour ps / colour eps / black-and-white ps / black-and-white eps /

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

Only measurements and average at high energy colliders:
colour ps / colour eps / black-and-white ps / black-and-white eps /

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

Only measurements and average at asymmetric B factories:
colour ps / colour eps / black-and-white ps / 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 chid 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 1.534 +- 0.013 ps.


colour ps / colour eps / black-and-white ps / black-and-white eps /


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B0s mixing: oscillations and mass difference

Combined results on Bs oscillations:

dms > 14.5 ps-1 at 95% CL
   xs > 20.8 at 95% CL
chis > 0.49885 at 95% CL
from all ALEPH, CDF, DELPHI, OPAL and SLD studies of dms with a combined 95% CL sensitivity on dms of 18.2 ps-1

The above limit on xs is derived from the results of the dms studies assuming a Bs lifetime of 1.469 +- 0.059 ps (the experimental average listed above). The above limit on chis is derived from the limit on xs assuming no CP violation in the mixing and no width difference in the Bs system.

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 14.5 ps-1) are excluded at 95% CL. The combined sensitivity for 95% CL exclusion (equal to 18.2 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.


colour ps / colour eps / colour ps (up to 20 ps-1 only) / colour eps (up to 20 ps-1 only) / ASCII file with numerical data /

Same, but using an additional unpublished result from SLD:
colour ps / colour eps / colour ps (up to 20 ps-1 only) / colour eps (up to 20 ps-1 only) / ASCII file with numerical data /

Same, but using only LEP data:
colour ps / colour eps / colour ps (up to 20 ps-1 only) / colour eps (up to 20 ps-1 only) / ASCII file with numerical data /

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 sensitivites 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 sensitivites for 95% CL exclusion limits.


colour ps / colour eps / black-and-white ps / black-and-white eps /

Same, but at dms=10 ps-1:
colour ps / colour eps / black-and-white ps / black-and-white eps /

Same, but at dms=19 ps-1:
colour ps / colour eps / black-and-white ps / black-and-white eps /


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Neutral B meson mixing: time-integrated results

Time-integrated probability for B0 mixing:

chid = 0.182 +- 0.015 from time-integrated measurements at ARGUS and CLEO
chid = 0.186 +- 0.003 average including time-dependent measurements of dmd and based on different assumptions, as explained above

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

chibar = 0.1257 +- 0.0042 LEP average from LEP EW WG
chibar = 0.152 +- 0.013 CDF measurement
chibar = 0.1282 +- 0.0077 weighted average of above two, with rescaled error according to PDG prescription



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B0 mixing: CP violation

Several different parameters can be used to descibe CP violation in B mixing: |q/p|, the so-called dilepton asymetry A_SL, and the real part of epsilon_B (noted here epsB). The relations between these parameters are as follows (all are exact except the last one which is an approximation valid for small CP violation):
   A_SL = (|p/q|**2 - |q/p|**2 ) / (|p/q|**2 + |q/p|**2 ) = ( 1 - |q/p|**4 ) / ( 1 + |q/p|**4 )
   |q/p| = ( (1-A_SL)/(1+A_SL) )**0.25
   epsilon_B = (p-q)/(p+q)
   q/p = (1-epsilon_B)/(1+epsilon_B)
   A_SL ~ 4 Re(epsB)/(1+|epsB|**2)

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.

|q/p| = 1.0013 +- 0.0034
A_SL = -0.0026 +- 0.0067
Re(epsB)/(1+|epsB|**2) = -0.0007 +- 0.0017
from measurements at LEP, CLEO, BABAR and BELLE


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b-hadron fractions

The fractions below are for 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 sqrt(s)=1.8 TeV. They have been obtained by combining direct rate measurements from LEP and CDF with all available mixing measurements from ALEPH, CDF, DELPHI, L3, OPAL as well as from ARGUS, CLEO, BABAR and BELLE. This includes the average value of chibar = 0.1282 +- 0.0077 listed in the previou section. 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) = 0.104 +- 0.015
b baryons f(b-baryon) = 0.100 +- 0.017 -0.176
B0 or B+ f(Bd) = f(Bu) = 0.398 +- 0.010 -0.566 -0.712

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 = 1.010 +- 0.038 after adjusting to a common B+/B0 lifetime ratio of 1.081 +- 0.015 (the current average given above). On the other hand, BABAR measured directly f00 = 0.486 +- 0.013 without assuming isospin invariance nor relying on the B+/B0 lifetime ratio.

f+-/f00 = 1.010 +- 0.038 from ratios of reconstructed B+ and B0 mesons at BABAR, BELLE and CLEO
(assumptions made, see text above)
f00 = 0.486 +- 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 Upsilon(4S) decay ratio
B+ B- f+- = 0.506 +- 0.008 f+-/f00 = 1.026 +- 0.032
B0 anti-B0 f00 = 0.494 +- 0.008



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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 consists mainly of the b hadron fractions and lifetimes given above.



Author: OS 04-Jul-2004
Latest mod. 29-Dec-2004