Results for the PDG 2006 review of particle physics


Only results published (or accepted in a refereed journal) before March 20, 2006 have been included in the averages computed by the lifetime and oscillations sub-group of the Heavy Flavour Average Group (HFAG) for the 2006 Particle Data Group review. The following material is available publicly:
The combination procedures are described in Chapter 3 of the following HFAG writeup: hep-ex/0603003 (this writeup describes the "end of 2005 averages", which also include preliminary results).


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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 1.530 +- 0.009 ps
B+ 1.638 +- 0.011 ps 1.071 +- 0.009
Bs 1.466 +- 0.059 ps 0.958 +- 0.039
Bc 0.46 +0.18 -0.16 ps
Lambda_b 1.230 +- 0.074 ps
Xi_b-, Xi_b0 mixture 1.39 +0.34 -0.28 ps
b-baryon mixture 1.209 +- 0.049 ps 0.790 +- 0.032
b-hadron mixture 1.568 +- 0.009 ps

The above Bs lifetime average includes all published measurements, except the ones performed using J/psi phi final states. It is "ill-defined" because it includes an unknown proportion of long and short components. Other (well-defined) averages are provided below:

mixture of the two Bs mass eigenstates average lifetime
Bs -> flavour specific 1.442 +- 0.066 ps
Bs -> J/psi phi 1.429 +- 0.088 ps

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

For both the B0 and Bs systems, the mean decay width and the decay width difference are defined here as &Delta&Gamma = &GammaL - &GammaH and &Gamma = (&GammaL + &GammaH)/2, where &GammaL (&GammaH) is the decay width of the light (heavy) mass eigenstate. In the Standard Model, one expects &Delta&Gamma > 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*&Delta&Gammad/&Gammad = 0.009 +- 0.037 from BABAR and DELPHI

The quantity s = sign(Re(&lambdaCP)), where &lambdaCP = (q/p)*AbarCP/ACP 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&Gammas/&Gammas, 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/&Gammas) * (1 + (&Delta&Gammas/&Gammas)2/4) / (1 - (&Delta&Gammas/&Gammas)2/4) to the flavour-specific Bs lifetime average:

Fit results from ALEPH,
CDF and DELPHI data
without constraint from
tau(Bs -> flavour specific)
with constraint from
tau(Bs -> flavour specific)
&Delta&Gammas/&Gammas (95% CL range) [ +0.01 ; +0.59 ]         [ -0.02 ; +0.60 ]        
&Delta&Gammas/&Gammas +0.35 +0.12 -0.16         +0.31 +0.11 -0.13        
&Delta&Gammas +0.25 +0.09 -0.11 ps-1 +0.22 +- 0.09 ps-1
1/&Gammas 1.42 +0.06 -0.07 ps    1.398 +0.049 -0.050 ps   
tau(short) = 1/&GammaL 1.21 +0.08 -0.09 ps    1.21 +- 0.09 ps   
tau(long) = 1/&GammaH 1.72 +- 0.19 ps    1.66 +0.11 -0.12 ps   

The left plot below shows 1-sigma contours in in the plane (1/&Gammas, &Delta&Gammas/&Gammas) for the average of all direct measurements (green), the constraint given by the Bs lifetime using flavour-specific final states (blue), and their combination (black). The right plot below shows the 1-sigma contour in the plane (1/&GammaL, 1/&GammaH) without (dashed red) and with (plain red) the flavour-specific Bs lifetime constraint (blue). In both cases, the blue band represents the average 1.450 +- 0.075 ps which includes all lifetime measurements with fralvour specific Bs decay, except those which are not independent of the direct measurements used in the &Delta&Gammas averaging.


(1/&Gammas, &Delta&Gammas/&Gammas)gif / (1/&GammaL, 1/&GammaH)gif / (1/&Gammas, &Delta&Gammas/&Gammas)eps / (1/&GammaL, 1/&GammaH)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 = 0.507 +- 0.005 ps-1 from time-dependent measurements at ALEPH, DELPHI, L3, OPAL, CDF, 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 1.530 +- 0.009 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

dmd = 0.507 +- 0.005 ps-1
   xd = 0.776 +- 0.008
&chid = 0.188 +- 0.003
from all ALEPH, DELPHI, L3, OPAL, CDF, 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 1.530 +- 0.009 ps.


colour gif / colour eps / black-and-white eps /

Same without average including time-integrated (&chid) 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 &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 1.530 +- 0.009 ps.


colour gif / colour eps / black-and-white eps /


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2D average of dmd and tau(B0)

BABAR and Belle have performed simultaneous measurements of dmd and tau(B0). The Belle analysis is actually a simultaneous measurement of dmd, tau(B0) and tau(B+), and has been converted, for the purpose of averaging with the BABAR results, into a 2D measurement of dmd and tau(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 dmd = 0.509 +- 0.006 ps-1 and tau(B0) = 1.527 +- 0.010 ps, with a total (stat+syst) correlation coefficient of -0.23 (note that this result on dmd is already included in the dmd world average quoted above).


colour gif / colour eps /


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B0s mixing: oscillations and mass difference

Combined results on Bs oscillations:

dms > 14.4 ps-1 at 95% CL
   xs > 19.9 at 95% CL
&chis > 0.49878 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 limit on xs is derived from the results of the dms studies assuming 1/&Gammas = 1.398 +0.049 -0.050 ps (the current experimental average). The limit on &chis is derived from the limit on xs assuming no CP violation in the mixing and &Delta&Gammas/&Gammas = +0.31 +0.11 -0.13 (the current experimental average).

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 14.4 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 gif / colour eps / ASCII file with numerical data /

Same, but using also unpublished results:
colour gif / colour eps / 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 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.


colour gif / colour eps / black-and-white eps /


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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| = 1.0026 +- 0.0059
A_SL = -0.0053 +- 0.0117
Re(epsB)/(1+|epsB|**2) = -0.0013 +- 0.0029
from measurements at LEP, CLEO and BABAR


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b-hadron fractions in Upsilon(4S) decays

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, 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 = 1.029 +- 0.035 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 = 1.029 +- 0.035 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 Upsilon(4S) decay ratio
B+ B- f+- = 0.509 +- 0.007 f+-/f00 = 1.037 +- 0.029
B0 anti-B0 f00 = 0.491 +- 0.007



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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 the time-integrated mixing probability averaged over an unbiased sample of semi-leptonic b-hadron decays, chibar = 0.1259 +- 0.0042 . This combination relies on the world average of &chid, on the assumption &chis = 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) = 0.102 +- 0.009
b baryons f(b-baryon) = 0.100 +- 0.017 +0.027
B0 or B+ f(Bd) = f(Bu) = 0.399 +- 0.010 -0.511 -0.873

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

chibar(LEP) = 0.1259 +- 0.0042 LEP average from LEP EW WG



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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 sqrt(s)=1.8 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, chibar = 0.1283 +- 0.0076 . This combination relies on the world average of &chid, on the assumption &chis = 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) = 0.103 +- 0.014
b baryons f(b-baryon) = 0.100 +- 0.020 -0.104
B0 or B+ f(Bd) = f(Bu) = 0.398 +- 0.012 -0.489 -0.816

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

chibar = 0.1259 +- 0.0042 LEP average from LEP EW WG
chibar = 0.152 +- 0.013 CDF measurement
chibar = 0.1283 +- 0.0076 weighted average of above two, with error rescaled by factor 1.9 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 27-Avr-2006
Latest mod. Mon May 1 01:20:19 CEST 2006