Results after the winter 2006 conferences

XX Rencontres de Physique de la Vallee d'Aoste, La Thuile, Italy, March 5-11, 2006
XLIst Rencontres de Moriond, Electroweak Interactions and Unified Theories, La Thuile, Italy, March 11-18, 2006
XLIst Rencontres de Moriond, QCD and High Energy Hadronic Interactions, La Thuile, Italy, March 18-25, 2006
4th Flavour Physics & CP violation conference (FPCP 2006), Vancouver, Canada, April 9-12, 2006


WARNING The averages presented on this page, performed after the Winter 2006 conferences, do not represent a complete set of averages. Only the Bs oscillation combination has been updated, based on the new dms results released by D0 in mid-March 2006 and by CDF in mid-April 2006. No other new measurement has been included in the averages presented on this page (as compared to the "end of 2005" averages published in hep-ex/0603003).

However, two sets of averages for chibar and for the b-hadron fractions at high-energy are now presented: one set using only measurements performed in Z decays, i.e. LEP measurements (new), and a second set including all measurements at LEP and Tevatron (as previously).


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:

The combination procedures are described in Chapter 3 of the following HFAG writeup: hep-ex/0603003 (this writeup decribes the "end of 2005" averages).


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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 1.527 +- 0.008 ps
B+ 1.643 +- 0.010 ps 1.076 +- 0.008
Bs 1.461 +- 0.040 ps 0.957 +- 0.027
Bc 0.469 +- 0.065 ps
Lambda_b 1.288 +- 0.065 ps
Xi_b-, Xi_b0 mixture 1.39 +0.34 -0.28 ps
b-baryon mixture 1.242 +- 0.046 ps 0.813 +- 0.030
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 1.454 +- 0.040 ps
Bs -> J/psi phi 1.404 +- 0.066 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 ]         [ +0.01 ; +0.57 ]        
&Delta&Gammas/&Gammas +0.35 +0.12 -0.16         +0.31 +0.10 -0.11        
&Delta&Gammas +0.25 +0.09 -0.11 ps-1 +0.22 +- 0.08 ps-1
1/&Gammas 1.42 +0.06 -0.07 ps    1.396 +0.044 -0.046 ps   
tau(short) = 1/&GammaL 1.21 +0.08 -0.09 ps    1.21 +- 0.08 ps   
tau(long) = 1/&GammaH 1.72 +- 0.19 ps    1.65 +0.07 -0.08 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 1.457 +- 0.042 ps which includes all lifetime measurements with flavour-specific Bs decay, except those which are not independent of the direct measurements used in the &Delta&Gammas averaging.


(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 = 0.508 +- 0.004 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 1.527 +- 0.008 ps (the experimental average listed above), all above measurements can be combined to yield the following world averages:

dmd = 0.507 +- 0.004 ps-1
   xd = 0.775 +- 0.008
&chid = 0.188 +- 0.002
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 1.527 +- 0.008 ps.


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 1.527 +- 0.008 ps.


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 1.643 +- 0.010 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 eps /


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B0s mixing: oscillations and mass difference

CDF has recently obtained the first direct evidence for Bs oscillations and performed the following preliminary measurement of dms:

dms = 17.33 +0.42 -0.21 (stat) +- 0.07 (syst) ps-1 CDF (Run II)

The plot below shows the Bs oscillation amplitude measured by CDF in Run II data as a function of dms. 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. A signal is clearly visible around 17.25 ps-1. The significance of this signal (computed as the measured amplitude divided by its total error at 17.25 ps-1) is 3.1 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 0.5%, corresponding to a 2.6 sigma significance. This analysis has the sensitivity to exclude dms values of to 25.3 ps.1, to get a 3-sigma evidence for a signal up to 17.7 ps-1, and to make a 5-sigma observation of a signal up to 10.0 ps-1.


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

The CDF result can be combined with other results performed at the Tevatron (old CDF Run I result and new D0 Run II result). This Tevatron combination exhibits a signal with a significance of 3.3 sigma at 17.75 ps-1 (defined as the maximal value of the combined amplitude divided by its total error, scanned in steps of 0.25 ps-1).
colour gif / colour eps / ASCII file with numerical data /

Note: There is some debate in the Tevatron community about the combination of results from analyses which have a proper-time dependent efficiency. This time-dependence is believed to cause some undershoot on either side of a signal or a fluctuation in the amplitude spectrum. Some people wonder whether the individual amplitude spectra need to be corrected for this effect before they are averaged. If CDF and D0 decide to provide "corrected" amplitude spectra, these will be used in future HFAG averages.

The plot below shows the world-averaged Bs oscillation amplitude as a function of dms, once all all published results from ALEPH, DELPHI, OPAL and SLD are included in addition to the Tevatron results. All measurements have been adjusted to the common set of inputs before averaging. Systematic correlations are taken into account. The signal has now an increased significance of 3.8 sigma at 17.5 ps-1. All values of dms up to 25 ps-1 except those between 16.7 ps-1 and 18.3 ps-1 (i.e. all values of dms for which the combined amplitude plus 1.645 times its total uncertainty is smaller than 1) are excluded at 95% CL.


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

The above world average spectrum can be converted into a negative log-likelihood curve. The minimum is close to 17.5 ps-1, perhaps between 17.25 and 17.50 ps-1 (?).
gif1 / eps1 / gif2 / eps2 / ASCII file with numerical data /

Note: A combination with a smaller step size would be needed to extract a measurement of dms corresponding to the world average. The Tevatron collaborations may still provide their results with a smaller step size, as this is no longer possible for the ALEPH, DELPHI, OPAL and SLD collaborations.

In the plot below, all individual measurements of the Bs oscillation amplitude at a fixed value of dms = 17.5 ps-1 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 /

A comparison of the amplitude spectra and sensitivities for each experiment is also available
gif / eps /

Finally, if the result of an unpublished SLD dms analysis (SLAC-PUB-8568) is included in the world average, one gets a Bs oscillation signal with a significance of 4.0 sigma at 17.5 ps-1.


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


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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| = 1.0015 +- 0.0039
A_SL = -0.0030 +- 0.0078
Re(epsB)/(1+|epsB|**2) = -0.0007 +- 0.0020
from measurements at LEP, CLEO, BABAR and BELLE


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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 = 1.020 +- 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.

f+-/f00 = 1.020 +- 0.034 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+- = 0.507 +- 0.007 f+-/f00 = 1.030 +- 0.029
B0 anti-B0 f00 = 0.493 +- 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) = 0.103 +- 0.009
b baryons f(b-baryon) = 0.098 +- 0.016 +0.049
B0 or B+ f(Bd) = f(Bu) = 0.399 +- 0.010 -0.522 -0.878

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) = 0.104 +- 0.013
b baryons f(b-baryon) = 0.099 +- 0.020 -0.097
B0 or B+ f(Bd) = f(Bu) = 0.398 +- 0.011 -0.499 -0.814

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 19-Mar-2006
Latest mod. Fri Apr 21 00:27:35 CEST 2006