Results after the summer and fall 2006 conferences ("end of 2006" results)

33nd International Conference on High Energy Physics, ICHEP06, Moscow (Russia), July 26 - August 2, 2006
11th International Conference on B-Physics at Hadron Machines, BEAUTY 2006, Oxford (UK), September 25-29, 2006
4th International Workshop on the CKM Unitarity Triangle, CKM 2006, Nagoya (Japan), December 12-16, 2006

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
Neutral B meson mixing: CP violation
b-hadron fractions in Upsilon(4S) decays
b-hadron fractions in Upsilon(5S) decays
b-hadron fractions in Z decays
b-hadron fractions at high energy
Notes on combination procedures

These "end of 2006" averages (and the combination procedures used to obtain them) are described in Chapter 3 of the following HFAG writeup: arXiv:0704.3575v1 [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	1.527 +- 0.008 ps
B+	1.643 +- 0.010 ps	1.076 +- 0.008
Bs	1.451 +0.029 -0.028 ps	0.950 +- 0.019
Bc	0.460 +- 0.066 ps
Lambda_b	1.393 +- 0.049 ps	0.912 +- 0.032
Xi_b-, Xi_b0 mixture	1.42 +0.28 -0.24 ps
b-baryon mixture	1.325 +- 0.039 ps	0.867 +- 0.026
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/Gamma_s, where Gamma_s = (Gamma_Light + Gamma_Heavy)/2 is the mean mean decay width of the Bs system. The Xi_b, 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	1.440 +- 0.036 ps
Bs -> Ds X	1.444 +- 0.036 ps
Bs -> J/psi phi	1.404 +- 0.066 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 &Delta&Gamma = &Gamma_L - &Gamma_H and &Gamma = (&Gamma_L + &Gamma_H)/2, where &Gamma_L (&Gamma_H) 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&Gamma_d/&Gamma_d = 0.009 +- 0.037

from BABAR and DELPHI

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 (CDF, D0, ALEPH 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 and the quantity &Gamma_L = &Gamma_s (1+&Delta&Gamma_s/(2&Gamma_s)) to the Bs -> K+K- lifetime:

Fit results from CDF, D0, ALEPH and DELPHI data	without constraint from tau(Bs -> flavour specific) and tau(Bs -> K+K-)	with constraint from tau(Bs -> flavour specific) and tau(Bs -> K+K-)
1/&Gamma_s	1.494 +0.055 -0.054 ps	1.451 +0.029 -0.028 ps
tau(short) = 1/&Gamma_L	1.354 +0.065 -0.062 ps	1.380 +0.060 -0.057 ps
tau(long) = 1/&Gamma_H	1.665 +0.143 +0.137 ps	1.531 +0.075 +0.069 ps
&Delta&Gamma_s (95% CL range)	[ 0.00 ; +0.27 ] ps-1	[ -0.04 ; +0.17 ] ps-1
&Delta&Gamma_s	+0.138 +0.068 -0.074 ps-1	0.071 +0.053 -0.057 ps-1
&rho(&Delta&Gamma_s,1/&Gamma_s)	+0.33	+0.08
&Delta&Gamma_s/&Gamma_s (95% CL range)	[ -0.01 ; +0.51 ]	[ -0.07 ; +0.25 ]
&Delta&Gamma_s/&Gamma_s	+0.206 +0.106 -0.111	+0.104 +0.076 -0.084
&rho(&Delta&Gamma_s/&Gamma_s,1/&Gamma_s)	+0.39	+0.08

The left plot below shows 1-sigma contours in the plane (1/&Gamma_s, &Delta&Gamma_s) for the average of all direct measurements (red), the constraint given by the Bs lifetime using flavour-specific final states (blue), the constraint given by the Bs -> K+K- lifetime (green), and their combination (black). The right plot below shows the same 1-sigma contours in the plane (1/&Gamma_L, 1/&Gamma_H). In both cases, the blue band represents the average 1.441 +- 0.037 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&Gamma_s averaging.

Above plots: (1/&Gamma_s, &Delta&Gamma_s) gif / (1/&Gamma_L, 1/&Gamma_H) gif / (1/&Gamma_s, &Delta&Gamma_s) eps / (1/&Gamma_L, 1/&Gamma_H) eps /
Another (1/&Gamma_s, &Delta&Gamma_s) 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 dmd (at high energy colliders and asymmetric B factories) and from time-integrated measurements of the mixing probability &chi_d 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
&chi_d = 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
&chi_d = 0.1877 +- 0.0024

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

Same without average including time-integrated (&chi_d) 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 &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 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).

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)

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 gif / colour eps /

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B0s mixing: oscillations and mass difference

In 2006, CDF has obtained the first direct evidence for and then the first observation of Bs oscillations. The measured value of dms is (A. Abulencia et al., Phys. Rev. Lett. 97, 242003 (2006)):

dms = 17.77 +- 0.10 (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 17.75 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 8e-8, corresponding to a 5.4 sigma significance.

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Several other experiments (D0, ALEPH, DELPHI, OPAL, SLD) have searched for Bs oscillations. The plot below the Bs oscillation amplitude as a function of dms for the CDF2 analysis (top, same as previous plot), for all analyses combined except the CDF2 analysis (middle), and for all analyses combined (bottom). The world average is dominated by the CDF2 analysis. The combination of all analyses except the CDF2 analysis (middle) is not sensitive enough yet to provide an independent confirmation of the CDF2 result, but is certainly consistent with a signal at around 17.75 ps-1.

colour gif / colour eps /
ASCII file with numerical data for CDF2 only /
ASCII file with numerical data for all combined expect CDF2 /
ASCII file with numerical data for world combination /

A hint for a signal between 15 ps-1 and 20 ps-1 has been around for many years, since the LEP times, but the Tevatron data was necessary to finally pin it down. The plot below shows the combined Bs amplitude spectrum at the end of the years 2000, 2005 and 2006.

In the plot below, all individual measurements of the Bs oscillation amplitude at a fixed value of dms = 17.75 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 here: gif / eps /

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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 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
   epsB = (p-q)/(p+q)
   q/p = (1-epsB)/(1+epsB)
   A_SL ~ 4 Re(epsB)/(1+|epsB|**2)

Averages are given below separately for the Bd and the Bs systems. Two sets of averages are given for the Bd system in the first table: a first set using only measurements performed at Upsilon(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 Bd and Bs parameters: the effect from the Bs is then isolated by using the value and error of the Bd parameter obtained at the B factories.

CP violation parameter in Bd mixing
\|q/p\| = 1.0024 +- 0.0023 A_SL = -0.0047 +- 0.0046 Re(epsB)/(1+\|epsB\|**2) = -0.0012 +- 0.0011	from measurements at CLEO, BABAR and BELLE
\|q/p\| = 1.0033 +- 0.0017 A_SL = -0.0064 +- 0.0034 Re(epsB)/(1+\|epsB\|**2) = -0.0016 +- 0.0009	same but adding measurements from ALEPH, OPAL and D0 (and assuming A_SL(Bs) = 0)

CP violation parameter in Bs mixing
\|q/p\| = 0.9998 +- 0.0046 A_SL = +0.0003 +- 0.0093	from measurements at CDF and D0 (and assuming A_SL(Bd) = -0.0047 +- 0.0046 )

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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 = 1.021 +- 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 = 1.021 +- 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 Upsilon(5S) decays

The table and plot below show the fraction fs(*)(*) of Bs(*) anti-Bs(*) events over all events with a pair of b-flavored mesons produced in e+e- collisions at a centre-of-mass energy equal to the Upsilon(5S) mass. Since all Bs* mesons decay to a Bs meson (by photon emission), this fraction is equal to the probability fs(Ups(5S)) that a weakly decaying b-hadron produced in such collisions be a Bs meson. The average for this fraction has been obtained by combining model-dependent estimates of CLEO3 and Belle based on the measurements of several inclusive Upsilon(5S) branching fractions, after performing adjustements to common external inputs. Most of this Bs production proceeds in the Bs* anti-Bs* channel, with the ratio of Bs* anti-Bs* events over Bs(*) anti-Bs(*) events (from Belle only) indicated in the table.

b hadron species	fraction in Upsilon(5S) decay	ratio
Bs() anti-Bs()	*fs()() = fs(Ups(5S)) = 0.199 +- 0.032*
Bs* anti-Bs*	fs**	fs/fs()() = 0.94 +0.06-0.09**

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

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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 &chi_d, on the assumption &chi_s = 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) = 0.104 +- 0.009
b baryons	f(b-baryon) = 0.091 +- 0.015	+0.029
B0 or B+	f(Bd) = f(Bu) = 0.402 +- 0.009	-0.534	-0.860

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 = 0.1284 +- 0.0069 . This combination relies on the world average of &chi_d, on the assumption &chi_s = 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) = 0.106 +- 0.013
b baryons	f(b-baryon) = 0.092 +- 0.018	-0.104
B0 or B+	f(Bd) = f(Bu) = 0.401 +- 0.010	-0.517	-0.798

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

chibar = 0.1259 +- 0.0042	LEP average from LEP EW WG
chibar = 0.147 +- 0.011	CDF measurement
chibar = 0.1284 +- 0.0069	weighted average of above two, with error rescaled by factor 1.8 according to PDG prescription

Note:

The above fractions at high energy are less precise than the fractions in Z decays, although they are obtained using more measurements. This is because the data from LEP and CDF are not entirely consistent with each other, and we apply the PDG prescription by rescaling errors based on a chi2. Two such scaling factors need to be applied independently in our procedure: a scaling factor of 1.8 when computing the world average of chibar and another scaling factor of 1.1 when combining the direct rate measurements at LEP and CDF.
This may be an indication that the fractions in high energy hadronic collisions may not be identical to those in Z decays.
We hope that, in the future, we can produce a set of fractions obtained only from measurements at the Tevatron.
For the time being, we recommend that our fractions at high energy (rather than our fractions in Z decays) be used by anyone who needs these fractions in the context of high energy hadronic collisions (Tevatron or LHC).

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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 26-Apr-2007

Latest mod. Tue Apr 3 23:08:52 CEST 2007