Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

10. Electroweak model and constraints on new physics 175
it is a loop-level process (in the SM) its sensitivity to new physics (and
SM parameters, such as heavy quark masses) is enhanced. The τ-lepton
lifetime and leptonic branching ratios are primarily sensitive to αs and
not affected significantly by many types of new physics. However, having
an independent and reliable low energy measurement of αs in a global
analysis allows the comparison with the Z lineshape determination of αs
which shifts easily in the presence of new physics contributions. By far the
most precise observable discussed here is the anomalous magnetic moment
of the muon (the electron magnetic moment is measured to even greater
precision, but its new physics sensitivity is suppressed by an additional
factor of m2 e/m2 μ). Its combined experimental and theoretical uncertainty
is comparable to typical new physics contributions. See the full Review for
more details.
10.5. Experimental results
The values for mt [6], MW [160,207], neutrino scattering [98,114–116],
the weak charges of the electron [125], cesium [132,133] and thallium [134],
the b → sγ observable [174–175], the muon anomalous magnetic
moment [189], and the τ lifetime are listed in Table 10.5. Likewise, the
principal Z pole observables can be found in Table 10.6 where the LEP 1
averages of the ALEPH, DELPHI, L3, and OPAL results include common
systematic errors and correlations [11]. The heavy flavor results of LEP 1
and SLD are based on common inputs and correlated, as well [11]. Note
that the values of Γ(ℓ + ℓ− ), Γ(had), and Γ(inv) are not independent of
ΓZ,theRℓ,andσhad and that the SM errors in those latter are largely
dominated by the uncertainty in αs. Also shown in both Tables are the
SM predictions for the values of MZ, MH, αs(MZ), Δα (3)
had and the heavy
quark masses shown in Table 10.4 in the full Review. The predictions
result from a global least-square (χ2 ) fit to all data using the minimization
package MINUIT [208] and the electroweak library GAPP [90]. In
most cases, we treat all input errors (the uncertainties of the values)
as Gaussian. The reason is not that we assume that theoretical and
systematic errors are intrinsically bell-shaped (which they are not) but
because in most cases the input errors are combinations of many different
(including statistical) error sources, which should yield approximately
Gaussian combined errors by the large number theorem. Thus, it suffices if
either the statistical components dominate or there are many components
of similar size. An exception is the theory dominated error on the τ
lifetime, which we recalculate in each χ2-function call since it depends
itself on αs. Sizes and shapes of the output errors (the uncertainties of
the predictions and the SM fit parameters) are fully determined by the fit,
and 1σ errors are defined to correspond to Δχ2 = χ2 − χ2 min = 1, and do
not necessarily correspond to the 68.3% probability range or the 39.3%
probability contour (for 2 parameters).
The agreement is generally very good. Despite the few discrepancies
discussed in the following, the fit describes well the data with a
χ2 /d.o.f. =43.0/44. Only the final result for gμ − 2fromBNLandA (0,b)
FB
from LEP 1 are currently showing large (2.5 σ and 2.7 σ) deviations.
In addition, A0 LR (SLD) from hadronic final states differs by 1.8 σ. The
SM prediction of σhad (LEP 1) moved closer to the measurement value
which is slightly higher. Rb, whose measured value deviated in the past
by as much as 3.7 σ from the SM prediction, is now in agreement, and
a2σ discrepancy in QW (Cs) has also been resolved. g2 L from NuTeV is