3 The Standard Model of Electroweak Interactions
67
Table 3.1 Summary of
electroweak precision
measurements at high Q 2 [8]
Observable
Measurement
SM fit
m Z [GeV]
91.1875 ± 0.0021
91.1875
Z [GeV]
2.4952 ± 0.0023
2.4957
σ 0
h [nb]
41.540 ± 0.037
41.477
R
0
l
20.767 ± 0.025
20.744
AF B
0,l
0.01714 ± 0.00095
0.01645
A l (SLD)
0.1513 ± 0.0021
0.1481
A l (P τ )
0.1465 ± 0.0032
0.1481
R
0
b
0.21629 ± 0.00066
0.21586
R 0
c
0.1721 ± 0.0030
0.1722
A
0,b
FB
0.0992 ± 0.0016
0.1038
A
0,c
FB
0.0707 ± 0.0035
0.0742
A b
0.923 ± 0.020
0.935
A c
0.670 ± 0.027
0.668
sin
2 θ eff (Q
had
FB )
0.2324 ± 0.0012
0.2314
m W [GeV]
80.398 ± 0.025
80.374
W [GeV]
2.140 ± 0.060
2.091
m t [GeV (p ¯
p)
170.9 ± 1.8
171.3
(5)
had (m 2
Z )
0.02758 ± 0.00035
0.02768
The first block shows the Z-pole measurements. The second
block shows additional results from other experiments: the
mass and the width of the W boson measured at the Tevatron
and at LEP-2, the mass of the top quark measured at the
Tevatron, and the contribution to α of the hadronic vacuum
polarization. The SM fit results are derived from the SM
analysis of these results
m t (here it is m W which is indirectly determined), and, finally, in column 3 a fit
of all the data listed in Table 3.1 (which is the most relevant fit for constraining
m H ). From the fit in column 1 of Table 3.2 we see that the extracted value of
m t is in good agreement with the direct measurement (see Table 3.1). Similarly
we see that the experimental measurement of m W in Table 3.1 is larger by about
one standard deviation with respect to the value from the fit in column 2. We
have seen that quantum corrections depend only logarithmically on m H . In spite
of this small sensitivity, the measurements are precise enough that one still obtains
a quantitative indication of the mass range. From the fit in column 3 we obtain:
log 10 m H (GeV) = 1.88 ± 0.16 (or m H = 76
+34
−24 GeV). This result on the Higgs
mass is particularly remarkable. The value of log 10 m H (GeV) is compatible with
the small window between ∼2 and ∼3 which is allowed, on the one side, by the
direct search limit (m H > 114 GeV from LEP-2 [8]), and, on the other side, by the
theoretical upper limit on the Higgs mass in the minimal SM, m H 600 −800 GeV
[51].
Thus the whole picture of a perturbative theory with a fundamental Higgs is well
supported by the data on radiative corrections. It is important that there is a clear
indication for a particularly light Higgs: at 95% c.l. m H 182 GeV (including
67
Table 3.1 Summary of
electroweak precision
measurements at high Q 2 [8]
Observable
Measurement
SM fit
m Z [GeV]
91.1875 ± 0.0021
91.1875
Z [GeV]
2.4952 ± 0.0023
2.4957
σ 0
h [nb]
41.540 ± 0.037
41.477
R
0
l
20.767 ± 0.025
20.744
AF B
0,l
0.01714 ± 0.00095
0.01645
A l (SLD)
0.1513 ± 0.0021
0.1481
A l (P τ )
0.1465 ± 0.0032
0.1481
R
0
b
0.21629 ± 0.00066
0.21586
R 0
c
0.1721 ± 0.0030
0.1722
A
0,b
FB
0.0992 ± 0.0016
0.1038
A
0,c
FB
0.0707 ± 0.0035
0.0742
A b
0.923 ± 0.020
0.935
A c
0.670 ± 0.027
0.668
sin
2 θ eff (Q
had
FB )
0.2324 ± 0.0012
0.2314
m W [GeV]
80.398 ± 0.025
80.374
W [GeV]
2.140 ± 0.060
2.091
m t [GeV (p ¯
p)
170.9 ± 1.8
171.3
(5)
had (m 2
Z )
0.02758 ± 0.00035
0.02768
The first block shows the Z-pole measurements. The second
block shows additional results from other experiments: the
mass and the width of the W boson measured at the Tevatron
and at LEP-2, the mass of the top quark measured at the
Tevatron, and the contribution to α of the hadronic vacuum
polarization. The SM fit results are derived from the SM
analysis of these results
m t (here it is m W which is indirectly determined), and, finally, in column 3 a fit
of all the data listed in Table 3.1 (which is the most relevant fit for constraining
m H ). From the fit in column 1 of Table 3.2 we see that the extracted value of
m t is in good agreement with the direct measurement (see Table 3.1). Similarly
we see that the experimental measurement of m W in Table 3.1 is larger by about
one standard deviation with respect to the value from the fit in column 2. We
have seen that quantum corrections depend only logarithmically on m H . In spite
of this small sensitivity, the measurements are precise enough that one still obtains
a quantitative indication of the mass range. From the fit in column 3 we obtain:
log 10 m H (GeV) = 1.88 ± 0.16 (or m H = 76
+34
−24 GeV). This result on the Higgs
mass is particularly remarkable. The value of log 10 m H (GeV) is compatible with
the small window between ∼2 and ∼3 which is allowed, on the one side, by the
direct search limit (m H > 114 GeV from LEP-2 [8]), and, on the other side, by the
theoretical upper limit on the Higgs mass in the minimal SM, m H 600 −800 GeV
[51].
Thus the whole picture of a perturbative theory with a fundamental Higgs is well
supported by the data on radiative corrections. It is important that there is a clear
indication for a particularly light Higgs: at 95% c.l. m H 182 GeV (including