Subatomic Physics

13.4. Tests of the Standard Model 415
Figure 13.1: Transverse energy distribution of
a Z 0 decay to e + e − in the (θ, φ) plane;[From
P. Bagnaia et al., (UA2 Collaboration), Phys.
Lett. 129B, 130 (1983).]
cross-section / pb
10 4
10 3
10 2
10
e + e - →hadrons
e + e - →µ + µ -
e + e - →τ + τ -
60 80 100 120 140 160 180
√s / GeV
200
Figure 13.2: Cross section versus invariant
mass for e + e − to hadrons and lepton pairs.
[From Rev. Mod. Phys. 71, s96 (1999).]
in a calorimeter as a function of polar and azimuthal angles relative to the proton
axis. Both W + and Z 0 were discovered at the predicted masses. In the
1990’s with data from e + e − colliders from SLAC and particularly LEP at CERN
the masses and the widths of the W + and Z 0 were determined with high accuracy.
The best measurements at present give mW c 2 =80.425 ± 0.038 GeV, and
mzc 2 =91.1876 ± 0.0021 GeV. (11) Figure 13.2 shows measurements of the cross
sections for e + e − to hadrons and lepton pairs produced by the experiments at the
LEP collider. The Z resonance is clearly visible.
In chapter 11, we focused on charged current weak interaction processes; these
are incorporated into the electroweak theory. In the last section we stressed the
neutral current parts of the electroweak theory because it is here that we find important
tests of the theory. Unlike their charged current counterparts, the neutral
current weak interactions are not simply left-handed or of the form V−A, but, because
of the mixing of weak and electromagnetic interactions (B 0 and W 0 ), involve
amixtureofV−Aand V + A. The mixture is determined by θW . For instance,
for the electron and its neutrino, the effective weak neutral current J n µ times its
coupling to leptons can be written as (see Eq. (13.29))
geffJ n µ =
g
4cosθW
[ψ ∗ νe (Vµ −Aµ)ψνe − ψ ∗ e Vµ(1 − 4sin 2 θW )ψe + ψe ∗ Aµψe]. (13.42)
The interference between the right- and left-handed components can be observed
by measuring, for example, the forward-backward asymmetry in e + e − → µ + µ − .
As shown in Fig. 13.3, the agreement with the prediction of the Standard Model is
very good.
11 PDG.