Subatomic Physics

13.4. Tests of the Standard Model 417
Figure 13.4: Feynman diagram for the elastic
scattering of muon neutrinos on electrons.
Figure 13.5: Feynman diagrams for elastic scattering
of electron neutrinos from electrons.
Similarly, we can compare elastic neutrino and antineutrino scattering on the proton.
At zero momentum transfer (forward scattering) there is no interference between
the vector and axial vector currents and the form factors are unity, so that
the ratio of antineutrino or neutrino scattering cross section due to neutral currents
to that for charged currents becomes
σ(νµp → νµp)
σ(νµp → µ + n) = σ(νµp → νµp)
σ(νµn → µ −p) 1
=
4cos 2 θC
� (1 − 4sin 2 θW ) 2 + g 2 A
1+g 2 A
�
, (13.46)
where gA ≈ 1.27.
The Weinberg angles obtained from the different processes described above
have been extracted and found to agree with the expectations from the standard
model. (12)
TheHiggsstructureofthetheory can be tested by measuring the parameter ρ0,
ρ0 = M 2 W /(M 2 Z cos2 θW ˆρ), (13.47)
which is unity in the WS theory, but could be different if the Higgs bosons were
not in a doublet. The factor ˆρ corresponds to calculated radiative corrections and
differs from unity by about one percent. Experimentally, the parameter ρ0 is found
to be 1 to within less than one tenth of one percent. 11 A major confirmation of
12 Measurements have become precise enough that radiative corrections need to be taken into
consideration. See SLAC E158 collaboration, Phys. Rev. Lett. 95, 081601 (2005). However,
measurements from scattering of ν and ν off nuclei disagree by more than 2σ with the expectations;
see NuTev collaboration, Phys. Rev. Lett. 88, 091802 (2002).