302
20. Introduction to the Phenomenology of Weak Interactions
and with
(
)
dσ
1
G
2
F
=
N μν E
μν
(20.81)
dΩ
64π 2 s
2
we finally obtain the result
dσ
G F
2 s
=
.
(20.82)
dΩ
4π 2
The total cross section is then
G
2
F s
σ =
.
(20.83)
π
Since t = −2p
2 (1 − cos θ), where p is the CM momentum and θ the CM
scattering angle, (20.82) can alternatively be written in invariant form as
(problem 20.7)
dσ
G
2
F
=
.
(20.84)
dt
π
All other purely leptonic processes may be calculated in an analogous fashion
(see Bailin 1982 and Renton 1990 for further examples).
When we discuss deep inelastic neutrino scattering in section 20.7.2, we
shall be interested in neutrino ‘laboratory’ cross sections, as in the electron
scattering case of chapter 9. A simple calculation gives s ⋍ 2m e E (neglecting
squares of lepton masses by comparison with m e E), where E is the ‘laboratory’
energy of a neutrino incident, in this example, on a stationary electron. It
follows that the total ‘laboratory’ cross section in this Fermi-like current–
current model rises linearly with E. We shall return to the implications of this
in section 20.7.2.
The process (20.45) was measured by Bergsma et al. (1983) using the
CERN wide band beam (E ν ∼ 20 GeV). The ratio of the observed number
of events to that expected for pure V-A was quoted as 0.98±0.12.
20.6 Leptonic weak neutral currents
−
The first observations of the weak neutral current process ¯
ν μ e
−
→ ν ¯ μ e were
reported by Hasert et al. (1973), in a pioneer experiment using the heavyliquid bubble chamber Gargamelle at CERN, irradiated with a ¯
ν μ beam. As
in the case of the charged currents, much detailed experimental work was
necessary to determine the precise form of the neutral current couplings. They
are, of course, predicted by the Glashow–Salam–Weinberg theory, as we shall
explain in chapter 22. For the moment, we continue with the current–current
approach, parametrizing the currents in a convenient way.
There are two types of ‘neutral current’ couplings, those involving neutrinos of the form ν ¯ ˆ l . . . ν ˆ l , and those involving the charged leptons of the form
20. Introduction to the Phenomenology of Weak Interactions
and with
(
)
dσ
1
G
2
F
=
N μν E
μν
(20.81)
dΩ
64π 2 s
2
we finally obtain the result
dσ
G F
2 s
=
.
(20.82)
dΩ
4π 2
The total cross section is then
G
2
F s
σ =
.
(20.83)
π
Since t = −2p
2 (1 − cos θ), where p is the CM momentum and θ the CM
scattering angle, (20.82) can alternatively be written in invariant form as
(problem 20.7)
dσ
G
2
F
=
.
(20.84)
dt
π
All other purely leptonic processes may be calculated in an analogous fashion
(see Bailin 1982 and Renton 1990 for further examples).
When we discuss deep inelastic neutrino scattering in section 20.7.2, we
shall be interested in neutrino ‘laboratory’ cross sections, as in the electron
scattering case of chapter 9. A simple calculation gives s ⋍ 2m e E (neglecting
squares of lepton masses by comparison with m e E), where E is the ‘laboratory’
energy of a neutrino incident, in this example, on a stationary electron. It
follows that the total ‘laboratory’ cross section in this Fermi-like current–
current model rises linearly with E. We shall return to the implications of this
in section 20.7.2.
The process (20.45) was measured by Bergsma et al. (1983) using the
CERN wide band beam (E ν ∼ 20 GeV). The ratio of the observed number
of events to that expected for pure V-A was quoted as 0.98±0.12.
20.6 Leptonic weak neutral currents
−
The first observations of the weak neutral current process ¯
ν μ e
−
→ ν ¯ μ e were
reported by Hasert et al. (1973), in a pioneer experiment using the heavyliquid bubble chamber Gargamelle at CERN, irradiated with a ¯
ν μ beam. As
in the case of the charged currents, much detailed experimental work was
necessary to determine the precise form of the neutral current couplings. They
are, of course, predicted by the Glashow–Salam–Weinberg theory, as we shall
explain in chapter 22. For the moment, we continue with the current–current
approach, parametrizing the currents in a convenient way.
There are two types of ‘neutral current’ couplings, those involving neutrinos of the form ν ¯ ˆ l . . . ν ˆ l , and those involving the charged leptons of the form