316
20. Introduction to the Phenomenology of Weak Interactions
CCFR data with the next-to-leading order calculation of Duke and Owens
(1984). This fit yields a value of α s at Q
2 = M
2 given by
Z
α s (M Z
2 ) = 0.111 ± 0.002 ± 0.003.
(20.153)
ν ¯p
νp
The Adler sum rule (Adler 1963) involves the functions F and F :
2
2
∫ 1 dx ν ¯p
νp
I A =
(F − F ).
(20.154)
2
2
x
0
In the simple model of (20.127)–(20.130), the right-hand side of I A is just
∫ 1
2
dx(u(x) + d ¯ (x) − d(x) − u ¯(x))
(20.155)
0
which represents four times the average of I 3 (isospin) of the target, which is
1 for the proton. This sum rule follows from the conservation of the charged
2
weak current (as will be true in the Standard Model, since this is a gauge
symmetry current, as we shall see in the following chapter). Its measurement,
however, depends precisely on separating the non-isoscalar contribution (I A
vanishes for the isoscalar average ‘N’). The BEBC collaboration (Allasia et al.
1984, 1985) reported:
I A = 2.02 ± 0.40;
(20.156)
in agreement with the expected value 2.
Relations (20.127)–(20.130) allow the F 2 functions for electron (muon) and
neutrino scattering to be simply related. From (9.58) and (9.61) we have
F
eN
1 (F
ep
en
5
1
=
+ F ) =
x(u + ¯
u + d + d ¯ ) + x(s + ¯
s) + · · ·
(20.157)
2
2
2
2
18
9
while (20.127) and (20.129) give
1
F
νN
νp + F
νn
+ ¯
≡ (F
) = x(u + d + ¯
u d).
(20.158)
2
2
2
2
Assuming that the non-strange contributions dominate, the neutrino and
charged lepton structure functions should be approximately in the ratio 18/5,
which is the reciprocal of the mean squared charged of the u and d quarks
in the nucleon. Figure 20.9 shows the neutrino results on F 2 and xF 3 together with those from several μN experiments scaled by the factor 18/5. The
agreement is satisfactory for a tree-level parton model calculation.
¯
From (20.127)–(20.130) we see that F
νN
− xF
νN = 2x(¯ u + d), which is just
2
3
the sea distribution; figure 20.9 shows that this is concentrated at small x, as
we already inferred in section 9.3.
We have mentioned QCD corrections to the simple parton model at several
points. Clearly the full machinery introduced in chapter 16, in the context
of deep inelastic charged lepton scattering, can be employed for the case of
neutrino scattering also. For further access to this area we refer to Ellis et al.
(1996), chapter 4, and Winter (2000) chapter 5.
20. Introduction to the Phenomenology of Weak Interactions
CCFR data with the next-to-leading order calculation of Duke and Owens
(1984). This fit yields a value of α s at Q
2 = M
2 given by
Z
α s (M Z
2 ) = 0.111 ± 0.002 ± 0.003.
(20.153)
ν ¯p
νp
The Adler sum rule (Adler 1963) involves the functions F and F :
2
2
∫ 1 dx ν ¯p
νp
I A =
(F − F ).
(20.154)
2
2
x
0
In the simple model of (20.127)–(20.130), the right-hand side of I A is just
∫ 1
2
dx(u(x) + d ¯ (x) − d(x) − u ¯(x))
(20.155)
0
which represents four times the average of I 3 (isospin) of the target, which is
1 for the proton. This sum rule follows from the conservation of the charged
2
weak current (as will be true in the Standard Model, since this is a gauge
symmetry current, as we shall see in the following chapter). Its measurement,
however, depends precisely on separating the non-isoscalar contribution (I A
vanishes for the isoscalar average ‘N’). The BEBC collaboration (Allasia et al.
1984, 1985) reported:
I A = 2.02 ± 0.40;
(20.156)
in agreement with the expected value 2.
Relations (20.127)–(20.130) allow the F 2 functions for electron (muon) and
neutrino scattering to be simply related. From (9.58) and (9.61) we have
F
eN
1 (F
ep
en
5
1
=
+ F ) =
x(u + ¯
u + d + d ¯ ) + x(s + ¯
s) + · · ·
(20.157)
2
2
2
2
18
9
while (20.127) and (20.129) give
1
F
νN
νp + F
νn
+ ¯
≡ (F
) = x(u + d + ¯
u d).
(20.158)
2
2
2
2
Assuming that the non-strange contributions dominate, the neutrino and
charged lepton structure functions should be approximately in the ratio 18/5,
which is the reciprocal of the mean squared charged of the u and d quarks
in the nucleon. Figure 20.9 shows the neutrino results on F 2 and xF 3 together with those from several μN experiments scaled by the factor 18/5. The
agreement is satisfactory for a tree-level parton model calculation.
¯
From (20.127)–(20.130) we see that F
νN
− xF
νN = 2x(¯ u + d), which is just
2
3
the sea distribution; figure 20.9 shows that this is concentrated at small x, as
we already inferred in section 9.3.
We have mentioned QCD corrections to the simple parton model at several
points. Clearly the full machinery introduced in chapter 16, in the context
of deep inelastic charged lepton scattering, can be employed for the case of
neutrino scattering also. For further access to this area we refer to Ellis et al.
(1996), chapter 4, and Winter (2000) chapter 5.