394
22. The GSW Gauge Theory of Electroweak Interactions
QCD corrections to (22.102) must as usual be included. Leading logarithms will make the distributions Q
2 -dependent, and they should be evaluated at Q
2 = M
2 . There will be further (O(α
2 )) corrections, which are often
W
s
accounted for by a multiplicative factor ‘K’, which is of order 1.5–2 at these
energies. O(α
2 ) calculations are presented in Hamberg et al. (1991) and by
s
van der Neerven and Zijlstra (1992); see also Ellis et al. (1996) section 9.4.
√
The total cross section for production of W
+ and W
− at s =630 GeV is
then of order 6.5 nb, while a similar calculation for the Z
0 gives about 2 nb.
Multiplying these by the branching ratios gives
σ(p¯ p → W + X → eνX) ⋍ 0.7 nb
(22.105)
+
σ(p¯ p → Z
0 + X → e e
− X) ⋍ 0.07 nb
(22.106)
√
at s =630 GeV.
The total cross section for p¯ p is about 70 mb at these energies: hence
(22.105) represents ∼ 10
−8 of the total cross section, and (22.106) is 10 times
smaller. The rates could, of course, be increased by using the q¯ q modes of
W and Z
0 , which have bigger branching ratios. But the detection of these is
very difficult, being very hard to distinguish from conventional two-jet events
produced via the mechanism discussed in section 14.3.2, which has a cross
section some 10
3 higher than (22.105). W and Z
0 would appear as slight
shoulders on the edge of a very steeply falling invariant mass distribution,
similar to that shown in figure 9.12, and the calorimetric jet energy resolution
capable of resolving such an effect is hard to achieve. Thus despite the unfavourable branching ratios, the leptonic modes provide the better signatures,
as discussed further in section 22.4.3.
22.4.2 Charge asymmetry in W ± decay
At energies such that the simple valence quark picture of (22.102) is valid, the
W
+ is created in the annihilation of a left-handed u quark from the proton
and a right-handed ¯
p (neglecting fermion masses). In the
d quark from the ¯
W
+
→ e
+ ν e decay, a right-handed e
+ and left-handed ν e are emitted. Referring to figure 22.16, we see that angular momentum conservation allows e
+
production parallel to the direction of the antiproton, but forbids it parallel
to the direction of the proton. Similarly, in W
−
→ e
− ν ¯ e , the e
− is emitted
preferentially parallel to the proton (these considerations are exactly similar
to those mentioned in section 20.7.2 with reference to νq and ¯
νq scattering).
The actual distribution has the form ∼ (1 + cos θ
∗ )
2 , where θ
∗ is the angle, in
e
e
the rest frame of the W, between the e
− and the p (for W
−
→ e
− ν ¯ e ) or the
+
e and the ¯
p (for W
+
→ e
+ ν e ).
22. The GSW Gauge Theory of Electroweak Interactions
QCD corrections to (22.102) must as usual be included. Leading logarithms will make the distributions Q
2 -dependent, and they should be evaluated at Q
2 = M
2 . There will be further (O(α
2 )) corrections, which are often
W
s
accounted for by a multiplicative factor ‘K’, which is of order 1.5–2 at these
energies. O(α
2 ) calculations are presented in Hamberg et al. (1991) and by
s
van der Neerven and Zijlstra (1992); see also Ellis et al. (1996) section 9.4.
√
The total cross section for production of W
+ and W
− at s =630 GeV is
then of order 6.5 nb, while a similar calculation for the Z
0 gives about 2 nb.
Multiplying these by the branching ratios gives
σ(p¯ p → W + X → eνX) ⋍ 0.7 nb
(22.105)
+
σ(p¯ p → Z
0 + X → e e
− X) ⋍ 0.07 nb
(22.106)
√
at s =630 GeV.
The total cross section for p¯ p is about 70 mb at these energies: hence
(22.105) represents ∼ 10
−8 of the total cross section, and (22.106) is 10 times
smaller. The rates could, of course, be increased by using the q¯ q modes of
W and Z
0 , which have bigger branching ratios. But the detection of these is
very difficult, being very hard to distinguish from conventional two-jet events
produced via the mechanism discussed in section 14.3.2, which has a cross
section some 10
3 higher than (22.105). W and Z
0 would appear as slight
shoulders on the edge of a very steeply falling invariant mass distribution,
similar to that shown in figure 9.12, and the calorimetric jet energy resolution
capable of resolving such an effect is hard to achieve. Thus despite the unfavourable branching ratios, the leptonic modes provide the better signatures,
as discussed further in section 22.4.3.
22.4.2 Charge asymmetry in W ± decay
At energies such that the simple valence quark picture of (22.102) is valid, the
W
+ is created in the annihilation of a left-handed u quark from the proton
and a right-handed ¯
p (neglecting fermion masses). In the
d quark from the ¯
W
+
→ e
+ ν e decay, a right-handed e
+ and left-handed ν e are emitted. Referring to figure 22.16, we see that angular momentum conservation allows e
+
production parallel to the direction of the antiproton, but forbids it parallel
to the direction of the proton. Similarly, in W
−
→ e
− ν ¯ e , the e
− is emitted
preferentially parallel to the proton (these considerations are exactly similar
to those mentioned in section 20.7.2 with reference to νq and ¯
νq scattering).
The actual distribution has the form ∼ (1 + cos θ
∗ )
2 , where θ
∗ is the angle, in
e
e
the rest frame of the W, between the e
− and the p (for W
−
→ e
− ν ¯ e ) or the
+
e and the ¯
p (for W
+
→ e
+ ν e ).