296
9. Deep Inelastic Electron–Nucleon Scattering and the Parton Model
(b) Introduce the Feynman scaling variable
x F = x 1 − x 2
with
2
q = sx 1 x 2
and show that
dq
2 dx F = (x 1 + x 2 )sdx 1 dx 2 .
Hence show that the Drell–Yan formula can be rewritten as
∑
d
2 σ
4πα
2
τ
2
=
e [q a (x 1 )¯ q a (x 2 ) + q ¯ a (x 1 )q a (x 2 )].
a
2
dq 2 dx F
9q 4 (x + 4τ ) 1/2
F
a
9.7 Verify that if the quarks participating in the Drell–Yan subprocess q¯ q →
γ → μμ ¯ had spin-0, the CM angular distribution of the final μ
+ μ
− pair would
be proportional to (1 − cos
2 θ).
9. Deep Inelastic Electron–Nucleon Scattering and the Parton Model
(b) Introduce the Feynman scaling variable
x F = x 1 − x 2
with
2
q = sx 1 x 2
and show that
dq
2 dx F = (x 1 + x 2 )sdx 1 dx 2 .
Hence show that the Drell–Yan formula can be rewritten as
∑
d
2 σ
4πα
2
τ
2
=
e [q a (x 1 )¯ q a (x 2 ) + q ¯ a (x 1 )q a (x 2 )].
a
2
dq 2 dx F
9q 4 (x + 4τ ) 1/2
F
a
9.7 Verify that if the quarks participating in the Drell–Yan subprocess q¯ q →
γ → μμ ¯ had spin-0, the CM angular distribution of the final μ
+ μ
− pair would
be proportional to (1 − cos
2 θ).