Question
Use (9.23) to show that the parton model predicts$$\left(\frac{d \sigma}{d x d y}\right)_{\mathrm{ep} \rightarrow \mathrm{eX}}=\frac{2 \pi \alpha^{2}}{Q^{4}} s\left[1+(1-y)^{2}\right] \sum_{i} e_{i}^{2} x f_{i}(x)$$
Step 1
23). For massless fermions the squared matrix element gives (e.g. from QED) |M|^2 = 2 e^4 e_i^2 (ŝ^2 + û^2)/t^2, so dσ̂/dt = (1/16π ŝ^2) |M|^2 = (2π α^2 e_i^2)/t^2 · (ŝ^2 + û^2)/ŝ^2. With t = −Q^2 and using û = −ŝ(1 − ŷ) one gets for the partonic differential in Show more…
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