Question

The fragmentation functions $D(z)$ describe properties of partons and are therefore the same, no matter how the partons are produced. Consider the inclusive leptoproduction cross section $\sigma(\mathrm{ep} \rightarrow \mathrm{hX})$ and show that $$ \frac{1}{\sigma} \frac{d \sigma}{d z}(\mathrm{ep} \rightarrow \mathrm{hX})=\frac{\sum_q e_q^2 f_q(x) D_q^h(z)}{\sum_q e_q^2 f_q(x)}, $$ where $f_q(x)$ are the proton structure functions of Chapter 9, see Fig. 11.6. The sum runs over the quarks and antiquarks that can be a parent of $h$.

   The fragmentation functions $D(z)$ describe properties of partons and are therefore the same, no matter how the partons are produced. Consider the inclusive leptoproduction cross section $\sigma(\mathrm{ep} \rightarrow \mathrm{hX})$ and show that
$$
\frac{1}{\sigma} \frac{d \sigma}{d z}(\mathrm{ep} \rightarrow \mathrm{hX})=\frac{\sum_q e_q^2 f_q(x) D_q^h(z)}{\sum_q e_q^2 f_q(x)},
$$
where $f_q(x)$ are the proton structure functions of Chapter 9, see Fig. 11.6. The sum runs over the quarks and antiquarks that can be a parent of $h$.

Quarks and leptons: introductory course in modern particle physics

Francis Halzen, Alan… 1st Edition

Chapter 11, Problem 2

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In the process $\mathrm{ep} \rightarrow \mathrm{hX}$, an electron (e) collides with a proton (p), resulting in the production of a hadron (h) and other particles collectively denoted as X. The variable $z$ is the fraction of the parton's momentum carried by the Show more…

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The fragmentation functions $D(z)$ describe properties of partons and are therefore the same, no matter how the partons are produced. Consider the inclusive leptoproduction cross section $\sigma(\mathrm{ep} \rightarrow \mathrm{hX})$ and show that $$ \frac{1}{\sigma} \frac{d \sigma}{d z}(\mathrm{ep} \rightarrow \mathrm{hX})=\frac{\sum_q e_q^2 f_q(x) D_q^h(z)}{\sum_q e_q^2 f_q(x)}, $$ where $f_q(x)$ are the proton structure functions of Chapter 9, see Fig. 11.6. The sum runs over the quarks and antiquarks that can be a parent of $h$.

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