Question

Using the notation $$ N_p^\pi(z) \equiv \frac{1}{\sigma} \frac{d \sigma}{d z}(\mathrm{ep} \rightarrow \pi \mathrm{X}) . $$ show that, in the valence quark approximation for $\mathrm{p}, \mathrm{n}$, $$ \frac{\int d z\left[N_n^{\pi^{+}}-N_n^{\pi^{-}}\right]}{\int d z\left[N_p^{\pi^{+}}-N_p^{\pi^{-}}\right]}=\frac{2}{7} . $$

   Using the notation
$$
N_p^\pi(z) \equiv \frac{1}{\sigma} \frac{d \sigma}{d z}(\mathrm{ep} \rightarrow \pi \mathrm{X}) .
$$
show that, in the valence quark approximation for $\mathrm{p}, \mathrm{n}$,
$$
\frac{\int d z\left[N_n^{\pi^{+}}-N_n^{\pi^{-}}\right]}{\int d z\left[N_p^{\pi^{+}}-N_p^{\pi^{-}}\right]}=\frac{2}{7} .
$$

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Quarks and leptons: introductory course in modern particle physics

Quarks and leptons: introductory course in modern particle physics

Francis Halzen, Alan… 1st Edition

Chapter 11, Problem 4

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The notation \( N_p^\pi(z) \equiv \frac{1}{\sigma} \frac{d \sigma}{d z}(\mathrm{ep} \rightarrow \pi \mathrm{X}) \) represents the normalized yield of pions (\(\pi\)) as a function of the variable \(z\) in electron-proton (\(\mathrm{ep}\)) collisions. The problem Show more…

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Using the notation $$ N_p^\pi(z) \equiv \frac{1}{\sigma} \frac{d \sigma}{d z}(\mathrm{ep} \rightarrow \pi \mathrm{X}) . $$ show that, in the valence quark approximation for $\mathrm{p}, \mathrm{n}$, $$ \frac{\int d z\left[N_n^{\pi^{+}}-N_n^{\pi^{-}}\right]}{\int d z\left[N_p^{\pi^{+}}-N_p^{\pi^{-}}\right]}=\frac{2}{7} . $$

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