If σ(v̅) / σ(v)=R, show that (∫x Q̅(x) d x)/(∫x Q(x) d x)=(3 R-1)/(3-R) . Detailed analyses show

Step 1: Understand the notation and the problem. - $sigma(bar{v})$ and $sigma(v)$ represent cros

Question

If $\sigma(\bar{v}) / \sigma(v)=R$, show that $$ \frac{\int x \bar{Q}(x) d x}{\int x Q(x) d x}=\frac{3 R-1}{3-R} . $$ Detailed analyses show that the functions $u(x), d(x), \ldots$, are indeed the same whether one extracts them from electroproduction or neutrino experiments. This is a definitive success of the parton model: the $u(x), d(x)$, describe the intrinsic structure of the hadronic target and are the same whatever experimental probe is used to determine them.

   If $\sigma(\bar{v}) / \sigma(v)=R$, show that
$$
\frac{\int x \bar{Q}(x) d x}{\int x Q(x) d x}=\frac{3 R-1}{3-R} .
$$
Detailed analyses show that the functions $u(x), d(x), \ldots$, are indeed the same whether one extracts them from electroproduction or neutrino experiments. This is a definitive success of the parton model: the $u(x), d(x)$, describe the intrinsic structure of the hadronic target and are the same whatever experimental probe is used to determine them.

Quarks and leptons: introductory course in modern particle physics

Francis Halzen, Alan… 1st Edition

Chapter 12, Problem 19

Instant Answer

Step 1

- $\sigma(\bar{v})$ and $\sigma(v)$ represent cross-sections for antineutrino and neutrino interactions, respectively. - $\bar{Q}(x)$ and $Q(x)$ are the parton distribution functions (PDFs) for antineutrinos and neutrinos. - The ratio $\sigma(\bar{v}) / \sigma(v) Show more…

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If $\sigma(\bar{v}) / \sigma(v)=R$, show that $$ \frac{\int x \bar{Q}(x) d x}{\int x Q(x) d x}=\frac{3 R-1}{3-R} . $$ Detailed analyses show that the functions $u(x), d(x), \ldots$, are indeed the same whether one extracts them from electroproduction or neutrino experiments. This is a definitive success of the parton model: the $u(x), d(x)$, describe the intrinsic structure of the hadronic target and are the same whatever experimental probe is used to determine them.

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