Discuss, on physical grounds, the behavior of fi(x) in the limit as x →1 when parton i carries a

Step 1: Understand the physical context of the problem. The parton distribution function $f_i(x)

Question

Discuss, on physical grounds, the behavior of $f_i(x)$ in the limit as $x \rightarrow 1$ when parton $i$ carries all the momentum of the proton. Counting rules have been proposed which argue that $$ f_i(x) \underset{x \rightarrow 1}{\longrightarrow}(1-x)^{2 n_s-1}, $$ where $n_s$ is the number of spectator valence quarks which share between them the residual, vanishingly small momentum of the proton. Contrast the $x \rightarrow 1$ behavior of $u^p(x)$ with that of $u^{\nabla}(x)$, the u-quark structure function of a $\pi^{+}$-meson.

   Discuss, on physical grounds, the behavior of $f_i(x)$ in the limit as $x \rightarrow 1$ when parton $i$ carries all the momentum of the proton. Counting rules have been proposed which argue that
$$
f_i(x) \underset{x \rightarrow 1}{\longrightarrow}(1-x)^{2 n_s-1},
$$
where $n_s$ is the number of spectator valence quarks which share between them the residual, vanishingly small momentum of the proton. Contrast the $x \rightarrow 1$ behavior of $u^p(x)$ with that of $u^{\nabla}(x)$, the u-quark structure function of a $\pi^{+}$-meson.

Quarks and leptons: introductory course in modern particle physics

Francis Halzen, Alan… 1st Edition

Chapter 9, Problem 11

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Step 1

The parton distribution function $f_i(x)$ describes the probability density of finding a parton (such as a quark or gluon) carrying a fraction $x$ of the total momentum of the proton. As $x \rightarrow 1$, the parton in question carries almost all the momentum of Show more…

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Discuss, on physical grounds, the behavior of $f_i(x)$ in the limit as $x \rightarrow 1$ when parton $i$ carries all the momentum of the proton. Counting rules have been proposed which argue that $$ f_i(x) \underset{x \rightarrow 1}{\longrightarrow}(1-x)^{2 n_s-1}, $$ where $n_s$ is the number of spectator valence quarks which share between them the residual, vanishingly small momentum of the proton. Contrast the $x \rightarrow 1$ behavior of $u^p(x)$ with that of $u^{\nabla}(x)$, the u-quark structure function of a $\pi^{+}$-meson.

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