Question

Verify (13.73). Assume that $k^2 \ll M_Z^2$ and that the target contains equal numbers of $u$ and $d$ quarks (i.e., it is an isoscalar target), and neglect antiquarks. Show that, in the standard model, $$ \begin{aligned} & a_1=-\frac{3}{4}\left(1-\frac{20}{9} \sin ^2 \theta_W\right), \\ & a_2=-\frac{3}{4}\left(1-4 \sin ^2 \theta_W\right) . \end{aligned} $$

   Verify (13.73). Assume that $k^2 \ll M_Z^2$ and that the target contains equal numbers of $u$ and $d$ quarks (i.e., it is an isoscalar target), and neglect antiquarks. Show that, in the standard model,
$$
\begin{aligned}
& a_1=-\frac{3}{4}\left(1-\frac{20}{9} \sin ^2 \theta_W\right), \\
& a_2=-\frac{3}{4}\left(1-4 \sin ^2 \theta_W\right) .
\end{aligned}
$$

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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 13, Problem 12

Instant Answer

Step 1

The target being isoscalar means it has equal numbers of $u$ and $d$ quarks, and we neglect antiquarks. The assumption $k^2 \ll M_Z^2$ simplifies the propagator of the $Z$ boson. Show more…

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Verify (13.73). Assume that $k^2 \ll M_Z^2$ and that the target contains equal numbers of $u$ and $d$ quarks (i.e., it is an isoscalar target), and neglect antiquarks. Show that, in the standard model, $$ \begin{aligned} & a_1=-\frac{3}{4}\left(1-\frac{20}{9} \sin ^2 \theta_W\right), \\ & a_2=-\frac{3}{4}\left(1-4 \sin ^2 \theta_W\right) . \end{aligned} $$

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