Show that 1-y=(p ·k^')/(p ·k) ≃(1)/(2)(1+cosθ), where θis the scattering angle in the electron-q

Step 1: Understand the variables and the context. - $y$ is a variable commonly used in deep inel

Question

Show that $$ 1-y=\frac{p \cdot k^{\prime}}{p \cdot k} \simeq \frac{1}{2}(1+\cos \theta), $$ where $\theta$ is the scattering angle in the electron-quark center-of-mass frame. Hence, identify the $(1-y)^2$ and 1 terms in (9.24) with scattering between an electron and quark with opposite helicities and with the same helicity, respectively. The parton model result $2 x F_1=F_2$ is known as the Callan-Gross relation. It is a consequence of the quarks having spin $\frac{1}{2}$ and is well borne out by the data.

   Show that
$$
1-y=\frac{p \cdot k^{\prime}}{p \cdot k} \simeq \frac{1}{2}(1+\cos \theta),
$$
where $\theta$ is the scattering angle in the electron-quark center-of-mass frame.
Hence, identify the $(1-y)^2$ and 1 terms in (9.24) with scattering between an electron and quark with opposite helicities and with the same helicity, respectively.

The parton model result $2 x F_1=F_2$ is known as the Callan-Gross relation. It is a consequence of the quarks having spin $\frac{1}{2}$ and is well borne out by the data.

Quarks and leptons: introductory course in modern particle physics

Francis Halzen, Alan… 1st Edition

Chapter 9, Problem 6

Instant Answer

Step 1

- $y$ is a variable commonly used in deep inelastic scattering, representing the fraction of the electron's energy lost in the proton's rest frame. - $p$ and $k$ are the four-momenta of the initial quark and electron, respectively, and $k'$ is the four-momentum of Show more…

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Show that $$ 1-y=\frac{p \cdot k^{\prime}}{p \cdot k} \simeq \frac{1}{2}(1+\cos \theta), $$ where $\theta$ is the scattering angle in the electron-quark center-of-mass frame. Hence, identify the $(1-y)^2$ and 1 terms in (9.24) with scattering between an electron and quark with opposite helicities and with the same helicity, respectively. The parton model result $2 x F_1=F_2$ is known as the Callan-Gross relation. It is a consequence of the quarks having spin $\frac{1}{2}$ and is well borne out by the data.

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