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I saw this question in a practice exam. I know that the structure functions are not linearly independent but that $F_2(x)=2xF_1(x)$ when the energy is in the order of GeV.

The question asks what would $F_1(x)/F_2(x)$ be if the spin of the quarks was 0.

On this matter my book says:

"...the underlying process in electron–proton inelastic scattering is the elastic scattering of electrons from point- like spin-half constituent particles within the proton, namely the quarks.."

but it doesn't explain how having spin-half comes into this.

Fernando Franco Félix
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2 Answers2

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The quarks of spin $\frac{1}{2}$ contribute to structure functions $F_{1}$ and $F_{3}$. ($F_{3}$ is parity-violating, so photon exchange does not contribute; only $W/Z$ boson.)

"IF" there were spin zero quarks, these would contribute to the longitudinal (scalar) structure-function $F_{L} = F_{2} - 2 x F_{1}$. But, because there are no spin zero quarks, $F_{L} = 0$ (at leading order), and thus $F_{2} = 2 x F_{1}$.

Additionally, if there were BOTH spin zero quarks and spin $\frac{1}{2}$ quarks, we would have: $F_{L} = F_{2} - 2 x F_{1}$ or $\frac{F_{1}}{F_{2}} = \frac{1 - \frac{F_{L}}{F_{2}}}{2x}$.

If there were NO spin $\frac{1}{2}$ quarks, and only spin $0$ quarks, $F_{1} = 0 = F_{3}$, and $F_{2} = F_{L}$ (Longitudinal).

ZaellixA
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Fredrick Olness
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I found the answer. Apparently when the spin of the quarks is 0 $F_1(x)=0$ as said here however I have to admit that i don't fully understand why is it 0

Fernando Franco Félix
  • 83