Question

The spin-flavor wavefunctions of the ground-state baryons are symmetric, and color was invoked to recover the required antisymmetric character. You should notice, however, and some people did, that we can construct a totally antisymmetric proton wavefunction, for example, $$ |\mathrm{p} \uparrow\rangle=\sqrt{\frac{1}{2}}\left[\mathrm{p}_A \chi\left(M_S\right)-\mathrm{p}_S \chi\left(M_A\right)\right] $$ and forget about color! Write this function in an explicit form, comparable to (2.71). Obtain $|\mathrm{n} \uparrow\rangle$, and hence show that $$ \frac{\mu_n}{\mu_p}=-2 . $$ So this option is ruled out by experiment. In fact, glancing at your derivation, you will notice that $\mu_p$ is negative. It is measured to be positive. Long live color.

   The spin-flavor wavefunctions of the ground-state baryons are symmetric, and color was invoked to recover the required antisymmetric character. You should notice, however, and some people did, that we can construct a totally antisymmetric proton wavefunction, for example,
$$
|\mathrm{p} \uparrow\rangle=\sqrt{\frac{1}{2}}\left[\mathrm{p}_A \chi\left(M_S\right)-\mathrm{p}_S \chi\left(M_A\right)\right]
$$
and forget about color! Write this function in an explicit form, comparable to (2.71). Obtain $|\mathrm{n} \uparrow\rangle$, and hence show that
$$
\frac{\mu_n}{\mu_p}=-2 .
$$

So this option is ruled out by experiment. In fact, glancing at your derivation, you will notice that $\mu_p$ is negative. It is measured to be positive. Long live color.

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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 2, Problem 18 ↓

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$\chi\left(M_S\right)$ and $\chi\left(M_A\right)$ are the mixed symmetry and mixed antisymmetry spin wavefunctions, respectively.  Show more…

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The spin-flavor wavefunctions of the ground-state baryons are symmetric, and color was invoked to recover the required antisymmetric character. You should notice, however, and some people did, that we can construct a totally antisymmetric proton wavefunction, for example, $$ |\mathrm{p} \uparrow\rangle=\sqrt{\frac{1}{2}}\left[\mathrm{p}_A \chi\left(M_S\right)-\mathrm{p}_S \chi\left(M_A\right)\right] $$ and forget about color! Write this function in an explicit form, comparable to (2.71). Obtain $|\mathrm{n} \uparrow\rangle$, and hence show that $$ \frac{\mu_n}{\mu_p}=-2 . $$ So this option is ruled out by experiment. In fact, glancing at your derivation, you will notice that $\mu_p$ is negative. It is measured to be positive. Long live color.
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