Magnetic Susceptibilty of Up Quarks

We can find analytic solutions for some parameters in terms of electron, muon and proton characteristics such as the mass $m$ and the magnetic moment $\mu$. This is done by writing out $\mu$ in terms of magnetic susceptibilities $\chi_{\it{m}}$ and quark coefficients, then solving the resulting equations to obtain

$\begin{align} \chi_{\it{m}}(\sf{u}) = \chi_{\it{m}}(\sf{e}) - \chi_{\it{m}}(\sf{g}) + \frac{\chi_{\it{m}}(\sf{t}) - \chi_{\it{m}}(\sf{b}) - \chi_{\it{m}}(\sf{s}) + \chi_{\it{m}}(\sf{c})}{\mathrm{2}} + \left( \frac{\mathrm{2} \pi \, \mu_{\sf{N}} }{\it{ he}} \right) \, \mu(\sf{e^{-}}) \, \it{m}(\sf{e^{-}}) \end{align}$

where $\mu_{\sf{N}}$ is the nuclear magneton and $\pi$, $h$ and $e$ are constants.