# Where can I find the measured magnetic moments of the quarks?

I read that the magnetic moment of the proton can be expressed as the sum of the magnetic moments of the three quarks like $\mu_p = \frac{4}{3}\mu_u - \frac{1}{3}\mu_d$. But I couldn't find a table listing the measured magnetic moments of the quarks. Can you point me to a reference?

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The magnetic moments of the nucleons are largely not the sum of the magnetic moments of the valence quarks in any microscopic model (the "constituent quark model" that Johannes talks about is a crude tool long since abandoned for most purposes). – dmckee♦ Apr 13 '11 at 18:30

## 2 Answers

Since a quark $q_i$ is a spin $\frac{1}{2}$ Dirac particle with charge $z_i e$ and constituent mass $m_i$ with $i=u,d,s...$ theory predicts its magnetic moment as

$\mu_i = \frac{z_i e \hbar}{2 m_i}$.

Note that the formula in your question is only valid in the constituent quark model where a baryon consists only of three constituent quarks. Therefore you have to use the constituent quark mass in the formula for the magnetic moment too. A list of constituent quark masses is eg. found here. These masses are obtained from hadron spectroscopy.

I am not aware of any direct measurements of quark magnetic moments.

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Is $z_i = \pm 1/3,\pm 2/3$ ? What about the $g$-factor for the different quarks? – asmaier Apr 13 '11 at 20:55

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Yes it is. The $g$-factor in this model is 2 for all quarks, because they are considered point particles with spin 1/2 obeying the Dirac equation (no QED). – Johannes Apr 13 '11 at 21:47
Can you point me to a reference describing the constituent quark model, where the equations for the magnetic moment according to this model are explained? – asmaier Apr 14 '11 at 12:17
You can read about this in just about every introductory particle physics book. For example the books of Griffiths (chapter 5.10) and Povh (chapter 15.4) cover it. – Johannes Apr 14 '11 at 14:37

Quarks are confined.

Any "measurements" come from the measurements of seen particles, utilizing the Dirac equation, Quantum Field Theory and the symmetries of the standard model to constrain the quantities of the quarks, be it masses or moments or charges.

The standard model was extremely well verified by the measurements at LEP up to the energies of LEP.

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