If we assume a non-relativistic model, the magnetic moment of a point quark is given by \(\mu_{i}=q_{i} / 2 m_{i}\), where \(q_{i}\) is the charge and \(m_{i}\) the effective mass of quark \(i\). Assume the magnetic moment of the proton to be given by the sum over valence quark contributions

where \(\left|p_{1 / 2}\rightangle\) denotes a proton in the \(M_{J}=J=\frac{1}{2}\) angular momentum state, and \(\sigma_{3}^{i}\) is a Pauli matrix operating on the spin wavefunction of the \(i\) th quark. Use the proton wavefunction constructed in Problem 9.7 to show that the proton magnetic moment is given by \(\mu_{p}=\frac{4}{3} \mu_{u}-\frac{1}{3} u_{d}\), where \(\mu_{u}\) and \(\mu_{d}\) are magnetic moments of the up and down quarks, respectively, and the \(u\) and \(d\) quark masses are assumed equal.

Data from Problem  9.7

Use the methods to construct a proton flavor-spin wavefunction that is symmetric with respect to flavor-spin exchange.

Transcribed Image Text:

3 Hp = (P1/2 HP1/2), i=1