0$. One should choose a form of the supermatrices that maintains the cancellation of valence and ghost quark loops with an operator insertion [@Tiburzi:2004mv; @Detmold:2005pt]. For the flavor changing contributions we consider below, however, these operator self-contractions automatically vanish. For our calculation we require the action of $J_\mu^{a}$ in only the valence sector, and specify the upper $2 \times 2$ block of $\ol T {}^{a}$ to be the usual isospin generators $T^a$. Henceforth we restrict our attention to the operator $J_\mu^{+} \equiv J_\mu^{1} + i J_\mu^{2}$.

In calculating the isovector magnetic moment of the nucleon at next-to-leading order in the chiral expansion, there are local operators that contribute at tree level. In , the leading isovector current operator is $$\d J_\mu^+ 
= 
\frac{\mu_1}{M} \partial_\nu 
\left( 
\ol N \sigma_{\mu \nu} T^+ N
\right)
.$$ In partially twisted , there are two terms in the leading isovector current operator $$\d J_\mu^+ 
= 
\frac{1}{M} \Dt_\nu 
\left[ 
\mu_\a \left(\ol \cBt \, \sigma_{\mu \nu} \cBt \, \ol T {}^+  \right)  
+  
\mu_\b \left(\ol \cBt \, \sigma_{\mu \nu}  \ol T {}^+ \cBt  \right) 
\right]
.$$ The contribution of these operators at tree level is proportional to the linear combination $\frac{1}{3} \mu_\a - \frac{1}{6} \mu_\b$, which is 