Dashen-Lee Sum Rules for Magnetic Moments

Abstract

This work stresses the importance of the contribution of an isotopic-spin-½ pion-nucleon intermediate state for the Dashen-Lee sum rules which are obtained from the commutation relations between various combinations of the isoscalar and isovector magnetic-moment operators $M^S$ and $M^V$. In particular, it is shown that the $M^S-M^V$ sum rule can be brought into agreement with experiment by introducing this contribution. Furthermore, it does not have much influence on the "good" $M^V-M^V$ sum rule ${\left(\frac{{{\mu }_p}^2}{2m}\right)}^2=\frac{{{〈r〉}_p}^2}{6}$, where ${\mu }_p$, $m$, and ${〈r〉}_p$ are the total magnetic moment, mass, and charge radius of the proton, respectively. The implications of these results for the commutation relations between space components of current densities are also discussed.