SU (3) breaking and baryon magnetic moments

We show that the magnetic moments of the octet baryons can be fitted to an accuracy of 1.5 % by a phenomenological Lagrangian in which SU(3) breaking corrections appear only linearly. This is in contrast to conventional chiral perturbation theory in which corrections non-analytic in SU(3) breaking dominate and tend to spoil the agreement with the data. Motivated by this observation, we propose a modified scheme for chiral perturbation theory that gives rise to a similar linear breaking of SU(3) symmetry. (Pacs 13.40.Em, 14.20.-c, 11.30.Rd) (hep-ph/9602251) The magnetic moments of the octet baryons were found to obey approximate SU(3) symmetry a long time ago by Coleman and Glashow [1]. In the SU(3) symmetric limit, the nine observable moments (including the transitional moment between Σ and Λ) can be parameterized in terms of two parameters, and as a result obey approximate relationships. As we will show later, the two parameter result of Coleman and Glashow can in fact fit the observed magnetic moments up to about the 20% level. However, since at present the moments have been measured with an accuracy of better than 1% [2], an improved theoretical understanding is clearly desirable. It is the goal of this paper to show how this can be achieved easily phenomenologically and in a scheme of chiral perturbation theory. Many attempts were made trying to improve the numerical predictions of Coleman and Glashow by including the SU(3) breaking effects using chiral perturbation theory (ChPT) [3, 4, 5, 6]. However, many of these efforts resulted in numerical fits worse than the leading order SU(3) invariant one by Coleman and Glashow. For example, Caldi and Pagels [3] found that the leading SU(3) breaking corrections, in their scheme for ChPT, appear in the non-analytic forms of √ ms and ms lnms. They showed that the √ ms corrections are in fact at least as large as the SU(3) invariant zeroth order terms, which casts doubt on the applicability of ChPT. Caldi and Pagels suggested that this “failure” of ChPT might be attributed to the large mass of kaon in the loops and the fact that the leading correction is of non-analytic form. Such non-analytic contributions were indeed pointed out earlier by Li and Pagels [7] and others [8], however, the non-analyticity appears only in the SU(3) invariant