Critical Analysis of Baryon Masses and Sigma-Terms in Heavy Baryon Chiral Perturbation Theory

Abstract

We present an analysis of the octet baryon masses and the $\pi N$ and $KN$ $\sigma$--terms in the framework of heavy baryon chiral perturbation theory. At next-to-leading order, ${\cal O}(q^3)$, knowledge of the baryon masses and $\sigma_{\pi N}(0)$ allows to determine the three corresponding finite low--energy constants and to predict the the two $KN$ $\sigma$--terms $\sigma^{(1,2)}_{KN} (0)$. We also include the spin-3/2 decuplet in the effective theory. The presence of the non--vanishing energy scale due to the octet--decuplet splitting shifts the average octet baryon mass by an infinite amount and leads to infinite renormalizations of the low--energy constants. The first observable effect of the decuplet intermediate states to the baryon masses starts out at order $q^4$. We argue that it is not sufficient to retain only these but no other higher order terms to achieve a consistent description of the three--flavor scalar sector of baryon CHPT. In addition, we critically discuss an SU(2) result which allows to explain the large shift of $\sigma_{\pi N}(2M_\pi^2) - \sigma_{\pi N}(0)$ via intermediate $\Delta (1232)$ states.