Abstract
$s$-wave meson-baryon scattering lengths to first order in symmetry breaking are investigated within the framework of the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ chiral algebra. We find that there are no renormalization effects in these scattering lengths to first order in symmetry breaking under the assumption of current commutation relations, the hypothesis of partially conserved axial-vector current, and the Ademollo-Gatto theorem for the vector-baryon---baryon coupling. However, if we do not assume the Ademollo---Gatto theorem, we do observe symmetry-breaking effects in the scattering-length sum rules.
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