The mass structure of SU(3) baryon antidecuplet and pion muon mass difference

Abstract

We show that the mass intervals among the pentaquark baryons $\Theta^{+}$, $N^{*}(1685)$ and $\Xi_{3/2}^{-}$ proposed to be the members of the SU(3) antidecuplet are exact integral multiples of the mass difference between a neutral pion and a muon i.e. 29.318 MeV, in agreement with the general tendency of the mass differences among elementary particles to be close integral/half integral multiple of this mass unit. Further our study reveals that the strength of the SU(3) breaking understood to give members of the same multiplet different masses takes values, discrete as integral multiple of the mass difference between a neutral pion and a muon, the first two massive elementary particles.