Bootstrap andSU(3)Assignment of2+Mesons

Abstract

For meson-meson scattering special properties of some submatrices of the total crossing matrix are derived. These properties are applied to the study of the bootstrap of $2^{+}$ mesons in the scattering system of two pseudoscalar octets. We find that self-consistency can be sustained by a $1^{-}$ octet, a $2^{+}$ singlet, and a $2^{+}$ octet. We assign $f^0\mathrm{}\left(1250\right)\mathrm{}$ to the $2^{+}$ singlet, and $A_2\mathrm{}\left(1310\right)\mathrm{}$ and $K^{*}\mathrm{}\left(1415\right)\mathrm{}$ to the $2^{+}$ octet, leaving an $I=0, 2^{+}$ particle yet to be found. Consequences of this assignment are discussed.