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The Mass of the Ninth Pseudoscalar Meson in the Frame of Broken Chiral SU(3) ⊗ SU(3)
Author(s) -
Rodenberg R.
Publication year - 1973
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19734830403
Subject(s) - physics , pseudoscalar , ansatz , particle physics , symmetry breaking , meson , pseudovector , scalar (mathematics) , chiral symmetry breaking , pseudoscalar meson , mathematical physics , geometry , mathematics
Using G ELL ‐M ANN 's ansatz for the SU (3)⊗ SU (3) symmetry breaking part H SB = ‐ u 0 ‐ cu 8 in the strong H AMILTONIAN density, where the operators u j ( j = 0, 1,…8) are the scalar part of a basis for the {(3,3 ★ ) ⊕ (3 ★ ,3)} representation of chiral SU (3)⊗ SU (3) and where the constant c is a measure for SU (3) breaking within the SU (3)⊗ SU (3) breaking, a sum rule for the spin zero spectral functions of the pseudoscalar axial vector current octet is derived. Saturating the sum rule with the lowest lying states, the mass of the ninth pseudoscalar meson can be estimated as m η1 = 950 MeV.