introduced some ambiguity through our choice of A ( z ) and Φ( z )). Requiring that the solution is simply normalizable gives us a discrete spectrum: where L m n are the associated Laguerre polynomials. The masses and decay constants are found using the same formulae in section 5.3.1, the only differ- ence being the presence of the non-zero dilaton, which changes the results to: Note that the mass spectrum goes like m 2 n ∼ n , as we set out to achieve. The treatment of the axial vector mesons follows that of section 5.3.2. We define the axial gauge field as A ≡ 1 2 ( A$_{L}$ − A$_{R}$ ), and the equation of motion is found to be with the linearized equation of motion for the Higgs-like field X ( z ) given by 82 5.5.2 Axial Vector Mesons ∂$_{z}$ ( e − z 2 z 3 ∂$_{z}$X ( z ) ) + 3 e − z 2 z 5 X ( z ) = 0 (5.34) ∂$_{z}$ ( e − z 2 z ∂$_{z}$a$_{n}$ ) + ( m 2 n − g 2 5 z $_{2}$X ( z ) 2 ) e − z 2 z a$_{n}$ = 0 (5.33) m 2 n = 4( n + 1) (5.31) F 2 ρ$_{n}$ = 8( n + 1) g 2 5 (5.32) v$_{n}$ ( z ) = z 2 √ 2 n + 1 L 1 $_{n}$( z $^{2}$) (5.30)