content_image/323226.jpg content_image/323224.jpg content_image/323225.jpg content_image/323223.jpg content_image/323222.jpg
introduced some ambiguity through our choice of A ( z ) and Φ( z )). Requiring that the solution is simply normalizable gives us a discrete spectrum: 

<img src='content_image/323226.jpg'>

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: 

<img src='content_image/323224.jpg'>

<img src='content_image/323225.jpg'>

Note that the mass spectrum goes like m 2 n ∼ n , as we set out to achieve. 

## 5.5.2 Axial Vector Mesons 

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 2 2 

<img src='content_image/323223.jpg'>

<img src='content_image/323222.jpg'>

