m^2 = u^4 \frac{\sqrt{1 + (1 - 2u \cos \phi + u^2)^2 - 2(1-u\cos \phi) (1 - 2u\cos \phi + u^2)^{1/2} }}{(1 - 2u \cos \phi + u^2)^2 (1 - 2u^2 \cos \phi + u^4)^{1/2}} = f(u,\phi)