5.6 Luescher analysis

The two pion energy states $omega_n$ are the roots of the Luecher quantization condition, which in the continuum for $l=1$ takes the for of $$\cot \delta (k_n) +\cot\phi(q_n)=0$$

with:

• $\omega_n=2\sqrt{k_n^2+m^2}$
• $q_n=\frac{k_nL}{2\pi}$
• $\cot\phi(q_n)=-\frac{Z_{00}(1,q_n^2)}{q_n \pi^{3/2}}$