## 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:

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