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:

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