23.25 two particle g0.25

23.25.1 fit $a$ from perturbative expansion

$$\frac{\Delta E_{2\phi_0} }{E_{2\phi_1}}=\frac{E_{2\phi_0}-2E_{2\phi_1}}{E_{2\phi_1}}= \frac{-2\pi a_0}{L^3} \left[ 1 +c_1 \frac{a_0}{L} + c_2 \frac{a_0^2}{L^2} \right]$$ $c_1=- 2.837297$ and $c_2= 6.375183$

$$\begin{gather} \chi^2/d.o.f.=1.46481 \\ P[0]=-0.834662\pm (0.0094) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 8.87e-05\\ \end{pmatrix} \end{gather}$$ }

23.25.2 Luescher analysis

$$\frac{k}{m} \cot{ \delta}=\frac{1}{a_0m}+\frac{r_0 m }{2}\frac{k^2}{m^2}$$ $P[0]=am$ , $P[1]=r_0m$

$$\begin{gather} \chi^2/d.o.f.=25.758 \\ P[0]=-0.107311\pm (0.001) \\ P[1]=-10.6811\pm (0.26) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 9.98e-07& 0.302\\ 0.302& 0.0701\\ \end{pmatrix} \end{gather}$$ }

23.25.3 energy level fit g=0.25

$$\begin{gather} \chi^2/d.o.f.=15.6572 \\ P[0]=-0.111071\pm (0.0016) \\ P[1]=-14.4885\pm (0.63) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 2.48e-06& 0.744\\ 0.744& 0.398\\ \end{pmatrix} \end{gather}$$ }