) (\text{c}_1 (n+2)+\text{c}_2 (n-2) \cosh \theta ) {\operatorname{csch}}^2\theta  \no
\\ & \qquad \qquad \qquad + 2\pi i (\text{c}_1+\text{c}_2) (\text{c}_1+\text{c}_2 \cosh \theta ) {\operatorname{csch}}^2 \theta+  (2 \text{c}_1^2-\text{c}_2^2 \cosh \theta +\text{c}_2^2) {\operatorname{csch}}\theta\big)\ . \no \vphantom{\frac{2i h^2}{\pi}} \end{aligned}$$ Having checked that the tree-level S-matrix satisfies the consistency condition , we can use the method of unitarity cuts described in Section \[sec:general\] with ${M},{N},\ldots = i,j,\ldots$ to find the following result $$\begin{aligned}
T_{\text{u.c.}}(\theta) &= 1 + 2 i h (\text{c}_1 + \text{c}_2) {\operatorname{csch}}\theta \no   \vphantom{\frac{2i h^2}{\pi}}
\\ & \quad \ \ \, + \frac{2ih^2}{\pi} \big(2 \text{c}_1 \text{c}_2 (i\pi - 2 \theta ) \coth \theta{\operatorname{csch}}\theta + i \pi  (2 \text{c}_1^2+2 \text{c}_1 \text{c}_2+\text{c}_2^2 (1+\cosh^2 \theta))  {\operatorname{csch}}^2\theta \no
\\ & \qquad \qquad \quad + (\text{c}_1+\text{c}_2) (4 \text{c}_1 + n (\text{c}_1+\text{c}_2))  {\operatorname{csch}}\theta \big) \ , \vphantom{\frac{2i h^2}{\pi}} \no
\\
R_{\text{u.c.}}(\theta) &= 2 i h (\text{c}_1 + \text{c}_2 \cosh\theta)  {\operatorname{csch}}\theta \vphantom{\frac{2i h^2}{\pi}} \label{s2com2}
\\ & \quad \ \ \, + \frac{2i h^2}{\pi}\big(\theta \, (\text{c}_1+\text{c}_2 \cosh \theta ) (\text{c}_1 (n+2)+\text{c}_2 (n-2) \cosh \theta ) {\operatorname{csch}}^2\theta \no
\\ & \qquad \qquad \qquad + 2\pi i (\text{c}_1+\text{c}_2) (\text{c}_1+\text{c}_2 \cosh \theta ) {\operatorname{csch}}^2 \theta+ 2 (\text{c}_1^2+\text{c}_2^2 \cosh \theta) {\operatorname{csch}}\theta\big) \ .\vphantom{\frac{2i h^2}{\pi}}\no\end{aligned}$$ Clearly and differ. Furthermore, they only agree for $\text{c}_2 = 0$. 