scaling limit is a continuous limit of the lattice model, $r_0\to 0$, with additional requirements: the velocity Eq. (\[velo\]) stays equal to unity and the gap Eq. (\[Gap\]) stays constant; hence $\gamma \to 0$ so that $\gamma_r=const$. In this limit, the effective theory describing the XYZ chain is a massive relativistic sine-Gordon model [@Luther76], $$\label{ham-sG}
 A_{sG}=\frac{1}{2} \int \mathrm{d^2} {{\bm{r}}}  ( \partial_{\mu} \Theta)^2   -2\mu \int \mathrm{d^2} {{\bm{r}}} \cos{ \sqrt{8 \pi \eta } \Theta}  .$$ To give explicit meaning to $\mu$ one has to specify normalization of fields. We will follow the approach developed by Zamolodchikov [@Zamolodchikov], where the dimension of field $[\cos{ \sqrt{8 \pi \eta } \Theta}]=r_0^{-2\eta}$ and the fields are normalized as follows at short distances, where perturbation is irrelevant [@comment]: $$\label{SDN}
\lim_{r\to 0}\langle  \cos{ \sqrt{8 \pi \eta } \Theta(0)}  \cos{ \sqrt{8 \pi \eta } \Theta(r)}  \rangle= \frac{1}{2}\frac{1}{r^{4\eta}}.$$

Explicit connection between the coupling constant $\mu$ and the soliton mass of the sine-Gordon model was obtained [@Zamolodchikov] by using the Bethe ansatz integrability of the sine-Gordon model in external uniform gauge field, with amplitude $A$, coupled to the conserved current [@JNW] and viewing the same model as a conformal field theory (Gaussian model for $\mu=0$) perturbed by a cosine term. In 