Higher order correction to the sine-Gordon soliton mass

We calculate in the 2-dimensional sine-Gordon theory

$\text{L}{}_{\mathrm{GC}}\text{=}\text{1}\text{2}\text{(?}{}^{\mathrm{\mu }}\text{φ)}{}^2\text{?(}\text{m}{}_4\text{λ}\text{)[1?cos(}\text{λ}\text{φ}\text{m}\text{)]}$

the soliton mass M_sol to order λ and compare it to the meson mass. We find

$\text{M}{}_{\mathrm{sol}}\text{m}{}_{\mathrm{menson}}\text{=}\text{8m}{}^2\text{λ}\text{?}\text{1}\text{π}\text{+}\text{λ}\text{192m}{}^2\text{+O(λ}{}^2\text{)}$

This supports the belief that the field-theoretic WKB approximation of Dashen, Hasslacher and Neveu gives the correct answer for the sine-Gordon problem.