  The two-loop correction to the mass of the $\phi^4$ kink is $0.0126\lambda/m$
in terms of the coupling $\lambda$ and the meson mass $m$ evaluated at the
minimum of the potential. This is calculated using a recently proposed
alternative to collective coordinates. Both the kink energy and the vacuum
energy are IR divergent at this order. To cancel the divergence, the two energy
densities are subtracted before integrating over space, or equivalently a
finite counterterm is added to the Hamiltonian density to cancel the vacuum
energy density. All spatial integrals are performed analytically. However in
the last step of our calculation, integrals over virtual momenta are performed
numerically.
