Higgs radial mass for a half-normalized quartic potential ($m_H^2=\lambda v^2$)

For $V=\frac{1}{2}\lambda ({\varphi }^{†}\varphi -v^2/2{)}^2$ and the canonically normalized radial field, the expansion is $V=\frac{1}{2}\lambda v^2{H}^2+\frac{1}{2}\lambda v{H}^3+\frac{1}{8}\lambda H^4$. Comparing the quadratic term with $m_H^2{H}^2/2$ gives the displayed mass. Replacing the prefactor $\lambda /2$ by $\lambda$ changes the answer to $2\lambda v^2$, so the potential's normalization must be retained.