Accidental massless scalar ($M^2\xi =0$)

An accidental massless scalar has zero quadratic mass without being required by the stated broken continuous symmetry. A singlet with potential $\kappa z^4$ around $z=0$ is an example: its Hessian matrix vanishes although no continuous symmetry of that single real field protects a mass term. Such a zero mass can require tuning once quantum corrections are included.