Two pseudo-Goldstone bosons in the Gildener-Weinberg model

In a dimensionless multi-scalar extension of the Standard Model, Gildener and Weinberg assumed that along a flat direction, there is only one classically massless scalar, known as the {\it scalon}, which acquires mass through radiative corrections \`a la Coleman-Weinberg, while all other scalars remain heavy. In this paper, by introducing a toy model with four scalar degrees of freedom we demonstrate the existence of {\it two} scalons along a specific flat direction that we construct. We present the effective potential for the model and provide the masses of the heavy scalars and two radiatively light pseudo-Goldstone bosons.