A note on Gravitational radiation in generalized Brans-Dicke theory: compact binary systems

This note revisits and corrects a previous analysis on gravitational radiation in compact binary systems within the framework of Brans-Dicke-f® theories-models featuring both massless and effectively massive scalar fields. We correct the lower bound on the Brans-Dicke coupling parameter ${\omega }_0$ presented in prior work, identifying teh issue that led to inverted constraints. By reanalyzing data from the binary system PSR J1012+5307, we present revised bounds on ${\omega }_0$ as a function of the geometrical scalar field mass $m_f$, emphasizing that the role of ${\omega }_0$ differs from its traditional interpretation in standard BD theory.