Beta boson

This work presents a minimal mass-closure scheme for a propagating scalar excitation associated with the structural channel beta within the visible action of the beta framework. The construction starts from the covariant visible sector, expanding the scalar potential around a locally stable branch to identify the branch curvature that defines the structural mass parameter. To resolve the dimensional tension between the role of beta as a structural quantity in the Yukawa hierarchy and its role as a dynamical scalar in the action, the structural variable is separated from a canonically normalized field B. A conservative effective ansatz is developed for the intrinsic structural block, the phi-B mixed sector, and the filtered contribution inherited from the deeper alpha reservoir. This approach yields a closed effective formula for the branch mass of the structural scalar and the mixed physical eigenvalues after diagonalization of the phi-B sector. In the weak-mixing regime, the observable state is identified as a beta-dominated scalar eigenmode. Finally, a benchmark realization is provided where the beta-dominated eigenmode lies near 285 GeV, with an internal spread of approximately 5 GeV under controlled parameter variations. This formulation establishes the branch mass and mixed eigenvalue spectrum of a structural scalar associated with the beta channel within the current effective framework.