Composite scalar boson mass dependence on the constituent mass anomalous dimension

Abstract

We perform a Bethe-Salpeter equation (BSE) evaluation of composite scalar boson masses in order to verify how these masses can be smaller than the composition scale. The calculation is developed with a constituent self-energy dependent on its mass anomalous dimension ($\gamma$), and we obtain a relation showing how the scalar mass decreases as $\gamma$ is increased. We also discuss how fermionic corrections to the BSE kernel shall decrease the scalar mass, whose effect can be as important as the one of a large $\gamma$. An estimate of the top quark loop effect that must appear in the BSE calculation gives a lower bound on the composite scalar mass.