Composite scalar boson mass dependence on the constituent mass anomalous dimension

TL;DR

This paper investigates how the mass of composite scalar bosons depends on the constituent fermion's mass anomalous dimension, revealing that larger $$ can lead to lighter scalar masses, with fermionic corrections also playing a significant role.

Contribution

It introduces a Bethe-Salpeter equation approach incorporating the mass anomalous dimension to analyze scalar boson masses, highlighting the impact of fermionic corrections.

Findings

Scalar mass decreases with increasing mass anomalous dimension $$.

Fermionic corrections to the BSE kernel significantly lower the scalar mass.

Top quark loop effects set a lower bound on the scalar mass.

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.