# A bound state model for a light scalar

## TL;DR

This paper introduces a Hamiltonian-based bound-state model to explain the emergence of a light scalar in near-conformal strong dynamics, connecting lattice results with theoretical predictions.

## Contribution

It presents a simple, interpolating model that captures the behavior of various mesonic states across different limits, highlighting the light scalar's origin.

## Key findings

- The scalar becomes lighter than spin 1 states near the chiral limit.
- Masses vanish in the conformal limit, characterized by scaling dimensions.
- The model relates form factors and decay constants to mass behavior.

## Abstract

Recent lattice studies of near-conformal strong dynamics suggest the existence of a light scalar. This provides motivation to consider a simple Hamiltonian-based bound-state model where the pseudoscalar, scalar, vector and axial-vector states are treated on an equal footing. The model interpolates between the non-relativistic limit and the highly relativistic chiral limit, where the pseudoscalar mass drops to zero. The fermion mass becomes purely dynamical at this point. When the gauge coupling is constant over a moderate range of scales the scalar becomes significantly lighter than the spin 1 states as the chiral limit is approached. We relate this result to the behavior of the form factors of the respective states and their decay constants. In the conformal limit of the model all masses vanish and the theory is characterized by scaling dimensions.