TL;DR
This paper explores the general formulation of gravity with independent metric and connection, identifying a unique light scalar or vector distortion field that can be phenomenologically relevant, including mixing with the Higgs.
Contribution
It uncovers a naturally light scalar or vector distortion field in gravity that can be dynamical and phenomenologically significant.
Findings
A unique light scalar or vector distortion field exists in general gravity theories.
The light scalar can naturally mix with the Higgs boson.
Most other fields are non-dynamical or very heavy, recovering general relativity at low energy.
Abstract
In the most general formulation of gravity, the metric and connection are independent degrees of freedom, and the connection may include torsion and non-metricity (or distortion, collectively) degrees of freedom, resulting in a huge number of possible dynamical fields. However, the most fields are either non-dynamical or extremely heavy and the general relativity is recovered at low energy. We find a unique naturally light vector- or scalar-like distortion field, which can be dynamical and have phenomenological implications. In particular, a light scalar particle that mixes with the Higgs boson naturally appears.
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