Bound States in Scalar Theory with Fourth-order Derivative Term

TL;DR

This paper investigates the existence of bound states in a scalar theory with a fourth-order derivative term, revealing conditions under which bound states form and discussing implications for quadratic gravity and unitarity.

Contribution

It demonstrates the formation of bound states in a scalar theory with higher derivatives and explores their relevance to quadratic gravity and unitarity issues.

Findings

Bound states appear at large coupling constants due to scalar attraction.

No bound states form for nearly massless normal particles like the graviton.

The model offers insights into ghost confinement and unitarity restoration in quadratic gravity.

Abstract

We consider a problem whether bound states are made in a scalar theory with a fourth-order derivative term or not. After rewriting the theory to a standard scalar theory with second-order derivative terms, we calculate a correlation function of the composite operators made out of massive ghosts with negative norm and massive normal fields with positive norm in the ladder approximation. It is shown that there appears a pole of the bound state in the correlation function of the both fields by attraction due to scalar field when the coupling constant is large whereas there does not so in the correlation function of almost massless normal particles corresponding to the graviton. We also point out the relationship between the scalar theory with a fourth-order derivative term and quadratic gravity. Our model may shed some light on the confinement of massive ghost in quadratic gravity, thereby enabling us to solve the problem of unitarity violation associated with the massive ghost.