Emergence of ghost in once-subtracted on-shell unitarization in glueball-glueball scattering

TL;DR

This paper studies scalar glueball scattering in pure Yang-Mills theory, revealing that a common unitarization method causes unphysical ghost states, and suggests a solution involving additional subtractions in the loop function.

Contribution

It identifies a problem with ghost states arising from single subtraction unitarization and proposes a modified subtraction scheme to resolve this issue.

Findings

Single subtraction unitarization leads to ghost states.

Adding an extra subtraction in the loop function removes ghosts.

The sign of the first-order term is crucial for physical unitarization.

Abstract

We investigate the scattering of two scalar glueballs in pure YM theory, using the well known dilaton potential. We perform the calculations considering a glueball mass of about $m_G \approx 1.7$ GeV, as predicted by lattice QCD. We begin with the tree-level theory, but the question about the presence of a bound state needs a deeper study to be answered. Thus we unitarize the theory through a self energy loop function consisting of a single subtraction at the single glueball resonance pole. We show that this choice is inconsistent as it leads to the emergence of a ghost-like state with negative norm. This problem is related with the sign of the coefficient in the first order term of the expansion of the reverse unitarized amplitude. We briefly discuss the solution which consists of an additional subtraction in the loop function, as presented in Eur.Phys.J.C 82 (2022) 5, 487.