On the analytic structure of scalar glueball operators at Born level

TL;DR

This paper analyzes the analytic structure of scalar glueball operators at the Born level, revealing branch cuts consistent with cut rules and showing spectral densities with cuts but no poles, using nonperturbative gluon propagators.

Contribution

It provides a detailed analysis of the two-point function of scalar glueball operators, incorporating nonanalytic structures and nonperturbative propagators, advancing understanding of glueball spectral properties.

Findings

Spectral densities exhibit cuts but no poles for lightlike momenta.

Branch points align with Cutkosky's cut rules.

Gluon propagators violate positivity, indicating absence from physical space.

Abstract

We study the analytic structure of the two-point function of the operator F2 which is expected to describe a scalar glueball. The calculation of the involved integrals is complicated by nonanalytic structures in the integrands, which we take into account properly by identifying cuts generated by angular integrals and deforming the contours for the radial integration accordingly. The obtained locations of the branch points agree with Cutkosky's cut rules. As input we use different nonperturbative Landau gauge gluon propagators with different analytic properties as obtained from lattice and functional calculations. All of them violate positivity and describe thus gluons absent from the asymptotic physical space. The resulting spectral densities for the glueball candidate show a cut but no poles for lightlike momenta, which can be attributed to the employed Born approximation.