Abstract
We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.
Highlights
The complete access to the hadronic bound state and resonance structure, as well as to the nonperturbative dynamics of QCD at finite temperature and density, requires the computation of timelike correlation functions
The ghost Dyson-Schwinger equations (DSEs) is solved for the three different input decoupling gluon spectral functions in Fig. 4 and propagators, labelled by GðAlatÞ resp. the infrared value of the related gluon propagators GAð0Þ 1⁄4 4.4; 1.91⁄2GeV−2
Our spectral DSE approach is based on the spectral DSE put forward in [1], and uses the spectral renormalization devised there
Summary
The complete access to the hadronic bound state and resonance structure, as well as to the nonperturbative dynamics of QCD at finite temperature and density, requires the computation of timelike correlation functions. The latter is protected by nonrenormalization, and shows a very mild momentum dependence. In the present work we approximate this vertex by its classical counterpart This leaves us with a rather stable set-up: the spectral ghost DSE is solved on the basis of given input gluon spectral functions, obtained by appropriately modifying the result of [4], which was reconstructed under the assumption of a KL representation of the gluon.
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