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Reliability of the Dyson-Schwinger gap equation in technicolor theories

Reliability of the Dyson-Schwinger gap equation in technicolor theories
Reliability of the Dyson-Schwinger gap equation in technicolor theories

This thesis is concerned with investigating the Dyson-Schwinger equation for the fermion propagator in the ladder approximation and beyond. The renormalization group improved ladder approximation to D-S equation has first been solved numerically in a general covariant gauge. Solution to this equation has been used to estimate the fermion condensate < PROB*LEM> and the technipion decay constant FπPROB*LEM. It was found that these estimates are extremely gauge dependent. The next order correction to the ladder approximation has been thoroughly examined with the hope that the gauge dependence may be reduced. The resulting system of integral equation for the mass function Σ*(p) and the wavefunction renormalization constant has been solved. We first determine the running critical coupling by examining the effective potential for each value of λ, the gauge parameter. This has been used as an input in the numerical analysis. The system of integral equations has been solved numerically subject to the boundary condition μ* = 2Σ*(0), where μ* is the threshold energy for the production of fermion condensate. In this analysis we found that while the decay constant is only moderately sensitive to the choice of λ, the gauge dependence of the condensate found in the ladder approximation is not reduced by the inclusion of next order terms.

University of Southampton
Kamli, Ali Ahmed
Kamli, Ali Ahmed

Kamli, Ali Ahmed (1991) Reliability of the Dyson-Schwinger gap equation in technicolor theories. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

This thesis is concerned with investigating the Dyson-Schwinger equation for the fermion propagator in the ladder approximation and beyond. The renormalization group improved ladder approximation to D-S equation has first been solved numerically in a general covariant gauge. Solution to this equation has been used to estimate the fermion condensate < PROB*LEM> and the technipion decay constant FπPROB*LEM. It was found that these estimates are extremely gauge dependent. The next order correction to the ladder approximation has been thoroughly examined with the hope that the gauge dependence may be reduced. The resulting system of integral equation for the mass function Σ*(p) and the wavefunction renormalization constant has been solved. We first determine the running critical coupling by examining the effective potential for each value of λ, the gauge parameter. This has been used as an input in the numerical analysis. The system of integral equations has been solved numerically subject to the boundary condition μ* = 2Σ*(0), where μ* is the threshold energy for the production of fermion condensate. In this analysis we found that while the decay constant is only moderately sensitive to the choice of λ, the gauge dependence of the condensate found in the ladder approximation is not reduced by the inclusion of next order terms.

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Published date: 1991

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Local EPrints ID: 460599
URI: http://eprints.soton.ac.uk/id/eprint/460599
PURE UUID: e0de283d-1d04-429b-b421-01bf05234ee7

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Date deposited: 04 Jul 2022 18:25
Last modified: 04 Jul 2022 18:25

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Author: Ali Ahmed Kamli

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