Summary
A cosmic-gauge-string model based upon aU(1)-Higgs theory containing a generic symmetry-breaking potential is considered. Dimensionless structure equations are obtained and examined for the case in which either an ordinary tree potential or a one-loop Coleman-Weinberg potential is incorporated. Asymptotic solutions are obtained for each case and compared.
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The boundary conditions given by eqs. (26) and (27) are valid for both the tree potential and the Coleman-Weinberg potential, which can be seen by examining the linear energy density of the system.
Note that η1 (a free parameter in the Coleman-Weinberg potential) need not be equal to η in eq. (38). For η1≠η, the replacement η→η1 can be made in eqs (28)–(31). Also note that the one-loop Coleman-Weinberg potentialU 1 can be built from a massless tree potentialU= λ′4! f 4 where λ′ need not be identified with λ in eq. (38). Adding loop corrections and forcingU 1 to minimize atf=η1 places a constraint upon λ′, allowing λ′ to be expressed in terms ofe 4.
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Morris, J.R. Structure equations for a cosmic-string model with a Coleman-Weinberg potential. Nuov Cim B 107, 453–461 (1992). https://doi.org/10.1007/BF02726995
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DOI: https://doi.org/10.1007/BF02726995