my question is what the energy density of a cosmic string in the abelian higgs model is? I have different sources (Scholarpedia Cosmic Strings, the book "Cosmic Strings and Topological Defects" from Vilenkin and Shellard, etc.), but they all give different values for the energy density. The formulas they give are similar, they all depend on the coupling parameter $\beta=\frac{\lambda}{2e}$, but they are definitely not the same. therefore I want to ask whether there even is a general formula for the energy density depending on $\beta$?
One a more specific note, not even the values for the critical coupling, $\beta=1$, agree with each other. Some sources say the energy density is $\mu=\pi\eta^2$ for this case while others have factors two or others in front.
