# Questions tagged [dimensional-regularization]

Dimensional regularization is a method of isolating divergencies in scattering amplitudes.

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### Renormalization of Two Scalar Field Theory at Tree-Level and One-Loop Levels

I have been given a problem on renormalization, but due to my inexperience, I don't understand what to do with it. Here is the statement: Consider a theory of two real scalar fields $\phi$ and $\Phi$ ...
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### Are large logarithms tied to dimensional regularization?

When introducing the renormalization group many textbooks start by stating that scattering amplitudes often contain logarithms of the form $\log\frac{\mu^2}{p^2}$, where $p^2$ is the characteristic ...
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### Expansion at first order ${\cal O}(\alpha_s)$ in counterterms for the QCD vertex renormalization at 1-loop

What is the meaning of the expansion at first order ${\cal O}(\alpha_s)$ in $\delta_2$ and $\delta_3$ at the second step in the last line? These quantities are not "small" - on the contrary,...
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### Epsilon dependence of the beta function

For some time now, I’ve been trying to prove that the beta function for a quantum field theory with coupling $g$ (in the typical case of a coupling with mass dimension $\varepsilon$ in dimensional ...
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### Operator mixing in dimensional regularization of EFTs

When renormalizing "non-renormalizable" operators within an effective field theory (EFT) one usually has to introduce additional (higher-dimensional) operators to the Lagrangian which act as ...
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### $1/\epsilon$ poles order in dimensional regularization of $\dfrac{\lambda}{4!}\phi^4$ theory
I have to find the order of 1/ε poles in dimensional regularization of $\dfrac{\lambda}{4!}\phi^4$ theory. The Feynman integral is the following: I(p)=-λ^6\int \frac{d^4p_1}{(2\pi)^4}\...