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A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem
by Matteo Becchetti
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Submission summary
| Authors (as registered SciPost users): | Matteo Becchetti |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2110.07339v2 (pdf) |
| Date accepted: | 2022-02-28 |
| Date submitted: | 2021-10-18 09:15 |
| Submitted by: | Becchetti, Matteo |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 15th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology (RADCOR2021) |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) = -\frac{\gamma(g)}{\beta(g)} =\frac{\gamma_0}{\beta_0}\frac{1}{g} + \cdots $ determines which different cases of operator mixing can occur, and we review their classification. We derive a sufficient condition for $A(g)$ to be set in the one-loop exact form $A(g) = \frac{\gamma_0}{\beta_0}\frac{1}{g}$. Finally, we discuss the consequences of the unitarity requirement in massless QCD-like theories, and we demonstrate that $\gamma_0$ is always diagonalizable if the theory is conformal invariant and unitary in its free limit at $g =0$.
Published as SciPost Phys. Proc. 7, 032 (2022)
Reports on this Submission
Strengths
The article reports on the work presented at RADCOR/LoopFest 2021. It fulfills all the requirements for publication in SciPost Proceedings.
Weaknesses
None.
Report
The article reports on the work presented at RADCOR/LoopFest 2021. It fulfills all the requirements for publication in SciPost Proceedings and therefore we recommend its publication.
Requested changes
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