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Anomalous Dimensions of Effective Theories from Partial Waves
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On-shell amplitude methods have proven to be extremely efficient for calculating anomalous dimensions. We further elaborate on these methods to show that, by the use of an angular momentum decomposition, the one-loop anomalous dimensions can be reduced to essentially a sum of products of partial waves. We apply this to the SM EFT, and show how certain classes of anomalous dimensions have their origin in the same partial-wave coefficients. We also use our result to obtain a generic formula for the one-loop anomalous dimensions of nonlinear sigma models at any order in the energy expansion, and apply our method to gravity, where it proves to be very advantageous even in the presence of IR divergencies.
Forward citations
Cited by 3 Pith papers
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Bootstrapping the Chiral-Gravitational Anomaly
Causality and unitarity force J≥4 resonances to appear below Λcaus approximately sqrt(MP Fπ/κg) in any EFT with a U(1)-gravitational anomaly.
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Positivity and partial wave unitarity bounds on ALP theories via amplitude methods
Complete partial-wave unitarity and positivity bounds are derived for ALP effective interactions up to dimension 8, with new SMEFT positivity constraints as a byproduct.
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Renormalization of effective field theories via on-shell methods: the case of axion-like particles
Complete one-loop anomalous dimension matrix for a CP-violating ALP effective field theory, derived via on-shell unitarity methods and extended to dimension-6 SMEFT operators.
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