Abstract
We use the on-shell S-matrix and form factors to compute anomalous dimensions of higher dimension operators in the Standard Model Effective Field Theory. We find that in many instances, these computations are made simple by using the on-shell method. We first compute contributions to anomalous dimensions of operators at dimension-six that arise at one-loop. Then we calculate two-loop anomalous dimensions for which the corresponding one-loop contribution is absent, using this powerful method.
Highlights
Subject to a Callan-Symanzik equation, a.k.a. renormalisation group equation (RGE), that depends on the anomalous dimensions
With blue arrows we indicate the two-loop anomalous dimensions that are computed in the sections indicated on top
In this work we have demonstrated how to retrieve the anomalous dimensions of the SM
Summary
We apply (1.7) in a series of examples of one-loop RGE mixing of the SM dimension-six operators. The one loop contributions to the right hand side of (1.7) involve a tree-level form factor and a tree-level S-matrix element, that are contracted with a twoparticle phase space integral. We should consider contributions that involve a scattering matrix with disconnected pieces. See for instance [11, 12] for further details on the spinor helicity formalism and on-shell scattering amplitudes techniques. The particles to the right of the last FF in (2.1) may involve tree-level interactions of the disconnected S-matrix, but we have absorbed those into the FF, such that both the S-matrix and the FF are connected. Where from here on we leave implicit the sum over all permutations of the external particles, and dLI is the Lorentz invariant integral measure over all the pi variables, in this case dLI =.
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