Abstract
We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.
Highlights
We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand
Since the UV divergences of one-loop amplitudes are only from massive (Ki2 = 0) and massless (Ki2 = 0) scalar bubble integrals and the bubble coefficients are related to the tree-level amplitudes, the on-shell method can be very convenient to obtain the renormalization group running of higher dimension operators
We demonstrate in detail how to extract the full UV divergences of the loop amplitudes
Summary
Since the renormalization of on-shell SMEFT is induced by UV divergent part of the amplitudes, we explain how to use unitarity cut to derive the UV divergences in one-loop amplitudes. The non-renormalizable interactions of the on-shell SMEFT can be described by the amplitude basis i ciMOi, where ci is the Wilson coefficient. To obtain the RG equations for ci, we consider the amplitude which receives tree-level contribution from MOi as well as loop contributions with another amplitude basis MOj insertion. The full amplitude takes the form of. +log μ come from the UV divergence and μ is the renormalization scale. By demanding the full amplitude being independent of the scale μ, one directly obtains renormalization group (RG) equation dci(μ) = d log μ j. 1 16π2 γijcj, where γij is the anomalous dimension matrix governing the RG running
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
