Two-loop renormalization of the SMEFT and the WET

The matching of the SMEFT onto the WET, i.e. expressing the WET parameters in terms of the SMEFT Wilson coefficients, is known since recently up to the one-loop level. These matching conditions depend however on unphysical entities and can therefore not be used in a consistent phenomenological analysis. In order to remove this scheme dependence the two-loop renormalization of the WET parameters needs to be taken into account, since it cancels this scheme dependence and therefore makes the results physical again. One objective of the current research project is to compute the full two-loop renormalization of the WET Wilson coefficients and implement the results in the public code wilson. A second objective of the research project is to conduct the full two-loop renormalization for the SMEFT parameters. Performing the two-loop renormalization is motivated by the fact that at this order many more SMEFT Wilson coefficients become phenomenologically accessible through running effects, which therefore allows for a broader and more precise NP search. Another goal of this computation is again to remove unphysical dependencies that are present in the matching conditions. Although the full one-loop matching from general BSM theories onto the SMEFT is currently unknown, it is, however, expected to be available in the very near future. Together with the proposed calculation these matching conditions can then be used to perform a consistent and completely general NLO analysis of SMEFT parameters.