Higher order corrections for precision observables

• Main Author: Cerdà Sevilla, M.
• Published: University of Liverpool 2017
• Subjects: 510
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.733885

Higher order corrections are a fundamental ingredient for the analysis of physical ob- servables. They are essential to improve the precision of theory predictions within the Standard Model which then lead to an increased sensitivity of these observables to physics beyond the Standard Model. In this thesis we compute higher order QCD corrections to the effective Lagrangian for weak decays. We combine previous results for the Next-to-Next-to-Leading order in the five-flavour theory with new matching calculations. This allows us to determine the effective Lagrangian in the four- and in the three-flavour theory for current-current and QCD penguin operators. We discuss explicitly the relevant steps required for a proper matching calculation, in particular the cancellation of the ultra-violet and infra-red divergences. We also introduce a new formalism that leads to scale and scheme independent intermediate results. Moreover the scheme change for the electroweak penguin operators at the Next-to-Leading or- der is calculated, and the one-loop and two-loop anomalous dimensions for a general number of flavours in the modern basis is presented for the first time in this thesis. In addition we present an updated QCD×QED running. Here a detailed discussion is provided to explain the problem with the singularities when the eigenvalues of the anomalous dimension matrix differ by a factor $2\beta_{00}^s$. Finally we apply the result to the theory prediction of the CP-conserving hadronic kaon decays, and the $\varepsilon^\prime/\varepsilon$ observable, reducing the perturbative uncertainty by a factor 0.12 at NNLO level.