Electroweak corrections relevant for semi-leptonic decays

by Ana Pereira (Universidade de Liverpool)

Wednesday 11 Dec 2024, 14:00 → 15:00 Portugal

Sala de Conferências (Departamento de Física FCTUC)

The project focus on the computation of 2-loop Electroweak corrections relevant for semi-leptonic decays, such as super allowed nuclear beta decays or $\Pi^+ -> e^+ \nu$. The decay rates of these processes are proportional to the modulus square Cabibbo–Kobayashi–Maskawa (CKM) matrix element $V_{ud}$ and are precisely measured. By normalizing these decay rates to the Fermi decay of the muon one extracts the modulus of $V_{ud}$ at tree-level accuracy. Quantum corrections will modify this extraction. Currently only 1-loop electroweak and 2-loop mixed electroweak QCD corrections are known. Given the size of the other corrections, one can estimate the effect of the currently unknown 2-loop electroweak corrections. Given this estimate we conclude that they will have an important impact on the extraction of $V_{ud}$. In order to calculate these 2-loop corrections, we will use an Effective Field Theory (EFT) approach. We already computed the 1-loop correction of the semi-leptonic decay using an EFT and renormalized the effective operator. We computed the 1-loop correction amplitude in the full Standard Model as well as the corresponding renormalization. We did the matching between the EFT and the SM theory for the 1-loop and obtained the relevant Wilson coefficients, which reproduce known results in the literature. As the final step, we currently are computing the 2-loop corrections in the EFT and the SM theory, the respective renormalization, and the corresponding matching between the EFT and the SM
theory. The process of diagram generation and computing amplitudes was done in Mathematica, using FeynArts and FeynCalc packages, although we are now developing our own code to compute the amplitudes.