Electroweak renormalization group corrections in high energy processes

At energies ($\sqrt{s}$) much higher than the electroweak gauge boson masses ($M$) large logarithmic corrections of the scale ratio $\sqrt{s}/M$ occur. While the electroweak Sudakov type double (DL) and universal single (SL) logarithms have recently been resummed, at higher orders the electroweak renormalization group (RG) corrections are folded with the DL Sudakov contributions and must be included for a consistent subleading treatment to all orders. In this paper we derive first all relevant formulae for massless as well as massive gauge theories including all such terms up to order ${\cal O} (\alpha^n \beta_0 \log^{2n-1} \frac{s}{M^2})$ by integrating over the corresponding running couplings. The results for broken gauge theories in the high energy regime are then given in the framework of the infrared evolution equation (IREE) method. The analogous QED-corrections below the weak scale $M$ are included by appropriately matching the low energy solution to the renormalization group improved high energy results. The corrections are valid for arbitrary external lines and largest in the scalar Goldstone and Higgs boson sector as well as for transverse gauge bosons. At TeV energies, these SL-RG terms change scattering cross sections in the percentile regime at two loops and are thus non-negligible for precision objectives at future linear colliders.