Two-Loop Electroweak NLL Corrections: from Massless to Massive Fermions

Recently the two-loop next-to-leading logarithmic (NLL) virtual corrections to arbitrary processes with massless external fermions have been calculated. Within the spontaneously broken electroweak theory the one-and two-loop mass singularities have been derived to NLL accuracy and expressed as universal correction factors depending only on the quantum numbers of the external particles. This talk summarizes the results for massless fermionic processes and presents new aspects arising in the extension of the corresponding loop calculations to massive external fermions. As a preliminary result, the Abelian form factor for massive fermions is given. Electroweak corrections at high energies Past and present collider experiments have explored high-energy processes at energy scales at the order of or below the masses M W and M Z of the weak gauge bosons. But the Large Hadron Collider (LHC) and the proposed International Linear Collider (ILC) will reach scattering energies in the TeV regime. For the first time, the characteristic energy Q of the reactions will be very large compared to M W . At these high energies Q M W , electroweak radiative corrections are enhanced by large logarithms ln(Q 2 /M 2 W ), which start to be sizable at energies of a few hundred GeV and increase with energy. At LHC and ILC, logarithmic electroweak effects can amount to tens of per cent at one loop and several per cent at two loops. In view of the expected experimental precision especially at ILC, theoretical predictions with an accuracy of about 1% are required, so the two-loop corrections are crucial. For sufficiently high Q, mass-suppressed terms of O(M 2 W /Q 2 ) become negligible and the electroweak corrections assume the form of a tower of logarithms with terms α l ln j (Q 2 /M 2 W ), 0 ≤ j ≤ 2l, at l loops. The leading logarithms (LLs) with power j = 2l are known as Sudakov logarithm