Electroweak corrections using effective field theory: Applications to the CERN LHC

Abstract

Electroweak Sudakov logarithms at high energy, of the form $(\ensuremath{\alpha}/{sin}^{2}{\ensuremath{\theta}}_{W}{)}^{n}{log}^{m}s/{M}_{Z,W}^{2}$, are summed using effective theory (EFT) methods. The exponentiation of Sudakov logarithms and factorization is discussed in the EFT formalism. Radiative corrections are computed to scattering processes in the standard model involving an arbitrary number of external particles. The computations include nonzero particle masses such as the $t$-quark mass, electroweak mixing effects which lead to unequal $W$ and $Z$ masses and a massless photon, and Higgs corrections proportional to the top-quark Yukawa coupling. The structure of the radiative corrections, and which terms are summed by the EFT renormalization group is discussed in detail. The omitted terms are smaller than 1%. We give numerical results for the corrections to dijet production, dilepton production, $t\overline{t}$ production, and squark pair production. The purely electroweak corrections are significant---about 15% at 1 TeV, increasing to 30% at 5 TeV, and they change both the scattering rate and angular distribution. The QCD corrections (which are well-known) are also computed with the EFT. They are much larger---about a factor of 4 at 1 TeV, increasing to a factor of 30 at 5 TeV. Mass effects are also significant; the $q\overline{q}\ensuremath{\rightarrow}t\overline{t}$ rate is enhanced relative to the light-quark production rate by 40%.