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Electroweak corrections using effective theory : factorization and application to LHC

Abstract

We study the infrared structure of perturbative amplitudes using the effective field theory (EFT) formalism and develop a general factorization scheme, frst for electroweak dynamics and then general gauge theories. We begin by discussing the factorization structure within the framework of the Soft-Collinear-Effective Theory. For the theories with a massive gauge boson, we introduce a (new) \[Delta\]-regulator to regulate the collinear singularities. In this way, we avoid the confusions in distinguishing different kinds of singularities which arise when considering unbroken theories. Consequently, we propose a factorization scheme to define a soft function free of collinear singularities and a jet function free of the soft singularities. We also clarify that heavy-quark effects change only the structure of collinear singularities and not the soft ones. With our definition of the soft function, we compute the one-loop soft anomalous dimension matrix for any fixed angle, multi- particle process by weighting the soft function with the proper group theory factor without additional calculation.Next, we use EFT methods to sum the Electroweak Sudakov logarithms at high energy, of the form (\[alpha\]/sin² \[theta\]w loĝm 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 non-zero 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-bar 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 four at 1 TeV, increasing to a factor of thirty at 5 TeV.

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