Factorization structure of gauge theory amplitudes and application to hard scattering processes at the LHC

Abstract

Previous work on electroweak radiative corrections to high-energy scattering using soft-collinear effective theory (SCET) has been extended to include external transverse and longitudinal gauge bosons and Higgs bosons. This allows one to compute radiative corrections to all parton-level hard scattering amplitudes in the standard model to next-to-leading-log order, including QCD and electroweak radiative corrections, mass effects, and Higgs exchange corrections, if the high-scale matching, which is suppressed by two orders in the log counting, and contains no large logs, is known. The factorization structure of the effective theory places strong constraints on the form of gauge theory amplitudes at high energy for massless and massive gauge theories, which are discussed in detail in the paper. The radiative corrections can be written as the sum of process-independent one-particle collinear functions, and a universal soft function. We give plots for the radiative corrections to q " q ! W T W T , Z T Z T , W L W L , and Z L H, and gg ! W T W T to illustrate our results. The purely electroweak corrections are large, ranging from 12% at 500 GeV to 37% at 2 TeV for transverse W pair production, and increasing rapidly with energy. The estimated theoretical uncertainty to the partonic (hard) cross section in most cases is below 1%, smaller than uncertainties in the parton distribution functions. We discuss the relation between SCET and other factorization methods, and derive the Magnea-Sterman equations for the Sudakov form factor using SCET, for massless and massive gauge theories, and for light and heavy external particles.

From webs to polylogarithms

“…In recent years we have seen significant progress towards determining the singularities of multi-leg amplitudes with general kinematics beyond the planar limit and beyond one loop [4,19,20,[25][26][27][28][29][30][31][32][33][34]41]. Complete two-loop results are now available for the soft anomalous dimension in both the massless and massive cases.…”

Running electroweak couplings as a probe of new physics

“…[73][74][75], relevant to the Drell-Yan process), and exist even in inclusive cross sections due to the fact that the initial states that are not electroweak singlets [76][77][78][79]. The form of these logarithms, and their resummation, can differ process-to-process, and requires careful treatment of the real electroweak radiation to ensure proper cancellation with numerically large contributions from virtual corrections (see, e.g., [80][81][82][83][84] for a general discussion of EW Sudakov logarithms in virtual corrections, or ref. [85] for a recent study on a set of specific processes).…”

“…Resummation of the EW Sudakov logarithms will bring perturbative stability to the cross section, and in refs. [82,83] it was suggested that this resummation along with QCD corrections can achieve a scale uncertainty within 1%. Hence, while these corrections are numerically important, resummation of these effects will give a well-controlled theoretical prediction for the EW corrections, and one expects small uncertainties on the result.…”

One-loop matching and next-to-next-to-leading log resummation for all partonic2→2processes in QCD

“…Processes with four hard partons in QCD separate into a number of color structures, corresponding to separate operators in SCET, which mix under RG evolution. Similar color mixing has already been studied for collinearlyregulated soft Wilson lines using the traditional approach to resummation [19], and for quark scattering [15], gauge boson production [20] and tt production [6] using SCET. For NNLL resummation, the renormalization group equations must be solved to least 2-loop order.…”

“…For NNLL resummation, the renormalization group equations must be solved to least 2-loop order. A general form for these RGEs is known [20,21,22,23,24,25], as is the related soft function evolution equation [19].…”