Abstract
We develop the framework to perform all-orders resummation of electroweak logarithms of Q/M for inclusive scattering processes at energies Q much above the electroweak scale M. We calculate all ingredients needed at next-to-leading logarithmic (NLL) order and provide an explicit recipe to implement this for 2 → 2 processes. PDF evolution including electroweak corrections, which lead to Sudakov double logarithms, is computed. If only the invariant mass of the final state is measured, all electroweak logarithms can be resummed by the PDF evolution, at least to LL. However, simply identifying a lepton in the final state requires the corresponding fragmentation function and introduces angular dependence through the exchange of soft gauge bosons. Furthermore, we show the importance of polarization effects for gauge bosons, due to the chiral nature of SU(2) — even the gluon distribution in an unpolarized proton becomes polarized at high scales due to electroweak effects. We justify our approach with a factorization analysis, finding that the objects entering the factorization theorem do not need to be SU(2) × U(1) gauge singlets, even though we perform the factorization and resummation in the symmetric phase. We also discuss a range of extensions, including jets and how to calculate the EW logarithms when you are fully exclusive in the central (detector) region and fully inclusive in the forward (beam) regions.
Highlights
At LHC energies, the effect of electroweak (EW) corrections on the cross section can be significant (∼ 10%)
We show the importance of polarization effects for gauge bosons, due to the chiral nature of SU(2) — even the gluon distribution in an unpolarized proton becomes polarized at high scales due to electroweak effects
Electroweak Sudakov logarithms were first studied in refs. [7,8,9,10,11], a recipe for the next-to-leading order (NLO) corrections was presented in refs. [12,13,14] and the two-loop logarithms for a four-fermion process were obtained in refs. [15, 16]
Summary
At LHC energies, the effect of electroweak (EW) corrections on the cross section can be significant (∼ 10%). These are dominated by EW Sudakov double logarithms, σ = σ0 cnm αwn lnm. [17, 18] developed a resummation framework using Soft-Collinear Effective Theory (SCET) [19,20,21,22], obtaining results at next-to-leading-logarithmic (NLL) plus NLO accuracy. For the nonsinglet PDFs there is a sensitivity to soft radiation This introduces rapidity divergences, and we use the rapidity renormalization group [39, 40] to resum the corresponding single logarithms of Q/M. In appendix B, we give examples of the possible PDF combinations which enter the production of a heavy particle in quark-antiquark annihilation
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