Electroweak Logarithms in Inclusive Cross Sections

TL;DR

This paper develops a comprehensive framework for resumming electroweak logarithms in high-energy inclusive scattering processes, including detailed calculations at NLL order and implications for PDFs, polarization, and experimental measurements.

Contribution

It introduces a method for all-orders electroweak logarithm resummation at NLL, including the effects of polarization and fragmentation, and extends factorization to non-singlet objects.

Findings

Electroweak logarithms can be resummed via PDF evolution at LL.

Polarization effects are significant for gauge bosons due to chiral SU(2) interactions.

Electroweak effects induce polarization in gluon distributions at high scales.

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 $\to$ 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) $\times$ 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.