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Sudakov Effects in Electroweak Corrections

P. Ciafaloni, D. Comelli

TL;DR

This work analyzes electroweak Sudakov double logarithms in perturbative corrections to e^+e^-→f f̄ in the Standard Model, comparing with SUSY-loop contributions. It distinguishes IR/collinear origins of the leading log terms in vertex and box diagrams and derives their high-energy behavior, showing that SM corrections can be several percent at TeV energies while SUSY contributions are power-suppressed. The authors provide explicit expressions for effective γ/Z f f̄ vertices and box amplitudes, along with numerical estimates for cross sections and forward-backward asymmetries, underscoring the need for resummation in precision analyses and the potential to probe chiral structures with polarized beams.

Abstract

In perturbation theory the infrared structure of the electroweak interactions produces large corrections proportional to double logarithms log^2 (s/m^2), similar to Sudakov logarithms in QED, when the scale s is much larger than the typical mass m of the particles running in the loops. These energy growing corrections can be particularly relevant for the planned Next Linear Colliders. We study these effects in the Standard Model for the process e+ e^->f fbar and we compare them with similar corrections coming from SUSY loops.

Sudakov Effects in Electroweak Corrections

TL;DR

This work analyzes electroweak Sudakov double logarithms in perturbative corrections to e^+e^-→f f̄ in the Standard Model, comparing with SUSY-loop contributions. It distinguishes IR/collinear origins of the leading log terms in vertex and box diagrams and derives their high-energy behavior, showing that SM corrections can be several percent at TeV energies while SUSY contributions are power-suppressed. The authors provide explicit expressions for effective γ/Z f f̄ vertices and box amplitudes, along with numerical estimates for cross sections and forward-backward asymmetries, underscoring the need for resummation in precision analyses and the potential to probe chiral structures with polarized beams.

Abstract

In perturbation theory the infrared structure of the electroweak interactions produces large corrections proportional to double logarithms log^2 (s/m^2), similar to Sudakov logarithms in QED, when the scale s is much larger than the typical mass m of the particles running in the loops. These energy growing corrections can be particularly relevant for the planned Next Linear Colliders. We study these effects in the Standard Model for the process e+ e^->f fbar and we compare them with similar corrections coming from SUSY loops.

Paper Structure

This paper contains 6 sections, 22 equations, 3 figures.

Table of Contents

  1. IR divergences: qualitative discussion
  2. Sudakov logarithms in the vertices
  3. Sudakov logarithms in the boxes
  4. Sudakov logarithms in the Standard model
  5. Sudakov logs in the cross section and in the forward backward asymmetry for $e^+\,e^-\rightarrow f\, \bar{f}$
  6. Conclusions

Figures (3)

  • Figure 1: Vertex diagram in SM (left) and SUSY (right) generating a $\log^2 \frac{s}{M^2}$. $p_1$ and $p_2$ are ingoing.
  • Figure 2: Box contribution for the SM and effective Feynman diagrams in the IR region
  • Figure 3: Box contribution for supersymmetry (the crossed diagram is also shown)