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Electroweak radiative corrections at high energies

Stefano Pozzorini

TL;DR

The thesis develops a complete, process-independent framework for one-loop electroweak radiative corrections at energies above the electroweak scale, focusing on universal leading and subleading logarithms and their mass dependences. It systematically separates sources of logarithms into soft/collinear mass singularities and parameter renormalization, using the eikonal and collinear Ward identities, the Goldstone-boson equivalence theorem, and an on-shell renormalization scheme. The work provides analytic formulas for double and single logarithms, including angular-dependent terms and Higgs/top mass effects, and validates them with explicit applications to $e^+e^-\to f\bar f$, $W^+W^-$, $ZZ$, $Z\gamma$, $\gamma\gamma$, and $\bar du\to W^+Z, W^+\gamma$ processes, among others. This framework enables precise high-energy predictions relevant for LHC and future linear colliders, including insights on gauge cancellations, Sudakov effects, and the interplay between broken and symmetric phases of the electroweak theory.

Abstract

This PhD thesis is concerned with one-loop virtual electroweak corrections to arbitrary processes in the high-energy limit. Complete results are presented for the leading and subleading logarithms of large ratios of energy scales to mass scales. These results include the logarithmic dependence on the photon and weak-boson masses, on the light-fermion masses, as well as on the Higgs- and top-masses in the heavy-Higgs and heavy-top limit. All sources of electroweak logarithmic corrections are taken into account, including the exchange of soft and/or collinear electroweak gauge bosons as well as the renormalization-group running of the gauge, scalar and Yukawa couplings. The logarithmic corrections are derived in a process-independent way, resulting in simple analytic formulas that apply to arbitrary electroweak processes that are not mass-suppressed in the high-energy limit. We also present analytical and numerical applications for the processes: e^+e^- \to f\bar{f}, e^+ e^- \to W^+W^-, ZZ, Zγ, γγand \bar{d}u \to W^+Z, W^+γ.

Electroweak radiative corrections at high energies

TL;DR

The thesis develops a complete, process-independent framework for one-loop electroweak radiative corrections at energies above the electroweak scale, focusing on universal leading and subleading logarithms and their mass dependences. It systematically separates sources of logarithms into soft/collinear mass singularities and parameter renormalization, using the eikonal and collinear Ward identities, the Goldstone-boson equivalence theorem, and an on-shell renormalization scheme. The work provides analytic formulas for double and single logarithms, including angular-dependent terms and Higgs/top mass effects, and validates them with explicit applications to , , , , , and processes, among others. This framework enables precise high-energy predictions relevant for LHC and future linear colliders, including insights on gauge cancellations, Sudakov effects, and the interplay between broken and symmetric phases of the electroweak theory.

Abstract

This PhD thesis is concerned with one-loop virtual electroweak corrections to arbitrary processes in the high-energy limit. Complete results are presented for the leading and subleading logarithms of large ratios of energy scales to mass scales. These results include the logarithmic dependence on the photon and weak-boson masses, on the light-fermion masses, as well as on the Higgs- and top-masses in the heavy-Higgs and heavy-top limit. All sources of electroweak logarithmic corrections are taken into account, including the exchange of soft and/or collinear electroweak gauge bosons as well as the renormalization-group running of the gauge, scalar and Yukawa couplings. The logarithmic corrections are derived in a process-independent way, resulting in simple analytic formulas that apply to arbitrary electroweak processes that are not mass-suppressed in the high-energy limit. We also present analytical and numerical applications for the processes: e^+e^- \to f\bar{f}, e^+ e^- \to W^+W^-, ZZ, Zγ, γγand \bar{d}u \to W^+Z, W^+γ.

Paper Structure

This paper contains 69 sections, 388 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Precision tests of the Electroweak Standard Model at high energies
  3. Universal logarithms in electroweak radiative corrections
  4. Existing literature
  5. Spontaneous symmetry breaking and high-energy limit
  6. Content and organization
  7. Universal logarithmic corrections at high energies
  8. Notation and conventions
  9. High-energy limit and logarithmic approximation
  10. Longitudinal gauge bosons in the high-energy limit
  11. Form and origin of universal logarithmic corrections
  12. Soft-collinear mass singularities
  13. Double-logarithmic mass singularities and eikonal approximation
  14. Leading soft--collinear contributions
  15. Subleading soft--collinear contributions
  16. ...and 54 more sections

Figures (2)

  • Figure 9: Dependence of the electroweak correction factors $\delta^{\mathrm{ew}}_{\bar{\mathrm{d}$d$}_\mathrm{L}\mathrm{u}$u$_\mathrm{L}\rightarrow \mathrm{W}$W$_{\mathrm{T}}^+\mathrm{A}$A$_{{\mathrm{T}}}}$, $\delta^{\mathrm{ew}}_{\bar{\mathrm{d}$d$}_\mathrm{L}\mathrm{u}$u$_\mathrm{L}\rightarrow \mathrm{W}$W$_{\mathrm{T}}^+\mathrm{Z}$Z$_{{\mathrm{T}}}}$, and $\delta^{\mathrm{ew}}_{\bar{\mathrm{d}$d$}_\mathrm{L}\mathrm{u}$u$_\mathrm{L}\rightarrow \mathrm{W}$W$_\mathrm{L}^+\mathrm{Z}$Z$_{\mathrm{L}}}$, on the scattering angle $\theta$ at $\sqrt{s}=1\,\mathrm{TeV}$.
  • Figure 10: Dependence of the electroweak correction factors $\delta^{\mathrm{ew}}_{\bar{\mathrm{d}$d$}_\mathrm{L}\mathrm{u}$u$_\mathrm{L}\rightarrow \mathrm{W}$W$_{\mathrm{T}}^+\mathrm{A}$A$_{{\mathrm{T}}}}$, $\delta^{\mathrm{ew}}_{\bar{\mathrm{d}$d$}_\mathrm{L}\mathrm{u}$u$_\mathrm{L}\rightarrow \mathrm{W}$W$_{\mathrm{T}}^+\mathrm{Z}$Z$_{{\mathrm{T}}}}$, and $\delta^{\mathrm{ew}}_{\bar{\mathrm{d}$d$}_\mathrm{L}\mathrm{u}$u$_\mathrm{L}\rightarrow \mathrm{W}$W$_\mathrm{L}^+\mathrm{Z}$Z$_{\mathrm{L}}}$, on the centre-of-mass energy $\sqrt{s}$ at $\theta=60^\circ$.