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Goldstone Equivalence and High Energy Electroweak Physics

by G. Cuomo, L. Vecchi, A. Wulzer

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Submission summary

Authors (as registered SciPost users): Luca Vecchi · Andrea Wulzer
Submission information
Preprint Link: scipost_202001_00045v3  (pdf)
Date accepted: 2020-05-06
Date submitted: 2020-03-21 01:00
Submitted by: Vecchi, Luca
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
Approach: Theoretical


The transition between the broken and unbroken phases of massive gauge theories, namely the rearrangement of longitudinal and Goldstone degrees of freedom that occurs at high energy, is not manifestly smooth in the standard formalism. The lack of smoothness concretely shows up as an anomalous growth with energy of the longitudinal polarization vectors, as they emerge in Feynman rules both for real on-shell external particles and for virtual particles from the decomposition of the gauge field propagator. This makes the characterization of Feynman amplitudes in the high-energy limit quite cumbersome, which in turn poses peculiar challenges in the study of Electroweak processes at energies much above the Electroweak scale. We develop a Lorentz-covariant formalism where polarization vectors are well-behaved and, consequently, energy power-counting is manifest at the level of individual Feynman diagrams. This allows us to prove the validity of the Effective $W$ Approximation and, more generally, the factorization of collinear emissions and to compute the corresponding splitting functions at the tree-level order. Our formalism applies at all orders in perturbation theory, for arbitrary gauge groups and generic linear gauge-fixing functionals. It can be used to simplify Standard Model loop calculations by performing the high-energy expansion directly on the Feynman diagrams. This is illustrated by computing the radiative corrections to the decay of the top quark.

Published as SciPost Phys. 8, 078 (2020)

Reports on this Submission

Anonymous Report 2 on 2020-4-22 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202001_00045v3, delivered 2020-04-22, doi: 10.21468/SciPost.Report.1635


The authors have answered my questions and clarified my doubts. They made a few requested changes to address the issues pointed out in my previous report. I find the changes appropriate.

However, they believe the clarity of the main text cannot be improved more, especially the discussion on page 17. This fact does not have any impact on the scientific content of the paper, which I consider high-level.

Therefore, I recommend the manuscript for publication in its present form.

  • validity: high
  • significance: high
  • originality: high
  • clarity: good
  • formatting: good
  • grammar: good

Anonymous Report 1 on 2020-4-21 (Invited Report)


I recommend that the manuscript is published in its present form.

  • validity: high
  • significance: top
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: good

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