Gauge-invariant Higgs mechanism via gradient-flow regularization
Abstract
We provide a manifestly gauge-invariant description of the Higgs mechanism in the Standard Model, casting it not as the breaking of a local symmetry, but as a smooth, analytic crossover from a high-temperature symmetric phase to a low-temperature Higgs phase. Taking the vacuum expectation value of a gauge-invariant local scalar operator and constructing composite quasi-particle states from the original fields of the Lagrangian usually introduces contact-term divergences. Previous attempts to circumvent this issue via bilocal operators remain unsatisfactory. Here we demonstrate that the gradient flow at a flow time t provides a clean, structurally sound, and Lorentz-covariant regularization that permits a consistent, renormalon-free matching onto the standard MS̅ scheme at a scale μ∼ 1/√(2t)≫ mt. Beyond its theoretical appeal, this construction clarifies a number of conceptional and practical questions. We demonstrate the utility of this framework at the one-loop level, thereby establishing the foundation for future electroweak precision physics in this approach.
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BibTeX
@misc{bali2026gaugeinvariant,
title = {{Gauge-invariant Higgs mechanism via gradient-flow regularization}},
author = {Gunnar S. Bali},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12877},
eprint = {2609.12877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12877},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gauge-invariant Higgs mechanism via gradient-flow regularization
AU - Gunnar S. Bali
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.12877
UR - https://arxiv.org/abs/2609.12877
AB - We provide a manifestly gauge-invariant description of the Higgs mechanism in the Standard Model, casting it not as the breaking of a local symmetry, but as a smooth, analytic crossover from a high-temperature symmetric phase to a low-temperature Higgs phase. Taking the vacuum expectation value of a gauge-invariant local scalar operator and constructing composite quasi-particle states from the original fields of the Lagrangian usually introduces contact-term divergences. Previous attempts to circumvent this issue via bilocal operators remain unsatisfactory. Here we demonstrate that the gradient flow at a flow time t provides a clean, structurally sound, and Lorentz-covariant regularization that permits a consistent, renormalon-free matching onto the standard MS̅ scheme at a scale μ∼ 1/√(2t)≫ m_t. Beyond its theoretical appeal, this construction clarifies a number of conceptional and practical questions. We demonstrate the utility of this framework at the one-loop level, thereby establishing the foundation for future electroweak precision physics in this approach.
ER -