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arXiv · 2609.12877

Gauge-invariant Higgs mechanism via gradient-flow regularization

Gunnar S. Bali
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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 $\overline{\text{MS}}$ scheme at a scale $μ\sim 1/\sqrt{2t}\gg m_t$. 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.

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Gunnar S. Bali. 2026-09-15. Gauge-invariant Higgs mechanism via gradient-flow regularization. https://arxiv.org/abs/2609.12877

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