European Physical Journal C: Particles and Fields (Jun 2023)

Gradient-flowed order parameter for spontaneous gauge symmetry breaking

  • Kengo Kikuchi,
  • Kenji Nishiwaki,
  • Kin-ya Oda

DOI
https://doi.org/10.1140/epjc/s10052-023-11553-4
Journal volume & issue
Vol. 83, no. 6
pp. 1 – 22

Abstract

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Abstract The gauge-invariant two-point function of the Higgs field at the same spacetime point can make a natural gauge-invariant order parameter for spontaneous gauge symmetry breaking. However, this composite operator is ultraviolet divergent and is not well defined. We propose using a gradient flow to cure the divergence from putting the fields at the same spacetime point. As a first step, we compute it for the Abelian Higgs model with a positive mass squared at the one-loop order in the continuum theory using the saddle-point method to estimate the finite part. The order parameter consistently goes to zero in the infrared limit of the infinite flow time.