Gradient-flowed order parameter for spontaneous gauge symmetry breaking

Kengo Kikuchi (RIKEN iTHEMS, Wako, Saitama, 351-0198, Japan) ; Kenji Nishiwaki (Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, 201314, India) ; Kin-ya Oda (Department of Mathematics, Tokyo Woman’s Christian University, Tokyo, 167-8585, Japan)

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.

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Published on:
02 June 2023
Publisher:
Springer
Published in:
European Physical Journal C , Volume 83 (2023)
Issue 6
Pages 1-22
DOI:
https://doi.org/10.1140/epjc/s10052-023-11553-4
arXiv:
arXiv:2303.10841
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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