Scientific article
Open access

Hilbert series, the Higgs mechanism, and HEFT

Published inThe journal of high energy physics, vol. 02, no. 2
Publication date2023
First online date2023-02-07

We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest at the level of the Hilbert series, as expected for the partition function of an S-matrix that is subject to the Goldstone equivalence theorem. In addition to massive vectors, we detail how other massive, spinning particles can be studied with Hilbert series; in particular, we spell out the ingredients for massive gravity in general spacetime dimensions. Further methodology is introduced to enable Hilbert series to capture the effect of spurion fields acquiring vevs. We apply the techniques to the Higgs Effective Field Theory (HEFT), providing a systematic enumeration of its operator basis. This is achieved both from a direct and a custodial symmetry spurion-based approach; we compare and contrast the two approaches, and our results to those appearing in previous literature.

  • Effective Field Theories
  • Gauge Symmetry
  • Higgs Properties
  • Spontaneous Symmetry Breaking
  • S-matrix
  • Partition function
  • Effective field theory
  • Higgs particle
  • Higgs mechanism
  • Symmetry: custodial
  • Goldstone particle: equivalence theorem
Citation (ISO format)
GRÁF, Lukáš et al. Hilbert series, the Higgs mechanism, and HEFT. In: The journal of high energy physics, 2023, vol. 02, n° 2. doi: 10.1007/jhep02(2023)064
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Article (Published version)
ISSN of the journal1029-8479

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