Effective field theory of electroweak symmetry breaking: Concepts and applications

• Applicant: Professor Dr. Gerhard Buchalla
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2014 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 261324988

• Final Report Year: 2024

Final Report Abstract

The unification of the subatomic weak interactions, central for the energy production in stars, with the theory of electromagnetism, familiar from everyday life and from its technological applications, is among the greatest achievements in physics in the past century. Those interactions are described in a unified framework as manifestations of the quantum theory of electroweak gauge fields, a generalization of Maxwell’s electromagnetic fields and potentials. A crucial difference between electromagnetic and weak-interaction phenomena is brought about by the Higgs mechanism: The spontaneous breaking of the electroweak gauge symmetry gives masses to the electroweak W and Z bosons (and the matter particles quarks and leptons) but leaves the photon of electromagnetism massless. Electromagnetic phenomena are therefore of long range and clearly apparent in the macroscopic world, while the direct effects of W and Z are restricted to the subatomic realm. The Higgs mechanism has a consistent and successful description in the Standard Model (SM) through the introduction of the scalar Higgs field, which develops a vacuum expectation value responsible for the masses of fundamental electroweak particles. However, a deeper understanding of the dynamical origin of such a field is still lacking and is a central goal for the experiments at the LHC collider at CERN. Possible deviations from the SM can be described using the methods of effective field theory (EFT). An EFT at the electroweak energy scale of a few hundred GeV allows us to formulate a theory of Higgs-boson properties that are more general than in the SM. The present project has established such an EFT, with the particular property to describe, in a systematic way, the non-standard Higgs couplings as the dominant effects of physics beyond the SM. The resulting EFT is technically referred to as an electroweak chiral Lagrangian with a light Higgs field (EWChL). Such an EFT is motivated since the Higgs sector is the least understood part of the SM and most likely to show unexpected results. In the first part of the project, the characteristic features of this EFT, its systematic construction (power counting) and the phenomenological implications have been developed. In the second part of the project, reported on here, the framework and its applications were further investigated and extended in new directions, centered mainly on three topics: The investigation of the quantum structure of the EWChL by deriving the complete one-loop renormalization and the renormalization-group equations; the implications of loop counting, central for the systematics of the EWChL, for other EFT formulations; and, finally, the analysis of higher-order QCD corrections to the Higgs decays into pairs of gluons or photons, emphasizing the consistent embedding of the calculations in the EFT framework.

Publications

• Higgs boson potential at colliders: Status and perspectives. Reviews in Physics, 5, 100045.
  Micco, Biagio Di; Gouzevitch, Maxime; Mazzitelli, Javier & Vernieri, Caterina
  
• Higgs-electroweak chiral Lagrangian: One-loop renormalization group equations. Physical Review D, 104(7).
  Buchalla, G.; Catà, O.; Celis, A.; Knecht, M. & Krause, C.
  
• Top-pair production via gluon fusion in the Standard Model effective field theory. Physical Review D, 104(9).
  Müller, Christoph
  
• h→gg and h→γγ with anomalous couplings at next-to-leading order in QCD. Physical Review D, 107(7).
  Buchalla, Gerhard; Höfer, Marius & Müller-Salditt, Christoph
  
• Loop counting matters in SMEFT. SciPost Physics, 15(3).
  Buchalla, Gerhard; Heinrich, Gudrun; Müller-Salditt, Christoph & Pandler, Florian