Complete NNLO Operator Bases in Higgs Effective Field Theory

Abstract

For the first time, we list the complete and independent set of operators at the next-to-next-to-leading order (NNLO) in the Higgs effective field theory (HEFT), also named as the electroweak chiral Lagrangian with the light Higgs boson. The Young tensor technique utilized in this work guarantees the completeness and independence of the on-shell amplitude basis while the Adler zero condition imposes non-linear symmetry on the Nambu-Goldstone bosons that play the central role in the chiral Lagrangian. The spurion fields are incorporated into the gauge structure of operators following the Littlewood-Richardson rule to accommodate custodial symmetry breaking. We enumerate 11506 (1927574) NNLO operators for one (three) flavor of fermions for the electroweak chiral Lagrangian with the light Higgs. Below the electroweak symmetry breaking scale, the dimension-8 standard model effective field theory (SMEFT) operators could be matched to these HEFT operators at both the NLO and NNLO orders.

arXiv comment419 pages, 3 tables

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• Opportunistic CP Violation
• The New Formulation of Higgs Effective Field Theory
• $C$ and $CP$ violation in effective field theories
• Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing
• The Art of Counting: a reappraisal of the HEFT expansion
• Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT
• HEFT approach to investigate the muon g-2 anomaly at a muon collider
• Higgs pair production in gluon fusion to higher orders in Higgs Effective Field Theory