Complete NNLO Operator Bases in Higgs Effective Field Theory

TL;DR

This paper systematically enumerates the complete set of NNLO operators in the Higgs effective field theory, providing a foundational basis for future theoretical and phenomenological studies involving the Higgs boson.

Contribution

It introduces a comprehensive and independent operator basis at NNLO in HEFT using Young tensor techniques and symmetry constraints, a first in the field.

Findings

Enumerates 11,506 NNLO operators for one fermion flavor.

Enumerates 1,927,574 NNLO operators for three fermion flavors.

Establishes a basis for matching SMEFT operators below the electroweak scale.

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.