All-Order Helicity Selection Rules in Effective Field Theories
Abstract
Using on-shell methods, we derive an all-order non-renormalization theorem for general four-dimensional effective field theories, relying on Poincaré invariance and unitarity. Each operator 𝒪 is assigned the weights (w,w̅)=(ℓ−h,ℓ+h), where ℓ and h are the number of particles and total helicity of its minimal configuration. At L loops, the mixing 𝒪j→𝒪i vanishes when ℓj−ℓi=L−1 and either wi<wj−2(L−1) or w̅i<w̅j−2(L−1), in the absence of non-holomorphic Yukawa couplings. These zeros follow entirely from tree-level data and are scheme independent under finite renormalizations that preserve the operator-length selection rule. For operators of dimensions five through eight, we identify broad classes of previously unknown zeros at higher loop orders, with particular emphasis on two loops, where the theorem provides direct checks on current calculations, as in the Standard Model Effective Field Theory.
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BibTeX
@misc{bresciani2026allorder,
title = {{All-Order Helicity Selection Rules in Effective Field Theories}},
author = {Luigi C. Bresciani and Nudzeim Selimovic},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20914},
eprint = {2609.20914},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20914},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - All-Order Helicity Selection Rules in Effective Field Theories
AU - Luigi C. Bresciani
AU - Nudzeim Selimovic
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20914
UR - https://arxiv.org/abs/2609.20914
AB - Using on-shell methods, we derive an all-order non-renormalization theorem for general four-dimensional effective field theories, relying on Poincaré invariance and unitarity. Each operator 𝒪 is assigned the weights (w,w̅)=(ℓ−h,ℓ+h), where ℓ and h are the number of particles and total helicity of its minimal configuration. At L loops, the mixing 𝒪_j→𝒪_i vanishes when ℓ_j−ℓ_i=L−1 and either w_i<w_j−2(L−1) or w̅_i<w̅_j−2(L−1), in the absence of non-holomorphic Yukawa couplings. These zeros follow entirely from tree-level data and are scheme independent under finite renormalizations that preserve the operator-length selection rule. For operators of dimensions five through eight, we identify broad classes of previously unknown zeros at higher loop orders, with particular emphasis on two loops, where the theorem provides direct checks on current calculations, as in the Standard Model Effective Field Theory.
ER -