Explicit conditions for diagnosing tree-level unitarity
- 1Quantum Universe Center (QUC)
- 2School of Physics
Abstract
A bstract : We explicitly present all coupling conditions required for tree-level unitarity (tree unitarity) in theories with a finite number of massive and massless particles of spin up to 1. They allow us to diagnose tree unitarity using only the particle content in the mass basis, without reconstructing the full Lagrangian. We show that all tree-unitary amplitudes except the four-scalar amplitude are on-shell constructible, allowing us to recursively construct four-point amplitudes with the four-scalar amplitude as a building block. From their high-energy behavior and Ward identities, we derive the coupling conditions for four-point amplitudes. Imposing these conditions, we use the Stückelberg formulation to derive those from all higher-point amplitudes and show that all tree unitarity conditions are fully captured up to five points. We apply our results to dark photon scenarios with dark matter particles of spin up to 1 and identify the essential features of their mass generation. We also examine simple theories without scalars in which tree unitarity requires an infinite tower of vectors or fermions. Finally, we briefly discuss tree unitarity and related issues in Higgs-portal vector dark matter.
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BibTeX
@article{jeong2026explicit,
title = {{Explicit conditions for diagnosing tree-level unitarity}},
author = {Jaehoon Jeong and Pyungwon Ko and Yu-Hui Zheng},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)073},
url = {https://link.springer.com/10.1007/JHEP10(2026)073},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Explicit conditions for diagnosing tree-level unitarity
AU - Jaehoon Jeong
AU - Pyungwon Ko
AU - Yu-Hui Zheng
PY - 2026
DA - 2026/10/07
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)073
UR - https://link.springer.com/10.1007/JHEP10(2026)073
AB - A bstract : We explicitly present all coupling conditions required for tree-level unitarity (tree unitarity) in theories with a finite number of massive and massless particles of spin up to 1. They allow us to diagnose tree unitarity using only the particle content in the mass basis, without reconstructing the full Lagrangian. We show that all tree-unitary amplitudes except the four-scalar amplitude are on-shell constructible, allowing us to recursively construct four-point amplitudes with the four-scalar amplitude as a building block. From their high-energy behavior and Ward identities, we derive the coupling conditions for four-point amplitudes. Imposing these conditions, we use the Stückelberg formulation to derive those from all higher-point amplitudes and show that all tree unitarity conditions are fully captured up to five points. We apply our results to dark photon scenarios with dark matter particles of spin up to 1 and identify the essential features of their mass generation. We also examine simple theories without scalars in which tree unitarity requires an infinite tower of vectors or fermions. Finally, we briefly discuss tree unitarity and related issues in Higgs-portal vector dark matter.
SN - 1029-8479
ER -