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Emergence of Unitarity and Locality from Hidden Zeros at One-Loop Order
Jeffrey V Backus1, Laurentiu Rodina2
1Princeton University, Joseph Henry Laboratories, Princeton, New Jersey 08544, USA.
Physical Review Letters
|October 12, 2025
Summary
Researchers extended "hidden zeros" to one-loop amplitudes in Tr(ϕ³) theory and the nonlinear sigma model (NLSM). These zeros are crucial for ensuring unitarity and locality, even beyond leading order in perturbation theory.
Area of Science:
- Theoretical High Energy Physics
- Quantum Field Theory
- String Theory
Background:
- Scattering amplitudes exhibit 'hidden zeros' at tree-level in various theories.
- These zeros represent kinematic points where amplitudes vanish.
- Previous work focused on tree-level amplitudes in Tr(ϕ³) theory, nonlinear sigma model (NLSM), and Yang-Mills theory.
Purpose of the Study:
- To extend the concept of hidden zeros to one-loop order.
- To investigate the role of hidden zeros in ensuring unitarity and locality at one-loop level.
- To explore if hidden zeros can uniquely determine loop integrands.
Main Methods:
- Utilized the 'surface integrand' technology developed by Arkani-Hamed et al.
- Analyzed one-loop integrands in Tr(ϕ³) theory and the NLSM.
- Investigated the relationship between hidden zeros, locality, and unitarity.
Main Results:
- Demonstrated that one-loop integrands in Tr(ϕ³) theory are unitary if and only if they satisfy loop hidden zeros, assuming locality.
- Provided evidence that hidden zeros inherently contain locality constraints.
- Observed simple factorization behavior near one-loop zeros, suggesting it fixes NLSM integrands.
Conclusions:
- Hidden zeros are extended to one-loop order in Tr(ϕ³) theory and the NLSM.
- Locality and unitarity emerge from hidden zeros even beyond leading order.
- This work provides the first extension of uniqueness results for loop integrands, driven by hidden zeros.
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