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Abstract
We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden “totally positive” structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra. This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the “EFT-hedron”. We initiate a systematic investigation of the boundary structure of the EFT-hedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFT-hedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.
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Details
1 Institute for Advanced Study, School of Natural Sciences, Princeton, USA (GRID:grid.78989.37) (ISNI:0000 0001 2160 7918)
2 California Institute of Technology, Walter Burke Institute for Theoretical Physics, Pasadena, USA (GRID:grid.20861.3d) (ISNI:0000000107068890)
3 National Taiwan University, Department of Physics and Astronomy, Taipei, Taiwan (GRID:grid.19188.39) (ISNI:0000 0004 0546 0241); National Tsing-Hua University, Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan (GRID:grid.38348.34) (ISNI:0000 0004 0532 0580)