Nima Arkani-HamedTzu-Chen HuangYU-TIN HUANG2021-07-282021-07-28202110298479https://www.scopus.com/inward/record.uri?eid=2-s2.0-85107016566&doi=10.1007%2fJHEP05%282021%29259&partnerID=40&md5=b15daaf4bc09ac4391f7f33c1a9e5357https://scholars.lib.ntu.edu.tw/handle/123456789/575279We 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. ? 2021, The Author(s).[SDGs]SDG7journal article10.1007/JHEP05(2021)2592-s2.0-85107016566