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2019 EJRNL PP MONICA PATE-1.pdf ]
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Asymptotic particle states in four-dimensional celestial scattering amplitudes are labeled by their SLð2;CÞ Lorentz/conformal weights ðh; ¯hÞ rather than the usual energy-momentum four-vector. These boost eigenstates involve a superposition of all energies. As such, celestial gluon (or photon) scattering cannot obey the usual (energetically) soft theorems. In this paper we show that tree-level celestial gluon scattering, in theories with sufficiently soft UV behavior, instead obeys conformally soft theorems involving h ? 0 or ¯h ? 0. Unlike the energetically soft theorem, the conformally soft theorem cannot be derived from low-energy effective field theory.