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Smoothly splitting amplitudes and semi-locality. (English) Zbl 1522.81225

Summary: In this paper, we study a novel behavior developed by certain tree-level scalar scattering amplitudes, including the biadjoint, NLSM, and special Galileon, when a subset of kinematic invariants vanishes without producing a singularity. This behavior exhibits properties which we call smooth splitting and semi-locality. The former means that an amplitude becomes the product of exactly three amputated Berends-Giele currents, while the latter means that any two currents share one external particle. We call these smooth splittings 3-splits. In fact, there are exactly \(\binom{n}{3}-n\) such 3-splits of an \(n\)-particle amplitude, one for each tripod in a polygon; as they cannot be obtained from standard factorization, they are a new phenomenon in Quantum Field Theory. In fact, the resulting splitting is analogous to the one first seen in Cachazo-Early-Guevara-Mizera (CEGM) amplitudes which generalize standard cubic scalar amplitudes from their \(\operatorname{Tr}G(2, n)\) formulation to \(\operatorname{Tr}G(k, n)\), where \(\operatorname{Tr}G(k, n)\) is the tropical Grassmannian. Along the way, we show how smooth splittings naturally lead to the discovery of mixed amplitudes in the NLSM and special Galileon theories and to novel BCFW-like recursion relations for NLSM amplitudes.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T18 Feynman diagrams
81U05 \(2\)-body potential quantum scattering theory
81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
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