Projectivity of planar zeros in field and string theory amplitudes

• Published in: The journal of high energy physics Vol. 2017; no. 5; pp. 1 - 29
• Main Authors: Jiménez, Diego Medrano, Vera, Agustín Sabio, Vázquez-Mozo, Miguel Á.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2017; Springer Nature B.V; SpringerOpen
• Subjects: Amplitudes; Classical and Quantum Gravitation; Elementary Particles; Emissions control; Helicity; High energy physics; Models of Quantum Gravity; Perturbative QCD; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; Scattering; Scattering Amplitudes; String Theory; Scattering Amplitudes; Models of Quantum Gravity; Perturbative QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2017)011

A bstract We study the projective properties of planar zeros of tree-level scattering amplitudes in various theories. Whereas for pure scalar field theories we find that the planar zeros of the five-point amplitude do not enjoy projective invariance, coupling scalars to gauge fields gives rise to tree-level amplitudes whose planar zeros are determined by homogeneous polynomials in the stereographic coordinates labelling the direction of flight of the outgoing particles. In the case of pure gauge theories, this projective structure is generically destroyed if string corrections are taken into account. Scattering amplitudes of two scalars with graviton emission vanish exactly in the planar limit, whereas planar graviton amplitudes are zero for helicity violating configurations. These results are corrected by string effects, computed using the single-valued projection, which render the planar amplitude nonzero. Finally, we discuss how the structure of planar zeros can be derived from the soft limit behavior of the scattering amplitudes.