Singular solutions in soft limits

• Main Authors: Freddy Cachazo, Bruno Umbert, Yong Zhang
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Journal of High Energy Physics
• Subjects: Differential and Algebraic Geometry; Scattering Amplitudes
• Online Access: http://link.springer.com/article/10.1007/JHEP05(2020)148

Abstract A generalization of the scattering equations on X (2, n), the configuration space of n points on ℂℙ1, to higher dimensional projective spaces was recently introduced by Early, Guevara, Mizera, and one of the authors. One of the new features in X (k, n) with k > 2 is the presence of both regular and singular solutions in a soft limit. In this work we study soft limits in X (3, 7), X (4, 7), X (3, 8) and X (5, 8), find all singular solutions, and show their geometrical configurations. More explicitly, for X (3, 7) and X (4, 7) we find 180 and 120 singular solutions which when added to the known number of regular solutions both give rise to 1 272 solutions as it is expected since X (3, 7) ∼ X (4, 7). Likewise, for X (3, 8) and X (5, 8) we find 59 640 and 58 800 singular solutions which when added to the regular solutions both give rise to 188 112 solutions. We also propose a classification of all configurations that can support singular solutions for general X (k, n) and comment on their contribution to soft expansions of generalized biadjoint amplitudes.