August 23, 2024 | Qu Cao, Jin Dong, Song He, Canxin Shi
This paper proposes a new splitting behavior for tree-level string and particle scattering amplitudes, particularly for massless scalars, gluons, and gravitons. The authors identify specific subspaces in the space of Mandelstam variables where the universal Koba-Nielsen factor splits into two parts, each with an off-shell leg. This splitting naturally leads to the factorization of both open- and closed-string amplitudes with Parke-Taylor factors into two stringy currents. The splitting implies the factorization of bi-adjoint $\phi^3$ amplitudes and, through a simple deformation, the factorization of amplitudes in the non-linear sigma model and Yang-Mills-scalar theory. The same splitting holds for scalar amplitudes without color, such as the special Galileon. Additionally, the Lorentz products involving polarizations for gluon and graviton amplitudes in bosonic and superstring theories also split into two stringy currents. A special case of this splitting implies soft theorems for gluons and gravitons, and more generally, it extends the recently proposed smooth splittings and factorizations near zeros to a wider context. The paper provides examples and detailed derivations for various theories, including bi-adjoint $\phi^3$, NLSM, YM, and gravity amplitudes, demonstrating the universality and generality of the 2-splitting behavior.This paper proposes a new splitting behavior for tree-level string and particle scattering amplitudes, particularly for massless scalars, gluons, and gravitons. The authors identify specific subspaces in the space of Mandelstam variables where the universal Koba-Nielsen factor splits into two parts, each with an off-shell leg. This splitting naturally leads to the factorization of both open- and closed-string amplitudes with Parke-Taylor factors into two stringy currents. The splitting implies the factorization of bi-adjoint $\phi^3$ amplitudes and, through a simple deformation, the factorization of amplitudes in the non-linear sigma model and Yang-Mills-scalar theory. The same splitting holds for scalar amplitudes without color, such as the special Galileon. Additionally, the Lorentz products involving polarizations for gluon and graviton amplitudes in bosonic and superstring theories also split into two stringy currents. A special case of this splitting implies soft theorems for gluons and gravitons, and more generally, it extends the recently proposed smooth splittings and factorizations near zeros to a wider context. The paper provides examples and detailed derivations for various theories, including bi-adjoint $\phi^3$, NLSM, YM, and gravity amplitudes, demonstrating the universality and generality of the 2-splitting behavior.