August 23, 2024 | Qu Cao, Jin Dong, Song He, Canxin Shi
This paper proposes a new "2-split" behavior for tree-level scattering amplitudes of massless scalars, gluons, and gravitons, including their string completions. The key idea is that by restricting Mandelstam variables to a subspace, the amplitude factorizes into the product of two currents. This behavior is shown to apply to both open- and closed-string amplitudes, and it implies the splitting of bi-adjoint $\phi^3$ amplitudes and extends to non-linear sigma model (NLSM) and Yang-Mills-scalar (YMS) theories. The same splitting applies to scalar amplitudes without color, such as the special Galileon. The 2-split behavior also leads to soft theorems for gluons and gravitons, and generalizes recent smooth splittings and factorizations near zeros to all these theories.
The 2-split behavior is demonstrated by splitting the scattering potential into "left" and "right" parts, each corresponding to a current with an off-shell leg. This splitting is shown to apply to both bosonic and supersymmetric string amplitudes of gluons and gravitons when Lorentz products involving their polarizations are similarly restricted. The 2-split behavior also explains the factorizations near zeros and extends to a wider context, including the special case of "skinny" zeros, which correspond to Adler zeros for Goldstone scalars.
The paper also discusses the splitting of scalar amplitudes in various theories, including NLSM, YMS, and the special Galileon. The splitting of these amplitudes is shown to follow from the splitting of the scattering potential and the corresponding measure. The results are illustrated with examples of 2-splits and factorizations near zeros, including the splitting of bi-adjoint $\phi^3$ amplitudes and the factorization of NLSM and YMS amplitudes.
The paper concludes with a discussion of the implications of the 2-split behavior for soft theorems and the potential for further generalizations to loop integrands and supersymmetric amplitudes. The results provide a unified framework for understanding the splitting behavior of scattering amplitudes in various theories, including string and particle amplitudes.This paper proposes a new "2-split" behavior for tree-level scattering amplitudes of massless scalars, gluons, and gravitons, including their string completions. The key idea is that by restricting Mandelstam variables to a subspace, the amplitude factorizes into the product of two currents. This behavior is shown to apply to both open- and closed-string amplitudes, and it implies the splitting of bi-adjoint $\phi^3$ amplitudes and extends to non-linear sigma model (NLSM) and Yang-Mills-scalar (YMS) theories. The same splitting applies to scalar amplitudes without color, such as the special Galileon. The 2-split behavior also leads to soft theorems for gluons and gravitons, and generalizes recent smooth splittings and factorizations near zeros to all these theories.
The 2-split behavior is demonstrated by splitting the scattering potential into "left" and "right" parts, each corresponding to a current with an off-shell leg. This splitting is shown to apply to both bosonic and supersymmetric string amplitudes of gluons and gravitons when Lorentz products involving their polarizations are similarly restricted. The 2-split behavior also explains the factorizations near zeros and extends to a wider context, including the special case of "skinny" zeros, which correspond to Adler zeros for Goldstone scalars.
The paper also discusses the splitting of scalar amplitudes in various theories, including NLSM, YMS, and the special Galileon. The splitting of these amplitudes is shown to follow from the splitting of the scattering potential and the corresponding measure. The results are illustrated with examples of 2-splits and factorizations near zeros, including the splitting of bi-adjoint $\phi^3$ amplitudes and the factorization of NLSM and YMS amplitudes.
The paper concludes with a discussion of the implications of the 2-split behavior for soft theorems and the potential for further generalizations to loop integrands and supersymmetric amplitudes. The results provide a unified framework for understanding the splitting behavior of scattering amplitudes in various theories, including string and particle amplitudes.