New relations for tree-level form factors and scattering amplitudes

TL;DR

This paper uncovers new structural relations between tree-level form factors and scattering amplitudes in Yang-Mills-scalar theory, offering an efficient computational framework and revealing hidden connections in gauge theories.

Contribution

It establishes novel relations between form factors and amplitudes in YMS theory, including decomposition formulas and expansion techniques, enhancing computational methods.

Findings

Form factors with ${\rm tr}(F^2)$ decompose into form factors with ${\rm tr}(\phi^2)$ and scalars.

Any form factor of ${\rm tr}(\phi^2)$ expands into higher-point YMS amplitudes.

Provides an efficient algorithm and CHY formulas for length-two form factors.

Abstract

We show that tree-level form factors with length-two operators in Yang-Mills-scalar (YMS) theory exhibit structures very similar to scattering amplitudes of gluons and scalars, which leads to new relations between them. Just like amplitudes, $n$-point Yang-Mills form factors with ${\rm tr}(F^2)$ operator can be decomposed as a linear combination of form factors with ${\rm tr}(\phi^2)$ operator and $r$ external scalars in YMS theory, where the coefficients are given by Lorentz products of the $r$ linearized field strengths. Moreover, we show that any such $n$-point form factor of ${\rm tr}(\phi^2)$ operator can be further expanded into $(n{+}1)$-point YMS amplitudes with an additional off-shell scalar leg. In addition to unravelling hidden structures, our results provide an efficient algorithm for computing all-multiplicity length-two form factors in any dimension, as well as their Cachazo-He-Yuan formulae via those of the YMS amplitudes.