New relations for tree-level form factors and scattering amplitudes

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 $\mathrm{tr}(F^2)$ operator can be decomposed as a linear combination of form factors with $\mathrm{tr}({\varphi }^2)$ 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 $\mathrm{tr}({\varphi }^2)$ 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.

27 pages+ appendices; ver2, minor modifications, typo corrected

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