New relations for tree-level form factors and scattering amplitudes

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 tr(F2) operator can be decomposed as a linear combination of form factors with tr(ϕ2) 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 tr(ϕ2) 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.