Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions

We present a systematic procedure to compute complete, analytic form factors of gauge-invariant operators at loop level in pure Yang-Mills. We consider applications to operators of the form TrFn where F is the gluon field strength. Our approach is based on an extension to form factors of the dimensional reconstruction technique, in conjunction with the six-dimensional spinor-helicity formalism and generalized unitarity. For form factors this technique requires the introduction of additional scalar operators, for which we provide a systematic prescription. We also discuss a generalization of dimensional reconstruction to any number of loops, both for amplitudes and form factors. Several novel results for one-loop minimal and nonminimal form factors of TrFn with n > 2 are presented. Finally, we describe the Mathematica package spinorHelicity6D, which is tailored to handle six-dimensional quantities written in the spinorhelicity formalism.