Analytic Multi-Loop Helicity Amplitudes in QCD Giuseppe De Laurentis The full physical information of a color-ordered helicity amplitude is in the finite remainder: Catani ('98) Becher, Neubert ('09) Gardi, Magnea ('09) Weinzierl ('11) $$ \textstyle \mathcal{R}^{\ell-\text{loop}}_{n-\text{point}}(|i⟩_{\alpha}, [i|_{\dot\alpha}) = \sum_i {\color{red}{r_{i}}}(|i⟩_{\alpha}, [i|_{\dot\alpha}) \, {\color{blue}{G_i}}(|i⟩_{\alpha} {\scriptsize\times} [i|_{\dot\alpha}) \, .