Abstract
We argue that no notion of flavor is necessary when performing amplitude calculations in perturbative QCD with massless quarks. We show this explicitly at tree level, using a flavor recursion relation to obtain multiflavored QCD from one-flavor QCD. The method relies on performing a color decomposition, under which the one-flavor primitive amplitudes have a structure which is restricted by planarity and cyclic ordering. An understanding of $SU(3{)}_{c}$ group theory relations between QCD primitive amplitudes and their organization around the concept of a Dyck tree is also necessary. The one-flavor primitive amplitudes are effectively $\mathcal{N}=1$ supersymmetric, and a simple consequence is that all of tree-level massless QCD can be obtained from Drummond and Henn's closed form solution to tree-level $\mathcal{N}=4$ super Yang-Mills theory.
Highlights
Fixed-order theoretical predictions for jet cross sections at the Large Hadron Collider (LHC) require the calculation of scattering amplitudes in perturbative QCD involving light QCD partons—gluons and quarks of different flavor
It has long been understood that some amplitudes in QCD are effectively supersymmetric at tree level [11,12], and, in a recent paper [13], it was shown that all QCD amplitudes with up to four quark lines of distinct flavor can be obtained from the formula of Drummond and Henn
It follows directly from the flavor recursion described in the previous section that the whole of massless QCD at tree level is obtainable from N 1⁄4 4 SYM, since oneflavor amplitudes are identical in QCD and N 1⁄4 4 SYM
Summary
Fixed-order theoretical predictions for jet cross sections at the Large Hadron Collider (LHC) require the calculation of scattering amplitudes in perturbative QCD involving light QCD partons—gluons and quarks of different flavor. It has long been understood that some amplitudes in QCD are effectively supersymmetric at tree level [11,12], and, in a recent paper [13], it was shown that all QCD amplitudes with up to four quark lines of distinct flavor (four being the number of gluino flavors in N 1⁄4 4 SYM) can be obtained from the formula of Drummond and Henn. Primitive amplitudes can be used explicitly in subtraction schemes, as formulated within the colorful [34] Frixione-Kunszt-Signer framework [35] Both a knowledge of a general basis and the flavor recursion described in this paper should be useful for multileg QCD calculations at leading and next-to-leading orders.
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