To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU(N ), N = 4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental representation, and use it to construct explicitly complete four-vector and four-scalar amplitudes at one loop. For fixed number of supercharges, graph-organized L-loop n-point integrands of all orbifold theories are given in terms of a fixed set of polynomials labeled by L representations of the orbifold group. In contrast to the standard duality-satisfying presentation of amplitudes of the N = 4 super Yang-Mills theory, each graph may appear several times with different internal states. The color and R-charge flow provide a way to deform the amplitudes of orbifold theories to those of more general quiver gauge theories which do not necessarily exhibit color/kinematics duality on their own.Based on the organization of amplitudes required by the duality between color and kinematics in orbifold theories we show how the amplitudes of certain non-factorized mattercoupled supergravity theories can be found through a double-copy construction.We also carry out a comprehensive search for theories with fields solely in the adjoint representation of the gauge group and amplitudes exhibiting color/kinematics duality for all external states and find an interesting relation between supersymmetry and existence of the duality.
We obtain, for the first time, the two-loop amplitudes for Higgs plus three gluons in Higgs effective field theory including dimension-seven operators. This provides the S-matrix elements for the top mass corrections for Higgs plus a jet production at LHC. The computation is based on the on-shell unitarity method combined with integration by parts reduction. We work in conventional dimensional regularization and obtain analytic expressions renormalized in the modified minimal subtraction scheme. The two-loop anomalous dimensions present operator mixing behavior. The infrared divergences agree with that predicted by Catani and the finite remainders take remarkably simple forms, where the maximally transcendental parts are identical to the corresponding results in N=4 super-Yang-Mills theory. The parts of lower transcendentality turn out to be also largely determined by the N=4 results.
We obtain the two-loop QCD corrections to Higgs plus three-parton amplitudes with dimension-seven operators in Higgs effective field theory. This provides the two-loop S-matrix elements for Higgs plus one-jet production at LHC with top-mass correction. We apply efficient unitarity plus IBP methods which are described in detail. We also study the color decomposition of the fermion cuts and find a connection between fundamental and adjoint representations which can reduce non-planar to planar unitarity cuts. We obtain final results in simple analytic form which exhibits intriguing hidden structure. The principle of maximal transcendentality is found to be satisfied for all results. The lower transcendentality parts also contain universal building blocks and can be written in compact analytic forms, suggesting further hidden structures.
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