Bern-Carrasco-Johansson relations for one-loop QCD integral coefficients

Abstract

We present a set of one-loop integral coefficient relations in QCD. The unitarity method is useful for exposing one-loop amplitudes in terms of tree amplitudes. The coefficient relations are induced by tree-level BCJ amplitude relations. We provide examples for box, triangle, and bubble coefficients. These relations reduce the total number of independent coefficients needed to calculate one-loop QCD amplitudes.

BCJ identities and d-dimensional generalized unitarity

“…In a similar way, the expansion for large-t of the ratio of propagators returns 27) which agrees with the t → ∞ expansion of (4.24d). The resulting contributions of the three cuts to A…”

“…In the framework of four-dimensional generalized unitarity, the BCJ identities for tree-level amplitudes were used in [26] to derive relations between coefficients of one-loop amplitudes in N = 4 super Yang-Mills theory and, more recently, in [27] these relations have been extended to integral coefficients for the cutconstructible part of one-loop QCD amplitudes by showing that tree-level the C/K-duality can significantly decrease the number of independent coefficients needed in one-loop computations. When moving to d-dimensional generalized unitarity, extensions of tree-level identities to one-loop amplitudes are expected to hold also between rational contributions, as it was investigated in [28,29].…”

Light-like scattering in quantum gravity

“…The consequence of the monodromy BCJ relations for one-loop integral coefficients have been studied in [45] and [46], while a string theory based systematic derivation of these relations was given in [47].…”

From Jacobi off-shell currents to integral relations

“…Similarly, new relations at oneloop level have been found with a clever use of the BCJ relations with string theory [24][25][26][27][28] and unitarity based methods [29,30].…”