Proof of the fundamental BCJ relations for QCD amplitudes

We present a set of relations between one-loop integral coefficients for dimensionally regulated QCD amplitudes. Within dimensional regularization, the combined use of color-kinematics duality and integrand reduction yields the existence of relations between the integrand residues of partial amplitudes with different orderings of the external particles. These relations can be established for the cut-constructible contributions as well for the ones responsible for rational terms. Starting from the general parametrization of one-loop residues and applying Laurent expansion in order to extract the coefficients of the amplitude decomposition in terms of master integrals, we show that the full set of relations can be obtained by considering the BCJ identities between d-dimensional tree-level amplitudes. We provide explicit examples for multi-gluon scattering amplitudes at one loop.

Section: Jhep04(2016)125mentioning

confidence: 95%

BCJ identities and d-dimensional generalized unitarity

Primo

Bobadilla

2016

“…The duality provides a rich structure to tree-level amplitudes [20,24,[35][36][37][38][39][40][41][42][43][44][45][46], most notably through the color-ordered n-point gluon amplitudes, which are constrained by the so-called BCJ relations [13,47,48] -these can be used to eliminate all but (n − 3)! independent amplitudes.…”

Section: Introductionmentioning

confidence: 99%

Unraveling conformal gravity amplitudes

Johansson

Mogull

Teng

2018

100

Conformal supergravity amplitudes are obtained from the double-copy construction using gauge-theory amplitudes, and compared to direct calculations starting from conformal supergravity Lagrangians. We consider several different theories: minimal N = 4 conformal supergravity, non-minimal N = 4 Berkovits-Witten conformal supergravity, mass-deformed versions of these theories, as well as supersymmetry truncations thereof. Coupling the theories to a Yang-Mills sector is also considered. For all cases we give the gravity Lagrangians that the double copy implicitly generates. The two main results are: we determine a Lagrangian for the non-minimal Berkovits-Witten theory, and we uncover the double-copy prescription for the minimal N = 4 conformal supergravity.

“…At tree level, it is proven [93,94] for gauge theories, in which color-ordered amplitudes satisfy the BCJ relations [61,[95][96][97]. For (super-)Yang-Mills theories with arbitrary fundamental matter, which is less studied, the corresponding BCJ relations [63,65] have been proven in the case of QCD [98].…”

Section: )mentioning

confidence: 99%

Two-loop $$ \mathcal{N} $$ = 2 SQCD amplitudes with external matter from iterated cuts

Kälin

Mogull

Ochirov³

2019

We develop an iterative method for constructing four-dimensional generalized unitarity cuts in N = 2 supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets (N = 2 SQCD). For iterated two-particle cuts, specifically those involving only four-point amplitudes, this implies simple diagrammatic rules for assembling the cuts to any loop order, reminiscent of the rung rule in N = 4 SYM. By identifying physical poles, the construction simplifies the task of extracting complete integrands. In combination with the duality between color and kinematics we construct all four-point massless MHV-sector scattering amplitudes up to two loops in N = 2 SQCD, including those with matter on external legs. Our results reveal chiral infrared-finite integrands closely related to those found using loop-level BCFW recursion. The integrands are valid in D ≤ 6 dimensions with external states in a four-dimensional subspace; the upper bound is dictated by our use of six-dimensional chiral N = (1, 0) SYM as a means of dimensionally regulating loop integrals.