Abstract
Planar zeros are studied in the context of the five-point scattering amplitude for gauge bosons and gravitons. In the case of gauge theories, it is found that planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta. This curve depends on the values of six independent color structures. Considering the gauge group SU(N) with N=2,3,5 and fixed color indices, the class of curves obtained gets broader by increasing the rank of the group. For the five-graviton scattering, on the other hand, we show that the amplitude vanishes whenever the process is planar, without imposing further kinematic conditions. A rationale for this result is provided using color-kinematics duality.
Highlights
The only study of planar zeros beyond the soft limit has been carried out in the interesting work [19], where the five parton amplitude in QCD was analyzed
In the case of gauge theories, it is found that planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta
We show that planar zeros are a “projective” property of the amplitude, in the sense that they are preserved by a simultaneous rescaling of the stereographic coordinates labeling the flight directions of the three outgoing gluons
Summary
We revisit the construction of the five-gluon amplitude g(p1, a1) + g(p2, a2) −→ g(p3, a3) + g(p4, a4) + g(p5, a5),. The tree level amplitude is computed in terms of 15 nonequivalent trivalent diagrams, leading to the expression. Where we have introduced the kinematic invariants sij = (pi + pj)2 = 2 pi · pj, i < j
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