Abstract
We find that scattering amplitudes in massive scalar QCD can manifest the duality between color and kinematics at loop-level. Specifically we construct the one-loop integrands for four-point scattering between two distinct massive scalars, and the five-point process encoding the first correction to massive scalar scattering with gluonic radiation. We find that factorization and the color-kinematics duality are sufficient principles to entirely bootstrap these calculations, allowing us to construct all contributions ultimately from the three-point tree-level amplitudes which are themselves entirely constrained by symmetry. Double-copy construction immediately provides the associated predictions for massive scalars scattering in the so called N=0 supergravity theory.
Highlights
Traditional methods of calculating quantum gravitational scattering amplitudes using Feynman rules quickly run into difficulties
We find that scattering amplitudes in massive scalar quantum chromodynamics (QCD) can manifest the duality between color and kinematics at loop-level
We found the first loop correction to scattering between two different massive scalar fields, as well as the first loop correction to such scattering with an emitted gluon
Summary
Traditional methods of calculating quantum gravitational scattering amplitudes using Feynman rules quickly run into difficulties. In gravitational double-copy amplitudes for massive external states, even at tree level, one can generically expect the contributions of dilatons [14] This state counting and attribution naturally fits in with the states that contribute to supergravity theories, which is why the naive double-copy of pure Yang-Mills is often called N 1⁄4 0 supergravity. The highest order correction in the gravitational coupling, GN, (often called post-Minkowskian [PM]) to conservative black hole binding energy (3 PM) was only made within the past couple of years and centered amplitudes insights (see [17,58] and references therein) This calculation required the classical remnant of the two-loop four-point scattering amplitude between two massive scalars.
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