BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
Yi-Jian Du, Bo Feng, Chih-Hao Fu
TL;DR
This paper provides a field theoretical proof of the KLT relation connecting gluon scattering amplitudes to scalar amplitudes, utilizing BCJ and KK relations with BCFW recursion, including an off-shell BCJ relation.
Contribution
It establishes the BCJ and KK relations for scalar amplitudes and proves the KLT relation for gluon amplitudes using BCFW recursion with boundary contributions.
Findings
Proof of BCJ and KK relations for scalar amplitudes
Verification of the KLT relation for gluon scattering
Development of an off-shell BCJ relation
Abstract
We present a field theoretical proof of the conjectured KLT relation which states that the full tree-level scattering amplitude of gluons can be written as a product of color-ordered amplitude of gluons and color-ordered amplitude of scalars with only cubic vertex. To give a proof we establish the KK relation and BCJ relation of color-ordered scalar amplitude using BCFW recursion relation with nonzero boundary contributions. As a byproduct, an off-shell version of fundamental BCJ relation is proved, which plays an important role in our work.
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