Higher-derivative relations between scalars and gluons. (English) Zbl 07917423
Summary: We extend the covariant color-kinematics duality introduced by C. Cheung and J. Mangan [J. High Energy Phys. 2021, No. 11, Paper No. 69, 46 p. (2021; Zbl 1521.81253)] to effective field theories. We focus in particular on relations between the effective field theories of gluons only and of gluons coupled to bi-adjoint scalars. Maps are established between their respective equations of motion and between their tree-level scattering amplitudes. An additional rule for the replacement of flavor structures by kinematic factors realizes the map between higher-derivative amplitudes. As an example of new relations, the pure-gluon amplitudes of mass dimension up to eight, featuring insertions of the \(F^3\) and \(F^4\) operators which satisfy the traditional color-kinematics duality, can be generated at all multiplicities from just renormalizable amplitudes of gluons and bi-adjoint scalars. We also obtain closed-form expressions for the kinematic numerators of the dimension-six gluon effective field theory, which are valid in \(D\) space-time dimensions. Finally, we find strong evidence that this extended covariant color-kinematics duality relates the \((DF)^2 + \mathrm{YM}(+\phi^3)\) theories which, at low energies, generate infinite towers of operators satisfying the traditional color-kinematics duality, beyond aforementioned \(F^3\) and \(F^4\) ones.
MSC:
| 81Txx | Quantum field theory; related classical field theories |
| 81Uxx | Quantum scattering theory |
| 83Exx | Unified, higher-dimensional and super field theories |
Citations:
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