Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents

Abstract: Our work focuses on utilizing the Berends-Giele currents to construct differential operators and unifying relations for 1-loop Feynman integrands. We successfully reproduce the known results for the unifying relations between Yang-Mills theory and Yang-Mills scalar theory, and extend the discussion to the (A)dS case for the scalar theory with minimal coupling to gluons.