One-loop Bern-Carrasco-Johansson numerators on quadratic propagators from the worldsheet

We introduce a novel approach for deriving one-loop Bern-Carrasco-Johansson (BCJ) numerators and reveal the world-sheet origin of the one-loop double copy. Our work shows that expanding Cachazo-He-Yuan half-integrands into generalized Parke-Taylor factors intrinsically generates BCJ numerators on quadratic propagators satisfying Jacobi identities. We validate our methodology by successfully reproducing one-loop BCJ numerators for the nonlinear sigma model as well as those of pure Yang-Mills theory in four dimensions with all-plus or single-minus helicities.