Kinematic Hopf algebra and Bern-Carrasco-Johansson numerators at finite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>α</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math>

We significantly extend recent work on the kinematic Hopf algebra, a structure that was shown to underlie the color-kinematics duality in Yang-Mills (YM) theory coupled to two heavy scalars, known as the heavy-mass effective theory (HEFT) limit. First, staying in the HEFT limit, we show the same kinematic Hopf algebra can be used to obtain Bern-Carrasco-Johansson (BCJ) numerators in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>DF</a:mi><a:mn>2</a:mn></a:msup><a:mo>+</a:mo><a:mrow><a:mi>YM</a:mi></a:mrow></a:math> theory, a theory containing an infinite number of higher derivative corrections to YM, used to obtain string amplitudes via the double copy. Second, we exploit the intricate structure induced by the massive poles to obtain an efficient and direct expression for local BCJ numerators in pure YM based on the same kinematic Hopf algebra. This demonstrates that the kinematic Hopf algebra works even beyond the HEFT limit, strongly suggesting this structure universally underlies the color-kinematics duality. Published by the American Physical Society 2024