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<p>In this work, we compute the one-loop four-graviton amplitudes with a massive abelian vector field (Proca) circulating in the loop. Instead of the conventional Einstein-Hilbert formulation, we employ the Landau-Lifshitz metric density approach, coupling gravity to the Proca field. Within this framework, we found that the resulting contact-terms-free <i>n</i>-gon numerators exhibit a manifest double-copy structure, provided the external gravitational trees satisfy this property. This structure enables the direct construction of the corresponding amplitudes with a scalar in the loop. We further show that these numerators can be consistently used to evaluate pure gravity amplitudes in the sectors where contact terms vanish, offering a simplified setting to explore double-copy relations at one loop level.</p>

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One-loop double copy from gravity coupled to a massive vector field

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  • 发表日期：

    2026年2月4日

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  • Cristhiam Lopez-Arcos

摘要

In this work, we compute the one-loop four-graviton amplitudes with a massive abelian vector field (Proca) circulating in the loop. Instead of the conventional Einstein-Hilbert formulation, we employ the Landau-Lifshitz metric density approach, coupling gravity to the Proca field. Within this framework, we found that the resulting contact-terms-free n-gon numerators exhibit a manifest double-copy structure, provided the external gravitational trees satisfy this property. This structure enables the direct construction of the corresponding amplitudes with a scalar in the loop. We further show that these numerators can be consistently used to evaluate pure gravity amplitudes in the sectors where contact terms vanish, offering a simplified setting to explore double-copy relations at one loop level.