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This study extends Kawai-Lewellen-Tye (KLT) and Bern-Carrasco-Johansson (BCJ) amplitude relations to loop integrands. It introduces a novel, invariant double-copy formulation for gauge theory and gravity loop amplitudes.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • Quantum Field Theory

Background:

  • The Kawai-Lewellen-Tye (KLT) and Bern-Carrasco-Johansson (BCJ) relations establish connections between scattering amplitudes in gauge theory and gravity at tree-level.
  • Extending these relations to loop integrands is crucial for a deeper understanding of quantum gravity and gauge theories.

Purpose of the Study:

  • To generalize the tree-level KLT and BCJ amplitude relations to the realm of loop integrands in gauge theory and gravity.
  • To develop a manifestly gauge- and diffeomorphism-invariant formulation of double-copy relations for loop integrands.

Main Methods:

  • Rearrangement of propagators within gauge and gravity loop integrands.
  • Development of a novel formulation for double-copy relations applicable to loop integrands.
  • Identification of gauge-invariant building blocks, termed 'partial integrands', for gravity loop amplitudes.

Main Results:

  • The first manifestly gauge- and diffeomorphism-invariant double-copy relations for loop integrands are proposed.
  • A one-loop KLT formula is derived, expressing gravity integrands via partial integrands derived from gauge theory amplitudes.
  • These partial integrands satisfy a one-loop analogue of the BCJ relations, demonstrating universality across dimensions and particle types.
  • One-loop integrands of Einstein-Yang-Mills theory are shown to be related to partial integrands of pure gauge theories.

Conclusions:

  • The study successfully extends KLT and BCJ relations to loop integrands, providing a unified framework for gauge theory and gravity.
  • The proposed double-copy formulation offers a powerful tool for investigating quantum gravity and gauge theories at loop level.
  • The universality of the derived relations highlights fundamental connections between different areas of theoretical physics.