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All-loop planar integrands in Yang-Mills theory from recursion
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All-loop planar integrands in Yang-Mills theory from recursion
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In this letter, we generalize the recursion methods based on cut equations arXiv:2412.21027, originally developed for scalar theories, to gluons in pure Yang-Mills theory. In gauge theories, planar loop integrands are subtle to defined and obtained due to the existence of scaleless integrals. A critical challenge arises when constructing higher-loop integrands via recursion methods: integrands with or without all scaleless terms both are incompatible with the reconstruction formalism in arXiv:2412.21027. To address this, we introduce a $\textit{refined}$ integrand by systematically removing specific scaleless contributions, and develop an algorithmic implementation of the recursion to all-loop level. We explicitly demonstrate the framework by three steps and obtain the recursion formula in pure Yang-Mills theory. In the ancillary files, we provide the results up to the two-loop five-point integrand and the simplified result in the large-$D$ limit for the three-loop four-point case.
Forward citations
Cited by 4 Pith papers
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Planar loop integrands from cuts in $D$ dimensions
A Möbius-inversion formula on the refinement poset reconstructs planar L-loop n-point integrands as sums over non-scaleless scalar graphs dressed by D-dimensional cuts, demonstrated for Yang-Mills theory.
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The bi-adjoint scalar $\ell$-loop planar integrand recursion and graded inverse variables
A new formalism with graded inverse variables refines the ℓ-loop planar integrand recursion in bi-adjoint scalar theory, allowing graph factors and symmetry factors to be read directly from monomials.
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Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
A recursion formula for ℓ-loop planar integrands in colored QFTs is derived from the classical equation of motion via comb components and loop kernels.
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Off-shell recursion for all-loop planar integrands in Yang-Mills theory
Yang-Mills planar loop integrands admit an off-shell recursion that organizes the pure-gluon sector into matrix form and incorporates ghost contributions, yielding a concrete two-loop strategy.
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