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Graphical functions with spin

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arxiv 2504.05850 v2 pith:P7DTK2FL submitted 2025-04-08 hep-th math-phmath.MP

Graphical functions with spin

Oliver Schnetz This is my paper
classification hep-th math-phmath.MP
keywords spintheoriesarticlefeynmanfunctionsgraphicalintegralstheory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The theory of graphical functions is generalized from scalar theories to theories with spin, leading to a numerator structure in Feynman integrals. The main part of this article treats the case of positive integer spin, which is obtained from spin $1/2$ theories after the evaluation of $\gamma$ traces. As an application (in this article used mainly to prove consistency and efficiency of the method), we calculate primitive Feynman integrals in Yukawa-$\phi^4$ (Gross-Neveu-Yukawa) theory up to loop order eight.

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Cited by 5 Pith papers

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    A leading-singularity bootstrap with single-valued polylog ansätze and region-expansion boundaries evaluates previously intractable four-loop conformal integrals, including non-planar sectors.

  2. Notes on the bootstrap of four-point conformal integrals

    hep-th 2026-07 conditional novelty 6.0

    A leading-singularity bootstrap workflow yields new analytic expressions for four-loop conformal integrals, including previously intractable non-planar sectors.

  3. Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion

    hep-th 2026-04 unverdicted novelty 6.0

    Four-loop anomalous dimension of φ^Q in scalar-QED computed via OPE, extending prior three-loop results and validating the method in a gauge theory.

  4. Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion

    hep-th 2026-04 unverdicted novelty 6.0

    Four-loop anomalous dimensions of φ^Q in scalar-QED are obtained via OPE, with beta functions and mass/field anomalous dimensions, validating OPE beyond pure scalar theories.

  5. Graphical Functions by Examples

    hep-th 2026-04 unverdicted novelty 2.0

    Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic com...