Pith. sign in

REVIEW 5 cited by

Evaluation of the general 3-loop vacuum Feynman integral

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1610.07720 v3 pith:SF5BCXE6 submitted 2016-10-25 hep-ph

Stephen P. Martin , David G. Robertson This is my paper · ORCID
classification hep-ph
keywords integralsbasisintegralloopvacuumevaluationgeneralmasses
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite basis integrals that are particularly convenient for expressing renormalized quantities. The basis integrals can be computed numerically by solving coupled first-order differential equations, using as boundary conditions the analytically known special cases that depend on only one mass scale. We provide the results necessary to carry this out, and introduce an implementation in the form of a public software package called 3VIL (3-loop Vacuum Integral Library), which efficiently computes the numerical values of the basis integrals for any specified masses. 3VIL is written in C, and can be linked from C, C++, or FORTRAN code.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bare effective potential and Goldstone boson anti-resummation

    hep-ph 2026-08 conditional novelty 7.0 of 10

    Treating Goldstone-boson squared masses as interaction vertices instead of propagator masses eliminates spurious infrared logarithms and imaginary parts, giving a consistent three-loop tadpole-free effective potential...

  2. Three-loop corrections to the Fermi decay constant in the $\overline{\rm{MS}}$ scheme

    hep-ph 2025-07 conditional novelty 7.0 of 10

    The leading three-loop corrections to the Fermi decay constant in the pure MS scheme are computed, shifting the Standard Model Higgs VEV down by about 3.5 MeV and cutting residual scale dependence to below 2e-6.

  3. Four-Loop Renormalisation of Chiral Gauge Theories with Non-Anticommuting $\gamma_5$ in the BMHV Scheme

    hep-ph 2025-06 conditional novelty 7.0 of 10

    First 4-loop BMHV renormalization of an Abelian chiral gauge theory, with explicit finite symmetry-restoring counterterms and an application to the SM fermionic sector.

  4. Full Three-Loop Electroweak Multiplet Contributions to the Electron Electric Dipole Moment

    hep-ph 2026-02 conditional novelty 6.0 of 10

    The full three-loop electron EDM from CP-violating SU(2)_L multiplet Yukawa interactions is exactly three times larger (at leading order) than the electroweak-Weinberg operator contribution alone.

  5. Heat Kernel Methods for Multiloop Calculations in Curved Spacetime: Nonzero Spin

    hep-th 2025-06 reject novelty 5.0 of 10

    This paper presents a master formula and the off-diagonal heat kernel expansion (eq. 4.10) that generalize the authors' scalar curved-spacetime multiloop formalism to nonzero-spin fields in general gauge and gravitati...

Pith tools