Pith. sign in

hub Canonical reference

Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals

Canonical reference. 83% of citing Pith papers cite this work as background.

16 Pith papers citing it
295 external citations · Pith
Background 83% of classified citations
abstract

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 supports Mathematica's arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica's Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FeynCalc and LoopTools.

hub tools

citation-role summary

background 5 method 1

citation-polarity summary

years

2026 10 2025 6

representative citing papers

Disperon QED

hep-ph · 2025-12-11 · unverdicted · novelty 6.0

Disperon QED is a new technique that feeds experimental data into higher-order QED loop calculations in Monte Carlo generators via dispersion relations and threshold subtraction.

Light new physics and the $\tau$ lepton dipole moments

hep-ph · 2025-11-05 · unverdicted · novelty 6.0

This work provides a comprehensive analysis of light new physics contributions to tau lepton dipole moments, detailing interpretations of asymmetry measurements for spin-0 and spin-1 bosons, their decoupling to the EFT limit, and a case study of a tauphilic vector boson at Belle II.

Improved Standard-Model predictions for $\eta^{(\prime)}\to \ell^+ \ell^-$

hep-ph · 2025-12-15 · accept · novelty 5.0

Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.

SubTropica

hep-th · 2026-04-22 · unverdicted · novelty 5.0

SubTropica is a software package that automates symbolic integration of linearly-reducible Euler integrals via tropical subtraction, supported by HyperIntica and an AI-driven Feynman integral database.

Neutrinoless double-beta decay of the $\Delta^-$ resonance

hep-ph · 2026-04-14 · unverdicted · novelty 5.0

Chiral EFT derivation of the Δ⁻ → p e⁻ e⁻ amplitude including long-range neutrino loops, short-range counterterms, pion-mass dependence for collinear electrons, and a long-range prediction in the degenerate Δ-nucleon mass limit.

Freeze-in at all couplings

hep-ph · 2026-06-17 · unverdicted · novelty 4.0

In low-reheating-temperature charged-parent freeze-in dark matter models, stronger couplings are viable if both dark matter and mediator number densities are tracked, with updated LHC and lepton-flavor-violation constraints.

The Polymorphic Chiral Anomaly

hep-ph · 2026-06-02 · unverdicted · novelty 4.0

Derives a generic chiral anomaly formula incorporating multiple Feynman diagrams, from which abelian, singlet, consistent, and covariant forms follow, with topological discussion and FeynCalc code.

citing papers explorer

Showing 16 of 16 citing papers.

  • Hyperon non-leptonic decays in relativistic Chiral Perturbation Theory with resonances hep-ph · 2026-04-01 · unverdicted · none · ref 79

    Relativistic ChPT at NLO with resonance saturation yields a good combined fit to hyperon non-leptonic s- and p-wave decay amplitudes.

  • Decay constants of $B_c$-mesons with vector and tensor currents hep-ph · 2026-06-24 · conditional · none · ref 33 · internal anchor

    QCD sum-rule computation of vector/axial-vector and tensor/axial-tensor decay constants for B_c, B_c*, B_c0*, B_c1 mesons, with refined power corrections and first tensor results.

  • Disperon QED hep-ph · 2025-12-11 · unverdicted · none · ref 64 · internal anchor

    Disperon QED is a new technique that feeds experimental data into higher-order QED loop calculations in Monte Carlo generators via dispersion relations and threshold subtraction.

  • Light new physics and the $\tau$ lepton dipole moments hep-ph · 2025-11-05 · unverdicted · none · ref 134 · internal anchor

    This work provides a comprehensive analysis of light new physics contributions to tau lepton dipole moments, detailing interpretations of asymmetry measurements for spin-0 and spin-1 bosons, their decoupling to the EFT limit, and a case study of a tauphilic vector boson at Belle II.

  • $\bar{B}_{s,d}^{0} \to J/\psi \mu^{+}\mu^{-}$ Decays in QCD Factorization hep-ph · 2025-10-01 · unverdicted · none · ref 56 · internal anchor

    Computes branching ratios of order 10^{-10} for Bs and 10^{-11} for Bd decays after NLO vertex corrections in QCD factorization, plus dimuon distributions and J/psi polarization.

  • Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $(g-2)_\mu$ hep-ph · 2025-09-09 · conditional · none · ref 49 · internal anchor

    Virtual electromagnetic corrections largely cancel radiative-channel contributions in data-driven HVP evaluations for muon g-2, reconciling timelike and spacelike methods via a VMD model.

  • Current and future constraints on heavy New Physics from $\tau$ weak dipole moments hep-ph · 2026-06-05 · unverdicted · none · ref 39 · internal anchor

    Tau weak dipole moments already rank among the leading probes of tau dipole operators and will become dominant at FCC-ee and HL-LHC.

  • Radiative Corrections to Elastic Lepton-Proton Scattering with Focus on Two-Photon-Exchange Diagrams hep-ph · 2026-05-29 · unverdicted · none · ref 72 · internal anchor

    Complete NLO QED radiative corrections to elastic lepton-proton scattering including TPE contributions with momentum-dependent form factors and numerical impact assessment.

  • Improved Standard-Model predictions for $\eta^{(\prime)}\to \ell^+ \ell^-$ hep-ph · 2025-12-15 · accept · none · ref 144 · internal anchor

    Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.

  • SubTropica hep-th · 2026-04-22 · unverdicted · none · ref 14

    SubTropica is a software package that automates symbolic integration of linearly-reducible Euler integrals via tropical subtraction, supported by HyperIntica and an AI-driven Feynman integral database.

  • Neutrinoless double-beta decay of the $\Delta^-$ resonance hep-ph · 2026-04-14 · unverdicted · none · ref 80

    Chiral EFT derivation of the Δ⁻ → p e⁻ e⁻ amplitude including long-range neutrino loops, short-range counterterms, pion-mass dependence for collinear electrons, and a long-range prediction in the degenerate Δ-nucleon mass limit.

  • Freeze-in at all couplings hep-ph · 2026-06-17 · unverdicted · none · ref 24 · internal anchor

    In low-reheating-temperature charged-parent freeze-in dark matter models, stronger couplings are viable if both dark matter and mediator number densities are tracked, with updated LHC and lepton-flavor-violation constraints.

  • Sensitivity to top-quark couplings in diboson production at lepton colliders hep-ph · 2026-06-10 · unverdicted · none · ref 61 · internal anchor

    NLO EW corrections to WW production from SMEFT top operators yield competitive sensitivity at LEP3 and FCC-ee relative to ZH production and existing LEP/LHC bounds.

  • The Polymorphic Chiral Anomaly hep-ph · 2026-06-02 · unverdicted · none · ref 93 · internal anchor

    Derives a generic chiral anomaly formula incorporating multiple Feynman diagrams, from which abelian, singlet, consistent, and covariant forms follow, with topological discussion and FeynCalc code.

  • Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations hep-ph · 2025-10-27 · unverdicted · none · ref 82 · internal anchor

    Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.

  • Light neutrinos, Dark matter and leptogenesis near electroweak scale and $Z_4$ symmetry hep-ph · 2026-04-06 · unverdicted · none · ref 28

    Z4-symmetric Type I seesaw fits neutrino data with minimal parameters and enables freeze-in dark matter plus resonant leptogenesis via soft symmetry breaking.