FeynHelpers: Connecting FeynCalc to FIRE and Package-X

Abstract

We present a new interface called FeynHelpers that connects FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and calculations in quantum field theory (QFT) to Package-X and FIRE. The former provides a library of analytic results for scalar 1-loop integrals with up to 4 legs, while the latter is a general-purpose tool for reduction of multi-loop scalar integrals using Integration-by-Parts (IBP) identities. With this add-on many types of calculations that were difficult or hardly feasible with FeynCalc previously, can now be done in a much simpler way. This is demonstrated with four different examples from QED, QCD and Higgs physics.

40 pages, 1 figure, updated to match the journal version. Accompanying Mathematica notebooks are bundled with the source files of this document. To obtain the program, see https://github.com/FeynCalc/feynhelpers

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Cited by in corpus (71)

• FeynCalc 9.3: New features and improvements
• Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals
• FeynCalc 10: Do multiloop integrals dream of computer codes?
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• FormTracer - A Mathematica Tracing Package Using FORM
• Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays
• Dimensional Regularization and Breitenlohner-Maison / 't Hooft-Veltman Scheme for ${\gamma }_5$ applied to Chiral YM Theories: Full One-Loop Counterterm and RGE Structure
• SMEFT Corrections to $Z$ Boson Decays
• DoFun 3.0: Functional equations in Mathematica
• Energy-energy correlation in hadronic Higgs decays: analytic results and phenomenology at NLO
• Higgs decay into a lepton pair and a photon revisited
• One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory
• Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting ${\gamma }_5$: Full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory
• Higgs portal to dark matter and $B\to K^{(\ast )}$ decays
• Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme
• Resummation of soft and Coulomb corrections for $t\bar{t}h$ production at the LHC
• Two-loop mass splittings in electroweak multiplets: winos and minimal dark matter
• Changing patterns in electroweak precision with new color-charged states: Oblique corrections and the $W$ boson mass
• The effective action for gauge bosons
• Radiative decays of the spin-$2$ partner of $X(3872)$
• Double insertions of SMEFT operators in gluon fusion Higgs boson production
• Introducing tools to test Higgs interactions via $WW$ scattering I: one-loop calculations and renormalization in the HEFT
• Bounds on photon scattering
• FeynGrav 2.0
• Minimal anomalous $\mathrm{U}(1)$ theories and collider phenomenology
• Non-relativistic and potential non-relativistic effective field theories for scalar mediators
• Revisiting the top quark chromomagnetic dipole moment in the SM
• Bound-state formation, dissociation and decays of darkonium with potential non-relativistic Yukawa theory for scalar and pseudoscalar mediators
• FeynOnium: Using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories
• Diboson production in the SMEFT from gluon fusion
• Lepton Phenomenology of Stueckelberg Portal to Dark Sector
• Production of the $X(4014)$ as the spin-2 partner of $X(3872)$ in $e^{+}{e}^{-}$ collisions
• Dispersion theoretic calculation of the $H\to Z+\gamma$ amplitude
• Quantum scale invariance in gauge theories and applications to muon production
• Pitfalls of iterative pole mass calculation in electroweak multiplets
• Maximal transcendental weight contribution of scattering amplitudes
• Anapole Moment of Majorana Fermions and Implications for Direct Detection of Neutralino Dark Matter
• Color-octet scalar decays to a gluon and an electroweak gauge boson in the Manohar-Wise model
• Precise Estimate of Charged Higgsino/Wino Decay Rate
• Models with two Higgs doublets and a light pseudoscalar:a portal to dark matter and the possible $(\mathbf{g}-2{)}_{\mu }$ excess
• Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories
• Dark SU(2) Stueckelberg portal
• Radiative Correction to Lepton Proton Scatterings in Manifestly Lorentz-Invariant Chiral Perturbation Theory
• Distinctive signals of frustrated dark matter
• Probing Dark Matter Electromagnetic Properties in Direct Detection Experiments
• Positivity bounds at one-loop level: the Higgs sector
• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• The $q_{\mathrm{T}}$ and $\Delta {\varphi }_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities
• Scalaron Decay in Perturbative Quantum Gravity
• Positivity bounds in scalar-QED EFT at one-loop level
• $B\to K+\text{axion-like particles}$: effective versus UV-complete models and enhanced two-loop contributions
• Two-loop corrections to the Carroll-Field-Jackiw term in a CPT-odd Lorentz-violating scalar QED
• On two body gravitational scattering within perturbative gravit
• Multi-loop calculations: numerical methods and applications
• Matching the Standard Model to Heavy-Quark Effective Theory and Nonrelativistic QCD
• Black Holes in Einstein-scalar-Gauss-Bonnet model probed with scattering amplitudes
• Z and Higgs boson decays with doubly-charged scalars at one-loop: current constraints, future sensitivities, and application to lepton-triality models
• Squark production with R-symmetry beyond NLO at the LHC
• Dynamical Lorentz Symmetry Breaking in a Scale-free Theory of Gravity
• Ultra-Planckian quark and gluon scattering in agravity
• Complete two-loop Yukawa-induced running of the Higgs-gluon coupling in SMEFT
• Two-loop renormalization of the CPT-even Lorentz-violating Scalar QED
• Higgs pair production in gluon fusion to higher orders in Higgs Effective Field Theory
• Quark-Gluon Backscattering in the Regge Limit at One-Loop
• Dihadron Angular Correlations in the $e^{+}{e}^{-}$ Collision
• Electroweak boson production at large transverse momentum in double polarized $pp$ scattering at next-to-leading order accuracy
• Scattering amplitudes in dimensionless quadratic gravity coupled to QED
• A Catalog of First-Order Electroweak Phase Transitions in the Standard Model Effective Field Theory
• Rare Higgs Decay into a Photon and a Z Boson in Radiatively-Driven Natural Supersymmetry
• Confining Quark Model with General Yang-Mills Symmetry and Inadequate Faddeev-Popov Ghost
• On the physical running of the electric charge in a dimensionless theory of gravity