Evaluation of multi-loop multi-scale Feynman integrals for precision physics

Abstract

Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders will require three-loop electroweak and mixed electroweak-QCD corrections to single-particle production and decay processes and two-loop electroweak corrections to pair production processes, all of which are beyond the reach of existing analytical and numerical techniques in their current form. This article presents a new semi-numerical approach based on differential equations with boundary terms specified at Euclidean kinematic points. These Euclidean boundary terms can be computed numerically with high accuracy using sector decomposition or other numerical methods. They are then mapped to the physical kinematic configuration with a series solution of the differential equation system. The method is able to deliver 8 or more digits precision, and it has a built-in mechanism for checking the accuracy of the obtained results. Its efficacy is illustrated with examples for three-loop self-energy and vertex integrals and two-loop box integrals.

References in corpus (53)

• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Feynman Graph Amplitudes
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Automatized analytic continuation of Mellin-Barnes integrals
• Kira - A Feynman Integral Reduction Program
• Integral Reduction with Kira 2.0 and Finite Field Methods
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• Mixed QCD-electroweak corrections to Higgs boson production in gluon fusion
• FIESTA 4: optimized Feynman integral calculations with GPU support
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• Reconstructing Rational Functions with $\text{FireFly}$
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• A quasi-finite basis for multi-loop Feynman integrals
• epsilon: A tool to find a canonical basis of master integrals
• Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• Complete electroweak two-loop corrections to Z boson production and decay
• Multiloop corrections for collider processes using auxiliary mass flow
• A non-planar two-loop three-point function beyond multiple polylogarithms
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Measurement of the weak mixing angle using the forward-backward asymmetry of Drell-Yan events in pp collisions at 8 TeV
• The two-loop electroweak bosonic corrections to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$
• Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• How to choose master integrals
• Standard Model Theory for the FCC-ee Tera-Z stage
• Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC
• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case
• Mixed strong$-$electroweak corrections to the Drell$-$Yan process
• Determine Arbitrary Feynman Integrals by Vacuum Integrals
• Evaluation of Feynman integrals with arbitrary complex masses via series expansions
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Mixed electroweak-QCD corrections to $e^{+}{e}^{-}\to HZ$ at Higgs factory
• Mixed QCD-EW corrections for Higgs boson production at $e^{+}{e}^{-}$ colliders
• Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy
• Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• NLO Corrections to Light-Quark Mixed QCD-EW Contributions to Higgs Production
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\mathrm{MS}}$-pole quark mass relation
• Three-loop mixed QCD-electroweak corrections to Higgs boson gluon fusion
• Two-loop mixed QCD-EW corrections to $gg\to Hg$
• Evaluating multi-loop Feynman integrals numerically through differential equations
• Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion
• Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation
• On the evaluation of two-loop electroweak box diagrams for $e^{+}{e}^{-}\to HZ$ production

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• Tropical Feynman integration in the Minkowski regime
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Automatic computation of Feynman integrals containing linear propagators via auxiliary mass flow
• One-loop QCD helicity amplitudes for $pp\to t\bar{t}j$ to $O({\epsilon }^2)$
• Third order correction to semileptonic $b\to u$ decay: fermionic contributions
• Learning Feynman integrals from differential equations with neural networks
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• Electroweak double-box integrals for Moller scattering
• Evaluation of three-loop self-energy master integrals with four or five propagators
• Monte Carlo evaluation of divergent one-loop integrals without contour deformation
• Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations