SIRENA -- Sum-Integral REductioN Algorithm

2026/05/07 by Luis Gil, Javier López Miras, Adrián Moreno-Sánchez · 1 voice
Physics and Astronomy · #hep-ph

paper · pdf

Abstract

We present SIRENA, a Python and C++ implementation of the Laporta algorithm for the automatic reduction of multi-loop sum-integrals via integration-by-parts identities. The method builds on established techniques for zero-temperature Feynman integrals and extends them to finite-temperature quantum field theory by consistently accounting for the Matsubara sum structure. We validate the framework by reproducing several known results from the literature up to 3-loop order, and we further provide, for the first time, reductions for selected 3-loop fermionic sum-integrals. In addition to the package, we derive an analytic factorization formula for arbitrary 2-loop fermionic sum-integrals, extending on a previous result for the bosonic case.

Citations

• Gauge-independent treatment of electroweak phase transition
• Electroweak phase transition in SMEFT: gravitational wave and collider complementarity
• Perturbative aspects of the electroweak phase transition with a complex singlet and implications for gravitational wave predictions
• A new approach to determine the thermodynamics of deconfined matter to high accuracy
• Electroweak phase transition enhanced by a CP-violating dark sector
• Two decades of algorithmic Feynman integral reduction
• Singularity-Free Feynman Integral Bases
• Hot news on the phase-structure of the SMEFT
• Cosmological phase transitions without high-temperature expansions
• Interpreting the 95 GeV resonance in the Two Higgs Doublet Model: Implications for the Electroweak Phase Transition
• Non-perturbative determination of the sphaleron rate for first-order phase transitions
• Kira 3: integral reduction with efficient seeding and optimized equation selection
• Phase Transitions in Dimensional Reduction up to Three Loops
• The High-Temperature Limit of the SM(EFT)
• Higher-dimensional operators at finite-temperature affect gravitational-wave predictions
• Finite-temperature bubble nucleation with shifting scale hierarchies
• Quark matter at four loops: hardships and how to overcome them
• A Guide to Functional Methods Beyond One-Loop Order
• One Loop Thermal Effective Action
• Perturbative gravitational wave predictions for the real-scalar extended Standard Model
• A Catalog of First-Order Electroweak Phase Transitions in the Standard Model Effective Field Theory
• Investigating two-loop effects for first-order electroweak phase transitions
• The g⁶ pressure of hot Yang-Mills theory: Canonical form of the integrand
• First-order Electroweak phase transition at finite density
• Nonperturbative study of the electroweak phase transition in the real scalar singlet extended Standard Model
• A nonperturbative test of nucleation calculations for strong phase transitions
• Factorizing two-loop vacuum sum-integrals
• Higher orders for cosmological phase transitions: a global study in a Yukawa model
• Perturbative effective field theory expansions for cosmological phase transitions
• NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals
• Tackling the infamous g⁶ term of the QCD pressure
• A QCD Debye mass in a broad temperature range
• On the validity of perturbative studies of the electroweak phase transition in the Two Higgs Doublet model
• Nonperturbative analysis of the gravitational waves from a first-order electroweak phase transition
• Soft thermal contributions to 3-loop gauge coupling
• Electroweak phase transition in the ΣSM - I: Dimensional reduction
• Three-dimensional effective theories for the two Higgs doublet model at high temperature
• Nonperturbative Analysis of the Electroweak Phase Transition in the Two Higgs Doublet Model
• Kira - A Feynman Integral Reduction Program
• Dimensional reduction of the Standard Model coupled to a new singlet scalar field
• Debye screening mass of hot Yang-Mills theory to three-loop order
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• A new three-loop sum-integral of mass dimension two
• A fresh look on three-loop sum-integrals
• IBP methods at finite temperature
• Three-loop matching coefficients for hot QCD: Reduction and gauge independence
• Open problems in hot QCD
• FeynRules – Feynman rules made easy
• Four-loop screened perturbation theory
• Four-loop pressure of massless O(N) scalar field theory
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• Asymptotic expansion of Feynman integrals near threshold
• Where the electroweak phase transition ends
• Is There a Hot Electroweak Phase Transition at m_H\gsim m_W?
• The Three-Loop Free Energy for High-Temperature QED and QCD with Fermions
• The Three-Loop Free Energy for Pure Gauge QCD
• The Three Loop Equation of State of QED at High Temperature
• The Effective Potential and First-Order Phase Transitions: Beyond Leading Order
• Integration by parts: The algorithm to calculate β-functions in 4 loops

Discussions

• Peter's Acronym of the Day: SIRENA -- Sum-Integral REductioN Algorithm arxiv.org/abs/2605.06775 [bsky, 0 points, 0 comments]

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