FEDILA
Automated calculation of Feynman Diagrams on the Lattice
Project Summary: FEDILA is a pioneering software solution designed to revolutionize analytic computations of the fundamental forces in the universe. Its design focuses on optimizing computations in the continuum but also in a discreted version of the theory on a spacetime lattice. FEDILA provides a flexible Mathematica package capable of handling a diverse spectrum of renormalization schemes, including a continumm Gauge Invariant Renormalization Scheme, as well as of extracting information from Supersymmetric Theories. This adaptability underlines the project's readiness to calculate Feynman diagrams across various renormalization schemes, for different theories, and for a variety of regularizations, such as dimensional and lattice. The primary goal of FEDILA is the utilization of Graph Theory principles. This intelligently designed methodology offers exceptional efficiency in perturbative computations, simplifying the time-consuming processes of calculations. The development of this software package will enrich our existing set of programs to encompass supersymmetric fields and incorporate features of improved lattice actions, as well as computations of Feynman diagrams beyond one-loop order. Written in the symbolic language Mathematica, the impact of FEDILA extends beyond research methodologies. The automation not only accelerates research processes but also enables professionals to explore different theories in-depth, such as Quantum Chromodynamics, Quantum Electrodynamics, and their supersymmetric versions. Through the automation of complex computations of Quantum Field Theories, FEDILA promotes richer educational experiences, providing researchers with a deeper understanding of the fundamental principles of the interaction of the subatomic particles and the properties of composite ones such as baryons, mesons and other supersymmetic theoretical particles.
Details:
| Programme | PROOF OF CONCEPT FOR TECHNOLOGY / KNOWHOW APPLICATIONS |
|---|---|
| Proposal Number | CONCEPT/0823/0052 |
| Proposal Acronym | FEDILA |
| Funding | Research and Innovation Foundation, Cyprus |
Paper: Gauge-invariant renormalization of four-quark operators
We study the renormalization of four-quark operators in one-loop perturbation theory. We employ a coordinate-space gauge-invariant renormalization scheme (GIRS), which can be advantageous compared to other schemes, especially in nonperturbative lattice investigations. From our perturbative calculations, we extract the conversion factors between GIRS and the modified minimal subtraction scheme (MS) at the next-to-leading order. As a by-product, we also obtain the relevant anomalous dimensions in the GIRS scheme. A formidable issue in the study of the four-quark operators is that operators with different Dirac matrices mix among themselves upon renormalization. We focus on both parity-conserving and parity-violating four-quark operators, which change flavor numbers by two units (ΔF = 2). The extraction of the conversion factors entails the calculation of two-point Green’s functions involving products of two four-quark operators, as well as three-point Green’s functions with one four-quark and two bilinear operators. The significance of our results lies in their potential to refine our understanding of QCD phenomena, offering insights into the precision of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and shedding light on the nonperturbative treatment of complex mixing patterns associated with four-quark operators.
Code: Automating Feynman diagrams in Quantum Field Theories
This file contains Mathematica command files (.m files) necessary for automating the computation of Feynman diagrams in Quantum Field Theories.