Source-linked AI summary
UFO - The Universal FeynRules Output
Céline Degrande, Claude Duhr, Benjamin Fuks, David Grellscheid, Olivier Mattelaer, Thomas Reiter
TL;DR
Existing BSM implementations require laborious, generator-specific translation, while text-based formats constrain the model structures they can represent. The paper introduces UFO, a generator-independent Python module produced automatically from FeynRules, and presents it as a generic format that preserves model information for direct linkage to matrix-element generators.
Problem
Implementing evolving BSM theories across matrix-element generators is tedious and error-prone because generators use different conventions and text formats struggle with general structures.
Method
UFO encodes particles, parameters, vertices, and related model information as abstract Python objects in a standalone, generator-independent module, with automatic output through FeynRules.
Results
UFO provides a generic model format that is not tied to a specific matrix-element generator and can accommodate arbitrary reasonable particle-physics model structures.
Takeaways & Limitations
The UFO interface preserves all model vertices and leaves generator-specific decisions about which structures are allowed to the matrix-element generator.
Takeaways & Limitations
The SILH example is truncated at O(ξ), so amplitudes of order O(ξ^n) with n ≥2 are generally unreliable without corresponding higher-order Lagrangian terms.
Abstract
from arXiv · showhide
We present a new model format for automatized matrix-element generators, the so- called Universal FeynRules Output (UFO). The format is universal in the sense that it features compatibility with more than one single generator and is designed to be flexible, modular and agnostic of any assumption such as the number of particles or the color and Lorentz structures appearing in the interaction vertices. Unlike other model formats where text files need to be parsed, the information on the model is encoded into a Python module that can easily be linked to other computer codes. We then describe an interface for the Mathematica package FeynRules that allows for an automatic output of models in the UFO format.
1 Introduction
Monte Carlo simulations are central to LHC physics, but implementing evolving BSM models across generators remains tedious and error-prone. UFO addresses these limitations with a generic, flexible model format encoded as accessible Python objects.
- Monte Carlo simulations support both searches for excesses over Standard Model backgrounds and phenomenological explanations of LHC observations.
- Implementing BSM models remains tedious because Feynman rules must be derived and separately adapted to generators with differing conventions and formats.
- Existing text-file interfaces are difficult to extend to higher-dimensional operators and non-standard color structures.
- UFO removes a priori assumptions about model structures by representing particles, parameters, and vertices as Python objects with extensible attributes.
2 The UFO format
The UFO format encodes particle-physics models as generator-independent Python modules, representing particles, parameters, interactions, and reusable structures without assuming specific model content. Its classes and linked object lists provide a modular implementation for matrix-element generators.
- 2 The UFO format: UFO represents model information as abstract Python objects in a standalone module that can link directly to matrix-element generators without modification.The format is generator-independent rather than tied to a specific generator’s conventions.
- 2 The UFO format: A UFO model separates identical model-independent Python modules from model-dependent files defining particles, parameters, vertices, couplings, Lorentz structures, and coupling orders.The model-independent files define shared classes, while model-dependent files instantiate the model content.
- 2.1 Initialization and structure of the objects and functions: The __init__.py file imports the complete model and links lists containing all particles, vertices, couplings, Lorentz structures, parameters, coupling orders, and functions.Creating an object instance automatically adds it to the corresponding list, enabling downstream access to the full model content.
- 2.1 Initialization and structure of the objects and functions: The core UFO implementation uses Particle, Parameter, Vertex, Coupling, Lorentz, and CouplingOrder classes derived from UFOBaseClass.The common base class supplies shared methods and attributes, including access to instance attributes such as a particle’s charge.
- 2.1 Initialization and structure of the objects and functions: User-defined functions are represented by Function objects with name, arguments, and expression attributes, while the library supplies functions such as complex conjugation and cosecant.Only functions expressible as single-line Python lambda functions are supported as user-defined functions.
- 2.2 Implementation of the particle content of a model: Particles are defined as Particle instances using mass eigenstates, with mandatory identity and quantum-number attributes plus optional model-dependent additive quantum numbers.The particle name identifies the object, while name and antiname are identical for self-conjugate particles.
- 2.4 Implementation of the interactions of the model: Vertices use reusable color and Lorentz tensors as bases, with couplings serving as coordinates for expressing interactions among particle objects.Color tensors are listed in the color attribute, while Lorentz structures are represented by Lorentz objects and listed in the lorentz attribute.
- 2.5 Controlling various types of couplings in a perturbative expansion: Coupling orders constrain the maximal number of couplings of a given type and classify interaction types by relative strength through integer hierarchies.The default maximal order is 99, and the example assigns QCD hierarchy 1 and QED hierarchy 2.
3 The FeynRules UFO interface
The FeynRules UFO interface automates exporting model information and vertices into the generator-independent UFO format. Unlike other FeynRules interfaces, it retains all model vertices and leaves generator-specific filtering to the matrix-element generator.
- Automated export: FeynRules can export a model directly to UFO, avoiding manual entry of every vertex.The interface uses the model’s particle and parameter information together with its interaction vertices.
- Coupling controls: The interface supports coupling-order controls through optional hierarchy and expansion settings, with defaults of 1 and 99 when unspecified.Expansion order limits the number of couplings of a type in a process, while hierarchy classifies interaction strengths.
- Automated export: WriteUFO takes one or more model Lagrangians plus interface options and internally computes their associated vertices.After obtaining the Feynman rules, FeynRules decomposes vertices into color ⊗ spin structures and identifies Lorentz and Coupling objects before writing the UFO files.
- Generator independence: The UFO interface is generator-agnostic and writes all model vertices, including structures that a particular matrix-element generator may not support.The downstream generator is responsible for deciding which vertices it can process.
4 The UFO format beyond tree level
The UFO format extends beyond tree-level calculations by representing renormalization information and counterterm vertices in a generator-independent way. The prescription supports perturbative expansions in multiple coupling constants, while relying on stated renormalization assumptions.
- Beyond tree level: The UFO format is not restricted to tree-level generators and has been interfaced with the one-loop generator GoSam.The interface translates UFO model information into model definitions for QGraf and Form; the paper reports applications to simple one-loop MSSM calculations.
- Renormalization data: Renormalization constants are represented as Laurent series in ǫ under dimensional regularization and can be associated with parameters and fields.Parameter counterterms use a counterterm attribute, while field renormalization constants are added to the Particle class.
- Perturbative expansion: The prescription supports corrections organized by arbitrary powers of multiple coupling constants, with only a small subset of expansion coefficients generally nonzero.The interaction-order attribute tracks the tree-level coupling power and excludes additional powers introduced by the perturbative sum.
- Counterterm representation: Counterterm interactions are encoded as two-point propagator counterterms and additional counterterm vertices with associated couplings.These objects are stored in ctvertices.py and ctcouplings.py, using the UFO Vertex and Coupling classes.
- Scope and extensions: The amendments provide the information needed for matrix-element generators to compute ultraviolet counterterms and may also accommodate rational R2 terms.The paper notes that the counterterm basis need not be unique and assumes zero on-shell particle mixing, with propagator mixing represented by two-point vertices.
5 An example
The SILH example demonstrates how UFO represents non-trivial Lorentz structures, coupling orders, and higher-dimensional interactions for matrix-element generation. It also validates the implementation while identifying the truncation boundary of the effective Lagrangian.
- 5 An example: A UFO vertex stores the particles, color structure, Lorentz structures, and couplings, allowing the HWW interaction to retain multiple non-standard terms.The example lists three Lorentz structures and separates their associated coupling coefficients.
- 5 An example: The SILH model extends Standard Model interactions through dimension-six operators and provides a test case for non-trivial Higgs interactions.The example focuses on the Higgs decay into two W bosons and uses the corresponding FeynRules implementation.
- 5 An example: Interaction orders separate Standard Model and new-physics contributions, enabling the SILH–Standard Model interference to be extracted from the relevant combinations.The interference is obtained by subtracting the pure Standard Model and pure SILH contributions from the combined contribution.
- 5 An example: Because the SILH Lagrangian is truncated at O(ξ), amplitudes at O(ξ^n) for n ≥2 are generally unreliable without adding higher-order terms.The W+W−→HH example contains two NP=1 vertices but also requires a missing O(ξ2) contribution.
- 5 An example: MadGraph 5 is used to validate the UFO model by computing the Higgs partial width into two W bosons with a dominant higher-dimensional contribution.The result is compared with hand-made analytical calculations, and the example relies on MadGraph’s Aloha module for higher-dimensional operators.
6 Conclusion
The conclusion presents UFO as a generator-independent Python-based model format designed to avoid assumptions about particle-physics interaction structures. It emphasizes extensibility beyond currently implemented color representations and support for Les Houches conventions.
- 6 Conclusion: UFO encodes model information in abstract Python classes that can accommodate reasonable particle-physics models without fixed color or Lorentz-structure assumptions.This distinguishes it from traditional table-based model formats used by many Monte Carlo codes.
- 6 Conclusion: The format is generator-independent, allowing the same model representation to be linked to existing matrix-element generators.UFO stores model information in a standalone Python module rather than a generator-specific format.
- 6 Conclusion: Although UFO currently implements only several color representations, extending it to more exotic QCD representations is described as straightforward without changing the format itself.The conclusion contrasts this extensibility with the difficulty of making similar changes in table-based formats.