UFO – The Universal FeynRules Output

Abstract

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.

Introduction

Monte Carlo simulations of the physics to be observed at the Large Hadron Collider (LHC) at CERN play a central role in the exploration of the electroweak scale, both from the experimental point of view of establishing an excesses over the expected Standard Model (SM) backgrounds as well as from the phenomenological point of view by providing possible explanations for the observations. For this reason, activities in the field of Monte Carlo simulations have been rather intense over the last fifteen years, resulting in many advances in the field. Automated tree-level matrix-element generators, such as Alpgen [1], Comix [2], CompHep/CalcHep [3], [4], [5], Helac [6], Herwig [7], [8], MadGraph/MadEvent [9], [10], [11], [12], [13], Sherpa [14], [15], or Whizard [16], [17], describing the hard scattering processes where the Beyond the Standard Model (BSM) physics is expected to show up have been developed. As a consequence, the problem of the automatic generation of tree-level matrix elements for a large class of Lagrangian-based BSM theories is solved, at least in principle.

Due to the numerous existing BSM theories based on ideas in constant evolution, the implementation of these models into Monte Carlo event generators remains a tedious and error-prone task. Feynman rules associated with a given BSM model must be derived and then implemented one at the time into the various codes, which often follow their own specific conventions and formats. A first step in the direction of automating this procedure by starting directly from the Lagrangian of the model has been made in the context of the LanHep package [18] linked to the CompHep and CalcHep programs. Recently, a new efficient framework going beyond this scheme has been developed. It is based on the FeynRules package [19], [20], [21], [22] and proposes a general and flexible environment allowing to develop a model, investigate its phenomenology and eventually confront it to data. Its virtue has been illustrated in the context of the CompHep/CalcHep, FeynArts/FormCalc [23], MadGraph/MadEvent, Sherpa and Whizard programs, by implementing several new physics theories in FeynRules and then passing them to the different tools for a systematic validation procedure. The approach is based on a modular structure where each node consists in an interface to a dedicated matrix-element generator. Since the latter have in general hard-coded information regarding the supported Lorentz and/or color structures, the interfaces check whether a given vertex is compliant with a given matrix-element generator, in which case the vertex is written to file in a format suitable for the generator. The final output consists then in a set of text files that can be used in a similar way to any other built-in model.

The procedure spelled out above, where communication between FeynRules and the matrix-element generators proceeds exclusively via a set of well-defined text files that must be parsed and interpreted, has some serious limitations. In particular, extending the format to include more general structures, like higher-dimensional operators and/or non-standard color structures, is difficult to incorporate into a static text-based format. In this paper we present a new format, dubbed the Universal FeynRules Output or the UFO, for model files that goes beyond existing formats in various ways. The format is completely generic and, unlike existing formats, it does not make any a priori assumptions on the structures that can appear in a model. The aim is to provide a flexible format, where all the information about a model is represented in an abstract form that can easily be accessed by other tools. The information on the particles, parameters and vertices of the model are stored in a set of Python objects, each of them being associated with a list of attributes related to their properties. This way of representing the model information has some benefits over the more traditional plain text table-based format, because it allows, e.g., to add a missing piece of information directly as a new attribute to an existing object. As an example, extending a table-based format to accommodate higher-point vertices requires to change the format of the table and to adapt the readers for the table accordingly. In an object-oriented format like the UFO, the same extension is trivial, as the number of particles entering a vertex is just an attribute of the vertex, so no extension of rewriting of the readers is necessary. Presently, the UFO format is already used by the MadGraph version 5 [13] and the GoSam generators [24], [25], [26], and will be used in a near future by Herwig++.

The paper is organized as follows. In Section 2, we describe the features of the UFO format as a stand-alone Python module, while Section 3 addresses the automation of writing an UFO model through FeynRules. Section 4 is dedicated to the UFO features beyond tree level and in Section 5, we provide an example of how to implement a model containing non-trivial Lorentz structures with the help of FeynRules into MadGraph 5. Our conclusions are drawn in Section 6.