New Developments in MadGraph/MadEvent
ABSTRACT We here present some recent developments of MadGraph/MadEvent since the latest published version, 4.0. These developments include: Jet matching with Pythia parton showers for both Standard Model and Beyond the Standard Model processes, decay chain functionality, decay width calculation and decay simulation, process generation for the Grid, a package for calculation of quarkonium amplitudes, calculation of Matrix Element weights for experimental events, automatic dipole subtraction for next-to-leading order calculations, and an interface to FeynRules, a package for automatic calculation of Feynman rules and model files from the Lagrangian of any New Physics model.
- SourceAvailable from: ArXivPhysical review D: Particles and fields 02/2011; 84.
- Physical review D: Particles and fields 05/2009;
- Physical review D: Particles and fields 12/2009;
New Developments in MadGraph/MadEvent
J. Alwall∗, P. Artoisenet†, S. de Visscher†, C. Duhr†, R. Frederix†, M. Herquet†and
∗SLAC, Stanford University, Menlo Park, CA 94025, E-mail: email@example.com
†Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
Abstract. We here present some recent developments of MadGraph/MadEvent since the latest published version, 4.0. These
developments include: Jet matching with Pythia parton showers for both Standard Model and Beyond the Standard Model
processes, decay chain functionality, decay width calculation and decay simulation, process generation for the Grid, a package
for calculation of quarkonium amplitudes, calculation of Matrix Element weights for experimental events, automatic dipole
subtraction for next-to-leading order calculations, and an interface to FeynRules, a package for automatic calculation of
Feynman rules and model files from the Lagrangian of any New Physics model.
Keywords: Monte Carlo Simulations, Beyond the Standard Model, New Physics, Matrix Element
PACS: 24.10.Lx, 13.85.Hd, 12.60.-i
With the imminent start of full-scale operation of the
LHC experiment, it has become increasingly important
to have efficient and versatile simulation tools, for
New Physics signals as well as Standard Model back-
grounds. Much effort has gone into the development
of new tools in recent years, resulting in a number of
packages addressing different issues. These include a
new generation of general-purpose tools (Sherpa,
Pythia8, Herwig++), automatized matrix ele-
ment generators and event generators (AlpGen,
MadGraph/MadEvent), and next-to-leading order
event generators (MCFM, MC@NLO).
MadGraph/MadEvent  is a fully automatized tool
for generation of cross sections and unweighted events
for processes, both in the Standard Model and for mod-
els of New Physics. MadGraph  takes as input a
process, specified in a simple syntax, and a model def-
inition. It is also possible to specify multi-particle la-
bels, the maximum order in the different couplings
(e.g. QCD and QED), and require or exclude inter-
mediate s-channel particles. MadGraph then produces
all Feynman diagrams for this process and all sub-
processes, as well as its matrix element expression in
the form of a Fortran subroutine with calls to the he-
licity amplitude library HELAS . MadEvent 
is used to perform the phase space integration of the
process (including any specified cuts) and produces
weighted and unweighted events, using a technique
dubbed “Single-diagram-enhanced multichannel integra-
tion”, which gives high unweighting efficiencies also for
multi-particle final states. This technique has the addi-
tional advantage that it is trivially parallelizable to run
on multi-processor clusters. Events are output to a text
file following the Les Houches Accord for event genera-
tion , and interfaces to Pythia , Herwig  and
PGS  allows for parton showering, hadronization and
fast detector simulation.
Event generation with MadGraph/MadEvent can be
done online over the Internet, on any of several dedicated
computer clusters around the world, using a simple but
powerful web interface. It is also possible to download
the source code to compile and run locally. Complete
event simulation using Pythia and PGS can be done
online, directly or in stages.
In version 4.0 of MadGraph/MadEvent , the structure
of MadGraph/MadEvent was modified to allow for im-
plementation of further models than the Standard Model,
and new models were implemented, including several
simple extensions of the Standard Model as well as the
completely general Two Higgs Doublet Model  and
the MSSM [20, 21]. Also a simple semi-automatized
framework for addition of user-defined extensions of the
Standard Model was provided. Automatization of the in-
clusion of new models in MG/ME has now been fur-
ther extended with the introduction of the interface to the
FeynRules package , see below.
Developments since version 4.0 include:
• Jet matching/merging between MG/ME and Pytha
parton showers for Standard Model  and Be-
yond the Standard Model processes [24, 25]
arXiv:0809.2410v1 [hep-ph] 14 Sep 2008
• Decay chain functionality, which generates only
the diagrams consistent with a specified decay
• Particle decay width calculation and decay simula-
tion directly in MG/ME 
• Creation of MadEvent process packages suitable for
event generation on the Grid 
• A repository of LHC events and Grid packages
for important Standard Model backgrounds to New
• MadOnium, calculation of quarkonium amplitudes
in NRQCD 
• MadWeight, a package for calculation of Matrix
Element weights of experimental events 
• MadDipole, automatic dipole subtraction for next-
to-leading order real correction calculations 
• Interface to FeynRules, a Mathematica package for
automatic calculation of Feynman rules and cre-
ation of event generator files directly from the La-
grangian of any New Physics model 
In the following we will discuss some of these devel-
opments in greater detail.
bremsstrahlung emissions has traditionally been done
using Parton Shower (PS) Monte Carlo programs such
as Pythia and Herwig, which describe parton radiation as
successive parton emissions using the soft and collinear
limit. This description is formally correct only in the
limit of soft and collinear emissions, but has been shown
to give a good description of much data also relatively
far away from this limit. However, for the production
of hard and widely separated jets in connection with
heavy particle production, this description breaks down
due to the lack of subleading terms and interference.
For that case, it is necessary to use the full tree-level
amplitudes for the heavy particle production plus addi-
tional partons. This description, however, diverges as
partons become soft or collinear. In order to describe
both these areas in phase space, the two descriptions
must be combined, without double counting or gaps
between different multiplicities. An additional physical
requirement is that such a procedure gives smooth dis-
tributions, and interpolates between the parton shower
description in the soft and collinear limits and the matrix
element description in the limit of hard and widely
separated partons. Several procedures have been pro-
posed, including the CKKW [34, 35], Lönnblad  and
Mangano  schemes. These different procedures are
in substantial agreement and give consistent results at
hadron colliders [23, 38].
Two matching schemes are implemented in Mad-
Graph/MadEvent interfaced to Pythia. The first is a ver-
sion of the Mangano scheme, but using kT jets instead
of cone jets in the jet matching step. The details of this
scheme is described in sec. 2.4 of . This scheme
now works with both the “old” (virtuality-ordered) and
the “new” (pT-ordered) Pythia parton showers. The sec-
ond is a new scheme, which uses the feature of the pT-
ordered parton showers of Pythia 6.4 that it stores the
kT of the first emission in the parton shower in a com-
mon block. An event is generated by MadEvent, with
QCD emission αsvalues calculated as done in the par-
ton shower, using the kT values of the event clustered
with the kT algorithm (as described in ). The event
is passed to Pythia and showered using the pT-ordered
shower, which reports the kT value of the first emis-
scale Qmatch, and the event is discarded if QPS
The exception is for the highest parton multiplicity sam-
ple, where the event is discarded only if QPS
than the lowest kT value in the matrix element multi-
parton event. This matching scheme, although simple,
effectively mimics the workings of the kT-jet Mangano
scheme. However, it more directly samples the Sudakov
form factor used in the shower. Furthermore, the treat-
ment of the highest multiplicity sample more closely
mimics that used in the CKKW matching scheme.
Both these schemes can be used in the Standard Model
ing in Beyond the Standard Model processes was re-
duction at the Tevatron [39, 40], where it was noted that
inclusion of Matrix Element corrections is crucial in the
to a near-degenerate LSP, and hence producing only soft
jets. In this case, the only way to generate large missing
transverse energy is when the whole gluino pair center-
of-mass system is boosted in the transverse direction due
to hard initial-state radiation, which is well described
only using jet matching.
Further studies of the effects of matching of jets in
gluino and squark production are underway, see [24, 25].
max. This value is then compared to the matching
For precision studies of production and decay of new
particles, many features can be important. In particular,
using kinematical differences in decay chains due to dif-
ferences of spins of the intermediate particles. For exam-
ple, studies have shown that invariant masses between
be generated using the decay chain functionality of Mad-
An example of a decay chain that can
lepton pairs  and leptons and b jets  can be used
to differentiate between Supersymmetry and Universal
Extra Dimensions. However, in order to correctly cap-
ture these differences in simulations, it is necessary that
the simulations keep the full spin correlations in the de-
cays. Also other effects can be important, such as finite-
width effects and interference effects from non-resonant
Since MadGraph/MadEvent uses the full set of Feyn-
man diagrams for any process, it automatically keeps all
spin correlations, as well as finite-width effects and inter-
ference effects. However, running MadGraph for many
final state particles has been forbiddingly slow, due to the
large number of diagrams and diagram topologies. This
situation has now been considerably improved through
the introduction of the new decay chain functionality,
which radically reduces diagram generation times for de-
cay chain-type processes, and allows for up to 10 exter-
nal particles in a process. An example of such a process
is shown in Fig. 1. This process can be specified using
the following syntax:
gg > (go > u (ul > un1))(go > b (b1 >
(b(n2 > mu+(mul− > mu−n1)))))
(without line break.) Only diagrams conforming to this
decay chain specification are generated. In the subse-
quent MadEvent event generation, all specified interme-
diate resonances are forced to be onshell (i.e., have a vir-
tuality at most a given number of widths off their pole
This technique for simulating decay chains has a num-
ber of advantages over conventional simulation methods:
• The full matrix element is used, automatically keep-
ing all spin correlations in production and decay
• Particle widths are correctly taken into account
• 1 → N decays are possible while still keeping all
• Non-resonant contributions can be included only
where they are relevant
It might be worthwhile to note that although this gen-
eration is considerably faster than generation of the full
multi-final state matrix element including all interfering
diagrams, it is still slower than the conventional genera-
tion of the central process with consecutive decays done
in a second step. For scalar particle production in par-
ticular, where no spin correlations are needed, it is more
efficient to use the MadGraph decay chain formalism up
to the production of the scalar particles, and then per-
form the decay of the scalar particles using some decay
tool such as BRIDGE  or the MadGraph/MadEvent
decay width functionality, described below.
As a complement to the decay chain formalism de-
scribed above, we have also implemented the calculation
of partial decay widths and simulation of decay for un-
stable particles. This is done by specifying the process
according to the syntax
A > BCD...
which indicates the decay of particle A to particles
BCD.... Multiparticle labels can be used as usual for
the decay products. When now MadEvent is run, it will
present the partial decay width instead of the cross sec-
tion, and generate events corresponding to the decay of
A in its rest frame. These decays can subsequently be
boosted and combined with an event file describing pro-
duction of A particles.
MadWeight  is a package, built on top of Mad-
Graph, to find the Matrix Element weight of experimen-
tal events for a large set of processes. This procedure,
also called the Matrix Element method, is aimed at de-
termining a set of free parameters α of a given theory
from a data sample. It maximizes the information that
can be extracted from the detector by defining for each
observed event x a conditional weight P(x|α) that quan-
tifies the agreement between the theoretical model with
parameters α and the experimental event x. In the defini-
tion of the weights, the parton-level high-energy collsion
is factorized from the detector-level event, by introduc-
ing the parton-level configuration y with a weight given
by the squared matrix element |Mα(y)|2. The evolution
of this parton-level configuration y into a reconstructed
event x in the detector is taken into account by a trans-
fer function W(y,x). As a result, the weight of a specific
150 155 160
likelihood (mtop=160 GeV)
of 20 Monte Carlo t¯ t events (semi-leptonic channel).
Extraction of the top quark mass from a sample
event x is of the form
where f1(w1)and f2(w2)arethepartondistributionfunc-
tions. The normalization by the total cross section σαen-
sures that P(x|α) is a probability density. Once the prob-
ability density P(xi|α) has been computed for each event
xi, the most likely value for α can be obtained through a
likelihood maximization method.
The numerical evaluation of the weights P(x|α) is in
general very complicated, since both the squared matrix
element and the transfer function are highly non-uniform
over the phase space. For an efficient Monte Carlo in-
tegration, phase-space points must be generated accord-
ing to the peak structure of the integrand. Therefore, a
specific phase-space generator, tuned to the shape of the
transfer function and the squared matrix element, is re-
quired. MadWeight decomposes the phase space topol-
ogy into substructures, where an efficient integration can
be achieved through suitable parametrizations.
Fig 2 provides an example of result that can be ob-
tained with MadWeight. The top-quark mass is extracted
from a (MC) sample of 20 t¯ t events with one lepton in
the final state, with mt= 160 GeV in the simulation. The
weights are computed with MadWeight and combined to
get the likelihood displayed in Fig. 2. The value of the
reconstructed mass of the top quark is 158.9±2.3 GeV.
include any pair-production processes with decay chains.
Also processes with three or more particles produced in
the central interaction can be handled, such as pair pro-
duction processes with radiation of an additional parton.
This provides for a large versatility and will allow for
Matrix Element methods to be used for many new types
MadDipole  is a tool for automatic calculation of
dipole-subtracted real corrections to next-to-leading or-
der calculation. Any next-to-leading (NLO) computation
in QCD includes the calculation of real contributions,
with the emission of an additional parton, and virtual
contributions, also called loop terms. In general these
suffer from soft and/or collinear singularities, which only
cancel after all contributions are summed. Because the
real contributions have one more particle in the final
state, numerical integrations over the phase spaces of the
real and virtual contributions need to be done indepen-
dently, and hence the divergencies must be extracted in
a form where their cancellation is explicit. One solution
to remove the divergences due to the phase space inte-
gration in the real contribution, is the subtraction scheme
proposed by Catani and Seymour . In this method,
the Born contribution times a dipole function is added to
both the real and the virtual contributions, schematically
where dσreal, dσBornand dσvirt.are the real, Born and
virtual matrix elements, respectively, and D is the dipole
function. The dipole functions are defined in such a
way that the real term plus subtraction term and the
virtual plus subtraction term are separately finite, and
the contributions from the subtraction terms cancel in the
sum of the real and virtual contributions.
MadDipole fully automatizes the calculation of the
dipole subtraction terms for massless and massive par-
tons in the MadGraph/MadEvent framework. The im-
plementation is done in such a way that the user only
needs to specify the desired (n+1)-particle process, and
MadDipole then returns a Fortran code for calculating all
dipoles, combined with possible Born processes which
can lead to the (n+1) process specified by the user. This
automation of the calculation of subtraction terms also
for the virtual contributions is underway.
Particles, symmetries, ...
Logical organization of FeynRules.
Interface to FeynRules
FeynRules  is a new package based on Mathe-
matica®1which takes a model file with the Lagrangian
as input and derives the interaction vertices associated
with this Lagrangian. The underlying algorithm, based
on canonical quantization formalism, is suitable not only
for renormalizable theories, but allows the derivation of
the Feynman rules in effective theories involving higher-
dimensional operators as well, which makes the package
a useful tool for developing models containing the SM as
a low-energy effective theory.
The basic input a user provides when implementing
his/her model into FeynRules is the so called model file,
a text file containing all the properties of the model (par-
using standard Mathematica commands, augmented by
some new symbols like Dirac matrices, which are neces-
sary when writing down a Lagrangian. The information
contained in the model file, together with the interaction
vertices computed inside Mathematica, are stored in a
generic format which is suitable for any further process-
ing of this information. In a second step, FeynRules can
translate this generic model (with the vertices) into the
model format of choice and allows in this way to imple-
ment the new model in any tool for which such an inter-
face exists. The organization of FeynRules is visualized
in Fig. 3.
This approach allows FeynRules to go beyond previ-
ous packages with similar functionality in several ways:
1. FeynRules is not tied to any existing Feynman dia-
2. The generic model format of FeynRules is suitable
to be translated to any other format.
1Mathematica is a registered trademark of Wolfram Research, Inc.
3. The user may choose his favorite Feynman diagram
calculator, according to the strength and advantages
of the latter.
4. The underlying Mathematica structure allows a
“theorist-friendly” environment, which makes the
package useful as a “sandbox” to develop new mod-
Graph/MadEvent and Sherpa, and more interfaces
will be added in the future.
idate the code, and extensive testing to check the inter-
faces is currently ongoing both between the output of
different Matrix Element generators using the results of
models. In particular the Standard Model and a higgs-
less three-site model have been carefully checked in this
way, to ensure the correctness of the package, and further
checks are ongoing for the MSSM and extradimensional
interfaces havebeen writtenfor
With the recent developments of, and additions to, Mad-
Graph/MadEvent, the package has taken several further
steps towards a full-fledged simulation tool for physics
beyond the Standard Model. These developments in-
clude, in particular, the FeynRules package which allows
easy implementation of any new model into MG/ME;
calculation of decay widths and decays for any model,ei-
directly; simulation of decay chain events, keeping full
spin correlations and finite width effects; matching of
jets between MG/ME multiparton generation and Pythia
parton showers; and not least the analysis of data events
using matrix element techniques. MG/ME can now fur-
thermore be used directly as a tool for simulations of the
real corrections to next-to-leading order QCD calcula-
tions for multiparticle processes in any model. Large-
scale simulations can be done using the Grid with the
new grid-pack functionality, which is especially impor-
tant for Standard Model background event generation.
The MadGraph/MadEvent philosophy includes a
strong emphasis of building a user community, not only
through fast response to questions and bugs, but also
by continuously develop the software and implement
requested features and functionalities. We also welcome
and support external efforts such as model implementa-
tions and development of external packages and tools.
And not least, we provide public clusters with personal
process databases, a Twiki site for communication, an
open CVS repository and, naturally, completely open
J.A. wishes to thank the organizers of SUSY08 for the
invitation and the generous support. J.A. is supported by
the Swedish Research Council.
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