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New Developments in MadGraph/MadEvent

J. Alwall∗, P. Artoisenet†, S. de Visscher†, C. Duhr†, R. Frederix†, M. Herquet†and

O. Mattelaer†

∗SLAC, Stanford University, Menlo Park, CA 94025, E-mail: alwall@slac.stanford.edu

†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

INTRODUCTION

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[1],

Pythia8[2], Herwig++[3]), automatized matrix ele-

ment generators and event generators (AlpGen[4],

CompHEP[5]/CalcHEP[6],

MadGraph/MadEvent[9]), and next-to-leading order

event generators (MCFM[10], MC@NLO[11]).

MadGraph/MadEvent [9] 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 [12] 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 [13]. MadEvent [14]

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-

Helac[7], Whizard[8],

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 [15], and interfaces to Pythia [16], Herwig [17] and

PGS [18] 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.

RECENT DEVELOPMENTS

In version 4.0 of MadGraph/MadEvent [9], 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 [19] 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 [22], see below.

Developments since version 4.0 include:

• Jet matching/merging between MG/ME and Pytha

parton showers for Standard Model [23] and Be-

yond the Standard Model processes [24, 25]

arXiv:0809.2410v1 [hep-ph] 14 Sep 2008

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• Decay chain functionality, which generates only

the diagrams consistent with a specified decay

chain [26]

• Particle decay width calculation and decay simula-

tion directly in MG/ME [27]

• Creation of MadEvent process packages suitable for

event generation on the Grid [28]

• A repository of LHC events and Grid packages

for important Standard Model backgrounds to New

Physics [29]

• MadOnium, calculation of quarkonium amplitudes

in NRQCD [30]

• MadWeight, a package for calculation of Matrix

Element weights of experimental events [31]

• MadDipole, automatic dipole subtraction for next-

to-leading order real correction calculations [32]

• 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 [33]

In the following we will discuss some of these devel-

opments in greater detail.

Jet matching

The simulation of jetproductionfromQCD

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 [36] and

Mangano [37] 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 [23]. 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 [23]). The event

is passed to Pythia and showered using the pT-ordered

shower, which reports the kT value of the first emis-

sion QPS

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

aswellasinprocessesinvolvingNewPhysics.Jetmatch-

ing in Beyond the Standard Model processes was re-

centlyusedinastudiesofmodel-independentgluinopro-

duction at the Tevatron [39, 40], where it was noted that

inclusion of Matrix Element corrections is crucial in the

caseofproductionofrelativelylightgluinoswhichdecay

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

max>Qmatch.

maxis higher

Decay chains

For precision studies of production and decay of new

particles, many features can be important. In particular,

differenttypesofNewPhysicscanoftenbedistinguished

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

Page 3

FIGURE 1.

be generated using the decay chain functionality of Mad-

Graph/MadEvent.

An example of a decay chain that can

lepton pairs [41] and leptons and b jets [42] 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

diagrams [43].

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

mass).

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

correlations

• 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 [44] 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

MadWeight [31] 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

Page 4

786

788

790

792

794

796

798

800

150 155 160

mtop

165 170

-ln(L)

likelihood (mtop=160 GeV)

fitted parameters:

mtop=158.9+-2.3 GeV

parabolic fit

FIGURE 2.

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

P(x|α) =

1

σα

?

dφ(y)|Mα(y)|2×

dw1dw2f1(w1)f2(w2)W(x,y),

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.

ThetypesofprocessesthatMadWeightcanbeusedfor

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

of processes.

MadDipole

MadDipole [32] 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 [45]. In this method,

the Born contribution times a dipole function is added to

both the real and the virtual contributions, schematically

σNLO=

?

m+1

?

?

dσreal−dσBorn⊗D

??

?

+

mloopdσvirt.+

?

1dσBorn⊗D

?

ε=0

,

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

worksforprocessesinanymodel.Animplementationfor

automation of the calculation of subtraction terms also

for the virtual contributions is underway.

Page 5

Modelfile

Particles, symmetries, ...

Lagangian

FeynRules

TeX

Feynman Rules

Interfaces

FeynArts

MadGraphCalcHep

Sherpa

...

FIGURE 3.

Logical organization of FeynRules.

Interface to FeynRules

FeynRules [22] 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-

ticles,parameters,etc.),andtheLagrangianwrittendown

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-

gram calculator.

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-

els.

Currently,

CalcHEP/CompHEP,

Graph/MadEvent and Sherpa, and more interfaces

will be added in the future.

Severalmodelshavebeenimplementedinordertoval-

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

FeynRules-generatedinputsandpreviouslyimplemented

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

models.

interfaceshave been writtenfor

FeynArts/FormCalc,Mad-

CONCLUSIONS

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-

therusingtheexternalBRIDGEpackage[44]orMG/ME

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

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open CVS repository and, naturally, completely open

source code.

ACKNOWLEDGMENTS

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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