Matching and Merging
Starting from a Born-level leading-order (LO) process, higher orders
can be included in various ways. The three basic approaches would be
- A formal order-by-order perturbative calculation, in each order
higher including graphs both with one particle more in the final
state and with one loop more in the intermediate state. This is
accurate to the order of the calculation, but gives no hint of
event structures beyond that, with more particles in the final state.
Today next-to-leading order (NLO) is standard, while
next-to-next-to-leading order (NNLO) is coming. This approach
thus is limited to few orders, and also breaks down in soft and
collinear regions, which makes it unsuitable for matching to
hadronization.
- Real emissions to several higher orders, but neglecting the
virtual/loop corrections that should go with it at any given order.
Thereby it is possible to allow for topologies with a large and
varying number of partons, at the prize of not being accurate to any
particular order. The approach also opens up for doublecounting,
and as above breaks down in soft and colliner regions.
- The parton shower provides an approximation to higher orders,
both real and virtual contributions for the emission of arbitrarily
many particles. As such it is less accurate than either of the two
above, at least for topologies of well separated partons, but it
contains a physically sensible behaviour in the soft and collinear
limits, and therefore matches well onto the hadronization stage.
Given the pros and cons, much of the effort in recent years has
involved the development of different prescriptions to combine
the methods above in various ways.
The common traits of all combination methods are that matrix elements
are used to describe the production of hard and well separated
particles, and parton showers for the production of soft or collinear
particles. What differs between the various approaches that have been
proposed are which matrix elements are being used, how doublecounting
is avoided, and how the transition from the hard to the soft regime
is handled. These combination methods are typically referred to as
"matching" or "merging" algorithms. There is some confusion about
the distinction between the two terms, and so we leave it to the
inventor/implementor of a particular scheme to choose and motivate
the name given to that scheme.
PYTHIA comes with methods, to be described next, that implement
or support several different kind of algorithms. The field is
open-ended, however: any external program can feed in
Les Houches events that
PYTHIA subsequently showers, adds multiparton interactions to,
and hadronizes. These events afterwards can be reweighted and
combined in any desired way. The maximum pT of the shower
evolution is set by the Les Houches scale
, on the one
hand, and by the values of the SpaceShower:pTmaxMatch
,
TimeShower:pTmaxMatch
and other parton-shower settings,
on the other. Typically it is not possible to achieve perfect
matching this way, given that the PYTHIA pT evolution
variables are not likely to agree with the variables used for cuts
in the external program. Often one can get close enough with simple
means but, for an improved matching,
User Hooks can be inserted to control
the steps taken on the way, e.g. to veto those parton shower branchings
that would doublecount emissions included in the matrix elements.
Zooming in from the "anything goes" perspective, the list of relevent
approaches actively supported is as follows.
- For many/most resonance decays the first branching in the shower is
merged with first-order matrix elements [Ben87, Nor01]. This
means that the emission rate is accurate to NLO, similarly to the POWHEG
strategy (see below), but built into the
timelike showers.
The angular orientation of the event after the first emission is only
handled by the parton shower kinematics, however. Needless to say,
this formalism is precisely what is tested by Z^0 decays at
LEP1, and it is known to do a pretty good job there.
- Also the spacelike showers
contain a correction to first-order matrix elements, but only for the
one-body-final-state processes
q qbar → gamma^*/Z^0/W^+-/h^0/H^0/A0/Z'0/W'+-/R0
[Miu99] and g g → h^0/H^0/A0, and only to
leading order. That is, it is equivalent to the POWHEG formalism for
the real emission, but the prefactor "cross section normalization"
is LO rather than NLO. Therefore this framework is less relevant,
and has been superseded the following ones.
- The POWHEG strategy [Nas04] provides a cross section
accurate to NLO. The hardest emission is constructed with unit
probability, based on the ratio of the real-emission matrix element
to the Born-level cross section, and with a Sudakov factor derived
from this ratio, i.e. the philosophy introduced in [Ben87].
While POWHEG is a generic strategy, the POWHEG BOX
[Ali10] is an explicit framework, within which several
processes are available. The code required for merging the PYTHIA
showers with POWHEG input can be found in
include/Pythia8Plugins/PowHegHooks.h
, and is further
described on a separate page.
A user example is found in examples/main31
.
- The other traditional approach for NLO calculations is the
MC@NLO one [Fri02]. In it the shower emission probability,
without its Sudakov factor, is subtracted from the real-emission
matrix element to regularize divergences. It therefore requires a
analytic knowledge of the way the shower populates phase space.
The aMC@NLO package [Fre11] offers an implementation for
PYTHIA 8, developed by Paolo Torrielli and Stefano Frixione. The
global-recoil option of the PYTHIA final-state shower has been
constructed to be used for the above-mentioned subtraction.
- Multi-jet merging in the CKKW-L approach [Lon01]
is directly available. Its implementation, relevant parameters
and test programs are documented on a
separate page.
- Multi-jet matching in the MLM approach [Man02, Man07]
is also available, either based on the ALPGEN or on the Madgraph
variant, and with input events either from ALPGEN or from
Madgraph. For details see
separate page.
- Unitarised matrix element + parton shower merging (UMEPS)
is directly available. Its implementation, relevant parameters
and test programs are documented on a
separate page.
- Next-to-leading order multi-jet merging (in the NL3 and UNLOPS approaches)
is directly available. Its implementation, relevant parameters
and test programs are documented on a
separate page.
- Next-to-leading order jet matching in the FxFx approach
is also available. For details see
separate page.
MC@NLO, jet matching, multi-jet merging and NLO merging with
main89.cc
A common Pythia main program for MC@NLO NLO+PS matching, MLM jet matching,
FxFx (NLO) jet matching, CKKW-L merging, UMEPS merging and UNLOPS (NLO)
merging is available through main89.cc
, together with the input
files main89mlm.cmnd
, main89fxfx.cmnd
,
main89ckkwl.cmnd
, main89umeps.cmnd
and
main89unlops.cmnd
. The interface to MLM jet matching relies
on MadGraph, while all other options of main89.cc
use aMC@NLO
input.
main89.cc
produces HepMC events [Dob01], that can be
histogrammed (e.g. using RIVET [Buc10]), or used as input for a
detector simulation. If the user is not familiar with HepMC analysis tools, it
is possible to instead use Pythia's histogramming routines. For this, remove
the lines referring to HepMC, and histogram events as illustrated (for CKKW-L)
for the histogram histPTFirstSum in main84.cc
, i.e.
using weight*normhepmc as weight.
All settings can be transferred to main89.cc
through an input
file. The input file is part of the command line input of
main89.cc
, i.e. you can execute main89
with the
command
./main89 myInputFile.cmnd myhepmc.hepmc
to read the input myInputFile.cmnd
and produce the output file
myhepmc.hepmc
. Since main89.cc
is currently a
"front-end" for different types of matching/merging, we will briefly discuss
the inputs for this sample program in the following.
Inputs
In its current form, main89.cc
uses LHEF input to transfer
(weighted) phase space points to Pythia. It is possible to include all
parton multiplicities in one LHEF sample. If e.g. UMEPS merging for
W-boson + up to two additional partons is to be performed, one LHE file
containing W+zero, W+one and W+two parton events is required.
All input settings are handed to main89.cc
in the form of an
input file. We have included the input settings files
main89mlm.cmnd
, which
illustrates the MLM jet matching interface,
main89ckkwl.cmnd
, which
illustrates the CKKW-L multi-jet merging interface,
main89umeps.cmnd
, which
illustrates the UMEPS multi-jet merging interface, and
main89fxfx.cmnd
, which
illustrates the FxFx NLO jet matching interface,
main89unlops.cmnd
, which
illustrates the UNLOPS multi-jet NLO merging interface.
Other settings (e.g. using main89.cc
as simple LO+PS or as MC@NLO
interface) are of course possible. In the following, we will briefly explain
how input for the five choices above are generated and handled.
MLM jet matching with main89.cc
For MLM jet matching, main89.cc
currently relies on LHEF input
from MadGraph. Due to the particular unweighting strategy performed in the
generation of these inputs, the sample program starts by estimating the
cross section. After this estimate, MLM jet matching within the Madgraph
approach is performed in a second Pythia run. Example MLM settings can be
found in main89mlm.cmnd
. Please consult
Jet Matching for more details.
CKKW-L merging with main89.cc
For CKKW-L merging, main89.cc
currently relies on LHEF inputs
generated with the leading-order mode of aMC@NLO (i.e. events should
be generated with ./bin/generate_events aMC@LO
).
No run to estimate the cross section estimate is needed. Example CKKW-L
settings can be found in main89ckkwl.cmnd
. Please consult
CKKW-L merging for more details.
UMEPS merging with main89.cc
For UMEPS merging, main89.cc
currently relies on LHEF inputs
generated with the leading-order mode of aMC@NLO as well (see above).
main89.cc
automatically assigns if an event will be used as
"standard" event or as "subtractive" contribution. Example UMEPS
settings can be found in main89umeps.cmnd
. Please
consult UMEPS merging and
CKKW-L merging for more details.
FxFx (NLO) jet matching with main89.cc
For FxFx jet matching, main89.cc
relies on MC@NLO input LHE
files generated with aMC@NLO. To produce FxFx outputs in aMC@NLO, the settings
PYTHIA8 = parton_shower
, 3 = ickkw
and
x = ptj
are necessary in your aMC@NLO run card. Here,
x
is the value of the matching scale in FxFx, i.e. has be
identical to JetMatching:qCutME
in the Pythia inputs.
Example FxFx settings for Pythia can be found in main89fxfx.cmnd
.
Please consult Jet Matching and
aMC@NLO matching for more details.
UNLOPS (NLO) merging with main89.cc
For UNLOPS merging, main89.cc
currently relies on LHEF inputs
generated with the aMC@NLO. The UNLOPS interface in main89.cc
requires a) leading-order inputs generated with the leading-order mode of
aMC@NLO, using the UNLOPS prescription, and b) next-to-leading-order inputs
generated with the NLO mode of aMC@NLO, using the UNLOPS prescription.
To produce UNLOPS outputs in aMC@NLO, the settings
PYTHIA8 = parton_shower
, 4 = ickkw
and
x = ptj
are necessary in your aMC@NLO run card. Here,
x
is the value of the merging scale in UNLOPS, i.e.
has be identical to Merging:TMS
in the Pythia inputs.
main89.cc
will then process NLO inputs and LO inputs
consecutively, and will automatically assign if an event will be used as
"standard" event or as "subtractive" contribution. Example UNLOPS
settings can be found in main89umeps.cmnd
. Please
consult UMEPS merging and
CKKW-L merging for more details.
Implementing an external ME+PS combination scheme and interfacing this
plugin with Pythia
For experts and developers of new matching/merging schemes, Pythia also offers
the possibility to completely replace its internal merging machinery with
a user-defined plugin code (much in the same way that parton shower plugins
(cf. Implement New Showers) are
possible). This allows for maximum flexibility while still benefiting from
the full Pythia event generation machinery. Note that the ME+PS merging with
the VINCIA and DIRE shower plugins make use of this flexibility, and might
thus provide helpful clarifications.
Of course, implementing your
own, new matching/merging scheme is a non-trivial task, and comprehensive
guidelines on how to proceed are impossible to set. However, it is important
that an external matching/merging plugin interfaces to Pythia in a simple and
well-defined manner. Here, we will document which C++ functions are necessary
to be able to use an external matching/merging (MM) plugin within Pythia.
To understand how to design a MM plugin for Pythia, it is useful to review
how Pythia's internal merging machinery is structured. The interaction between
the core Pythia and the merging code is governed by the
Merging
and MergingHooks
classes. Note that for
moderately complex requirements, it may be sufficient to only replace Pythia's
instance of MergingHooks
with a pointer to an external class (cf.
CKKW-L merging). The latter two classes
are supplemented with the helper classes History
and
HardProcess
. The latter gathers information on the (user-supplied
information about the) hard core scattering process to which hard jets are
added
by ME+PS merging. It is only used as a helper to the MergingHooks
class. The History
class contains the implementation of all
internal (LO or NLO) merging schemes. The Merging
class
acts as a bridge between the implementation in the History
class
and the rest of the Pythia code.
To implement an external MM plugin, you will have to write classes that derive
from the Merging
, MergingHooks
and
HardProcess
classes of Pythia. For special cases, it might also
be permissible to only implement a replacement of the Merging
class, while still using Pythia's implementation of the other two classes.
The external MM plugin can then be transferred to and
used by Pythia much in the same way as UserHooks
classes or
shower plugins. More concretely, an external MM code will
be used if a pointer to an instance of the external classes is transferred to
Pythia via the methods
Pythia::setMergingPtr( Merging* myMerging)
Pythia::setMergingHooksPtr( MergingHooks* myMergingHooks)
MergingHooks::setHardProcessPtr( HardProcess* myHardProcess)
The option to only use a user-defined MergingHooks
instance is
already documented in the item CKKW-L merging
and will not be discussed further. We will now focus on how to implement
external Merging
, MergingHooks
and
HardProcess
classes that can be used as a complete
replacement of the Pythia methods.
Let us assume that you want to create a class of type MyMerging
,
and you call its instance myMerging
. For this external ME+PS
merging class to be interfaced to Pythia, the class needs to inherit from the
Pythia8::Merging
base class. It is further necessary to define
the following functions that serve as interface to Pythia:
virtual ~MyMerging()
A destructor for your ME+PS class. If not defined, the base class's empty
destructor will be used.
virtual void MyMerging::init()
A method that is used to initialize your merging class. Pythia will call
this function during its initialization and after all pointers to
internal classes (e.g. to instances of the Info
and
ParticleData
classes) have been set up.
virtual void statistics()
This function can be used to collect and print merging information at the
end of the event generation. Pythia will call this function in the execution
of a Pythia::stat()
call.
virtual int MyMerging::mergeProcess( Event& process)
This function should be the main interface of Pythia to the MM plugin.
Pythia will execute this function once the partonic (fixed-order) scattering
has been constructed (or read from LHEF). The partonic scattering is
transferred via the process
argument. The external MM plugin
should then, based on the process
, implement the matching/merging
strategy. It is permissible that this function changes process
.
In this case, Pythia will continue the event generation with the changed
process
as starting point. The return value of the function
steers how Pythia should proceed after the function execution. The following
return values are supported:
-1 : Reject the event and exit the generation/processing of the current
event
0: Reject the event but continue with the generation/processing of the
current event.
1: Keep the event but continue with the generation/processing of the
current event.
2: Reject the event but continue with the generation/processing of the
current event. However, re-evaluate resonance decays before any other
event generation step. This option can be necessary if the merging code
removes or changes resonant particles from process
.
Note that because this function is the main interface between the MM plugin
and Pythia, it is necessary to use this function to set up all the information
that you might later need (merging weights, particle counters, etc) in this
call already.
For more details on how to design your MyMerging
class, and to
understand the interface to Pythia, studying Pythia's internal code is
unavoidable. Each potential developer of a MM plugin should do so.
The other main ingredient of the interface to MM plugins is a new
implementation
of the MergingHooks
class. Let us assume that you want to
create a class of type MyMergingHooks
, and you call its
instance myMergingHooks
. For this class to be interfaced to
Pythia, it will need to inherit from the Pythia8::MergingHooks
base class.
virtual ~MyMergingHooks()
A destructor for your MergingHooks class. If not defined, the base class's
empty destructor will be used.
virtual void MyMergingHooks::init()
A method that is used to initialize your MyMergingHooks
class.
Pythia will call this function during its initialization and after all
pointers to internal classes (e.g. to instances of the Info
and
ParticleData
classes) have been set up.
virtual bool MyMergingHooks::canVetoStep()
This function will be used to tell Pythia if a CKKW-L-style event veto
after the first parton shower emission should be checked. If so, the function
should return true, and false otherwise.
virtual bool MyMergingHooks::doVetoStep( const Event& process, const Event& event, bool doResonance = false )
This function will be used to implement the check of a CKKW-L-style event veto
after the first parton shower emission, i.e. to check if the first parton
shower emission is above the merging scale.
If the input event event
after emission should be kept, then false should be returned. If you want
instead to veto the event and continue with a completely now hard scattering
event, true should be returned.
virtual bool MyMergingHooks::canVetoEmission()
This function will be used to tell Pythia if a veto of emissions should
potentially be applied.
virtual bool MyMergingHooks::doVetoStep( const Event& event)
This function will be used to implement the check if shower emissions should
be discarded, as e.g. necessary in UMEPS or UNLOPS merging.
You can study the input event event
after emission, and return
true if the emission is valid, and false if you want to reject the emission.
Note that this veto does not lead to event rejections, only in potentially
removing certain emissions during shower evolution.
virtual bool MyMergingHooks::setShowerStartingScales( bool isTrial, bool doMergeFirstEmm, double& pTscaleIn, const Event& event, double& pTmaxFSRIn, bool& limitPTmaxFSRin, double& pTmaxISRIn, bool& limitPTmaxISRin, double& pTmaxMPIIn, bool& limitPTmaxMPIin )
This function allows to set the starting scales for timelike and spacelike
showering as well as multiparton interactions. It is thus necessary to
properly start trial showers (that generate necessary no-emission
probabilities), and for setting the correct starting conditions for parton
showering of accepted (non-zero weight) events.
The input event
gives the hard process before showers and MPI
are attempted.
If isTrial=true
, this means that the function is currently called
from within a trial shower object (to produce no-emission probabilities). If
doMergeFirstEmm=true
, then the function is called to set starting
conditions for the shower evolution of an (accepted) event. The double
arguments pTscaleIn
, pTmaxFSRIn
,
pTmaxISRIn
and pTmaxMPIIn
are tentative values
for the starting scales of FSR, ISR and MPI. The function may overwrite
these with the desired values. Similarly, limitPTmaxFSRin
,
limitPTmaxFSRin
and limitPTmaxMPIin
inform Pythia
if the phase space for FSR/ISR/MPI is restricted (true) or unrestricted
(false). Again, the tentative values can be overwritten.
The MergingHooks
base class allows for further virtual functions
that are not directly called by Pythia, and are hence
not necessary to define. Th usage of these functions within
Pythia's Merging
and History
classes is documented
in CKKW-L merging. The additional (optional)
virtual functions are:
virtual double dampenIfFailCuts( const Event& inEvent )
virtual bool canCutOnRecState()
virtual bool doCutOnRecState( const Event& event )
virtual bool canVetoTrialEmission()
virtual bool doVetoTrialEmission( const Event&, const Event& )
virtual double hardProcessME( const Event& inEvent )
virtual double MyMergingHooks::tmsDefinition( const Event& event)
virtual int MyMergingHooks::getNumberOfClusteringSteps(const Event& event, bool resetNjetMax = false)
virtual bool useShowerPlugin()
The internal implementation of MergingHooks
in Pythia heavily
relies on the HardProcess
helper class. It is in principle
not necessary to follow the same strategy when implementing a derived
MyMergingHooks
class. However, to benefit from the Pythia
implementation, and to allow for a structure similar to the internal code also
for an external MM plugin, it is also possible to effectively replace (in the
MergingHooks
class) the pointer to an instance of
HardProcess
with a pointer to an external implementation.
Let us assume that you want to create a class of type
MyHardProcess
, and you call its instance
myHardProcess
. For this class to be interfaced to
MergingHooks
(or the derived MyMergingHooks
class),
it will need to inherit from the Pythia8::HardProcess
base class.
virtual ~MyHardProcess()
A destructor for your HardProcess class. If not defined, the base class's
empty destructor will be used.
virtual void MyHardProcess::initOnProcess( string process, ParticleData* particleData)
This function can be used to initialize the instance of your HardProcess
class. In the internal Pythia implementation, this acts as a wrapper around
the next function.
virtual void MyHardProcess::translateProcessString( string process)
This function will use the string argument to set up the hard process
bookkeeping, e.g. how many incoming/outgoing particles of which flavour are
contained in the core (lowest multiplicity) scattering process.
virtual void MyHardProcess::storeCandidates( const Event& event, string process)
This function studies the input event and book-keeps the particles that
may be considered as part of the core scattering process. For this, it may
use the four next functions.
virtual bool MyHardProcess::allowCandidates(int iPos, vector<int> Pos1, vector<int> Pos2, const Event& event)
This function uses the input vectors of positions of particles in the input
event to decide if the particle with iPos
could be member
of the core scattering. If the particle with position iPos
cannot be part of the core scattering (e.g. because it is a final state
parton, while the core scattering contains final state leptons only), then
the function should return false. Else, return true to allow this candidate.
Note that it might be possible to find multiple equally good core scattering
candidates. In this case, all candidates should be found (with the
findOtherCandidates
function), and can be potentially be
replaced (with exchangeCandidates
).
virtual bool MyHardProcess::matchesAnyOutgoing(int iPos, const Event& event)
This function may be used to check if the particle with position
iPos
in the input event should be considered an outgoing particle
of the core scattering.
virtual bool MyHardProcess::findOtherCandidates(int iPos, const Event& event, bool doReplace)
The argument iPos
specifies the position of a particle in the
input event which is tagged as part of the core scattering. This function may
be used to check the role of iPos
as core scattering member may
be filled by another particle in the event record. If so, and if
doReplace=true
, then iPos
will no longer be
book-kept as part of the core scattering. An example where this functionality
is helpful is if the input event is g g -> b b~ b b~, and the core scattering
is g g -> b b~. Not swapping the hard process candidates could in this case
mean that not all parton shower histories can be found.
The function should return false if no replacements can be found, and true
otherwise.
virtual bool MyHardProcess::exchangeCandidates( vector<int> candidates1, vector<int> candidates2, map<int, int> further1, map<int, int> further2)
This function implements the replacement of a list of core scattering
candidates by another list of candidates.