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<h2>CKKW-L Merging</h2>
CKKW-L merging [<a href="Bibliography.html" target="page">Lon01</a>] allows for a consistent merging of parton
showers with
matrix elements to include multiple well-separated partons. The
algorithm implemented in PYTHIA is described in [<a href="Bibliography.html" target="page">Lon11</a>]. To
perform matrix element merging, the user has to supply LHE
files [<a href="Bibliography.html" target="page">Alw07</a>] for the hard process and the corresponding
process with up to N additional jets.
<p/> The usage of the merging procedure is illustrated in a few
example main programs
(<code>main81.cc</code>, <code>main82.cc</code>,
<code>main83.cc</code>, <code>main84.cc</code> and <code>main85.cc</code>,
together with the input files <code>main81.cmnd</code>,
<code>main82.cmnd</code>, <code>main84.cmnd</code> and
<code>main85.cmnd</code>). These examples should of course only serve
as an illustration, and as such will not make use of the merging in
all possible ways. For full generality, the example programs link to
LHAPDF, FastJet and HepMC. Of course the user is welcome to remove
these dependencies. To remove the FastJet dependence, the functions
calculating example observables have to be deleted. Removing the
LHAPDF dependence requires changing the cmnd input files to choose an
inbuilt PDF, as outlined in the
<a href="PDFSelection.html" target="page">PDF documentation</a>. The
HepMC dependence can be removed by erasing the code allowing for HepMC
output.
<p/> Please note that a detailed tutorial on merging in Pythia is available
from
<a href="http://home.thep.lu.se/~torbjorn/pythia8/mergingworksheet8160.pdf">
http://home.thep.lu.se/~torbjorn/pythia8/mergingworksheet8160.pdf</a>.
<p/> Three very short LHE files (<code>w+_production_lhc_0.lhe</code>,
<code>w+_production_lhc_1.lhe</code>, <code>w+_production_lhc_2.lhe</code>)
are included in the distribution. These files are not intended for
physics studies, but only serve as input for the example main
programs. For realistic studies, the user has to supply LHE files.
<p/> In the generation of LHE files, the value of the factorisation
scale used in the PDFs is not important, since the cross section will
be multiplied by ratios of PDFs to adjust to the PYTHIA starting
scales. The same is true for the renormalisation scale (and starting
value <i>α<sub>s</sub>(M<sub>Z</sub>)</i>) used to evaluate
<i>α<sub>s</sub></i>. Coupling and scale choices by the user
will be transferred to the merging routines.
<p/> Multi-jet events can suffer from infrared divergences in the
calculation. Sensible matrix element generator (MEG) outputs should not
contain phase space points in which the calculation is ill-defined, meaning
infrared regions need to be removed by cuts. This is most conveniently done
by disallowing the MEG to produce partons below a
minimal parton-parton separation in a certain jet algorithm. Using
dedicated cuts to regularise MEG output is of course possible as well. Any
regularisation criterion defines the matrix element region: The parts of
phase space in which the fixed order calculation is considered valid and
preferable to the parton shower. Matrix element merging is combining
MEG events in the matrix element region with parton shower events in regions
outside the regularisation cut (often called parton shower region). Because
the regularisation cut defines a boundary between the matrix element
and parton shower regions, i.e. the regions to be merged into one inclusive
sample, it is usually called <i> merging scale </i>. Since many different
cut choices may regularise the MEG calculation, many different merging scale
definitions are possible. A few standard choices are listed below, as well as
documentation on how to use a user-defined cut criterion. In combining matrix
element and parton shower regions, the CKKW-L prescription tries to minimise
the dependence on the merging scale. This can only be achieved if the
combination of MEG events and parton shower populates the whole phase space.
Additional cuts on the partons in the LHEF generation should hence be
avoided as much as possible, meaning that the merging scale cut should always
pose a more stringent cut than all other cuts on the partons. Of course, if
the hard process itself is divergent, cuts need to be made. However, this
should be chosen in such a way as to not exclude regions that will be
available to the matrix elements with additional jets. An example is QCD
di-jet production with additional jets: Say the <i>2 → 2</i> process is
regularised with a <i>pTmin</i> cut of pTminCut = 100 GeV, and
the <i>2 - >3</i> sample is regularised with a <i>kTmin</i>-cut of
kTminCut = 50 GeV. This would mean that when reclustering
the emission in the 2 → 3 sample, we could end up with a
<i>pT</i> value <i>pTminNow</i> of the 2 → 2 configuration with
<i>pTminCut > pTminNow</i>, which is excluded in the
2 → 2 sample. Thus, the 2 → 3 sample will include a
Sudakov factor not included in the 2 → 2 sample, resulting
in merging scale dependencies. Such dependencies can be avoided if
the additional cuts on the hard process are minimal.
<p/> Of course, additional cuts on electroweak particles are
allowed. These should be the same for all samples with
<i>0 <= n <= N</i> additional partons.
<p/> If it is not possible to generate LHE files with minimal cuts,
the user can choose to use the <code>MergingHooks</code> structures in
order to decide how much influence to attribute to parton shower
histories in which the reclustered lowest multiplicity process does
not pass the matrix element cuts. This is described below.
<p/> When generating LHE files, we advise against putting
unstable particles (e.g. massive gauge bosons) in the final state.
Rather, specify a resonance by its decay products, e.g. if Les Houches
events for the <i>pp → Z + jets → e+e- + jets</i> process
are desired, generate the matrix element events with the <i>Z</i> decay
included. From a physical point of view, on-shell final massive gauge
bosons should not be considered part of a hard process, since only
the boson decay products will be detectable. Furthermore,
non-narrow-width approximation contributions are not present if the
ME generator only produces on-shell bosons. Interference effects
between different production channels for the decay products would
also be neglected. These points seem an unnecessary restriction on
the accuracy of the ME calculation. In addition, there is a
technical reason for this strategy. Since some matrix element
generators choose to put additional information on intermediate
bosons into Les Houches events, depending on if they pass a certain
criterion (e.g. being close to the mass shell), without exact
knowledge of this criterion, the only feasible way of bookkeeping the
hard process is by identifying outgoing decay products.
<p/> Despite these considerations, (massive) gauge bosons in the final state
are allowed in the hard process definition. This is useful particularly for
Higgs physics, when different decays of the Higgs boson need to be simulated
after the LHEF generation.
<p/> For all merging purposes, processes with different charge of
outgoing leptons are considered different processes. That means
e.g. that <i>e+ν<sub>e</sub>+ jets</i> and
<i>e-ν̄<sub>e</sub> + jets</i>
are considered independent processes. If the user wishes to generate
distributions including effects of more than one process, merged
samples for all independent processes should be generated separately
and added afterwards. Alternatively, to combine simple processes,
combined LHE files can be used in conjunction with flexible containers (see
below).
<p/> When the matrix element merging is used to produce HepMC
[<a href="Bibliography.html" target="page">Dob01</a>] files to be analysed with RIVET [<a href="Bibliography.html" target="page">Buc10</a>],
special care needs to taken in how the cross section is read by RIVET
(see below).
<p/> To specify the merging conditions, additionally information on
the merging scale value and the functional definition of the merging
scale is needed. A few standard definitions of merging scales are
available. We hope this makes the user interface less cumbersome.
<p/> Different choices intrinsic to the CKKW-L merging procedure might
be relevant for the user as well. The base
class <code>MergingHooks</code> gives the user the opportunity to
define the functional form of the merging scale. In the following,
the usage of the merging machinery to consistently include LHE files
with additional jets into PYTHIA will be discussed.
<br/><br/><hr/>
<h3>Merging scale definitions</h3>
<p/> The quickest way to include processes with additional jets is to
produce LHE files with one of the standard ways to define the merging
scale. Three standard ways to define a merging scale (minimal <i>kT</i>,
minimal evolution <i>pT</i> and by three cuts) are implemented. All of these
prescriptions are equivalent - different definitions have only been introduced
for the convenience of users, who might be limited by which cuts can be used
in the generation of LHE files. Below, we describe how to switch on and use
these different merging scale definitions.
<h4>Merging with merging scale defined in kT:</h4>
<p/><code>flag </code><strong> Merging:doKTMerging </strong>
(<code>default = <strong>off</strong></code>)<br/>
If the additional jets in the LHE files have been regulated by
a <i>kT</i> cut, the user can supply the merging scale definition by
setting this flag to on. <i>kT</i> here and below means cutting on
Durham <i>kT</i> for <i>e+e-</i> collisions, and cutting on
longitudinally invariant <i>kT</i> for hadronic collisions. Please note
that this particular merging scale definition will check <i>kT</i> between
all pairs of <i>u,d,c,s,b,g</i> partons.
</p>
Currently, the name longitudinally invariant <i>kT</i> is used
for a few jet recombination algorithms with slightly different
jet measures. A specific form can be chosen by setting the switch
<p/><code>mode </code><strong> Merging:ktType </strong>
(<code>default = <strong>1</strong></code>; <code>minimum = 1</code>; <code>maximum = 3</code>)<br/>
Precise functional definition of longitudinally
invariant <i>kT</i>. For e+e- collisions, <i>Durham kT</i> is
always defined by the square root of <i>min{ 2*min[ </sub>
E<sub>i</sub><sup>2</sup>, E<sub>j</sub><sup>2</sup>] * [ 1 -
cosθ<sub>ij</sub>] }</i>, so that this switch will have no effect.
<br/><code>option </code><strong> 1</strong> : Longitudinally invariant <i>kT</i> is defined by
the square root of the minimum of minimal jet kinematic <i>pT</i>
(<i>p<sub>Tkin,min</sub><sup>2</sup> = min{ p<sub>T,i</sub><sup>2</sup> }
</i>) and <i>p<sub>Tlon,min</sub><sup>2</sup> =
min{ min[ p<sub>T,i</sub><sup>2</sup>, p<sub>T,j</sub><sup>2</sup>] *
[ (Δy<sub>ij</sub>)<sup>2</sup> +
(Δφ<sub>ij</sub>)<sup>2</sup> ] / D<sup>2</sup> }</i> , i.e.
<i>kT = min{ √p<sub>Tkin,min</sub><sup>2</sup>,
√p<sub>Tlon,min</sub><sup>2</sup> }</i> for hadronic collisions. Note
that the true rapidity of partons is used.
<br/><code>option </code><strong> 2</strong> : Longitudinally invariant <i>kT</i> is defined by
the square root of the minimum of minimal jet kinematic <i>pT</i>
(<i>p<sub>Tkin,min</sub><sup>2</sup> = min{ p<sub>T,i</sub><sup>2</sup>
} </i>) and <i>p<sub>Tlon,min</sub><sup>2</sup> =
min{ min[ p<sub>T,i</sub><sup>2</sup>,
p<sub>T,j</sub><sup>2</sup>] * [
(Δη<sub>ij</sub>)<sup>2</sup> +
(Δφ<sub>ij</sub>)<sup>2</sup> ] / D<sup>2</sup> }</i>, i.e.
<i>kT = min{ √p<sub>Tkin,min</sub><sup>2</sup>,
√p<sub>Tlon,min</sub><sup>2</sup> }</i>
for hadronic collisions. Note that the pseudorapidity of partons is used.
<br/><code>option </code><strong> 3</strong> : Longitudinally invariant <i>kT</i> is defined by
the square root of the minimum of minimal jet kinematic <i>pT</i>
(<i>p<sub>Tkin,min</sub><sup>2</sup> = min{ p<sub>T,i</sub><sup>2</sup>
} </i>) and
<i>p<sub>Tlon,min</sub><sup>2</sup> =
min{ min[ p<sub>T,i</sub><sup>2</sup>,
p<sub>T,j</sub><sup>2</sup>] * [ cosh(Δη<sub>ij</sub>) -
cos(Δφ<sub>ij</sub>) ] / D<sup>2</sup> } </i>, i.e.
<i>kT = min{ √p<sub>Tkin,min</sub><sup>2</sup>
, √p<sub>Tlon,min</sub><sup>2</sup> }</i>
for hadronic collisions.
<p/><code>parm </code><strong> Merging:Dparameter </strong>
(<code>default = <strong>1.0</strong></code>)<br/>
The value of the <i>D</i> parameter needed in the definition of
longitudinally invariant <i>kT</i> separation.
<p/><code>mode </code><strong> Merging:nJetMax </strong>
(<code>default = <strong>0</strong></code>; <code>minimum = 0</code>)<br/>
Maximal number of additional jets in the matrix element
<p/><code>parm </code><strong> Merging:TMS </strong>
(<code>default = <strong>0.0</strong></code>)<br/>
The value of the merging scale. The name is inspired by the scale in
evolution equations, which is often called 't', and the suffix 'MS' stands
for merging scale. In the particular case of <i>kT</i>-merging, this
would be the value of the <i>kT</i>-cut in GeV. For any merging scale
definition, this input is considered the actual value of the merging
scale.
<p/><code>word </code><strong> Merging:Process </strong>
(<code>default = <strong>void</strong></code>)<br/>
The string specifying the hard core process, in MG4/ME notation.
</p>
If e.g. <i>W + jets</i> merging should be performed, set this to
<code>pp>e+ve</code> (<i>without white spaces or quotation marks</i>).
This string may contain resonances in the MG/ME notation, e.g. for merging
<i>pp→Z W<sup>+</sup>→q q̄ e+ν<sub>e</sub> + jets</i>,
the string <code>pp>(z>jj)(w+>e+ve)</code> would be applicable.
<p/>
A lot more flexible hard process definitions are possible. To not dwell too
much on these details here, we will come back to the process string at the end
of this section.
<p/><code>flag </code><strong> Merging:doMGMerging </strong>
(<code>default = <strong>off</strong></code>)<br/>
Even easier, but highly non-general, is to perform the merging with
MadGraph/MadEvent-produced LHE files, with a merging scale defined by
a <i>kT</i> cut. For this, set this switch to on. The merging scale
value will be read from the +1 jet LHE file by searching for the
string <code>ktdurham</code>, and extracting the value from <code>
value = ktdurham</code>. Also, the hard process will be read from
the +0 jet LHE file, from the line containing the string <code>@1</code>
(the tag specifying the first process in the MadGraph process card).
For this to work, PYTHIA should be initialised on LHE files called
<code>NameOfYourLesHouchesFile_0.lhe</code> (+0 jet sample) and
<code>NameOfYourLesHouchesFile_1.lhe</code> (+1 jet sample) and the
same naming convention for LHE files with two or more additional jets.
Since for this option, the merging scale value is read from the
LHEF, no merging scale value needs to be supplied by setting <code>
Merging:TMS </code>. Also, the hard process is read from LHEF, the
input <code>Merging::Process</code> does not have to be defined.
However, the maximal number of merged jets still has to be supplied by
setting <code>Merging:nJetMax</code>.
<h4>Merging with merging scale defined in Pythia evolution <i>pT</i>:</h4>
If the LHE file has been regularised by cutting on the minimal Pythia
evolution <i>pT</i> in the state, this can also be used as a merging scale
right away. For this, change the switch
<p/><code>flag </code><strong> Merging:doPTLundMerging </strong>
(<code>default = <strong>off</strong></code>)<br/>
The merging scale is then defined by finding the minimal Pythia evolution
<i>pT</i> between sets of radiator, emitted and recoiler partons. For this
particular merging scale definition, <i>u,d,c,s,b,g</i> are considered
partons. The Pythia evolution <i>pT</i> of a single three-parton set is
defined by
<p/>
<i>pT<sub>evol</sub> = z<sub>ijk</sub>(1-z<sub>ijk</sub>)
Q<sub>ij</sub><sup>2</sup></i> for FSR, where <i>i</i> is the radiating
parton, <i>j</i> is the emitted parton and <i>k</i> is the recoiler,
and
<i> Q<sub>ij</sub><sup>2</sup> =
(p<sub>i</sub> + p<sub>j</sub>)<sup>2</sup> </i>, and
<i>z<sub>ijk</sub> =
x<sub>i,jk</sub> / (x<sub>i,jk</sub> + x<sub>j,ik</sub>)</i> with
<i>x<sub>i,jk</sub> =
2 p<sub>i</sub> (p<sub>i</sub> + p<sub>j</sub> + p<sub>k</sub>)
/ (p<sub>i</sub> + p<sub>j</sub> + p<sub>k</sub>)<sup>2</sup> </i>
<p/>
<i>pT<sub>evol</sub> = (1-z<sub>ijk</sub>)
Q<sub>ij</sub><sup>2</sup></i> for ISR, where <i>i</i> is the radiating
parton, <i>j</i> is the emitted parton and <i>k</i> is the second
initial state parton, and
<i> Q<sub>ij</sub><sup>2</sup> =
-(p<sub>i</sub> - p<sub>j</sub>)<sup>2</sup> </i>, and
<i>z<sub>ijk</sub> =
(p<sub>i</sub> - p<sub>j</sub> + p<sub>k</sub>)<sup>2</sup>
/ (p<sub>i</sub> + p<sub>k</sub>)<sup>2</sup> </i>.
<p/>
When using this option, the merging scale is defined by the minimum
<i>pT<sub>evol</sub></i> for all combinations of three partons in the event,
irrespective of flavour or colour-connections. The merging scale value will
be read from the <code>Merging:TMS</code> parameter, so that this needs to be
set just as in the case of the <i>kT</i>-merging prescription. Of course you
will also need to set <code>Merging:Process</code> and the maximal number of
additional matrix element jets <code>Merging:nJetMax</code>.
<h4>Merging with merging scale defined by a combination of cuts:</h4>
It is possible to regularise QCD divergences in a LHE file by applying cuts
to the kinematical <i>pT</i> of jets (<i>pT<sub>i</sub></i>), combined
with a cut on <i> ΔR<sub>ij</sub></i> between jets and a cut on
invariant mass <i> Q<sub>ij</sub></i> of jet pairs. The combination of
these standard cuts can also serve as a merging scale. For this, use this
setting
<p/><code>flag </code><strong> Merging:doCutBasedMerging </strong>
(<code>default = <strong>off</strong></code>)<br/>
This switch will use cuts on (<i>pT<sub>i</sub></i>),
<i> ΔR<sub>ij</sub></i> and
<i> Q<sub>ij</sub></i> to define when parton shower emissions are allowed.
Please note for this particular merging scale definition, only light jets
(<i>u,d,c,s,g</i>) are checked.
<p/>
The values of the cuts will then be read from
<p/><code>parm </code><strong> Merging:QijMS </strong>
(<code>default = <strong>0.0</strong></code>)<br/>
The value of the invariant mass cut <i> Q<sub>ij</sub></i> of pairs of final
state partons used in the matrix element generation.
<p/><code>parm </code><strong> Merging:pTiMS </strong>
(<code>default = <strong>0.0</strong></code>)<br/>
The value of the minimal transverse momentum cut <i> pT<sub>i</sub></i> on
final state partons, as used in the matrix element generation.
<p/><code>parm </code><strong> Merging:dRijMS </strong>
(<code>default = <strong>0.0</strong></code>)<br/>
The value of the minimal <i> ΔR<sub>ij</sub></i> separation between
pairs of final state partons used in the matrix element generation, where
<i> ΔR<sub>ij</sub><sup>2</sup> = (Δy<sub>ij</sub>)<sup>2</sup> +
(Δφ<sub>ij</sub>)<sup>2</sup></i>.
<p/>
With knowledge of these values, and <code>Merging:doCutBasedMerging</code>,
Pythia will use these cuts as a separation between matrix element phase space
and parton shower region. If e.g. the Les Houches Events have been generated
with the cuts <i> ΔR<sub>ij</sub> = 0.1 </i>,
<i>pT<sub>i</sub>= 20 GeV</i> and <i> Q<sub>ij</sub> = 40 GeV</i>, set
<code>Merging:QijMS=40.</code>,
<code>Merging:pTjMS=20.</code>,
<code>Merging:dRijMS=0.1</code> to perform a cut-based merging. Of course
you will also need to set <code>Merging:Process</code> and the
maximal number of additional matrix element jets
<code>Merging:nJetMax</code>.
<h4>Les Houches events outside the matrix element region</h4>
</p>
Before continuing, we would like to point out that in general, the user
should make sure that the events in the Les Houches file are actually
calculated using the regularisation cut definition and value(s) supplied to
Pythia as merging scale definition and value(s). However, if LH files with
a large number of events and loose merging scale cuts are available, it
might be useful to choose a higher merging scale value, e.g. for merging
scale variations as part of uncertainty assessments. If CKKW-L merging is
enabled, Pythia will by default check if events read from Les Houches file
are in the matrix element region as defined by the merging scale definition
and merging scale value. Events outside the matrix element region will be
discarded. This will lead to warnings of the form "<code>Les Houches Event
fails merging scale cut. Cut by rejecting event</code>". These warnings
should, in this case, rather be regarded as information.
To change the default behaviour, use the flag
<p/><code>flag </code><strong> Merging:enforceCutOnLHE </strong>
(<code>default = <strong>on</strong></code>)<br/>
This will check if the events read from LHE file are in the matrix element
region as defined by the merging scale definition and value(s). If on, LHE
input outside the matrix element region will be rejected. If off, every
event is assumed to pass the merging scale cut.
<h4>Defining the hard process</h4>
To perform CKKW-L matrix element merging, the user has to decide on a hard
process, and communicate this choice to Pythia. This is done by setting the
input <code>Merging:Process</code>
<p/>
For single processes in the Standard Model or the MSSM, MG4/ME notation is
applicable. However, for some purposes, using a single simple process
string is not satisfactory. Mixed W<sup>+</sup> and W<sup>-</sup> events
in a single LHE file is a common example. For this case, it would of course
be perfectly allowed to perform twice, once for W<sup>+</sup> production and
once for W<sup>-</sup> production, and then add the results. Nevertheless, it
seems reasonable to alleviate difficulties by allowing for less restrictive
hard process definitions. Two generalisations of the process tag are
available: Containers and user-defined particle tags. The syntax of these
settings is described below.
<p/>
In case you want multiple processes in a LHE file to be treated on equal
footing (e.g. <i>W<sup>+</sup> + jets</i> and
<i>W<sup>-</sup> + jets</i>), you should use flexible containers do
specify the hard process. So far, we allow the use of the containers
<code>LEPTONS</code>, <code>NEUTRINOS</code>, <code>BQUARKS</code>. If you
use these containers, the hard process definition is relatively flexible,
meaning that Pythia will attempt a merging of QCD jets for each event in
the LHE file, and assume that all particles matching one of the containers
are products of the hard process. This is best explained by examples.
If you want to have both <i>pp → e+ ν<sub>e</sub> + jets</i>
and <i>pp → e- ν̄<sub>e</sub> + jets</i> events in a single
file, you can set <code>Merging:Process=pp>LEPTONS,NEUTRINOS</code> as hard
process (note that for readability, you are allowed to use commata to separate
container names). Combining e.g. the processes
<i>pp → e+ ν<sub>e</sub></i> and
<i>pp → μ+ ν<sub>μ</sub></i> is possible with the hard process
definition <code>pp>LEPTONS,NEUTRINOS</code>.
<p/>
For maximal flexibility, the definition of the hard process by these
containers does not mean that each Les Houches event needs to contain
particles to match each container. It is enough if one container is matched.
This means that with the string <code>pp>LEPTONS,NEUTRINOS</code>, you can
immediately process <i>pp → e+ e- </i> events mixed with
<i>pp → e+ ν<sub>e</sub></i> events, since particles matching at
least one container can be found in both cases. Another example for the usage
of containers is mixing <i>pp → e+ ν<sub>e</sub></i> and
<i>pp → tt̄ → e+ ν<sub>e</sub> e- ν̄<sub>e</sub>
bb̄</i>. This can be accommodated by the hard process string
<code>Merging:Process=pp>LEPTONS,NEUTRINOS,BQUARKS</code>.
<p/>
There is however a conceptual limitation to containers: The hard process
definition is necessary to ensure that when constructing lower multiplicity
states (that will be used to calculate the correct merging weight), the
structure of the hard process will be preserved. If e.g. we want the hard
process to be <i>pp → Z → bb̄ </i>, we should ensure that
the lowest multiplicity state contains a colour-singlet bb̄-pair. When
reconstructing intermediate lower multiplicity states from multi-jet matrix
elements, we should thus always be able to find at least one bb̄-pair. By
mixing different processes in a LHE file, this requirement might already be
violated at the level of Les Houches events. Flexible containers cannot give
strong conditions which flavours should be preserved in the construction of
the hard process. In order to avoid non-sensible results, it is hence <i>
assumed that all</i> particles matching any of the containers will be part
of the lowest multiplicity process. This implies that if you decide to use the
<code>BQUARKS</code> container, all b-quarks in the LHE file will be
interpreted as hard process particles, and never as additional radiation.
<p/>
Another way to specify the hard process particles is to explicitly define the
particle names and identifiers. This is necessary if the matrix element
merging in Pythia does not contain the particles of interest. To make sure
that the hard process is still treated correctly, it is possible to define
particles in the process string. If you e.g. want the hard process to contain
a particle "zeta~" with PDG identifier "12345", produced in proton collisions,
you have to include a user-defined particle tag by setting the process string
to <code>pp>{zeta~,12345}</code>. The user-defined particle is enclosed in
curly brackets, with syntax
<code>{particle_name,particle_identifier}</code>, where "particle_name"
and "particle_identifier" are the particle name and particle identifier used
for this particle in the input LHE file. User-defined particles are only
allowed in the final state. You are free to fix user-defined particles with
more common ones, as long as user-defined particles are put before more common
particles in the process string. This means that if you e.g. wanted the hard
process to contain a graviton in association with a positron and an
electron-neutrino, you have to define the hard process as
<code>pp>{G,39}e+ve</code>.
<p/>
Below you can find a list of particles predefined in the merging. If you wish
to include a hard process with different final state particles, you may use
the "curly bracket notation" outlined above.
<p/>
The set of incoming particles us limited to:
<code>e-</code> (electron), <code>e+</code> (positron), <code>mu-</code>
(muon), <code>mu+</code> (antimuon), <code>p</code> (proton, container to
hold all initial state coloured particles), <code>p~</code> (identical to
<code>p</code> container).
<p/>
The following intermediate particles are allowed:
<code>a</code> (photon), <code>z</code> (Z boson),
<code>w-</code> (W<sup>-</sup> boson), <code>w+</code> (W<sup>+</sup> boson),
<code>h</code> (scalar Higgs boson), <code>W</code> (container to hold both
W<sup>-</sup> and W<sup>+</sup> boson), <code>t</code> (top quark),
<code>t~</code> (anti-top),
<code>dl</code>, <code>dl~</code>, <code>ul</code>, <code>ul~</code>,
<code>sl</code>, <code>sl~</code>, <code>cl</code>, <code>cl~</code>,
<code>b1</code>, <code>b1~</code>, <code>t1</code>, <code>t1~</code>,
<code>dr</code>, <code>dr~</code>, <code>ur</code>, <code>ur~</code>,
<code>sr</code>, <code>sr~</code>, <code>cr</code>, <code>cr~</code>,
<code>b2</code>, <code>b2~</code>, <code>t2</code>, <code>t2~</code>
(all MSSM squarks).
<p/>
We have pre-defined the outgoing particles:
<code>e+</code>, <code>e-</code>, <code>ve~</code>,
<code>ve</code>, <code>mu+</code>, <code>mu-</code>,
<code>vm~</code>, <code>vm</code>, <code>ta+</code>, <code>ta-</code>,
<code>vt~</code>, <code>vt</code> (all SM leptons and neutrinos),
<code>j~</code> (container to hold all final state coloured particles),
<code>j</code> (container to hold all final state coloured particles),
<code>NEUTRINOS</code> (container to hold all final state neutrinos and
anti-neutrinos), <code>LEPTONS</code> (container to hold all final state
leptons and anti-leptons), <code>BQUARKS</code> (container to hold final
state b-quarks), <code>d~</code>, <code>d</code>, <code>u~</code>,
<code>u</code>, <code>s~</code>, <code>s</code>, <code>c~</code>,
<code>c</code>, <code>b~</code>, <code>b</code>, <code>t~</code>,
<code>t</code> (all SM quarks), <code>a</code>, <code>z</code>,
<code>w-</code>, <code>w+</code> (all SM electro-weak bosons),
<code>h</code> (scalar Higgs boson), <code>W</code> (container to hold both
W<sup>-</sup> and W<sup>+</sup> boson), <code>n1</code> (MSSM neutralino),
<code>dl~</code>, <code>dl</code>, <code>ul~</code>, <code>ul</code>,
<code>sl~</code>, <code>sl</code>, <code>cl~</code>, <code>cl</code>,
<code>b1~</code>, <code>b1</code>, <code>t1~</code>, <code>t1</code>,
<code>dr~</code>, <code>dr</code>, <code>ur~</code>, <code>ur</code>,
<code>sr~</code>, <code>sr</code>, <code>cr~</code>, <code>cr</code>,
<code>b2~</code>, <code>b2</code>, <code>t2~</code>, <code>t2</code>
(all MSSM squarks). Other outgoing particles are possible if you use the
"curly bracket notation" described earlier.
<br/><br/><hr/>
<h3>Histogramming the events</h3>
After the event has been processed, histograms for observables of interest
need to be filled. In order to achieve good statistical accuracy for all jet
multiplicities and all subprocesses contributing to one jet multiplicity,
generally a fixed number of unit-weighted events is read from each Les
Houches Event file. To then arrive at the correct prediction, for each of
these events, histogram bins should be filled with the corresponding cross
section, or weighted with unit weight and normalised at the end to
the generated cross section for each jet multiplicity separately.
<p/> Still another, even more important, event weight that has to
applied on an event-by-event basis is the CKKW-L-weight. This
corrective weight is the main outcome of the merging procedure and
includes the correct no-emission probabilities, PDF weights and
α<sub>s</sub> factors. This means that the merging
implementation will generate weighted events. The CKKW-L-weight can be
accessed by the following function:
<p/><strong> double Info::mergingWeight() </strong> <br/>
Returns the CKKW-L weight for the current event.
<p/> Note that to avoid confusion, this function does not include the
the weight of a phase space point (given
by <strong>Info::weight()</strong>). This weight will differ from
unity when reading in weighted Les Houches events. In this case, the
full weight with which to fill histogram bins is
<strong>Info::mergingWeight() * Info::weight()</strong>.
<p/> Finally, to arrive at a correct relative normalisation of the
contributions from different number of additional jets in the matrix
element, each histogram should be rescaled with the accepted cross
section given by
<strong>Info::sigmaGen()</strong>. The accepted cross section includes
the effect of vetoes generating Sudakov form factors for the matrix
elements, and is in general only known after the run.
<p/> This final step can of course be skipped if the accepted cross
section had been estimated before the histogramming run, and histogram
bins had instead been filled with the weight
<strong>Info::mergingWeight() * σ<sub>est</sub>(number of
additional jets in current ME sample)</strong>. This is the way HepMC
events should be weighted to produce correct relative weights of
events (see below, and particularly examine the example programs
<code>main84.cc</code> and <code>main85.cc</code>).
<p/> Examples how to use these options are given in <code>main81.cc</code>
(<i>kT</i> merging), <code>main84.cc</code> (automatic MG/ME merging
for RIVET usage), and <code>main85.cc</code> (HepMC output for RIVET usage).
<br/><br/><hr/>
<h3>Merging with user-defined merging scale function</h3>
<p/> For all other merging scale definitions, the procedure is
slightly more complicated, since the user has to write a small piece
of code defining the merging scale. To allow for a user defined
procedure, set the input
<p/><code>flag </code><strong> Merging:doUserMerging </strong>
(<code>default = <strong>off</strong></code>)<br/>
General user defined merging on/off.
</p>
Then, set
the <strong>Merging:nJetMax</strong>, <strong>Merging:TMS</strong>
and <strong>Merging:Process</strong> input as before.
<p/> Since during execution, PYTHIA needs to evaluate the merging
scale with the definition of the user, the user interface is designed
in a way similar to the
<code>UserHooks</code> strategy. The class controlling the merging
scale definition is called <code>MergingHooks</code>.
<h4>Initialisation</h4>
<p/> To initialise the merging with user-defined merging scale, we
should construct a class derived from <code>MergingHooks</code>, with
a constructor and destructor
<p/>
<a name="method1"></a>
<p/><strong>MergingHooks::MergingHooks() </strong> <br/>
<a name="method2"></a>
<p/><strong>virtual MergingHooks::~MergingHooks() </strong> <br/>
The constructor and destructor do not need to do anything.
<p/> For the class to be called during execution, a pointer to an
object of the class should be handed in with the
<br/><code><a href="ProgramFlow.html" target="page">
Pythia::setMergingHooksPtr( MergingHooks*)</a></code> method.
An examples of this procedure are given in <code>main82.cc</code>.
<h4>Defining a merging scale</h4>
<p/> Then, in the spirit of the <code>UserHooks</code> class, the user
needs to supply the process to be merged by defining a methods to
evaluate the merging scale variable.
<a name="method3"></a>
<p/><strong>virtual double MergingHooks::tmsDefinition(const Event& event) </strong> <br/>
This method will have to calculate the value of the merging scale
defined in some variable from the input event record. An example of
such a function is given in <code>main82.cc</code>.
<p/> The base class <code>MergingHooks</code> contains many functions
giving information on the hard process, to make the definition of the
merging scale as easy as possible:
<a name="method4"></a>
<p/><strong>int MergingHooks::nMaxJets() </strong> <br/>
Return the maximum number of additional jets to be merged.
<a name="method5"></a>
<p/><strong>int MergingHooks::nHardOutPartons() </strong> <br/>
Returns the number of outgoing partons in the hard core process.
<a name="method6"></a>
<p/><strong>int MergingHooks::nHardOutLeptons() </strong> <br/>
Returns the number of outgoing leptons in the hard core process.
<a name="method7"></a>
<p/><strong>int MergingHooks::nHardInPartons() </strong> <br/>
Returns the number of incoming partons in the hard core process.
<a name="method8"></a>
<p/><strong>int MergingHooks::nHardInLeptons() </strong> <br/>
Returns the number of incoming leptons in the hard core process.
<a name="method9"></a>
<p/><strong>int MergingHooks::nResInCurrent() </strong> <br/>
The number of resonances in the hard process reconstructed from the
current event. If e.g. the ME configuration was
<i>pp → (w+→e+ve)(z → mu+mu-)jj</i>, and the ME generator put
both intermediate bosons into the LHE file, this will return 2.
<a name="method10"></a>
<p/><strong>double MergingHooks::tms() </strong> <br/>
Returns the value used as the merging scale.
<p/> Filling output histograms for the event then proceeds along the
lines described above in "Histogramming the events".
<p/> The full procedure is outlined in <code>main82.cc</code>. Special
care needs to be taken when the output is stored in the form of HepMC
files for RIVET usage.
<h4>Defining a cut on lowest jet multiplicity events</h4>
<p/> It can sometimes happen that when generating LHE files, a fairly
restrictive cut has been used when generating the lowest multiplicity
matrix element configurations. Then, it can happen that states that
are (in the generation of a parton shower history) constructed by
reclustering from higher multiplicity configurations, do not pass
this matrix element cut.
<p/> Consider as an example pure QCD dijet merging, when up to one
additional jet should be merged. Three-jet matrix element
configurations for which the reclustered two-jet state does not pass
the cuts applied to the two-jet matrix element would never have been
produced by showering the two-jet matrix element. This means that the
three-jet matrix element includes regions of phase space that would
never have been populated by the parton shower. Thus, since the
matrix element phase space is larger than the shower phase space,
merging scale dependencies are expected. A priori, this is not
troublesome, since the aim of matrix element merging is to include
regions of phase space outside the range of the parton shower
approximation into the shower. An example is the inclusion of
configurations with only unordered histories.
<p/> Clearly, if the parton shower phase space is very constrained by
applying stringent cuts to the two-jet matrix element, merging scale
dependencies can become sizable, as was e.g. seen in [<a href="Bibliography.html" target="page">Lon11</a>]
when forcing shower emissions to be ordered both in the evolution
variable and in rapidity. To influence the effect of large phase
space differences for shower emissions and matrix element
configurations due to LHEF generation cuts, the user has to write a
small piece of code overwriting method
<a name="method11"></a>
<p/><strong>virtual double MergingHooks::dampenIfFailCuts(const Event& event) </strong> <br/>
multiplicity reclustered state as an input Event. From this input
event, the user can then check if matrix element cuts are
fulfilled. The return value will be internally multiplied to the
CKKW-L weight of the current event. Thus, if the user wishes to
suppress contributions not passing particular cuts, a number smaller
than unity can be returned.
<p/> Note that this method gives the user access to the lowest
multiplicity state, which ( e.g. in the case of incomplete histories)
does not have to be a <i>2 → 2</i> configuration. Also, changing the
weight of the current event by hand is of course a major intervention
in the algorithm, and should be considered very carefully. Generally,
if this facility would have to be used extensively, it is certainly
preferable to be less restrictive when applying additional,
non-merging-scale-related cuts to the matrix element.
<p/> An example how to force a cut on lowest multiplicity reclustered
states for pure QCD matrix element configurations is given by
<code>main83.cc</code> (to be used with e.g. <code>main82.cmnd</code>).
<h4>Influencing the construction of all possible histories</h4>
<p/> Even more powerful - and dangerous - is influencing the construction
of histories directly. This should only be attempted by expert users. If you
believe manipulations completely unavoidable, we advise you to take great care
when redefining the following functions.
<a name="method12"></a>
<p/><strong>virtual bool MergingHooks::canCutOnRecState() </strong> <br/>
In the base class this method returns false. If you redefine it
to return true then the method <code>doCutOnRecState(...)</code>
will be called for each reclustered state encountered in the generation of
all possible histories of the matrix element state.
<a name="method13"></a>
<p/><strong>virtual bool MergingHooks::doCutOnRecState(const Event& event) </strong> <br/>
This routine will be supplied internally with every possible reclustered
event that can be reached by reclustering any number of partons in
the matrix element input state. The new, reclustered, states can then be
analysed. If the method returns false, the history to which the state belongs
will be treated as if it were unordered, i.e. this path will only be chosen
if no other histories are available. In this way, the number of histories
not fulfilling the user criterion will be minimised.
<p/>
Clearly, these methods are highly intrusive. It could e.g. happen that no
history is allowed, which would make merging impossible. One example where
this method could be useful is if cuts on the core <i>2 → 2</i>
processes have to be checked, and the method
<code>MergingHooks::dampenIfFailCuts(const Event& event)</code> is not
sufficiently effective.
<h4>Defining the hard process matrix element</h4>
<p/> The MergingHooks class also allows the expert user to define the matrix
element of the hard process, by defining the method
<a name="method14"></a>
<p/><strong>virtual double MergingHooks::hardProcessME(const Event& inEvent) </strong> <br/>
This routine will be supplied internally with the reconstructed
lowest-multiplicity event. From this, it is possible to calculate the squared
matrix element of the hard process, by using the information stored in the
event record. The function should return a <code>double</code> value that
corresponds to the matrix element at the phase space point given by the input
event record. This number will then be multiplied to the product of splitting
functions that define the probability of the current path of the parton
shower history. In this way, the hard process configuration can be taken into
account when choosing the parton shower history, which is, internally, used
to generate the "merging weight".
<p/> The inclusion of the hard process matrix element into the choice
of histories becomes relevant when the hard process matrix element has very
strong phase space dependencies. QCD dijet cross sections for example strongly
depend on the transverse momentum of the jets. So far, the authors have not
encountered any changes upon inclusion of the full hard process matrix
element, even for the QCD dijet case.
<br/><br/><hr/>
<h3>Matrix element merging and HepMC output for RIVET</h3>
Examples how to produce matrix element merged events to be analysed
with RIVET are given by <code>main84.cc</code> and <code>main85.cc</code>.
<p/> The main issue is that the output of separate RIVET runs can not
in general be combined. To perform a matrix element merging, we
however need to runs over different LHE files. The solution to this
problem (so far) is to only perform one RIVET run for all matrix
elements, i.e. print the events for all ME parton multiplicities,
with the correct weights, to a single HepMC file. Since the correct
weight includes the cross section of the different samples after
Sudakov vetoes --- which is not a priori known --- the cross sections
have to be estimated in a test run, before the actual production run
is performed. Finally, the cross section of the last event in the
HepMC file has to be taken as the full merged cross section
<i>sigma_merge = Sum_{i=0}^N Sum_{j=0}*^{nEvents}
sigma_est(i)*wckkwl(j)</i>.
<p/> This procedure is outlined in <code>main84.cc</code>.
Input LHE files with only very inclusive cuts pose further difficulties. For
such files (which were already addressed under the heading <strong>Les Houches
events outside the matrix element region</strong>), the cross section after
the merging scale cut is not known before the cut is performed. Using Pythia's
<code>UserHooks</code> facilities, it is possible to produce a valid estimate
of the cross section after cuts. This however entails a careful cut definition
by the user, which might become cumbersome for some in-built merging scale
definitions. A reasonable alternative is using the switch
<p/><code>flag </code><strong> Merging:doXSectionEstimate </strong>
(<code>default = <strong>off</strong></code>)<br/>
If on, estimate cross section after merging scale cut. This switch has to be
used in conjunction with a merging scale definition (e.g.
<code>Merging:doPTLundMerging = on</code>). Then, this merging scale
definition will be used as a cut on the input events. After the requested
number of Monte Carlo events, the cross section after the cut can be extracted
by inferring the <code>Info::sigmaGen()</code> method, and the number of
accepted events by using <code>Info::nAccepted()</code>
<p/>
This switch also relies on knowledge on how many partons a LHE file should
contain. This is important for real-emission kinematics in the case of
NLO merging. The number of (additional) partons in a LHE file can be set with
<p/><code>mode </code><strong> Merging:nRequested </strong>
(<code>default = <strong>-1</strong></code>; <code>minimum = -1</code>)<br/>
Exact number of additional jets requested for a particular LHE file. If
a file should for example only contain <i>W<sup>+</sup> g g </i> events,
this switch should be set to "2" for this LHE file. For NLO merging
schemes (see <a href="NLOMerging.html" target="page">NLO Merging</a>), this number has to
be set.
<p/>
The usage of these switches to obtain the necessary cross section estimate is
illustrated in <code>main85.cc</code>. The example <code>main85.cc</code>
program is intended as a "front-end" for CKKW-L merging in Pythia8, so we will
discuss the program briefly. <code>main85.cc</code> should be used together
with an input file (like <code>main85.cmnd</code>). The executable should be
invoked with three arguments: the input file, the "name" of the input LHE
files, and the name of the output HepMC event file. To use the LHE files that
are shipped with the Pythia distribution, a valid usage would be
</p>
<code>./main85.exe ./main85.cmnd ./w_production ./myhepmc.hepmc</code>
</p>
If you want to use other input LHE files, note
that <code>main85.cc</code> assumes the naming
convention <i>name_tree_#nAdditionalJets.lhe</i>. All settings can
be included though the input file, so that <code>main85.cc</code> does not
have to be changed explicitly. <code>main85.cc</code> first switches off
showers, multiparton interactions and hadronisation, and estimates the cross
sections (after enforcing the merging scale cut) of samples for different
numbers of additional jets. Then, showers, MPI and hadronisation are switched
on again, and the CKKW-L merging procedure is performed. Events will be read
in a decreasing sequence of jet multiplicities, which also means that e.g.
events with two additional partons in the LHE file will be printed to the
HepMC file before events with one additional parton.
<br/><br/><hr/>
<h3>Further variables</h3>
For more advanced manipulations of the merging machinery, all
parameter changes that were investigated in [<a href="Bibliography.html" target="page">Lon11</a>] are
supplied. Please check [<a href="Bibliography.html" target="page">Lon11</a>] for a detailed discussion of
the switches.
<p/> These switches allow enthusiastic users to perform a systematic
assessment of the merging prescription. Apart from this, we advise the
non-expert user to keep the default values.
<p/><code>mode </code><strong> Merging:nQuarksMerge </strong>
(<code>default = <strong>5</strong></code>; <code>minimum = 2</code>; <code>maximum = 5</code>)<br/>
This switch controls which quarks flavours (labelled by PDG id's) are
considered additional partons. If e.g. set to 4, then u-, d-, c- and s-quarks
will be merged, while b-quarks will not be considered in the merging
(corresponding to a 4-flavour merging scheme). We advise caution when
changing this number. In particular, please ensure that the allowed flavour
for additional partons in the input LHE file does not exceed this value, since
unnecessary double-counting might occur otherwise.
<p/><code>flag </code><strong> Merging:includeMassive </strong>
(<code>default = <strong>on</strong></code>)<br/>
If on, use the correct massive evolution variable and massive
splitting kernels in the reconstruction and picking of parton shower
histories of the matrix element. If off, reconstruct evolution
scales, kinematics and splitting kernels as if all partons were
massless.
<p/><code>flag </code><strong> Merging:enforceStrongOrdering </strong>
(<code>default = <strong>off</strong></code>)<br/>
If on, preferably pick parton shower histories of the matrix element
which have strongly ordered consecutive splittings, i.e. paths in
which consecutive reclustered evolution scales are separated by a
user-defined factor.
<p/><code>parm </code><strong> Merging:scaleSeparationFactor </strong>
(<code>default = <strong>1.0</strong></code>; <code>minimum = 1.0</code>; <code>maximum = 10.0</code>)<br/>
The factor by which scales should differ to be classified as strongly
ordered.
<p/><code>flag </code><strong> Merging:orderInRapidity </strong>
(<code>default = <strong>off</strong></code>)<br/>
If on, preferably pick parton shower histories of the matrix element
with consecutive splittings ordered in rapidity and <i>pT</i>.
<p/><code>flag </code><strong> Merging:pickByFullP </strong>
(<code>default = <strong>on</strong></code>)<br/>
If on, pick parton shower histories of the matrix element by the full
shower splitting kernels, including potential ME corrections and
Jacobians from joined evolution measures.
<p/><code>flag </code><strong> Merging:pickByPoPT2 </strong>
(<code>default = <strong>off</strong></code>)<br/>
If on, pick parton shower histories of the matrix element by the
shower splitting kernels divided by the evolution <i>pT</i>.
<p/><code>flag </code><strong> Merging:pickBySumPT </strong>
(<code>default = <strong>off</strong></code>)<br/>
If on, exclusively pick parton shower histories of the matrix element
for which have the smallest sum of scalar evolution <i>pT</i> for
consecutive splittings has been calculated.
<p/><code>flag </code><strong> Merging:includeRedundant </strong>
(<code>default = <strong>off</strong></code>)<br/>
If on, then also include PDF ratios and <i>α<sub>s</sub></i>
factors in the splitting probabilities used for picking a parton shower
history of the matrix element, when picking histories by the full shower
splitting probability. As argued in [<a href="Bibliography.html" target="page">Lon11</a>], this should not
be done since a reweighting with PDF ratios and <i>α<sub>s</sub></i>
factors will be performed. However, it can give useful insight in how
sensitive the results are to the prescription on how to choose PS
histories.
<p/><code>parm </code><strong> Merging:nonJoinedNorm </strong>
(<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 10.0</code>)<br/>
Normalisation factor with which to multiply splitting probability for
splittings without joined evolution equation.
<p/><code>parm </code><strong> Merging:fsrInRecNorm </strong>
(<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 10.0</code>)<br/>
Normalisation factor with which to multiply splitting probability for
final state splittings with an initial state recoiler.
<p/><code>parm </code><strong> Merging:aCollFSR </strong>
(<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 10.0</code>)<br/>
Factor with which to multiply the scalar <i>pT</i> of a final state
splitting, when choosing the history by the smallest sum of scalar
<i>pT</i>. Default value taken from Herwig++ [<a href="Bibliography.html" target="page">Tul09</a>].
<p/><code>parm </code><strong> Merging:aCollISR </strong>
(<code>default = <strong>0.9</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 10.0</code>)<br/>
Factor with which to multiply the scalar <i>pT</i> of an initial state
splitting, when choosing the history by the smallest sum of scalar
<i>pT</i>. Default value taken from Herwig++ [<a href="Bibliography.html" target="page">Tul09</a>].
<p/><code>mode </code><strong> Merging:unorderedScalePrescrip </strong>
(<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 1</code>)<br/>
When the parton shower history of the matrix element contains a
sequence of splittings which are not ordered in evolution <i>pT</i>
(called an unordered history), this sequence is interpreted as a combined
emission. Then, a decision on which starting scale for trial emissions
off reconstructed states in this sequence of unordered splittings has
to be made. Two options are available:
<br/><code>option </code><strong> 0</strong> : Use larger of the two reconstructed (unordered)
scales as starting scale.
<br/><code>option </code><strong> 1</strong> : Use smaller of the two reconstructed (unordered)
scales as starting scale.
<p/><code>mode </code><strong> Merging:unorderedASscalePrescrip </strong>
(<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 1</code>)<br/>
Prescription which scale to use to evaluate <i>α<sub>s</sub></i>
weight for splittings in a sequence of splittings which are not ordered
in evolution <i>pT</i>.
<br/><code>option </code><strong> 0</strong> : Use the combined splitting scale as argument in
<i>α<sub>s</sub></i>, for both splittings.
<br/><code>option </code><strong> 1</strong> : Use the true reconstructed scale as as argument in
<i>α<sub>s</sub></i>, for each splitting separately.
<p/><code>mode </code><strong> Merging:unorderedPDFscalePrescrip </strong>
(<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 1</code>)<br/>
Prescription which scale to use to evaluate ratios of parton distributions
for splittings in a sequence of splittings which are not ordered
in evolution <i>pT</i>.
<br/><code>option </code><strong> 0</strong> : Use the combined splitting scale as argument in PDF ratios,
for both splittings.
<br/><code>option </code><strong> 1</strong> : Use the true reconstructed scale as argument in PDF
ratios, for each splitting separately.
<p/><code>mode </code><strong> Merging:incompleteScalePrescrip </strong>
(<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
When no complete parton shower history (i.e. starting from a
<i>2 → 2</i> process) for a matrix element with additional jets
can be found, such a configuration is said to have an incomplete history.
Since in incomplete histories, not all shower starting scales are
determined by clusterings, a prescription for setting the starting scale
of trial showers in incomplete histories is needed. Three options are
provided.
<br/><code>option </code><strong> 0</strong> : Use factorisation scale as shower starting scale
for incomplete histories.
<br/><code>option </code><strong> 1</strong> : Use <i>sHat</i> as shower starting scale for
incomplete histories.
<br/><code>option </code><strong> 2</strong> : Use <i>s</i> as shower starting scale for
incomplete histories.
<p/><code>flag </code><strong> Merging:allowColourShuffling </strong>
(<code>default = <strong>off</strong></code>)<br/>
If on, this will allow the algorithm to swap one colour index in the state,
when trying to find all possible clusterings, if no clustering has been
found, but more clusterings had been requested. In this way, some incomplete
histories can be avoided. Generally, we advise the non-expert user to not
touch this switch, because a slight change in the colour structure can change
the radiation pattern. To however study the sensitivity of the predictions on
these effects, allowing for colour reshuffling can be useful.
<p/><code>flag </code><strong> Merging:usePythiaQRenHard </strong>
(<code>default = <strong>on</strong></code>)<br/>
If on, this will allow the algorithm to use a dynamical renormalisation scale
to evaluate the strong couplings of the core hard process in dijet and
prompt photon events.
This means that the value of <i>α<sub>s</sub></i> used as coupling
of the hard process in the matrix element generation will be replaced with
a running coupling evaluated at the geometric mean of the squared transverse
masses of the two outgoing particles, as is the default prescription in
Pythia.
<p/><code>flag </code><strong> Merging:usePythiaQFacHard </strong>
(<code>default = <strong>on</strong></code>)<br/>
If on, this will allow the algorithm to use a dynamical factorisation scale
to evaluate parton distributions associated with the hadronic cross section
of the core hard process in dijet and prompt photon events.
In the calculation of PDF ratios as part of the CKKW-L weight of an event,
parton distributions that should be evaluated at the scale of the core
2 - >2 process will be evaluated using the dynamical factorisation scale
Pythia would attribute to this process. This means that the hard process
factorisation scale is set to the smaller of the squared transverse masses
of the two outgoing particles.
<p/><code>flag </code><strong> Merging:mayRemoveDecayProducts </strong>
(<code>default = <strong>off</strong></code>)<br/>
Remove products of resonances in the hard process, in case Pythia generates
decay products before merging. This makes merging possible even for an
indeterminate final state, if Pythia itself has produced the decay products.
The merging methods will instead be invoked on the "non-decayed" event,
thus removing the limitation to only one decay channel when performing
the merging.
This switch is necessary e.g. for slepton pair production in association with
additional QCD jets, if the input LHE file contains the resonant sleptons,
and Pythia decides on a decay according to the branching fractions read from
SLHA input.
<p/><code>flag </code><strong> Merging:allowSQCDClustering </strong>
(<code>default = <strong>off</strong></code>)<br/>
Allow clustering of gluon emission off squarks.
<p/><code>flag </code><strong> Merging:allowWClustering </strong>
(<code>default = <strong>off</strong></code>)<br/>
Allow clustering of W boson, if interpreted as a final state emission. This
switch should not be used until electro-weak showers become available.
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