Update to pythi8.170

[u/mrichter/AliRoot.git] / PYTHIA8 / pythia8170 / xmldoc / MatrixElementMerging.xml

<chapter name="Matrix Element Merging">

<h2>Matrix Element Merging</h2>

CKKW-L merging <ref>Lon01</ref> 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 <ref>Lon11</ref>. To
perform matrix element merging,  the user has to supply LHE
files <ref>Alw07</ref> 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> and <code>main84.cc</code>, together with  the
input files <code>main81.cmnd</code>, <code>main82.cmnd</code> and 
<code>main84.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
<strong>http://home.thep.lu.se/~torbjorn/pythia8/mergingworksheet8160.pdf
</strong>

<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 <ei>&alpha;<sub>s</sub>(M<sub>Z</sub>)</ei>)  used to evaluate
<ei>&alpha;<sub>s</sub></ei>. 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 <ei> merging scale </ei>. 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 <ei>2 -> 2</ei> process is
regularised with a <ei>pTmin</ei> cut of pTminCut = 100 GeV, and
the <ei>2 - >3</ei> sample is regularised with a <ei>kTmin</ei>-cut of 
kTminCut = 50 GeV. This would mean that when reclustering
the  emission in the 2 -> 3 sample, we could end up with a 
pT value <ei>pTminNow</ei> of the 2 -> 2 configuration with 
<ei>pTminCut > pTminNow</ei>, 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
 <ei>0 &lt;= n &lt;= N</ei>  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 <ei>pp &rarr; Z + jets &rarr; e+e- + jets</ei> process
are desired, generate the matrix element events with the <ei>Z</ei> 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 <ei>e+&nu;<sub>e</sub>+ jets</ei> and 
<ei>e-&nu;&#772;<sub>e</sub> + jets</ei>
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
<ref>Dob01</ref> files to be analysed  with RIVET <ref>Buc10</ref>, 
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 <ei>kT</ei>,
minimal evolution <ei>pT</ei> 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>

<flag name="Merging:doKTMerging" default="off">
If the additional jets in the LHE files have been regulated by
a <ei>kT</ei> cut, the user can supply the merging scale definition by
setting this flag to on. <ei>kT</ei> here and below means cutting on
Durham <ei>kT</ei> for <ei>e+e-</ei>  collisions, and cutting on 
longitudinally invariant <ei>kT</ei> for hadronic  collisions. Please note 
that this particular merging scale definition will check <ei>kT</ei> between
all pairs of <ei>u,d,c,s,b,g</ei> partons. 
</flag>

</p>
Currently, the name longitudinally invariant <ei>kT</ei> is used
for a few jet recombination algorithms with slightly different
jet measures. A specific form can be chosen by setting the switch

<modepick name="Merging:ktType" default="1" min="1" max="3">
Precise functional definition of longitudinally
invariant <ei>kT</ei>. For e+e- collisions, <ei>Durham kT</ei> is
always defined by the square root of <ei>min{ 2*min[ </sub>
E<sub>i</sub><sup>2</sup>, E<sub>j</sub><sup>2</sup>] * [ 1 -
cos&theta;<sub>ij</sub>] }</ei>, so that this switch will have no effect.
<option value="1"> Longitudinally invariant <ei>kT</ei> is defined by
the  square root of the minimum of minimal jet kinematic <ei>pT</ei>
(<ei>p<sub>Tkin,min</sub><sup>2</sup> = min{ p<sub>T,i</sub><sup>2</sup> }
 </ei>) and <ei>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>] *
 [ (&Delta;y<sub>ij</sub>)<sup>2</sup> + 
(&Delta;&phi;<sub>ij</sub>)<sup>2</sup> ] / D<sup>2</sup> }</ei> , i.e. 
<ei>kT = min{ &radic;p<sub>Tkin,min</sub><sup>2</sup>,
 &radic;p<sub>Tlon,min</sub><sup>2</sup> }</ei> for hadronic collisions. Note 
that the true rapidity of partons is used.
</option>
<option value="2">Longitudinally invariant <ei>kT</ei> is defined by
the  square root of the minimum of minimal jet kinematic <ei>pT</ei>
(<ei>p<sub>Tkin,min</sub><sup>2</sup> = min{ p<sub>T,i</sub><sup>2</sup>
 } </ei>) and <ei>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>] * [
(&Delta;&eta;<sub>ij</sub>)<sup>2</sup> +
(&Delta;&phi;<sub>ij</sub>)<sup>2</sup> ] / D<sup>2</sup> }</ei>, i.e. 
<ei>kT = min{ &radic;p<sub>Tkin,min</sub><sup>2</sup>,
 &radic;p<sub>Tlon,min</sub><sup>2</sup> }</ei> 
for hadronic collisions. Note that the pseudorapidity of partons is used.
</option>
<option value="3"> Longitudinally invariant <ei>kT</ei> is defined by
the  square root of the minimum of minimal jet kinematic <ei>pT</ei>
(<ei>p<sub>Tkin,min</sub><sup>2</sup> = min{ p<sub>T,i</sub><sup>2</sup>
 } </ei>) and
<ei>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(&Delta;&eta;<sub>ij</sub>) -
cos(&Delta;&phi;<sub>ij</sub>) ] / D<sup>2</sup> } </ei>,  i.e. 
<ei>kT = min{ &radic;p<sub>Tkin,min</sub><sup>2</sup>
, &radic;p<sub>Tlon,min</sub><sup>2</sup> }</ei> 
for hadronic collisions.
</option>
</modepick>

<modeopen name="Merging:nJetMax" default="0" min="0">
Maximal number of additional jets in the matrix element
</modeopen>

<parm name="Merging:TMS" default="0.0">
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 <ei>kT</ei>-merging, this
would be the value of the <ei>kT</ei>-cut  in GeV. For any merging scale
definition, this input is considered the actual value of the merging
scale.
</parm>

<word name="Merging:Process" default="void">
The string specifying the hard core process, in MG4/ME notation. 
</word>

</p>
If e.g. <ei>W + jets</ei> 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 
<ei>pp&rarr;Z W<sup>+</sup>&rarr;q q&#772; e+&nu;<sub>e</sub> + jets</ei>, 
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.


<flag name="Merging:doMGMerging" default="off">
Even easier, but highly non-general, is to perform the merging with
MadGraph/MadEvent-produced LHE files, with a merging scale defined by
a <ei>kT</ei> 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>.
</flag>


<h4>Merging with merging scale defined in Pythia evolution pT:</h4>

If the LHE file has been regularised by cutting on the minimal Pythia evolution
pT in the state, this can also be used as a merging scale right away. For this,
change the switch

<flag name="Merging:doPTLundMerging" default="off">
The merging scale is then defined by finding the minimal Pythia evolution pT
between sets of radiator, emitted an recoiler partons. For this
particular merging scale definition, <ei>u,d,c,s,b,g</ei> are considered
partons. The Pythia evolution pT of a single three-parton set is defined by
<p/>
<ei>pT<sub>evol</sub> = z<sub>ijk</sub>(1-z<sub>ijk</sub>)
   Q<sub>ij</sub><sup>2</sup></ei> for FSR, where <ei>i</ei> is the radiating
   parton, <ei>j</ei> is the emitted parton and <ei>k</ei> is the recoiler, and
   <ei> Q<sub>ij</sub><sup>2</sup> =
      (p<sub>i</sub> + p<sub>j</sub>)<sup>2</sup> </ei>, and
   <ei>z<sub>ijk</sub> = 
      x<sub>i,jk</sub> / (x<sub>i,jk</sub> + x<sub>j,ik</sub>)</ei> with
   <ei>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> </ei>
<p/>
<ei>pT<sub>evol</sub> = (1-z<sub>ijk</sub>)
   Q<sub>ij</sub><sup>2</sup></ei> for ISR, where <ei>i</ei> is the radiating
   parton, <ei>j</ei> is the emitted parton and <ei>k</ei> is the second initial
   state parton, and
   <ei> Q<sub>ij</sub><sup>2</sup> =
     -(p<sub>i</sub> - p<sub>j</sub>)<sup>2</sup> </ei>, and
   <ei>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> </ei>.

<p/>
When using this option, the merging scale is defined by the minimum 
<ei>pT<sub>evol</sub></ei> for all combinations of three partons in the event, 
irrespectively 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 <ei>kT</ei>-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>.
</flag>

<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 pT of jets (<ei>pT<sub>i</sub></ei>), combined with a cut on 
<ei> &Delta;R<sub>ij</sub></ei> between jets and a cut on invariant mass
<ei> Q<sub>ij</sub></ei> of jet pairs. The combination of these standard cuts
can also serve as a merging scale. For this, use this setting

<flag name="Merging:doCutBasedMerging" default="off">
This switch will use cuts on (<ei>pT<sub>i</sub></ei>), 
<ei> &Delta;R<sub>ij</sub></ei>  and
<ei> Q<sub>ij</sub></ei> to define when parton shower emissions are allowed.
Please note for this particular merging scale definition, only light jets
(<ei>u,d,c,s,g</ei>) are checked.
</flag>

<p/>
The values of the cuts will then be read from

<parm name="Merging:QijMS" default="0.0">
The value of the invariant mass cut <ei> Q<sub>ij</sub></ei> of pairs of final
state partons used in the matrix element generation.
</parm>

<parm name="Merging:pTiMS" default="0.0">
The value of the minimal transverse momentum cut <ei> pT<sub>i</sub></ei> on 
final state partons, as used in the matrix element generation. 
</parm>

<parm name="Merging:dRijMS" default="0.0">
The value of the minimal <ei> &Delta;R<sub>ij</sub></ei> separation between
pairs of final state partons used in the matrix element generation, where
<ei> &Delta;R<sub>ij</sub><sup>2</sup> = (&Delta;y<sub>ij</sub>)<sup>2</sup> + 
(&Delta;&phi;<sub>ij</sub>)<sup>2</sup></ei>.
</parm>

<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 <ei> &Delta;R<sub>ij</sub> = 0.1 </ei>, 
<ei>pT<sub>i</sub>= 20 GeV</ei> and <ei> Q<sub>ij</sub> = 40 GeV</ei>, 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. To change this default behaviour, use the flag

<flag name="Merging:enforceCutOnLHE" default="on">
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. 
</flag>

<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 <strong>Merging:Process</strong>
 
<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. <ei>W<sup>+</sup> + jets</ei> and <ei>W<sup>-</sup> + jets</ei>),
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 <ei>pp &rarr; e+ &nu;<sub>e</sub> + jets</ei>
 and <ei>pp &rarr; e- &nu;&#772;<sub>e</sub> + jets</ei> 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
<ei>pp &rarr; e+ &nu;<sub>e</sub></ei> and
<ei>pp &rarr; &mu;+ &nu;<sub>&mu;</sub></ei> 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 
<ei>pp &rarr; e+ e- </ei> events mixed with 
<ei>pp &rarr; e+ &nu;<sub>e</sub></ei> events, since particles matching at
least one container can be found in both cases. Another example for the usage
of containers is mixing <ei>pp &rarr; e+ &nu;<sub>e</sub></ei> and
<ei>pp &rarr; tt&#772; &rarr; e+ &nu;<sub>e</sub> e- &nu;&#772;<sub>e</sub>
  bb&#772;</ei>. 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 <ei>pp &rarr; Z &rarr; bb&#772; </ei>, we should ensure that the lowest
multiplicity state contains a colour-singlet bb&#772;-pair. When
reconstructing intermediate lower multiplicity states from multi-jet matrix
elements, we should thus always be able to find at least one bb&#772;-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 <ei>
assumed that all</ei> 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
&alpha;<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() &nbsp;</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() * &sigma;<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 program
<code>main84.cc</code>).

<p/> Examples how to use these options are given in <code>main81.cc</code> 
(<ei>kT</ei> merging) and <code>main84.cc</code> (automatic MG/ME merging 
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

<flag name="Merging:doUserMerging" default="off">
General user defined merging on/off.
</flag>

</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/>
<method name="MergingHooks::MergingHooks()">
</method>
<method name="virtual MergingHooks::~MergingHooks()">
</method>
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.

<method name="virtual double MergingHooks::tmsDefinition(const Event& event)">
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>.
</method>

<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:

<method name="int MergingHooks::nMaxJets()">
Return the maximum number of additional jets to be merged.
</method>

<method name="int MergingHooks::nHardOutPartons()">
Returns the number of outgoing partons in the hard core process.
</method>

<method name="int MergingHooks::nHardOutLeptons()">
Returns the number of outgoing leptons in the hard core process.
</method>

<method name="int MergingHooks::nHardInPartons()">
Returns the number of incoming partons in the hard core process.
</method>

<method name="int MergingHooks::nHardInLeptons()">
Returns the number of incoming leptons in the hard core process.
</method>

<method name="int MergingHooks::nResInCurrent()">
The number of resonances in the hard process reconstructed from the
current event. If e.g. the ME configuration was 
<ei>pp -> (w+->e+ve)(z -> mu+mu-)jj</ei>, and the ME generator put 
both intermediate bosons into the LHE file, this will return 2.
</method>

<method name="double MergingHooks::tms()">
 Returns the value used as the merging scale.
</method>

<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 <ref>Lon11</ref>
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

<method 
  name="virtual double MergingHooks::dampenIfFailCuts(const Event&
event)"> This routine will be supplied internally with the lowest
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.
</method>

<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 <ei>2 &rarr; 2</ei> 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.

<method name="virtual bool MergingHooks::canCutOnRecState()">
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.  
</method>

<method name="virtual bool MergingHooks::doCutOnRecState(const Event&
event)">
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. 
</method>

<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 <ei>2 -> 2</ei> processes
have to be checked, and the method 
<code>MergingHooks::dampenIfFailCuts(const Event& event)</code> is not 
sufficiently effective.


<br/><br/><hr/>
<h3>Matrix element merging and HepMC output for RIVET</h3>

An example how to produce matrix element merged events to be analysed
with RIVET is given by <code>main84.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
<ei>sigma_merge = Sum_{i=0}^N Sum_{j=0}*^{nEvents} 
sigma_est(i)*wckkwl(j)</ei>.

<p/> This procedure is outlined in <code>main84.cc</code>.

<br/><br/><hr/>
<h3>Further variables</h3>

For more advanced manipulations of the merging machinery, all
parameter  changes that were investigated in <ref>Lon11</ref> are
supplied. Please  check <ref>Lon11</ref> 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.

<flag name="Merging:includeMassive" default="on">
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.
</flag>

<flag name="Merging:enforceStrongOrdering" default="off">
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.
</flag>

<parm name="Merging:scaleSeparationFactor" default="1.0" min="1.0" max="10.0">
The factor by which scales should differ to be classified as strongly
ordered.
</parm>

<flag name="Merging:orderInRapidity" default="off">
If on, preferably pick parton shower histories of the matrix element
with  consecutive splittings ordered in rapidity and <ei>pT</ei>.
</flag>

<flag name="Merging:pickByFullP" default="on">
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.
</flag>

<flag name="Merging:pickByPoPT2" default="off">
If on, pick parton shower histories of the matrix element by the
shower  splitting kernels divided by the evolution <ei>pT</ei>.
</flag>

<flag name="Merging:pickBySumPT" default="off">
If on, exclusively pick parton shower histories of the matrix element
for which have the smallest sum of scalar evolution <ei>pT</ei> for consecutive
splittings has been calculated.
</flag>

<flag name="Merging:includeRedundant" default="off">
If on, then also include PDF ratios and <ei>&alpha;<sub>s</sub></ei> 
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  <ref>Lon11</ref>, this should not
be done since a reweighting with PDF ratios and <ei>&alpha;<sub>s</sub></ei>
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.
</flag>

<parm name="Merging:nonJoinedNorm" default="1.0" min="0.0" max="10.0">
Normalisation factor with which to multiply splitting probability for
splittings without joined evolution equation.
</parm>

<parm name="Merging:fsrInRecNorm" default="1.0" min="0.0" max="10.0">
Normalisation factor with which to multiply splitting probability for
final state splittings with an initial state recoiler.
</parm>

<parm name="Merging:aCollFSR" default="1.0" min="0.0" max="10.0">
Factor with which to multiply the scalar <ei>pT</ei> of a final state
splitting, when choosing the history by the smallest sum of scalar
<ei>pT</ei>. Default value taken from Herwig++ <ref>Tul09</ref>.
</parm>

<parm name="Merging:aCollISR" default="0.9" min="0.0" max="10.0">
Factor with which to multiply the scalar <ei>pT</ei> of an initial state
splitting, when choosing the history by the smallest sum of scalar
<ei>pT</ei>. Default value taken from Herwig++ <ref>Tul09</ref>.
</parm>

<modepick name="Merging:unorderedScalePrescrip" default="0" min="0" max="1">
When the parton shower history of the matrix element contains a
sequence of splittings which are not ordered in evolution <ei>pT</ei> 
(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:
<option value="0"> Use larger of the two reconstructed (unordered)
scales as  starting scale.
</option>
<option value="1"> Use smaller of the two reconstructed (unordered)
scales as  starting scale.
</option>
</modepick>

<modepick name="Merging:unorderedASscalePrescrip" default="1" min="0" max="1">
Prescription which scale to use to evaluate <ei>&alpha;<sub>s</sub></ei> 
weight for  splittings in a sequence of splittings which are not ordered 
in evolution <ei>pT</ei>.
<option value="0"> Use the combined splitting scale as argument in
<ei>&alpha;<sub>s</sub></ei>, for both splittings.
</option>
<option value="1"> Use the true reconstructed scale  as as argument in
<ei>&alpha;<sub>s</sub></ei>, for each splitting separately.
</option>
</modepick>

<modepick name="Merging:unorderedPDFscalePrescrip" default="0" min="0" max="1">
Prescription which scale to use to evaluate ratios of parton distibutions 
for splittings in a sequence of splittings which are not ordered 
in evolution <ei>pT</ei>.
<option value="0"> Use the combined splitting scale as argument in PDF ratios,
for both splittings.
</option>
<option value="1"> Use the true reconstructed scale as argument in PDF
ratios, for each splitting separately.
</option>
</modepick>

<modepick name="Merging:incompleteScalePrescrip" default="0" min="0" max="2">
When no complete parton shower history (i.e. starting from a 
<ei>2 &rarr; 2</ei> 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.
<option value="0"> Use factorisation scale as shower starting scale
for  incomplete histories.
</option>
<option value="1"> Use <ei>sHat</ei> as shower starting scale for  
incomplete histories.
</option>
<option value="2"> Use <ei>s</ei> as shower starting scale for  
incomplete histories.
</option>
</modepick>

<flag name="Merging:allowColourShuffling" default="off">
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.
</flag>

<flag name="Merging:usePythiaQRenHard" default="on">
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 <ei>&alpha;<sub>s</sub></ei> 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.
</flag>

<flag name="Merging:usePythiaQFacHard" default="on">
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. 
</flag>

</chapter>

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