source: git/external/fastjet/contribs/RecursiveTools/README@ a63afb1

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RecursiveTools FastJet contrib
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The RecursiveTools FastJet contrib aims to provide a common contrib
for a number of tools that involve recursive reclustering/declustering
of a jet for tagging or grooming purposes.

Currently it contains:

- ModifiedMassDropTagger
  This corresponds to arXiv:1307.0007 by Mrinal Dasgupta, Alessandro
  Fregoso, Simone Marzani and Gavin P. Salam

- SoftDrop
  This corresponds to arXiv:1402.2657 by Andrew J. Larkoski, Simone
  Marzani, Gregory Soyez, Jesse Thaler

- RecursiveSoftDrop
- BottomUpSoftDrop
  This corresponds to arXiv:1804.03657 by Frederic Dreyer, Lina
  Necib, Gregory Soyez and Jesse Thaler

- IteratedSoftDrop
  This corresponds to arXiv:1704.06266 by Christopher Frye, Andrew J.
  Larkoski, Jesse Thaler, Kevin Zhou

- Recluster
  A generic tool to recluster a given jet into subjets
  Note: a Recluster class is available natively in FastJet since v3.1.
        Users are therefore encouraged to use the FastJet version
        rather than this one which is mostly provided for
        compatibility of this contrib with older versions of FastJet.

The interface for these tools is described in more detail below, with
all of the available options documented in the header files.

One note about nomenclature.  A groomer is a procedure that takes a
PseudoJet and always returns another (non-zero) PseudoJet.  A tagger is
a procedure that takes a PseudoJet, and either returns another PseudoJet
(i.e. tags it) or returns an empty PseudoJet (i.e. doesn't tag it).

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ModifiedMassDropTagger
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The Modified Mass Drop Tagger (mMDT) recursively declusters a jet,
following the largest pT subjet until a pair of subjets is found that
satisfy the symmetry condition on the energy sharing

   z > z_cut

where z_cut is a predetermined value.  By default, z is calculated as
the scalar pT fraction of the softest subjet.  Note that larger values
of z_cut correspond to a more restrictive tagging criteria.

By default, mMDT will first recluster the jet using the CA clustering
algorithm, which means that mMDT can be called on any jet, regardless
of the original jet finding measure.

A default mMDT can be created via

   double z_cut = 0.10;
   ModifiedMassDropTagger mMDT(z_cut);

More options are available in the full constructor.  To apply mMDT,
one simply calls it on the jet of interest.

   PseudoJet tagged_jet = mMDT(original_jet);

Note that mMDT is a tagger, such that tagged_jet will only be non-zero
if the symmetry cut z > z_cut is satisfied by some branching of the
clustering tree.  

To gain additional information about the mMDT procedure, one can use

   tagged_jet.structure_of<ModifiedMassDropTagger>()

which gives access to information about the delta_R between the tagged
subjets, their z value, etc.

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SoftDrop
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The SoftDrop procedure is very similar to mMDT, albeit with a 
generalised symmetry condition:
 
   z > z_cut * (R / R0)^beta

Note that larger z_cut and smaller beta correspond to more aggressive
grooming of the jet.

SoftDrop is intended to be used as a groomer (instead of as a tagger),
such that if the symmetry condition fails throughout the whole
clustering tree, SoftDrop will still return a single particle in the
end.  Apart from the tagger/groomer distinction, SoftDrop with beta=0 is
the same as mMDT.

A default SoftDrop groomer can be created via:

   double z_cut = 0.10;
   double beta  = 2.0;
   double R0    = 1.0; // this is the default value
   SoftDrop sd(z_cut,beta,R0);

and acts on a desired jet as

   PseudoJet groomed_jet = sd(original_jet);

and additional information can be obtained via

   groomed_jet.structure_of<SoftDrop>()

SoftDrop is typically called with beta > 0, though beta < 0 is still a
viable option.  Because beta < 0 is infrared-collinear unsafe in
grooming mode, one probably wants to switch to tagging mode for negative
beta, via set_tagging_mode().

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RecursiveSoftDrop
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The RecursiveSoftDrop procedure applies the Soft Drop procedure N times 
in a jet in order to find up to N+1 prongs.  N=0 makes no modification
to the jet, and N=1 is equivalent to the original SoftDrop.

Once one has more than one prong, one has to decide which will be
declustered next.  At each step of the declustering procedure, one
undoes the clustering which has the largest declustering angle
(amongst all the branches that are searched for substructure). [see
"set_fixed_depth" below for an alternative]

Compared to SoftDrop, RecursiveSoftDrop takes an extra argument N
specifying the number of times the SoftDrop procedure is recursively
applied. Negative N means that the procedure is applied until no
further substructure is found (i.e. corresponds to taking N=infinity).

   double z_cut = 0.10;
   double beta  = 2.0;
   double R0    = 1.0; // this is the default value
   int N        = -1;  
   RecursiveSoftDrop rsd(z_cut, beta, N, R0);

One then acts on a jet as

   PseudoJet groomed_jet = rsd(jet)

and get additional information via

   groomed_jet.structure_of<RecursiveSoftDrop>()

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IteratedSoftDrop
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Iterated Soft Drop (ISD) is a repeated variant of SoftDrop.  After
performing the Soft Drop procedure once, it logs the groomed symmetry
factor, then recursively performs Soft Drop again on the harder
branch.  This procedure is repeated down to an (optional) angular cut
theta_cut, yielding a set of symmetry factors from which observables
can be built.

An IteratedSoftDrop tool can be created as follows:

  double beta = -1.0;
  double z_cut = 0.005;
  double theta_cut = 0.0;
  double R0 = 0.5;        // characteristic radius of jet algorithm
  IteratedSoftDrop isd(beta, z_cut, double theta_cut, R0);

By default, ISD applied on a jet gives a result of type
IteratedSoftDropInfo that can then be probed to obtain physical
observables

  IteratedSoftDropInfo isd_info = isd(jet);

  unsigned int multiplicity = isd_info.multiplicity();
  double kappa = 1.0;     // changes angular scale of ISD angularity
  double isd_width = isd_info.angularity(kappa);
  vector<pair<double,double> > zg_thetags = isd_info.all_zg_thetag();
  vector<pair<double,double> > zg_thetags = isd_info();
  for (unsigned int i=0; i< isd_info.size(); ++i){
    cout << "(zg, theta_g)_" << i << " = "
         << isd_info[i].first << " " <<  isd_info[i].second << endl;
  }

Alternatively, one can directly get the multiplicity, angularity, and
(zg,thetag) pairs from the IteratedSoftDrop class, at the expense of
re-running the declustering procedure:

  unsigned int multiplicity = isd.multiplicity(jet);
  double isd_width = isd.angularity(jet, 1.0);
  vector<pair<double,double> > zg_thetags = isd.all_zg_thetag(jet);


Note: the iterative declustering procedure is the same as what one
  would obtain with RecursiveSoftDrop with an (optional) angular cut
  and recursing only in the hardest branch [see the "Changing
  behaviour" section below for details], except that it returns some
  information about the jet instead of a modified jet as RSD does.


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BottomUpSoftDrop
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This is a bottom-up version of the RecursiveSoftDrop procedure, in a
similar way as Pruning can be seen as a bottom-up version of Trimming.

In practice, the jet is reclustered and at each step of the clustering
one checks the SoftDrop condition

   z > z_cut * (R / R0)^beta

If the condition is met, the pair is recombined. If the condition is
not met, only the hardest of the two objects is kept for further
clustering and the softest is rejected.

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Recluster
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  *** NOTE: this is provided only for backwards compatibility ***
  *** with FastJet <3.1. For FastJet >=3.1, the native        ***
  *** fastjet::Recluster is used instead                      ***

The Recluster class allows the constituents of a jet to be reclustered
with a different recursive clustering algorithm.  This is used
internally in the mMDT/SoftDrop/RecursiveSoftDrop/IteratedSoftDrop
code in order to recluster the jet using the CA algorithm.  This is
achieved via

  Recluster ca_reclusterer(cambridge_algorithm,
                        JetDefinition::max_allowable_R);
  PseudoJet reclustered_jet = ca_reclusterer(original_jet);

Note that reclustered_jet creates a new ClusterSequence that knows to
delete_self_when_unused.

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Changing behaviour
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The behaviour of the all the tools provided here
(ModifiedMassDropTagger, SoftDrop, RecursiveSoftDrop and
IteratedSoftDrop) can be tweaked using the following options:

SymmetryMeasure = {scalar_z, vector_z, y, theta_E, cos_theta_E}
  [constructor argument]
  : The definition of the energy sharing between subjets, with 0
    corresponding to the most asymmetric.
    . scalar_z = min(pt1,pt2)/(pt1+pt2)   [default]
    . vector_z = min(pt1,pt2)/pt_{1+2}
    . y = min(pt1^2,pt2^2)/m_{12}^2  (original y from MDT)
    . theta_E     = min(E1,E2)/(E1+E2),
           with angular measure theta_{12}^2
    . cos_theta_E = min(E1,E2)/(E1+E2),
           with angular measure 2[1-cos(theta_{12})]
    The last two variants are meant for use in e+e- collisions,
    together with the "larger_E" recursion choice (see below)

RecursionChoice = {larger_pt, larger_mt, larger_m, larger_E}
  [constructor argument]
  : The path to recurse through the tree after the symmetry condition
    fails. Options refer to transverse momentum (pt), transverse mass
    (mt=sqrt(pt^2+m^2), mass (m) or energy (E). the latter is meant
    for use in e+e- collisions

mu_cut   [constructor argument]
  : An optional mass drop condition

set_subtractor(subtractor*) [or subtractor as a constructor argument]
  : provide a subtractor. When a subtractor is supplied, the
    kinematic constraints are applied on subtracted 4-vectors. In
    this case, the result of the ModifiedMassDropTagger/SoftDrop is a
    subtracted PseudoJet, and it is assumed that
    ModifiedMassDropTagger/SoftDrop is applied to an unsubtracted jet.
    The latter default can be changed by calling
    set_input_jet_is_subtracted().

set_reclustering(bool, Recluster*)
  : An optional setting to recluster a jet with a different jet
    recursive jet algorithm.  The code is only designed to give sensible
    results with the CA algorithm, but other reclustering algorithm
    (especially kT) may be appropriate in certain contexts. 
    Use at your own risk.

set_grooming_mode()/set_tagging_mode()
  : In grooming mode, the algorithm will return a single particle if the
    symmetry condition fails for the whole tree.  In tagging mode, the
    algorithm will return an zero PseudoJet if no symmetry conditions
    passes.  Note that ModifiedMassDropTagger defaults to tagging mode
    and SoftDrop defaults to grooming mode.

set_verbose_structure(bool)
  : when set to true, additional information will be stored in the jet
    structure. This includes in particular values of symmetry,
    delta_R, and mu of dropped branches

For the specific case of RecursiveSoftDrop, additional tweaking is
possible via the following methods

set_fixed_depth_mode(bool)
  : when this is true, RSD will recurse (N times) into all the
    branches found during the previous iteration [instead of recursing
    through the largest declustering angle until N prongs have been
    found]. This yields at most 2^N prong. For infinite N, the two
    options are equivalent.

set_dynamical_R0(bool)
  : By default the angles in the SD condition are normalised to the
    parameter R0. With "dynamical R0", RSD will dynamically adjust R0
    to be the angle between the two prongs found during the previous
    iteration.

set_hardest_branch_only(bool)
  : When substructure is found, only recurse into the hardest of the
    two branches for further substructure search. This uses the class
    RecursionChoice.

set_min_deltaR_squared(double):
  : set a minimal angle (squared) at which we stop the declustering
    procedure.  This cut is ineffective for negative values of the
    argument.

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Technical Details
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Both ModifiedMassDropTagger and SoftDrop inherit from
RecursiveSymmetryCutBase, which provides a common codebase for recursive
declustering of a jet with a symmetry cut condition.  A generic 
RecursiveSymmetryCutBase depends on the following (virtual) functions
(see header file for exact full specs, including constness):

double symmetry_cut_fn(PseudoJet &, PseudoJet &)
  : The function that defines the symmetry cut. This is what actually 
    defines different recursive declustering schemes, and all classes
    that inherit from RecursiveSymmetryCutBase must define this
    function.

string symmetry_cut_description() 
  : the string description of the symmetry cut.

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