| 1 | --------------------------------------------------------------------------------
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| 2 | Nsubjettiness Package
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| 3 | --------------------------------------------------------------------------------
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| 4 |
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| 5 | The Nsubjettiness package is based on the physics described in:
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| 6 |
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| 7 | Identifying Boosted Objects with N-subjettiness.
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| 8 | Jesse Thaler and Ken Van Tilburg.
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| 9 | JHEP 1103:015 (2011), arXiv:1011.2268.
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| 10 |
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| 11 | Maximizing Boosted Top Identification by Minimizing N-subjettiness.
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| 12 | Jesse Thaler and Ken Van Tilburg.
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| 13 | JHEP 1202:093 (2012), arXiv:1108.2701.
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| 14 |
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| 15 | New in v2.0 is the winner-take-all axis, which is described in:
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| 16 |
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| 17 | Jet Observables Without Jet Algorithms.
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| 18 | Daniele Bertolini, Tucker Chan, and Jesse Thaler.
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| 19 | JHEP 1404:013 (2014), arXiv:1310.7584.
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| 20 |
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| 21 | Jet Shapes with the Broadening Axis.
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| 22 | Andrew J. Larkoski, Duff Neill, and Jesse Thaler.
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| 23 | JHEP 1404:017 (2014), arXiv:1401.2158.
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| 24 |
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| 25 | Unpublished work by Gavin Salam
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| 26 |
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| 27 | New in v2.2 are new measures used in the XCone jet algorithm, described in:
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| 28 |
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| 29 | XCone: N-jettiness as an Exclusive Cone Jet Algorithm.
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| 30 | Iain W. Stewart, Frank J. Tackmann, Jesse Thaler,
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| 31 | Christopher K. Vermilion, and Thomas F. Wilkason.
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| 32 | arXiv:1508.01516.
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| 33 |
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| 34 | Resolving Boosted Jets with XCone.
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| 35 | Jesse Thaler and Thomas F. Wilkason.
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| 36 | arXiv:1508.01518.
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| 37 |
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| 38 | --------------------------------------------------------------------------------
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| 39 | Core Classes
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| 40 | --------------------------------------------------------------------------------
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| 41 |
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| 42 | There are various ways to access N-(sub)jettiness variables, described
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| 43 | in more detail below:
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| 44 |
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| 45 | Nsubjettiness [Nsubjettiness.hh]:
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| 46 | A FunctionOfPseudoJet<double> interface to measure the
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| 47 | N-subjettiness jet shape
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| 48 | (Recommended for most users)
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| 49 |
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| 50 | NsubjettinessRatio [Nsubjettiness.hh]:
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| 51 | A FunctionOfPseudoJet<double> interface to measure ratios of
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| 52 | two different N-subjettiness (i.e. tau3/tau2)
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| 53 | (Recommended for most users)
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| 54 |
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| 55 | XConePlugin [XConePlugin.hh]:
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| 56 | A FastJet plugin for using the XCone jet algorithm.
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| 57 | (Recommended for most users)
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| 58 |
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| 59 | NjettinessPlugin [NjettinessPlugin.hh]:
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| 60 | A FastJet plugin for finding jets by minimizing N-jettiness.
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| 61 | Same basic philosophy as XCone, but many more options.
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| 62 | (Recommended for advanced users only.)
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| 63 |
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| 64 | Njettiness [Njettiness.hh]:
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| 65 | Access to the core Njettiness code.
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| 66 | (Not recommended for users, since the interface might change)
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| 67 |
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| 68 | The code assumes that you have FastJet 3, but does not (yet) require FastJet 3.1
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| 69 |
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| 70 | --------------------------------------------------------------------------------
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| 71 | Basic Usage: Nsubjettiness and NsubjettinessRatio [Nsubjettiness.hh]
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| 72 | --------------------------------------------------------------------------------
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| 73 |
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| 74 | Most users will only need to use the Nsubjettiness class. The basic
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| 75 | functionality is given by:
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| 76 |
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| 77 | Nsubjettiness nSub(N, AxesDefinition, MeasureDefinition)
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| 78 | // N specifies the number of (sub) jets to measure
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| 79 | // AxesDefinition is WTA_KT_Axes, OnePass_KT_Axes, etc.
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| 80 | // MeasureDefinition is UnnormalizedMeasure(beta),
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| 81 | // NormalizedMeasure(beta,R0), etc.
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| 82 |
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| 83 | // get tau value
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| 84 | double tauN = nSub.result(PseudoJet);
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| 85 |
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| 86 | Also available are ratios of N-subjettiness values
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| 87 | NsubjettinessRatio nSubRatio(N, M, AxesDefinition,
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| 88 | MeasureDefinition)
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| 89 | // N and M give tau_N / tau_M, all other options the same
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| 90 |
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| 91 | For example, if you just want the tau_2/tau_1 value of a jet, using recommended
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| 92 | parameter choices, do this:
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| 93 |
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| 94 | PseudoJet this_jet = /*from your favorite jet algorithm*/;
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| 95 | double beta = 1.0;
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| 96 | NsubjettinessRatio nSub21(2,1,
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| 97 | OnePass_WTA_KT_Axes(),
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| 98 | UnnormalizedMeasure(beta));
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| 99 | double tau21 = nSub21(this_jet);
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| 100 |
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| 101 | --------------------------------------------------------------------------------
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| 102 | AxesDefinition [NjettinessDefinition.hh]
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| 103 | --------------------------------------------------------------------------------
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| 104 |
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| 105 | N-(sub)jettiness requires choosing axes as well as a measure (see below). There
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| 106 | are a number of axes choices available to the user, though modes with a (*) are
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| 107 | recommended. Arguments in parentheses are parameters that the user must set.
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| 108 |
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| 109 | Axes can be found using standard recursive clustering procedures. New in v2 is
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| 110 | the option to use the "winner-take-all" recombination scheme:
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| 111 | (*) KT_Axes // exclusive kt axes
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| 112 | CA_Axes // exclusive ca axes
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| 113 | AntiKT_Axes(R0) // inclusive hardest axes with antikt, R0 = radius
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| 114 | (*) WTA_KT_Axes // exclusive kt with winner-take-all recombination
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| 115 | WTA_CA_Axes // exclusive ca with winner-take-all recombination
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| 116 |
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| 117 | New in v2.2 are generalized recombination/clustering schemes:
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| 118 | GenET_GenKT_Axes(delta, p, R0 = inf)
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| 119 | WTA_GenKT_Axes(p, R0 = inf)
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| 120 | GenKT_Axes(p, R0 = inf)
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| 121 | Here, delta > 0 labels the generalized ET recombination scheme (delta = 1 for
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| 122 | standard ET scheme, delta = 2 for ET^2 scheme, delta = infinity for WTA scheme)
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| 123 | p >= 0 labels the generalized KT clustering metric (p = 0 for ca, p = 1 for kt),
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| 124 | R0 is the radius parameter, and the clustering is run in exclusive mode. The
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| 125 | GenKT_Axes mode uses standard E-scheme recombination. By default the value of
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| 126 | R0 is set to "infinity", namely fastjet::JetDefinition::max_allowable_R.
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| 127 |
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| 128 | Also new in v2.2 is option of identifying nExtra axes through exclusive
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| 129 | clustering and then looking at all (N + nExtra) choose N axes and finding the
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| 130 | one that gives the smallest N-(sub)jettiness value:
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| 131 | Comb_GenET_GenKT_Axes(nExtra, delta, p, R0 = inf)
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| 132 | Comb_WTA_GenKT_Axes(nExtra, p, R0 = inf)
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| 133 | Comb_GenKT_Axes(nExtra, p, R0 = inf)
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| 134 | These modes are not recommended for reasons of speed.
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| 135 |
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| 136 | Starting from any set of seed axes, one can run a minimization routine to find
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| 137 | a (local) minimum of N-(sub)jettiness. Note that the one-pass minimization
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| 138 | routine is tied to the choice of MeasureDefinition.
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| 139 | (*) OnePass_KT_Axes // one-pass minimization from kt starting point
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| 140 | OnePass_CA_Axes // one-pass min. from ca starting point
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| 141 | OnePass_AntiKT(R0) // one-pass min. from antikt starting point,R0=rad
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| 142 | (*) OnePass_WTA_KT_Axes // one-pass min. from wta_kt starting point
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| 143 | OnePass_WTA_CA_Axes // one-pass min. from wta_ca starting point
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| 144 | OnePass_GenET_GenKT_Axes(delta, p, R0 = inf) // one-pass min. from GenET/KT
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| 145 | OnePass_WTA_GenKT_Axes(p, R0 = inf) // one-pass min from WTA/GenKT
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| 146 | OnePass_GenKT_Axes(p, R0 = inf) // one-pass min from GenKT
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| 147 |
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| 148 | For one-pass minimization, OnePass_CA_Axes and OnePass_WTA_CA_Axes are not
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| 149 | recommended as they provide a poor choice of seed axes.
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| 150 |
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| 151 | In general, it is difficult to find the global minimum, but this mode attempts
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| 152 | to do so:
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| 153 | MultiPass_Axes(NPass) // axes that (attempt to) minimize N-subjettiness
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| 154 | // (NPass = 100 is typical)
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| 155 | This does multi-pass minimization from KT_Axes starting points.
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| 156 |
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| 157 | Finally, one can set manual axes:
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| 158 | Manual_Axes // set your own axes with setAxes()
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| 159 | OnePass_Manual_Axes // one-pass minimization from manual starting point
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| 160 | MultiPass_Manual_Axes(Npass) // multi-pass min. from manual
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| 161 |
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| 162 | If one wants to change the number of passes used by any of the axes finders, one
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| 163 | can call the function
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| 164 | setNPass(NPass,nAttempts,accuracy,noise_range)
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| 165 | where NPass = 0 only uses the seed axes, NPass = 1 is one-pass minimization, and
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| 166 | NPass = 100 is the default multi-pass. nAttempts is the number of iterations to
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| 167 | use in each pass, accuracy is how close to the minimum one tries to get, and
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| 168 | noise_range is how much in rapidity/azimuth the random axes are jiggled.
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| 169 |
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| 170 | For most cases, running with OnePass_KT_Axes or OnePass_WTA_KT_Axes gives
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| 171 | reasonable results (and the results are IRC safe). Because it uses random
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| 172 | number seeds, MultiPass_Axes is not IRC safe (and the code is rather slow).
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| 173 | Note that for the minimization routines, beta = 1.1 is faster than beta = 1,
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| 174 | with comparable performance.
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| 175 |
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| 176 | --------------------------------------------------------------------------------
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| 177 | MeasureDefinition [NjettinessDefinition.hh]
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| 178 | --------------------------------------------------------------------------------
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| 179 |
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| 180 | The value of N-(sub)jettiness depends crucially on the choice of measure. Each
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| 181 | measure has a different number of parameters, so one has to be careful when
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| 182 | switching between measures The one indicated by (*) is the one recommended for
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| 183 | use by users new to Nsubjettiness.
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| 184 |
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| 185 | The original N-subjettiness measures are:
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| 186 | NormalizedMeasure(beta,R0) //default normalized measure with
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| 187 | //parameters beta and R0 (dimensionless)
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| 188 | (*) UnnormalizedMeasure(beta) //default unnormalized measure with just
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| 189 | //parameter beta (dimensionful)
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| 190 |
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| 191 | There are also measures that incorporate a radial cutoff:
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| 192 | NormalizedCutoffMeasure(beta,R0,Rcutoff) //normalized measure with
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| 193 | //additional Rcutoff
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| 194 | UnnormalizedCutoffMeasure(beta,Rcutoff) //unnormalized measure with
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| 195 | //additional Rcutoff
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| 196 |
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| 197 | For all of the above measures, there is an optional argument to change from the
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| 198 | ordinary pt_R distance measure recommended for pp collisions to an
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| 199 | E_theta distance measure recommended for ee collisions. There are also
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| 200 | lorentz_dot and perp_lorentz_dot distance measures recommended only for
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| 201 | advanced users.
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| 202 |
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| 203 | New for v2.2 is a set of measures defined in arXiv:1508.01516. First, there is
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| 204 | the "conical measure":
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| 205 |
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| 206 | ConicalMeasure(beta,R0) // same jets as UnnormalizedCutoffMeasure
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| 207 | // but differs in normalization and specifics
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| 208 | // of one-pass minimization
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| 209 |
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| 210 | Next, there is the geometric measure (as well as a modified version to yield
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| 211 | more conical jet regions):
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| 212 |
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| 213 | OriginalGeometricMeasure(R) // not recommended for analysis
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| 214 | ModifiedGeometricMeasure(R)
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| 215 |
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| 216 | (Prior to v2.2, there was a "GeometricMeasure" which unfortunately had the wrong
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| 217 | definition. These have been commented out in the code as
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| 218 | "DeprecatedGeometricMeasure" and "DeprecatedGeometricCutoffMeasure", but they
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| 219 | should not be used.)
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| 220 |
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| 221 | Next, there is a "conical geometric" measure:
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| 222 |
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| 223 | ConicalGeometricMeasure(beta, gamma, Rcutoff)
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| 224 |
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| 225 | This is a hybrid between the conical and geometric measures and is the basis for
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| 226 | the XCone jet algorithm. Finally, setting to the gamma = 1 default gives the
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| 227 | XCone default measure, which is used in the XConePlugin jet finder
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| 228 |
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| 229 | (*) XConeMeasure(beta,Rcutoff)
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| 230 |
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| 231 | where beta = 2 is the recommended default value and beta = 1 is the recoil-free
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| 232 | default.
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| 233 |
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| 234 | --------------------------------------------------------------------------------
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| 235 | A note on beta dependence
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| 236 | --------------------------------------------------------------------------------
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| 237 |
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| 238 | The angular exponent in N-subjettiness is called beta. The original
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| 239 | N-subjettiness paper advocated beta = 1, but it is now understood that different
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| 240 | beta values can be useful in different contexts. The two main choices are:
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| 241 |
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| 242 | beta = 1: aka broadening/girth/width measure
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| 243 | the axes behave like the "median" in that they point to the hardest cluster
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| 244 | wta_kt_axes are approximately the same as minimizing beta = 1 measure
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| 245 |
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| 246 | beta = 2: aka thrust/mass measure
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| 247 | the axes behave like the "mean" in that they point along the jet momentum
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| 248 | kt_axes are approximately the same as minimizing beta = 2 measure
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| 249 |
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| 250 | N.B. The minimization routines are only valid for 1 < beta < 3.
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| 251 |
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| 252 | For quark/gluon discrimination with N = 1, beta~0.2 with wta_kt_axes appears
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| 253 | to be a good choice.
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| 254 |
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| 255 | --------------------------------------------------------------------------------
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| 256 | XConePlugin [XConePlugin.hh]
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| 257 | --------------------------------------------------------------------------------
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| 258 |
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| 259 | The XCone FastJet plugin is an exclusive cone jet finder which yields a
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| 260 | fixed N number of jets which approximately conical boundaries. The algorithm
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| 261 | finds N axes, and jets are simply the sum of particles closest to a given axis
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| 262 | (or unclustered if they are closest to the beam). Unlike the NjettinessPlugin
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| 263 | below, the user is restricted to using the XConeMeasure.
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| 264 |
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| 265 | XConePlugin plugin(N,R,beta=2);
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| 266 | JetDefinition def(&plugin);
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| 267 | ClusterSequence cs(vector<PseudoJet>,def);
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| 268 | vector<PseudoJet> jets = cs.inclusive_jets();
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| 269 |
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| 270 | Note that despite being an exclusive jet algorithm, one finds the jets using the
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| 271 | inclusive_jets() call.
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| 272 |
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| 273 | The AxesDefinition and MeasureDefinition are defaulted in this measure to
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| 274 | OnePass_GenET_GenKT_Axes and XConeMeasure, respectively. The parameters chosen
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| 275 | for the OnePass_GenET_GenKT_Axes are defined according to the chosen value of
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| 276 | beta as delta = 1/(beta - 1) and p = 1/beta. These have been shown to give the
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| 277 | optimal choice of seed axes. The R value for finding the axes is chosen to be
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| 278 | the same as the R for the jet algorithm, although in principle, these two radii
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| 279 | could be different.
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| 280 |
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| 281 | N.B.: The order of the R, beta arguments is *reversed* from the XConeMeasure
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| 282 | itself, since this ordering is the more natural one to use for Plugins. We
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| 283 | apologize in advance for any confusion this might cause.
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| 284 |
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| 285 | --------------------------------------------------------------------------------
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| 286 | Advanced Usage: NjettinessPlugin [NjettinessPlugin.hh]
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| 287 | --------------------------------------------------------------------------------
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| 288 |
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| 289 | Same as the XConePlugin, but the axes finding methods and measures are the same
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| 290 | as for Nsubjettiness, allowing more flexibility.
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| 291 |
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| 292 | NjettinessPlugin plugin(N, AxesDefinition, MeasureDefinition);
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| 293 | JetDefinition def(&plugin);
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| 294 | ClusterSequence cs(vector<PseudoJet>,def);
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| 295 | vector<PseudoJet> jets = cs.inclusive_jets();
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| 296 |
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| 297 | --------------------------------------------------------------------------------
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| 298 | Very Advanced Usage: Njettiness [Njettiness.hh]
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| 299 | --------------------------------------------------------------------------------
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| 300 |
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| 301 | Most users will want to use the Nsubjettiness or NjettinessPlugin classes to
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| 302 | access N-(sub)jettiness information. For direct access to the Njettiness class,
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| 303 | one can use Njettiness.hh directly. This class is in constant evolution, so
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| 304 | users who wish to extend its functionality should contact the authors first.
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| 305 |
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| 306 | --------------------------------------------------------------------------------
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| 307 | TauComponents [MeasureDefinition.hh]
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| 308 | --------------------------------------------------------------------------------
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| 309 |
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| 310 | For most users, they will only need the value of N-subjettiness (i.e. tau)
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| 311 | itself. For advanced users, they can access individual tau components (i.e.
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| 312 | the individual numerator pieces, the denominator, etc.)
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| 313 |
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| 314 | TauComponents tauComp = nSub.component_result(jet);
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| 315 | vector<double> numer = tauComp.jet_pieces_numerator(); //tau for each subjet
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| 316 | double denom = tauComp.denominator(); //normalization factor
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| 317 |
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| 318 | --------------------------------------------------------------------------------
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| 319 | Extra Recombiners [ExtraRecombiners.hh]
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| 320 | --------------------------------------------------------------------------------
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| 321 |
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| 322 | New in v2.0 are winner-take-all axes. (These have now been included in
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| 323 | FastJet 3.1, but we have left the code here to allow the plugin to work under
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| 324 | FJ 3.0). These axes are found with the help of the WinnerTakeAllRecombiner.
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| 325 | This class defines a new recombination scheme for clustering particles. This
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| 326 | scheme recombines two PseudoJets into a PseudoJet with pT of the sum of the two
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| 327 | input PseudoJet pTs and direction of the harder PseudoJet. This is a
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| 328 | "recoil-free" recombination scheme that guarantees that the axes is aligned with
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| 329 | one of the input particles. It is IRC safe. Axes found with the standard
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| 330 | E-scheme recombiner at similar to the beta = 2 minimization, while
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| 331 | winner-take-all is similar to the beta = 1 measure.
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| 332 |
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| 333 | New in v2.2 is the GeneralEtSchemeRecombiner, as defined in arxiv:1506.XXXX.
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| 334 | This functions similarly to the Et-scheme defined in Fastjet, but the reweighting
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| 335 | of the sum of rap and phi is parameterized by an exponent delta. Thus, delta = 1
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| 336 | is the normal Et-scheme recombination, delta = 2 is Et^2 recombination, and
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| 337 | delta = infinity is the winner-take-all recombination. This recombination scheme
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| 338 | is used in GenET_GenKT_Axes, and we find that optimal seed axes for minimization
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| 339 | can be found by using delta = 1/(beta - 1).
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| 340 |
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| 341 | Note that the WinnerTakeAllRecombiner can be used outside of Nsubjettiness
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| 342 | itself for jet finding. For example, the direction of anti-kT jets found
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| 343 | with the WinnerTakeAllRecombiner is particularly robust against soft jet
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| 344 | contamination. That said, this functionality is now included in FJ 3.1, so this
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| 345 | code is likely to be deprecated in a future version.
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| 346 |
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| 347 | --------------------------------------------------------------------------------
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| 348 | Technical Details
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| 349 | --------------------------------------------------------------------------------
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| 350 |
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| 351 | In general, the user will never need access to these header files. Here is a
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| 352 | brief description about how they are used to help the calculation of
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| 353 | N-(sub)jettiness:
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| 354 |
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| 355 | AxesDefinition.hh:
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| 356 |
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| 357 | The AxesDefinition class (and derived classes) defines the axes used in the
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| 358 | calculation of N-(sub)jettiness. These axes can be defined from the exclusive
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| 359 | jets from a kT or CA algorithm, the hardest jets from an anti-kT algorithm,
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| 360 | manually, or from minimization of N-jettiness. In the future, the user will be
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| 361 | able to write their own axes finder, though currently the interface is still
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| 362 | evolving. At the moment, the user should stick to the options allowed by
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| 363 | AxesDefinition.
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| 364 |
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| 365 | MeasureDefinition.hh:
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| 366 |
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| 367 | The MeasureDefinition class (and derived classes) defines the measure by which
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| 368 | N-(sub)jettiness is calculated. This measure is calculated between each
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| 369 | particle and its corresponding axis, and then summed and normalized to
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| 370 | produce N-(sub)jettiness. The default measure for this calculation is
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| 371 | pT*dR^beta, where dR is the rapidity-azimuth distance between the particle
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| 372 | and its axis, and beta is the angular exponent. Again, in the future the user
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| 373 | will be able to write their own measures, but for the time being, only the
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| 374 | predefined MeasureDefinition values should be used. Note that the one-pass
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| 375 | minimization algorithms are defined within MeasureDefinition, since they are
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| 376 | measure specific.
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| 377 |
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| 378 | --------------------------------------------------------------------------------
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| 379 | Known Issues
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| 380 | --------------------------------------------------------------------------------
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| 381 |
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| 382 | -- The MultiPass_Axes mode gives different answers on different runs, since
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| 383 | random numbers are used.
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| 384 | -- For the default measures, in rare cases, one pass minimization can give a
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| 385 | larger value of Njettiness than without minimization. The reason is due
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| 386 | to the fact that axes in default measure are not defined as light-like
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| 387 | -- Nsubjettiness is not thread safe, since there are mutables in Njettiness.
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| 388 | -- If the AxesDefinition does not find N axes, then it adds zero vectors to the
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| 389 | list of axes to get the total up to N. This can lead to unpredictable
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| 390 | results (including divide by zero issues), and a warning is thrown to alert
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| 391 | the user.
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| 392 |
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| 393 | --------------------------------------------------------------------------------
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| 394 | --------------------------------------------------------------------------------
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