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Lund Jet Plane

The Lund jet plane (arXiv:1807.04758) is a simple and intuitive way to visualize how a jet breaks up into smaller components. Each point in the plane represents a branching in the jet, helping understand how energy and angles are distributed within.

Decluster

decluster(jet::T, clusterseq::ClusterSequence{T}) where {T <: FourMomentum} -> Tuple{PseudoJet}

Recursively declusters a jet into two parent subjets using a provided clustering sequence. The subjets are ordered by decreasing transverse momentum squared (pt²).

j1, j2 = decluster(jet, clusterseq)
  • If no parents are found, the function returns nothing for one or both subjets.

Useful for building recursive jet trees and jet grooming algorithms.

Generate Lund Emissions

generate_lund_emissions(jet::PseudoJet, cs::ClusterSequence{PseudoJet}) -> Vector{NamedTuple}

Constructs the Lund plane emissions of a jet. The result is a list of declustering steps, each represented by a named tuple of physics observables.

lund_points = generate_lund_emissions(jet, cluster_seq)

Each named tuple includes:

  • h_pt: transverse momentum of the harder branch
  • s_pt: transverse momentum of the softer branch
  • z: momentum fraction
  • delta: angular distance ΔR
  • kt: transverse momentum of the softer branch relative to the harder
  • psi: azimuthal angle between the two splittings
  • kappa: z × ΔR

These values are useful for visualization and physics analysis of jet splittings.

Visualisation of Lund Jet Plane

examples/lundplane/lund-plane-visualisation.jl provides an example for generating and plotting the average lund image.

generate_average_lund_image(njets::Int, delta_array::Vector{Vector{Real}}, kt_array::Vector{Vector{Real}}; xrange::Tuple{Real}, yrange::Tuple{Real}, bins::Int) -> (xgrid, ygrid, avg_image)

Computes the average Lund image over a set of jets, by binning (log(1/ΔR), log(kt)) values from each jet into a 2D histogram and averaging the histograms per jet.

x, y, avg_image = generate_average_lund_image(njets, delta_array, kt_array; bins=25)
  • delta_array and kt_array should be arrays of arrays: one per jet.
  • The output is a tuple of x and y bin edges, and a 2D image array.
  • This is useful for creating heatmaps to compare jet substructure distributions.

For further examples and advanced use cases, see the documentation in the examples/lundplane/ directory