add Lb2pKg model

docs/.gitignore

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+*.html
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+execute-results/
+site_libs/

docs/_quarto.yml

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       - section: Julia
         contents:
           - julia/lc2pkpi.qmd
+          - julia/lb2pkg.qmd
       - section: Python
         contents:
           - python/lc2pkpi.qmd

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docs/julia/lb2pkg.qmd

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+---
+jupyter: julia-amplitude-serialization-1.10
+---
+
+# $\Lambda_b^0 \to p K^- \gamma$
+
+This page demostrates deserialization and evaluation of an amplitude model for the decay $\Lambda_b^0 \to p K^- \gamma$. The resonant structure is studied using proton-proton collision data recorded at centre-of-mass energies of $7$, $8$, and $13$ TeV collected with the LHCb detector, [INSPIRE-HEP 2765817](https://inspirehep.net/literature/2765817).
+
+```{julia}
+#| code-fold: true
+#| code-summary: Activate environment
+#| output: false
+import Pkg
+Pkg.activate(@__DIR__)
+Pkg.instantiate()
+
+using ThreeBodyDecaysIO
+using ThreeBodyDecaysIO.ThreeBodyDecays
+using ThreeBodyDecaysIO.HadronicLineshapes
+using ThreeBodyDecaysIO.Parameters
+using ThreeBodyDecaysIO.DataFrames
+using ThreeBodyDecaysIO.JSON
+using Measurements
+using Statistics
+using QuadGK
+using Plots
+
+theme(:wong2, frame=:box, grid=false, minorticks=true,
+    guidefontvalign=:top, guidefonthalign=:right,
+    foreground_color_legend=nothing,
+    xlim=(:auto, :auto), ylim=(:auto, :auto),
+    lab="")
+```
+
+## Function definitions
+
+Non-standard lineshapes are used to model resonances that do not conform to a simple `BreitWigner` distributions, or a `MultichannelBreitWigner` has to be defined explicitly.
+The code below defines a new lineshape, and its deserialization method.
+
+```{julia}
+struct NonResonant <: HadronicLineshapes.AbstractFlexFunc
+    m::Float64
+end
+function (BW::NonResonant)(σ)
+    @unpack m = BW
+    1.0
+end
+function ThreeBodyDecaysIO.dict2instance(::Type{NonResonant}, dict)
+    @unpack mass = dict
+    return NonResonant(mass)
+end
+```
+
+## Deserialization of Objects to a Workspace
+
+Model components are deserialized from a JSON file into computational objects within a workspace for further manipulation. First, functions representing lineshapes and formfactors are built. Following this, distributions are processed and added to the workspace.
+
+```{julia}
+input = open(joinpath(@__DIR__, "..", "..", "models", "Lb2pKg.json")) do io
+    JSON.parse(io)
+end
+
+workspace = Dict{String,Any}()
+
+@unpack functions = input
+for fn in functions
+    @unpack name, type = fn
+    instance_type = eval(Symbol(type))
+    workspace[name] = dict2instance(instance_type, fn)
+end
+
+@unpack distributions = input
+for dist in distributions
+    @unpack name, type = dist
+    instance_type = eval(Symbol(type))
+    workspace[name] = dict2instance(instance_type, distributions[1]; workspace)
+end
+```
+
+## Validation
+
+The integrity of the model is checked by validating the value of distributions at a few phase space points.
+The table lists the validation checkes and their status ("🟢" or "🔴").
+
+```{julia}
+#| code-fold: true
+#| code-summary: A loop over validation points
+df = let
+    @unpack misc, parameter_points = input
+    @unpack amplitude_model_checksums = misc
+
+    map(amplitude_model_checksums) do check_point_info
+        @unpack name, value, distribution = check_point_info
+        #
+        # pull distribution
+        dist = workspace[distribution]
+
+        # pull correct parameter point
+        parameter_points_dict = array2dict(parameter_points; key="name")
+        # find the point in the list of points
+        parameter_point = parameter_points_dict[name]
+        # compute, compare
+        _parameters = array2dict(parameter_point["parameters"];
+            key="name", apply=v -> v["value"])
+        #
+        function label_diff(diff; levels=[1e-2, 1e-4])
+            _diff = abs(diff)
+            _diff < levels[2] && return '🟢'
+            _diff < levels[1] && return '🟡'
+            return '🔴'
+        end
+        computed_value = dist(_parameters)
+        status = label_diff(value - computed_value)
+        (; Distribution=distribution, Reference=value, Computed_value=computed_value,
+            Point=name, Status=status)
+    end |> DataFrame
+end
+```
+
+## Visualization
+
+The model descibing the decay is fetched from the workspace
+
+```{julia}
+model_dist = [v for (k, v) in workspace if v isa HadronicUnpolarizedIntensity] |> first;
+```
+
+### Dalitz plot
+
+The Dalitz plot shows the probability distribution across two dimensional phase space of the decay.
+
+```{julia}
+#| code-fold: true
+#| code-summary: Dalitz plot plotting
+let iσx = 3, iσy = 2
+    xlab = ((i, j) = ij_from_k(iσx);
+    "m²($i$j) [GeV²]")
+    ylab = ((i, j) = ij_from_k(iσy);
+    "m²($i$j) [GeV²]")
+    model = model_dist.model
+
+    plot(masses(model), Base.Fix1(unpolarized_intensity, model);
+        iσx, iσy, xlab, ylab)
+end
+```
+
+Test that the NonResonant part is implemented correctly.
+
+```{julia}
+let
+    model = model_dist.model
+    @assert model.chains[74].Xlineshape(3.5^2) == 1.0 "Not computed / normalized correctly"
+end
+```