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* json file for Lb2pKg * Updated json file and docs .qmd file for Lb2pKg * Add .qmd file and modified json file * [pre-commit.ci] auto fixes from pre-commit.com hooks * update deps. - no Graphs - up TBDsIO.jl, HadronicLineshapes.jl * introduced MomentumPower for FF * test of lineshape computation * MAINT: make page name lower case * MAINT: git-ignore Quaro output files * DOC: switch Julia notebook order * MAINT: remove temporary files * update masses to approximate * fix couplings weights * add BlattWeisskopf for 1405 * add Dalitz and projections to docs --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Mikhail Mikhasenko <[email protected]> Co-authored-by: Remco de Boer <[email protected]>
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| .jupyter_cache/ | ||
| *.html | ||
| *.ipynb | ||
| /.quarto/ | ||
| execute-results/ | ||
| site_libs/ |
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| --- | ||
| jupyter: julia-amplitude-serialization-1.10 | ||
| --- | ||
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| # $\Lambda_b^0 \to p K^- \gamma$ | ||
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| 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). | ||
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| ```{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="") | ||
| ``` | ||
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| ## Function definitions | ||
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| 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 `NonResonant` lineshape, and its deserialization method. In this case this is just a constant. | ||
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| ```{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 | ||
| ``` | ||
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| ## Deserialization of Objects to a Workspace | ||
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| 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. | ||
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| ```{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 | ||
| ``` | ||
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| ## Validation | ||
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| 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 ("🟢" ($<10^{-12}$), "🟡" ($<10^{-2}$) or "🔴" $\ge10^{-2}$) for the difference between the reference and computed values. | ||
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| ```{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-12]) | ||
| _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 | ||
| ``` | ||
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| ## Visualization | ||
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| The model descibing the decay is fetched from the workspace | ||
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| ```{julia} | ||
| model_dist = [v for (k, v) in workspace if v isa HadronicUnpolarizedIntensity] |> first; | ||
| model = model_dist.model | ||
| ``` | ||
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| ### Dalitz plot | ||
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| The Dalitz plot shows the probability distribution across two dimensional phase space of the decay in the range of mass $m_{pK^{-}}$ from $1.5$ to $2.5 GeV/c^2$. | ||
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| ```{julia} | ||
| #| code-fold: true | ||
| #| code-summary: Dalitz plot plotting | ||
| let | ||
| ms = masses(model) | ||
| # | ||
| σ3v = range(lims3(ms)[1], 2.5^2, 100)[2:end-1] | ||
| σ2v = range(5, 27, 30)[2:end-1] | ||
| # | ||
| _model = model | ||
| f(σs) = Kibble(σs, ms^2) > 0 ? NaN : unpolarized_intensity(model, σs) | ||
| calv = [ | ||
| f(Invariants(ms; σ3, σ2)) for σ2 in σ2v, σ3 in σ3v] | ||
| heatmap(σ3v, σ2v, calv) | ||
| end | ||
| ``` | ||
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| The projection of the model onto a mass variable is shown by black line. | ||
| Contributions from individual resonances are shown by the colored lines. | ||
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| ```{julia} | ||
| #| code-fold: true | ||
| #| code-summary: Computation of projections | ||
| let k = 3 | ||
| i, j = ij_from_k(k) | ||
| xlab = "m($i$j) [GeV]" | ||
| model = model_dist.model | ||
| # | ||
| mlims = (sqrt(lims(3, masses(model))[1]), 2.5) | ||
| mv = range(mlims..., 200) |> shift_by_half | ||
| # | ||
| plot() | ||
| plot!(mv, lab="Total") do m | ||
| I = Base.Fix1(unpolarized_intensity, model) | ||
| m * quadgk(projection_integrand(I, masses(model), m^2; k), 0, 1)[1] | ||
| end | ||
| chain_names = Set(model.names) |> collect |> sort | ||
| for name in chain_names | ||
| _model = model[model.names.==name] | ||
| plot!(mv, lab=name) do m | ||
| I = Base.Fix1(unpolarized_intensity, _model) | ||
| m * quadgk(projection_integrand(I, masses(_model), m^2; k), 0, 1)[1] | ||
| end | ||
| end | ||
| plot!(; xlab) | ||
| end | ||
| ``` |
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