compass, replace Katchaev Sigma by expression string

docs/julia/x2pipipi-compass-1391643.qmd

@@ -37,44 +37,6 @@ theme(:wong2, frame=:box, grid=false, minorticks=true,
     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}
-@with_kw struct KatchaevSigma <: HadronicLineshapes.AbstractFlexFunc
-    poles::Vector{Float64}
-    residues::Vector{Float64}
-    nonpole_expansion_coeffs::Vector{Float64}
-end
-function (bw::KatchaevSigma)(σ::Number)
-    mπ = 0.13956755
-    mπ2 = mπ^2
-
-    @unpack poles, residues, nonpole_expansion_coeffs = bw
-    M00 = 0.0
-    for i = 1:length(poles)
-        M00 += residues[i] / (σ - poles[i])
-    end
-    #
-    mK = 0.493677
-    mK0 = 0.497614
-    scale = (σ / (4 * ((mK + mK0) / 2.0)^2)) - 1.0
-    for (i, ci) in enumerate(nonpole_expansion_coeffs)
-        M00 += scale^(i - 1) * ci
-    end
-
-    rho00 = sqrt(Kallen(σ, mπ2, mπ2)) / σ
-    return 1.0 / (M00 - 1im * rho00)
-end
-function ThreeBodyDecaysIO.dict2instance(::Type{KatchaevSigma}, dict)
-    @unpack poles, residues, nonpole_expansion_coeffs, x = dict
-    return NamedArgFunc(;
-      f=KatchaevSigma(poles, residues, nonpole_expansion_coeffs),
-      variable_names=[x])
-end
-```
 
 ## Deserialization of Objects to a Workspace
 

models/x2pipipi-compass-1391643.json

@@ -991,11 +991,8 @@
       "name": "R(1690)"
     },
     {
-      "type": "KatchaevSigma",
-      "x": "m_12_sq",
-      "poles": [-0.0073999, 0.9828001],
-      "residues": [0.1131, 0.0],
-      "nonpole_expansion_coeffs": [0.0337, -0.3185, -0.0942, -0.5927],
+      "type": "generic_function",
+      "expression": "1.0 / (0.1131 / (m_12_sq + 0.0073999) + 0.0337 - 0.3185 * (m_12_sq / 0.982657846681 - 1.0) - 0.0942 * (m_12_sq / 0.982657846681 - 1.0)^2 -0.5927 * (m_12_sq / 0.982657846681 - 1.0)^3 - i * sqrt(1 - 4*0.13956755^2 / m_12_sq))",
       "name": "R(600)"
     },
     {