[HS3] Add a new `analytic_convolution_dist` Streamer/Factory

[Phmonski]

Feature description

Proposal: add analytic_convolution_dist to HS3 / RooFitHS3

RooFit currently serializes RooDecay via a dedicated decay_dist key. This is somewhat special-case: RooDecay is not just an exponential distribution, but a RooAbsAnaConvPdf that declares analytic basis functions to be convolved with a RooResolutionModel.

I propose introducing a generic analytic_convolution_dist node that represents the RooAbsAnaConvPdf concept directly:

• observable/convolution variable
• resolution model
• list of analytic basis terms
• coefficient expression/function per term

Example for RooDecay(DoubleSided):

{
  "name": "decay_gm",
  "type": "analytic_convolution_dist",
  "x": "dt",
  "resolution_model": "gm",
  "terms": [
    {
      "coefficient": "1",
      "basis": {
        "type": "exp_decay",
        "tau": "tau",
        "side": "both"
      }
    }
  ]
}

This generic node could support the following Classes:

• RooDecay
• RooBMixDecay
• RooBDecay
• RooBCPGenDecay
• RooBCPEffDecay
• RooNonCPEigenDecay

Requirements

This feature requires serializable categorical variables to fully support these classes in a clean way.

@cburgard @stalbrec

[cburgard]

I'm not sure I understand why this requires serializable categorical variables. Could you elaborate?

[Phmonski]

They become required if analytic_convolution_dist is intended to cover the broader RooAbsAnaConvPdf family listed above. Several of these classes have coefficients that depend on RooAbsCategory proxies. For example, RooBMixDecay has terms like

• (1 - tagFlav * delMistag) * exp_basis
• mixState * (1 - 2 * mistag) * cos_basis

where tagFlav and mixState are categorical observables with numeric state values. Similarly, RooBCPGenDecay, RooBCPEffDecay, and RooNonCPEigenDecay depend on tag/rho categories.

So categorical serialization is not needed for the analytic convolution mechanism itself, but it is needed to represent the coefficient functions of most nontrivial RooAbsAnaConvPdf subclasses in a clean, generic, and round-trippable way.