[RF][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.

[cburgard]

What is the interplay of this issue with #20245 ?

[Phmonski]

As far as I understood, creating a RooAbsAnaConvPdf creates additional servers in the computational graph that are picked up by the export logic running through the dependencies. These servers are automatically generated and don't follow the HS3 naming convention.