Serialize lineshape functions

[redeboer]

The section functions defines the lineshapes that should be inserted into parametrization of the propagators. Example:

https://github.com/RUB-EP1/amplitude-serialization/blob/9fcd26e8c7cd487d93f902529c5513c977e03e62/Lc2ppiK.json#L42

https://github.com/RUB-EP1/amplitude-serialization/blob/9fcd26e8c7cd487d93f902529c5513c977e03e62/Lc2ppiK.json#L756-L776

Currently, the format specifications do not yet include an exact definition of the function tree, only a type description (here: BreitWigner). Some solution ideas:

• Define the full mathematical operations in JSON format in the model file under functions. Disadvantage: the JSON file might become very large (human-readable?). Advantage: all information is contained within a single file.
• Provide an extra file with lineshape definitions. Advantage: smaller model JSON file and option to use a more common format like MathML (XML-based) Disadvantage: the model definition becomes split over multiple files

In either case, we preferably serialize to a common mathematical markup language. Afaics, for JSON, there is only MathJSON, which is not widely adopted. OpenMath and MathML are more widely adopted (especially in web applications), but use XML, which is hard to read. But then again, lineshape expressions can be large and JSON won't be pretty either.

[redeboer]

Note: HS3 specifications probably won't help us here yet, because complex-valued functions are not supported.

[mmikhasenko]

I see great benefits in defining all functions fully in the format, there are cons as well. It would make it possible for different files to have different "BreitWigner"s, which is something I would not want.

I see that it might be challenging to convince the community to stick with a single definition of the BW. But it would be nice. For now, I would like to try that, i.e. treat all non-standard parametrization as exceptions

[mmikhasenko]

Btw, there is already a way to code simple functions in HS3. They are strings.

  "distributions": [
    {
      "expression": "1/((m*m-s)^2+(m*G)^2)",
      "name": "BreitWigner",
      "type": "generic_dist"
    }
  ],