Generalize convolutions for both initial and final states

[cschwan]

This generalization will require the following changes:

• add support for new scale(s): fragmentation function scale. Requires changing the order structure, which is related to Add support for additional couplings #98. This is being addressed in Implement v1 file format #299.
• the PDF-PDF-FF case will require a generalization of the SparseArray3 structure; we need SparseArray4, and then it's possibly better to even think about SparseArrayN; this is done with Add new type PackedArray #275.
• what is currently called 'luminosities' should really haven been 'channels' from the start, and this part will need to be reworked to support the case of three PIDs, also for the case of three convolutions; partly addressed in commit aef0982, remainder requires file-format changes that are being addressed in Implement v1 file format #299.
• the CLI needs to support two or three different PDFs: Add support for different initial-state hadrons in the CLI #174
• the evolution code (Grid::evolve*) needs to be changed in order to support time-like EKOs. For that to work we should discuss the possible interfaces and probably first merge Add method(s) to support larger EKOs #244; partly addressed in Accommodate for two different EKOs in Evolution #289. The remaining bits will be addressed in Implement v1 file format #299.

[enocera]

@cschwan You're way too efficient. The idea is to have a dedicated meeting to discuss this in detail.

[cschwan]

The implementation might take a while 😄. But I anticipate to introduce a new file format soon to accommodate a number of changes/simplications (see #118) and it would be ideal to know what changes roughly are required to support them in said file format. I think the meeting would indeed be perfect to discuss that point.

[cschwan]

@enocera: which of the following scenarios do you see to be relevant in the future:

1. lepton-hadron collisions with one fragmentation function,
2. lepton-hadron collisions with two fragmentation functions,
3. hadron-hadron collisions with one fragmentation function,
4. hadron-hadron collisions with two fragmentation functions?

Basically my questions is: how many 'convolutions' (with PDFs and/or fragmentation functions) will we need to support in PineAPPL?

[alecandido]

I guess there is also SIA case, i.e. "lepton-lepton collisions with *".

[cschwan]

What does SIA stand for?

[felixhekhorn]

semi-inclusive annihilation

[enocera]

@enocera: which of the following scenarios do you see to be relevant in the future:

1. lepton-hadron collisions with one fragmentation function,

Yes. This is called semi-inclusive deep-inelastic scattering (SIDIS)

2. lepton-hadron collisions with two fragmentation functions,

No. This is a process that occurs, but it cannot be described within collinear factorisation. The object that is introduced is called di-hadron fragmentation function. Let's forget about it.

3. hadron-hadron collisions with one fragmentation function,

Yes. This is relevant for the LHC.

4. hadron-hadron collisions with two fragmentation functions?

No. For the same reason as in 2.

On top of these processes, there is hadron production in electron-positron annihilation (SIA=single-inclusive annihilation), so one FF (and no PDF).

Basically my questions is: how many 'convolutions' (with PDFs and/or fragmentation functions) will we need to support in PineAPPL?

Here's a summary:
SIA : one FF (it's like DIS, but with a FF instead of a PDF);
SIDIS: one PDF and one FF (it's like DY, but with a FF in lieu of one PDF);
PP: two PDFs and one FF (this has no counterpart).
In principle, for SIDIS the PDF can be either unpolarised or polarised; for PP the PDFs can be both unpolarised, both polarised, or one unpolarised and the other polarised. The FF is always unpolarised.

[cschwan]

I had a brief chat with @t7phy yesterday, and there are a couple of points that require answering:

1. In which (file-)format are the fragmentation functions available? Is there a library like LHAPDF that supports it? Or can one (ab)use LHAPDF?
2. If the fragmentation function is like a PDF it will have an associated scale, $\mu_\mathrm{Frag} $. How do you set this scale, and specifically do you set it different than $\mu_\mathrm{R} = \mu_\mathrm{F} = \mu_\mathrm{Frag}$?
3. Would polarized FFs/PDFs make a difference in the convolution? If yes, where can I read the details?
4. How do FK tables with FF look like? Can we use the same EKOs as we do for PDFs?