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Deduplicate scale variations #220

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alecandido opened this issue Aug 11, 2023 · 0 comments
Open

Deduplicate scale variations #220

alecandido opened this issue Aug 11, 2023 · 0 comments
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@alecandido
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alecandido commented Aug 11, 2023

Current factorization scale variations are implemented obtaining an operator from integrating an x-space expression. Renormalization scale variations are fully superseded by Pineko's implementation.

This involves integrating a matrix anyhow, and coding all the x-space expressions for the anomalous dimensions.
The exact same task could be performed by using EKOs, and integrating them in matrices. The procedure leading to a matrix will be different, since EKO will use N-space kernels while currently x-space ones are adopted, but the result is in both cases x-space, converted using two interpolation bases (input and output, assumed to be the same, otherwise reshaped), so the result will be the exact same.

The only further complication is that we should support integrals of the anomalous dimensions' products, arising from the expansion of the exponential. Currently, these are not present in EKO, which it has its own solution kernels. However, they should correspond to the expanded scale variation kernel, at present joint with a solution kernel. Once decoupled, we should be able to use that one for both of the tasks (i.e., scale variations in EKO and yadism, once expanded they are the exact same).

Last note: once implemented through EKO, this fact scale variation approach could be directly applied at PineAPPL level. I would develop first in yadism, as a replacement of the current one. But once available, we could move this to Pineko, extending the scale variations generator. The advantage is that it will work for any process, by virtue of PDFs universality, with the extra care of extending it to the double hadronic case.

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