NNPDF / nnusf

An open source machine learning framework that provides predictions for all-energy neutrino structure functions.
https://nnpdf.github.io/nnusf/
GNU General Public License v3.0
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Add module that corrects isoscalarity for a given PDF set #67

Closed Radonirinaunimi closed 1 year ago

Radonirinaunimi commented 1 year ago

As agreed for $A=1$ we need to use a free isoscalar nucleon with nNNPDF30_nlo_as_0118_p that contains constraints from the LHCb data. To do so, we need to create a functionality that enforces isoscalarity on a given PDF set.

Such a constraint is enforced by replacing each PDF flavour with a linear combination of the proton- and neutron-bound PDFs as follows: $$f^{\rm iso}_i (x, Q^2) = \left( \frac{ f^{p}_i (x, Q^2) + f^{n}_i (x, Q^2) }{2} \right)$$

Assuming isospin symmetry the proton-bound $f^p_i$ and neutron-bound $f^n_i$ PDFs are related: $$u^n (x, Q^2) = d^p (x, Q^2) \, d^n (x, Q^2) = u^p (x, Q^2)~\text{(same relations hold for anti-u and anti-d)}$$ and $f^n_i (x, Q^2) = f^p_i (x, Q^2)$ for other flavours.

juanrojochacon commented 1 year ago

indeed, this is what needs to be done. In this respect, a proton is quite different from an isoscalar A=1 free nucleon, so it is important to get it right.