Questions on toys and fit biases

[MarcelHoh]

Dear experts,

I'm using pyhf for my B -> Xu l nu via weak annihilation study at Belle II. I'm running some toy studies and observe some biases in the fits. I've uploaded a small spec here.

[Edit: my question on toys was answered here: https://hep-physics.rockefeller.edu/~luc/technical_reports/cdf5776_pulls.pdf]

Running my fit on the toys, I observe biases which seem to be related to certain nuisance parameters. In the spec attached in the gist I have included just one nuisance parameter, ff_Omega[3] which is one such problematic parameter. Generating 10000 toys and plotting the pulls I find an odd structure:

Which seems to have caused biases in my two parameters of interest, mu_wa_charged, and mu_wa_mixed.

I'm a little lost as to what causes this bias. The change in shape to the Xulnu template caused by the nuisance parameter is similar to the shape of the WA_Charged/Mixed samples but I would expect this to just be associated with a large uncertainty as the fit cannot distinguish between the weak annihilation events and changes to this form factor.
I would also naively expect the structure in the ff_Omega[3] pulls to be somewhat mirrored in the weak annihilation yields rather than a biased but still normal distribution.

I'm unsure where to go from here, any tips or tricks to fix this bias would be appreciated!
Thanks in advance!

Cheers,
Marcel

Edit:
To add some more information, the fitted central values look correct, like a correlated multi-normal distribution as expected. The errors however seem to group into two clusters, depending on the fitted value of the ff_Omega[3] nuisance parameter.

[kratsg]

Did this get answered by https://hep-physics.rockefeller.edu/~luc/technical_reports/cdf5776_pulls.pdf? Can you elaborate more - so we can mark as answered?