BTag Shape Uncs Mishandled

[aebid]

Ak4 BTagging uncertainties showed 1 sided impacts in recent limit setting. This was followed down other being a bug in the BTagShape application.

It shows up in uncertainties but not in the central when trying to make the relative up/down values in FLAF.

In the end, the code ends up doing this

norm_Central = Σ(w0)          / Σ(w0·SFc)      ← correct, SFs == SFc so it collapses
norm_s       = Σ(w0·SFc/SFs)  / Σ(w0·SFc)      ← wrong

That is from applying the weight_before/weight_after twice:

1. FLAF/Analysis/AnalysisCacheAggregator.py

   Line 53 in 593bc11

   weight_before / weight_after if weight_after != 0 else 1

2. FLAF/Analysis/BtagShapeProducer.py

   Line 39 in 593bc11

   f"return {branch_name} != 0.0 ? {total_weight} / {branch_name} : 0.0",

The applied correction is therefore ⟨1/ (SF_syst/SF_central) ⟩ where it should be 1/⟨ (SF_syst/SF_central) ⟩.

[aebid]

Further on Ak4 btagging uncs
Right now the normalization is being done on ALL events, but we will not use Ak4 b-tagging on the boosted events. In this logic, would the normalization only need to use the resolved in both numerator and denominator? If this is the case -- then the normalization is currently wrong.

But then if this is the case, the BTagShape code which is shared in FLAF will need some analysis-specific flag for a boosted event or not, making it a little messy.