Recoil calibration for the V+jets backgrounds, plus two options and a nuisance naming fix

[davidwalter2]

Summary

The recoil calibration was applied to the W signal only. This branch applies it to the V+jets backgrounds as well, fixes two bugs found along the way, and adds two options used to study the calibration.

Backgrounds in the calibration (88394e5a)

wprocs_recoil now contains Wtaunu, Ztautau, Zmumu and Zmumu10to50 in addition to the signal. The proxy for the boson differs per process:

process	invisible momentum	boson proxy
W→μν	gen ν	gen ν + reco μ
W→τν, Z→ττ	sum of all post-FSR neutrinos	Σν + reco μ
Z→μμ	partner muon, if it is not in the MET	gen partner μ + reco μ

For the tau processes the charge partner used for W→μν picks up the muon neutrino only and misses the tau neutrinos (|pdgId| = 16), hence the sum over postfsrNeutrinos_mom4.

For Z→μμ the partner muon is subtracted from the MET like the selected muon whenever it is inside the tracker acceptance: it leaves a track and is part of the PF MET even when it fails the muon reconstruction, the CVH refit or the veto selection, and also for 2.4 < |η| < 2.5 where there is a track but no muon. Treating it as invisible instead gave a large tail in the residual above qT = 50 GeV (mean +16 instead of +7 GeV, rms 25 instead of 20, 6.6% instead of 1.2% beyond |u| = 60 GeV).

Effect on the mT categories of the extended ABCD (mt_corr_rec / mt_corr_xy, isolated region):

process	mT<20	20-40	>40
Wminusmunu / Wplusmunu	0.875 / 0.918	0.932 / 0.926	1.003 / 1.003
Wminustaunu / Wplustaunu	0.934 / 0.951	0.963 / 0.944	1.015 / 1.016
Ztautau	0.891	1.008	1.101
Zmumu	0.911	0.970	1.014

The recoil uncertainty in setupRabbit is applied to the processes for which the variations are stored instead of to the signal samples only, so it follows the list above while older histmaker outputs keep working.

Bug fixes

• v_gen_phi was aliased to the proxy pt instead of the proxy phi in setup_gen_reco_vars_Z, corrupting the gen recoil columns of the Z path (88394e5a)
• the wlike histmaker booked nominal_noSF unconditionally although nominal_weight_noSF is only defined together with the auxiliary histograms, so --onlyMainHistograms crashed at graph build (88394e5a)
• recoil_stat and recoil_syst both used systAxes = ["recoil_unc"] and therefore produced nuisances with the same names. Since rabbit collects the names in a set and overwrites dict_logk, the two background variations silently replaced the stat variations 0 and 1, and both names ended up in both impact groups: the fit of 260609_abcd has 1100 parameters matching recoil for 1102 booked variations. They are now recoil_stat[0-1099] and recoil_calibration_bkg[0-1] (8534fbac). This renames the parameters, so pulls and impacts of older fits cannot be compared by name.

Two options, both off by default

• --recoilQtMax (0495eaa9) evaluates the calibration at min(ptV, RECOILQTMAX). The calibration is derived from Z events and has no statistics above ~150 GeV, where the model extrapolates: for DeepMETPVRobust the response correction at ut_para+qT = 0 grows from +3.4 GeV at qT = 80 to +6.8 at 120, +13.1 at 150, +32.1 at 200 and +68.0 at 300, while the slope of the map collapses from 1.05 to 0.12. Only the conditioning variable of the model is capped; the true boson pt and phi are kept for the decomposition, so that the transformation stays invertible. The uncapped calibration is stored as nominal_recoilQtExtrap and added as a mirrored nuisance. Measured with a cap at 100 GeV: the cap affects 0.62% of the events and changes their MET by up to -41 GeV, but the migration matrix between the mT categories is exactly diagonal, so the variation is null in the nominal binning and only becomes relevant with a finer binning in mT.
• --recoilGenProxy (734ba8b3) applies the calibration in the Z analyses along the gen boson proxy, as done for the W, instead of the reconstructed dilepton. This is a closure test of the W application on Z events; it changes the central value of the Z analyses (corrected MET mean by -2 MeV, transverse mass mean by +0.7 MeV, parallel recoil residual mean by -27 MeV, at most 0.05% migration between W-like MET bins) and adds no variation.

Validation

All numbers above come from histmaker runs on this branch (1 to 300 files per dataset, --recoilHists). The signal templates are unchanged by the refactoring: the mT migration factors of Wplusmunu and Wminusmunu are identical to four decimals before and after.

Not addressed here

The calibration is conditional on the boson pt only, while the residual depends on more than that: in MC the response differs by ~0.7% of qT between W and Z (300 files each, e.g. +0.343 ± 0.045 GeV at qT = 40-50), and by as much between W+ and W- (+0.449 ± 0.024 GeV at qT = 30-40). A transfer/parametrisation uncertainty of that size is still missing.

🤖 Generated with Claude Code

[cippy]

I only had a minor comment, otherwise this PR looks good to me (I didn't double check the correctness of all the Defines, but the logic seems correct and I am sure the AI is better than me for that).

Edit: an additional comment, the nominal_weight_noSF was mainly intended to be able to plot the nominal histograms with no scale factors applied (it came up during the journal review), to show the effect of the efficiency corrections on the event yields and better highlight the smallness of the residual discrepancies with respect to the uncorrected case. These plots are probably (or possible to produce) only when using the standard external scale factors. That said, I think it is fine to produce them only when not calling --onlyMainHistograms.

[cippy]

Is it worth checking lep_corr_charge > 0 instead of == 1? It is practically the same, but more general in case future developments introduce charges different from unity (but I don't know if we currently expect invalid charge values like -99 o +99, although the current code would not discard them and would simply pick the second alternative already).
Same comments apply to few similar lines below