Yield fits for Full Run 2

Yield estimation

Bs and Bd yields were estimated in two ways - from run 1 SM expectations and from 15/16 SM expectations using formula:

N_exp = N_run1 * (σ_FR2/σ_run1) * (eff_FR2/eff_run1) * (L_FR2/L_run1)

I.e. taking into account increase in B-production cross-section due to increase in centre-of-mass energy, difference in trigger efficiencies and available integrated luminosities.

The calculation is performed here (spreadsheet): expCands_Run2.xlsx

The results from both approaches are 400 Bs and 44 Bd candidates to be expected in FR2 dataset.

Something to remember: the lifetime correction for the D_ref values in 15/16 paper (and internal note as well) are switched between Bs and Bd - perhaps the labels got switched, Resulting in larger D_ref value presented for Bd while it should have been so for the Bs.

Pseudo MC production

The toy datasets are produced directly from the extended RooSimultaneous. The generation is done in two variables - the RooRealVar mass and RooCategory corresponding to bin. A type flag is added to each generated component - pdg id for Bd and Bs decays and 999 for background. The expected numbers to be generated are first Poisson-fluctuated prior to the RooSimultaneous::generate() call. The relative population of the various bins in the generated dataset is taken automatically from the extended parameters of the RooSimultaneous. This works well as long as we're generating large enough sample so that every bin has at least one event. This is however not the case for the Bd component, where it often happens that a bin should be empty. When all the desired events are generated and some of the bins remain with no events left to be generated, a number corresponding to the extended term of the RooSimultaneous belonging to that bin is generated instead of 0. That is highly undesirable of course, so a measure dealing with this has been implemented to remove events generated this way.

A projection of 500 toys generated this way is shown here:

500 toys put together

Average BDT and ETA values for each bin are also needed in order to parametrize the shape dependences. Therefore, at the fitting time, each event is assigned a random BDT/eta value sampled from the corresponding MC taking into account the actual BDT & ETA bin (i.e. for an event generated from the Bd pdf into BDT 2 ETA 3 bin, a random BDT & ETA value is sampled from BDT bin 2 ETA bin 3 in the Bd MC). That way we get a fluctuating average BDT and ETA for each toy.

Fitting 15/16 statistics toys

First a set of toys was generated using the procedure described above with the 15/16 statistics, and subsequently were flushed into single ETA bin, reproducing the 15/16 BDT binning. These were then fitted with the 15/16 model. The fit was performed in two steps - first, background-only was initialized with the 15/16 parameters and then fitted to the sidebands. In the next step then the full model was fitted starting from the 15/16 SM expected yields for the signal components. Pulls and residuals were then investigated. Results here are for 200 toys.

Residuals

Pulls

Subsequent fits and checks for pulls and residuals in Bs/Bd yield revealed certain bugs, such as that exponential constant was fixed and not determined by the fit. After fixing these, a comparison was made between fits using the randomized BDT averages (as described above) and fixed BDT averages as used in the 15/16 analysis, and the differences between the two resulting pulls and residuals were found to be rather negligible.

BUG FIX 16.4.2021: the random BDT for bkg was actually drawn from Bd MC. This was fixed and figures updated. No significant impact was observed due to this bug.

The pulls and residuals with randomized BDT:

Randomized BDT

Randomized BDT

Yields correlation: -0.625143
Resids correlation: -0.690806
Pulls correlation: -0.690563

And with the 15/16 fixed bdt mean:

Fixed BDT

Fixed BDT

Yields correlation: -0.625483
Resids correlation: -0.691427
Pulls correlation: -0.69106

NOTE: the TH1 means/rms's are calculated only from the plotted range while those in the TH2s include also the over/underflows.

-- OndrejKovanda - 2021-03-29