Background Estimation
Overview
Teaching: 20 min
Exercises: 40 minQuestions
What are the source of background for MDS?
How do we estimate the background contribution?
Objectives
Understand background sources for MDS
Understand ABCD method
ABCD method
As you’ve seen in the previous exercise, the main background is from clusters produced in pilup interactions. To estimate the background, we use a fully data-driven background estimation method, the ABCD method, that make use of two independent variables for background: $N_{\text{hits}}$ and $\Delta\phi\text{(cluster, MET)}$.
The ABCD plane is illustrated in Figure 5.1, where bin A is the signal-enhanced region, with large values of $N_{\text{hits}}$ and small values of $\Delta\phi\text{(cluster, MET)}$. The estimation of the number of events in each bin is expressed by:
\[\\ \begin{align} N_A &= c_1\times c_2 \times Bkg_C +\mu \times SigA\nonumber\\ N_B &= c_1\times Bkg_C +\mu \times SigB\nonumber\\ N_C &= Bkg_C +\mu \times SigC\nonumber\\ N_D &= c_2\times Bkg_C +\mu \times SigD\nonumber\\ \end{align} \\\]where:
- SigA, SigB, SigC, SigD are the number of signal events expected in bin A, B, C, and D, taken from the signal MC prediction.
- $\mu$ is the signal strength (the model parameter of interest)
- $c_1$ is the ratio between background in B and C; $c_2$ is the ratio between background in D and C; Both c1 and c2 are essentially interpreted as nuisance parameters that are unconstrained in the fit.
- BkgC is the number of background events in bin C
Figure 5.1
Diagram of the ABCD plane, where bin A is the signal region, $c_1$ is the ratio between background in B and C, and $c_2$ is the ratio between background in D and C.
Validation of the ABCD method
We have shown the previous episode that if the background clusters are from pileup interaction than the two variables $N_{\text{hits}}$ and $\Delta\phi\text{(cluster, MET)}$ should be independent of each other. To validate this assumption and the only background sources are from pileup interactions, we create an out-of-time validation region that is enriched with background and perform ABCD method to check that the prediction from ABCD matches with the observation.
Open a notebook
For this part, open the notebook called
ABCD_validation.ipynband define the OOT control region and perform the validation test by scanning both $N_{\text{hits}}$ and $\Delta\phi\text{(cluster, MET)}$ thresholds.
Discussion 5.1
Does the prediction agree with the observation?
Key Points
The ABCD method requires the use of two independent variables for background, which implies the only source of background should be low pT particles
The method has been validated in the out-of-time validation region, allowing us to proceed to statistical analysis in the signal region