Model Independent Search for Deviations from the Standard Model ...

92 Search Algorithm
probability
0.04
0.035
0.03
0.025
0.02
0.015
0.01
N
0.005
data
p as a function of σ
N MC b
0
0 20 40 60 80 100 120 140 160
number of events in region
Figure 7.1: Schematic view illustrating the computation of the statistical estimator p.
measured and b is expected. In this case this integral is very large, which shows that the
p-valueriseswiththewidth δN MC . If N MC isitselfuncertainbecauseofsystematicerrors,
then a small dierence between N MC and N data is very common, and the p-value is close
to 0.5.
After the p-value is dened it is calculated for all possible regions in all event class distributions.
The Region of Interest is simply the region with the smallest p-value pmin. This
regionrepresentsthegreatestdeviationofdatafromtheSMpredictioninthespecicevent
data
class and its MET or ∑ p T distribution. If the p-value is very small, this deviation cannot
be explained by statistical or systematic errors, and the region is a potential candidate
for physics beyond the Standard Model. As this p-value is a convolution of a Gaussian
and a Poisson distribution, its value cannot be directly translated into terms of sigmas
corresponding to the deviation.
It has to be stressed that a small p-value itself does not suce to identify a region of possibleNewPhysics.
The p min obtainedisrelatedtoasingle specic regioninthedistribution.
Itestimateshowprobableadeviationisinthespecicregion. Besidesthis, thesignicance
of this deviation has to be tested by considering how probable such a deviation is in any
of the connected regions. This is what the second step of the algorithm evaluates.