Significance Calculation and a New Analysis Method in Searching for New Physics at the LHC

The ATLAS and CMS experiments at the LHC have great physics potential in discovering many possible new particles in a very large mass range up to the TeV scale. We are familar with the significance calculation in searching for and observation of a physics signal with known location and shape. The same calculation is no longer valid when either the location or the shape of the signal is unknown. Using a physics signal with known shape but unknown location as an example, we demonstrate in detail why the current significance calculation fails. We find the significance calculation of the current "Sliding-Window" method at the LHC is over-estimated. The significance and sensitivity of the "Sliding-Window" method also strongly depend on the specifics of the method and the situation it applies to. We describe general procedures for significance calculation and comparing different search schemes. We then apply the procedures to compare the "Sliding-Window" method with a new analysis method in searching for a signal with known shape but unknown location. The new method uses maximum likelihood fits with floating pararmeters and scans the parameter space for the best fit to the entire sample. We find that the new maximum likelihood scan method is significantly more sensitive than current "Sliding-Window" approaches. Unlike the "Sliding-Window" method, the sensitivity of the new method is insensitive to the exact location of the new physics signal we search. Detailed comparison results are given.