Influence on Higgs mass resolution and significance

 With the different methods for finding the primary vertex developed it is easy to compare the power of them. The significance of a Higgs signal is determined by the mass resolution and the amount of signal events outside a $\pm$ 1.4$\sigma$ window as shown in section7.1.

  

Figure 7.12: Distribution of the reconstructed Higgs mass at high luminosity for the options Beam constraint (a), Calorimeter (b), Calorimeter & Conversions (c) and Beam, Conv & Global (d). The values of the fits can be found in table tab:Results.

As a reference point results, with vertex information taken from the average position of the beam spot only, will be used. This is the worst case scenario with a mass resolution of 1.66 GeV and with 75% of the events inside the signal peak. The last number should be compared to the 84% expected from a perfect Gaussian. Events with one or both photons in a crack of the calorimeter are excluded from the analysis, i.e. the accepted regions in $\eta$ for reconstructed clusters are 0.08 < |$\eta$| < 1.37 and 1.52 < |$\eta$| < 2.45 .

Some selected mass distributions in the high luminosity case can be found in fig. 7.12.

High luminosity  

Resolution Fraction Relative

Method used (GeV) in peak significance

Beam constraint 1.66 0.75 1.00

Calorimeter 1.54 0.74 1.01

Calorimeter & Conversions 1.40 0.77 1.11

Calorimeter & Global 1.57 0.74 1.01

Calo, Conv & Global 1.40 0.77 1.11

Beam & Conversions 1.63 0.80 1.07

Beam & Global 1.67 0.76 1.01

Beam, Conv & Global 1.42 0.77 1.10

True vertex 1.40 0.72 1.04

True vertex & Conversions 1.27 0.76 1.15

 

In table 7.1 the results are summarised for a large set of different conditions at high luminosity:

Beam constraint

A primary vertex position of (0,0,0) used in all positions. Conversions are not identified.

Calorimeter

The pointing from the calorimeter used but conversions are not identified.

Calorimeter & Conversions

Same as above but identified conversions are used both for pointing and for separate energy calibrations.

Calorimeter & Global

Global track reconstruction used in addition to the calorimeter pointing.

Calo, Conv & Global

All information available used for both energy calibration and primary vertex determination.

Beam & Conversions

The beam constraint and information from conversions used. No pointing from the calorimeter.

Beam & Global

The beam constraint and global track reconstruction used. Conversions are not identified.

Beam, Conv & Global

All information except the pointing from the calorimeter used.

True vertex

The true vertex position used.

True vertex & Conversions

The true vertex information used and identified conversions used for separate energy calibration.

In the high luminosity case, the calorimeter performance alone can be compared to the situation with adding information from the Inner Detector. The main improvement is from identifying conversions such that an independent energy calibration can be done for converted and non-converted photons in the calorimeter. It is seen that the best performance achievable using only the global track reconstruction (row Beam, Conv & Global) and using only the calorimeter (row Calorimeter & Conversions) for pointing are nearly equal. However, combining the two methods (row Calo, Conv & Global) gives no further improvement.

That the same significance of the Higgs signal is achievable at high luminosity with the calorimeter pointing having a worse resolution than expected, confirms the robustness of the ATLAS detector for finding a Higgs particle in the H $\rightarrow$ $\gamma$$\gamma$ decay channel.

The uncertainties in the kinematics of the underlying event was treated by artificially changing the amount of events where the Higgs vertex was identified correctly from the global tracking. Varying it the interval from 23% to 55%, which was estimated to be the maximum uncertainty in section 7.4.3, changes the relative significance for the combined pointing with ^{+ 4.0%}_{- 0.5%} for the most optimal pointing with and without the calorimeter pointing. The important point is that the estimate from the full simulation on the influence of the signal significance using global tracking is a pessimistic estimate.

In the multiple interaction model with a hard core proton the upper bound for the option with pointing from the calorimeter, conversions and global tracking (row Calo, Conv & Global in table 7.1) is 1.14 in the relative significance or nearly the same as using the true vertex position (row True vertex & Conversions). The option with pointing from the calorimeter and from conversions (row Calorimeter & Conversions) is clearly unaffected by the treatment of multiple interactions.

As a conclusion the combined approach using both the calorimeter and the Inner Detector for pointing is clearly better than using the calorimeter alone when the hard core proton model is considered for multiple interactions.

Inside the ATLAS collaboration a fast simulation program of the ATLAS detector is under development which will include the resolutions and correlations in the tracking parameters and the track finding efficiencies. The program will be an important tool to continue the study of the significance of the H $\rightarrow$ $\gamma$$\gamma$ signal as the particle level simulations directly from the Monte Carlo do not give enough information on the problems with global track reconstruction, and the full simulation is too slow for simulating the many different kinematic models of the underlying event.

Low luminosity  

Resolution Fraction Relative

Method used (GeV) in peak significance

Beam constraint 1.66 0.82 1.00

Calorimeter 1.25 0.72 1.06

Calorimeter & Conversions 1.15 0.76 1.18

Calorimeter & Global 1.15 0.69 1.08

Calo, Conv & Global 1.04 0.77 1.26

Beam & Conversions 1.44 0.78 1.08

Beam & Global 1.15 0.70 1.08

Beam, Conv & Global 1.04 0.77 1.25

True vertex 1.14 0.69 1.08

True vertex & Conversions 1.03 0.77 1.26

 

At low luminosity the improvement in the H $\rightarrow$ $\gamma$$\gamma$ significance is much better than at high luminosity. The results in table 7.2 are obtained with only the Higgs event in the simulation. For the purpose here the situation is quite close to the low luminosity case where only a few overlapping events are expected in the silicon and pixel detectors. The effect of adding pointing from the global tracking now adds 7% to the significance compared to using only the calorimeter for pointing, and 16% when using only the beam spot constraint. From this it is seen that the global tracking is essential in the search for H $\rightarrow$ $\gamma$$\gamma$ decays at low luminosity. Some selected mass distributions can be found in fig. 7.13.

  

Figure 7.13: Distribution of the reconstructed Higgs mass at low luminosity for the options Beam constraint (a), Calorimeter (b), Calorimeter & Conversions (c) and Beam, Conv & Global (d). The values of the fits can be found in table tab:ResultsLowLum.