Vector boson reconstruction

 The two vector bosons in the four jet decay are reconstructed from the energies deposited in the calorimeters. The two vector bosons will be nearly back-to-back with a high boost along the vector boson direction and the two jets from each vector boson decay will thus be close together and appear as sub-jets inside jets with a large cone size. The event structure is illustrated in fig. 8.2.

  

Figure 8.2: The structure of a Higgs event with the Higgs decaying to two vector bosons which in turn decay hadronicly. The central region contains two large-cone jets from each vector boson each with two sub-jets from the fragmentation of the quarks in the vector boson decay. Tag jets (section sec:TagJet) and the proton remnants are seen in the forward region.

The first step in the reconstruction is to identify two high energy jets with the energy collected in a large cone of radius 0.5 centred on the jet axis. The jets are quite central and as shown in fig. 8.3 a selection inside the region |$\eta$| < 2.5 maintains nearly the full signal.

  

Figure: The pseudorapidity distribution of the jet with highest transverse energy in H $\rightarrow$ W ⁺W ^- $\rightarrow$ 4j events before any kinematic cuts.

  

Figure: The transverse energy distribution of the jet with highest transverse energy in H $\rightarrow$ W ⁺W ^- $\rightarrow$ 4j and QCD-jet events before any kinematic cuts.

The transverse energy distribution of the jet with highest transverse energy is shown in fig. 8.4 for the Higgs signal together with the background from QCD-jets. The number of events with transverse energy below 300 GeV in the jet sample is strongly biased by the simulation technique. The significance of the signal has a broad maximum for a cut on the jet transverse energy in the interval from 300-400 GeV and the central value of 350 GeV was chosen for the cut.

In a second iteration jets are reconstructed with the energy collected in more narrow cones of radius 0.2. The purpose is to look for two individual sub-jets inside each of the high energy jets, caused by the independent fragmentation of the two quarks in the vector boson decay. For the H $\rightarrow$ W ⁺W ^- $\rightarrow$ 4j events the search for sub-jets with transverse momentum above 50 GeV in both W jets retain 75% of the events, while it keeps 13% of the QCD-jet background. The significance of the signal is almost unaffected by changing the cut in the region from 50 to 125 GeV.

The invariant mass of the large-cone jets are reconstructed by treating each cell of the calorimeter inside the jet cone as a massless 4-vector; the squared mass of a jet is then
 $$\begin{align} m_{j}^2 &= (\sum_i P_i)^2, \\ \intertext{with} P_i &= (\sqrt{p_{x_i}^2+p_{y_1}^2+p_{z_i}^2}, p_{x_i},p_{y_i},p_{z_i})\end{align}$$
the massless 4-vectors of each cell inside the jet. The mass distribution for W jets reconstructed using ATLFAST is shown in fig. 8.5. The resolution is 7.9 GeV and no systematic shift is observed. This should be compared to a resolution of (7.7+-0.4) GeV for a full simulation of a small sample of H $\rightarrow$ W ⁺W ^- $\rightarrow$ 4j events at high luminosity [4].

  

Figure: The mass distribution of reconstructed W-jets in H $\rightarrow$ W ⁺W ^- $\rightarrow$ 4j decays using the ATLFAST program.

  

Figure 8.6: An illustration of tag jets created in Higgs production through vector boson fusion. The hard scattering process can be any of the processes in fig:WWscatterDiagrams.