Vector Boson Fusion Production of the Standard Model Higgs at the LHC

Vector Boson Fusion (VBF) Higgs boson production is the second largest production mechanism at the LHC. The cross section measurements of the VBF process, $VV\to H$ ($qq\to qqH$), followed by Higgs boson decays into $\tau \tau$, $WW$ and $\gamma \gamma$ will significantly extend the possibility of Higgs boson coupling measurements [1, 2].

Events produced by VBF are characterized by a distict topology of the final state: two forward jets with little extra hadronic activity and the decay products of the Higgs boson. The rapidity distribution of the 3rd jet with respect to the two forward jets, ${\eta }_{j3}^{\ast }$, is shown in Fig. 1 (left) which shows a double-peak structure for the electroweak processes, including the VBF signal, and is more central for the QCD background samples. Applying a central jet veto (CJV) is a poweful rejection method against the QCD background. To avoid considering jets from pile-up events in the CJV, jets are associated to the signal vertex using tracks. For every extra jet one can define the quantity ${\alpha }_{j3}=\Sigma p_{Ttrk}/E_{Tj3}$, where $p_{Ttrk}$ is the $p_T$ of tracks from the signal vertex within the jet cone and $E_{Tj3}$ is the jet measured raw $E_T$. Figure 1 (right) shows ${\alpha }_{3j}$ tends to peak at low values for non-signal jets. The efficiency of the veto for the background samples versus the signal efficiency is shown in Figure 2 (left) for events containg a 3rd jet with $E_T$ larger than different threshold values. An optimal threshold where the signal process has $\sim$80% efficiency while the backgrounds are suppressed below 50% is used [3]. An alternative approach is to consider a track counting veto (TCV) [4], where the number of tracks between the two leading jets is counted with different $p_T$ thresholds. Figure 2 (right) shows the performance of the TCV algorithm, i.e the efficiency of selecting the signal versus the background for events with an increasing cut on the track multiplicity and $p_T$. The black star indicates the performance of the CJV based on calorimeter jets. The TCV algorithm can reach similar discrimination power than the central jet veto.

The observability of the VBF Higgs boson production has been studied with the full CMS detector simulation in the $H\to \tau \tau$, $\gamma \gamma$ and $WW$ decay channels [5]. VBF $H\to \tau \tau$ production has been studied in the Higgs mass range of 115 to 145 GeV in the lepton plus ${\tau }_{jet}$ final state. Figure 3 (left) shows the expected di-$\tau$ mass distribution using the collinear approximation [3] for a luminosity of 30 fb${}^{-1}$. Figure 3 (right) shows the significance of the expected number of signal events for different Higgs masses. A statistical signal significance of 3.9$\sigma$ is expected for a Higgs mass of 135 GeV.

VBF $H\to WW$ production in the lepton plus two jet final state has been studied in the Higgs mass range between 120 and 250 GeV. Figure 4 (left) shows the signal significance expected with 30 fb${}^{-1}$ for different central jet veto selections [6]. In the mass range between 140-200 GeV a 5$\sigma$ significance can be achieved. VBF $H\to \gamma \gamma$ production has also been studied in the Higgs mass range between 115 and 150 GeV [7]. Figure 4 (right) shows the signal significance expected with 30 and 60 fb${}^{-1}$. With 60 fb${}^{-1}$ of collected data a 3$\sigma$ significance can be achieved for a low mass Higgs in the range 115 to 130 GeV.

A selection strategy for the search of VBF Higgs $\to \tau \tau \to lepton+{\tau }_{jet}$ with 1 fb${}^{-1}$ has been developed and is described in detail in [8]. The di-$\tau$ invariant mass will be analyzed to search for the presence of a Higgs boson in the region above the $Z\to \tau \tau$ mass peak. It is important to know well the shape of the $Z\to \tau \tau$ background. The dominant uncertainty comes from the modeling of the missing transverse momentum related to the effects of pile-up, underlying event and the calorimeter noise and response. A method to model the di-$\tau$ mass has been developed [4]. $Z\to \mu \mu$ data events are selected and the muons are removed from the real event. Di-$\tau$ Monte Carlo events are generated with the same kinematics as the real muons and their detector response is fully simulated. Finally the real $Z\to \mu \mu$ events with the muons removed and the simulated di-$\tau$ events are super-imposed to form one event, $Z\to {\tau }_{\mu }{\tau }_{\mu }$, and the di-$\tau$ mass is calculated. The reconstructed di-$\tau$ mass for real and fake $Z\to \tau \tau$ events for inclusive Drell-Yan and $Z$+jets events are shown in Fig. 5. A good agreement between the di-$\tau$ mass shapes is obtained.

The expected di-$\tau$ mass distribution for the background and the Higgs signal for 1 fb${}^{-1}$ is shown in Fig. 6 (left). A profile likelihood method is used to evaluate the upper limit on the number of signal events. Figure 6 (right) shows the expected 95% $CL$ limit on the cross section times branching ratio as a function of the Higgs boson mass.

A selection strategy for the Standard Model Higgs boson produced in vector boson fusion decaying to a pair of $\tau$ leptons with 1 fb${}^{-1}$ of early CMS data at the LHC has been presented. No signal evidence is expected and upper limit on the cross section times branching ratio is evaluated. Prospective analyses for the $H\to \gamma \gamma$, $WW$ and $\tau \tau$ decay channels for a luminosity of 30 fb${}^{-1}$ have also been discussed. For a Higgs boson mass in the range 115 to 140 GeV, an observation with a significance above 2 standard deviations is expected in the H to $\gamma \gamma$ channel, and above 3 standard deviations in the H to $\tau \tau$ channel. The H to WW channel offers a discovery reach above 5 sigma in the mass range of 140 to 200 GeV.