Koji Ebina and Kohei Yorita
Waseda University, Japan

[Public Document]

 We search for the Standard Model Higgs boson associated with vector boson using all lepton decay mode. Signal processes are WH → lν+ττ and ZH → ll+ττ. We select 3 or 4 leptons including hadronic τ to pick candidate events out. To improve search sensitivity, we adopt Support Vector Machine (SVM) to discriminate signals from backgrounds.

 Using 6.2 fb^-1 data, there was not a clear discrepancy between data and our background estimation. Therefore, we extract cross section limits on the Standard Model Higgss production at 95% confidence level. The observed upper limit on assumption of M_H = 115GeV/c² is 18.5 × σ^SM at 95% confidence level while the expectation is 17.3, which is within one standard deviation.

Introduction

 We can search the Standard Model (SM) Higgs boson in several capable production channels and decay modes. Our target M_H region is [100,150] GeV/c² which we call low-mass search region because M_H = 89⁺³⁵_-26 GeV/c² (68% confidence level) as of July 2010, as which top quark mass and W boson mass constrain, indirectly. In the low-mass search region the standard model Higgs boson dominantly decays into b quark pair, but it can also decay into a Tau pair (~7% for M_H = 120 GeV/c²).

 Here, we show the results of a search for the standard model Higgs boson associated with vector boson using all leptonic decay modes. The final states considered are lν+ττ and ll+ττ.

Event Selection

 We require event quality, topological condition and kinematical condition. At first, we require vertex quality, enough distance between leptons in η-φ plane (ΔR>0.2) and leptons come from same z-vertex position. Topological condition requirements are the number of leptons in an event, which is 3 or 4 leptons for WH and ZH processes respectively. We also require the sum charge of leptons must be ± 1 for WH case and be 0 for ZH case. About kinematical condition requirement, we require transverse missing energy significance just to clean up events, especially Drell-Yan process, QCD process and so on.

• Vertex quality
• N(vertex) ≥ 1
• |Δz(vertex)| < 60.0 cm
• N(Lep) = 3 or N(Lep) = 4, which include hadronic τ
  • |Δz(vertex, lepton)| < 4.0 cm
  • |Δz(lepton, lepton)| < 4.0 cm
  • ΔR(lepton, lepton) > 0.2
• |Σ Q_lep| = 1 for N(Lep) = 3 or |Σ Q_lep| = 0 for N(Lep) = 4
• Met/√ΣE_T > 1

These are minimum requirement to save signals as many as possible. Then, we use a multivariate technique later to discriminate signals from backgrounds.

After we select candidate events, we categorize these events to 5 sets; lll, llτ, eμτ, lττ and LLLL, which l denotes e or μ, and L denotes e, μ or τ.

Control Regions (To top)

To check analysis method and modeling, we define control region as below plot, in which CR denotes control region and SR does signal region (our candidate events).

Expected Signal (To top)

We describe the expected number of signal events at 6.2fb^-1, here. Plot shows the expected number of VH → All + ττ events for different mass samples. We also got the expected number of VBF→jj+ττ and H→ττ but these expected events are less than 0.1 events for entire lepton categories at 6.2fb^-1.

  For instance with this criteria, more than 1 SM Higgs event assuming M_H ∈ [100 GeV/c², 115 GeV/c²] is expected.

Background Estimation (To top)

After applying event selection cuts, the expected number of events is shown in below Table. Dominant background process for all categories is Drell-Yan process, which includes 2 real lepton and jet(s) faking leptons. Errors shown in Table include all systematic uncertainties.

Kinematics in Control Regions (To top)

Exact 2 leptons events

3 or 4 lepton with Met significance < 1.0

Kinematics in Signal Regions (To top)

3 or 4 lepton with Met significance ≥ 1.0

Systematic Uncertainties

Systematic uncertainties for our analysis is listed as below.

• Luminosity
• Theoretical Cross Section
• Acceptance
  • z-vertex efficiency
  • trigger efficiency
  • lepton identification
  • Monte Calro Sample statistics
  • fake lepton
  • ISR/FSR (Initial State Radiation/Final State Radiation) modeling for signal process
  • PDF (Parton Distribution Function) modeling for signal process

Systematic Uncertainties are also categorized to 5 sets of lepton combination; lll, llτ, eμτ, lττ and LLLL

lll case (To top)

llτ case (To top)

eμτ case (To top)

lττ case (To top)

LLL case (To top)

Discriminant

To discriminate signals from backgrounds in candidate events, we use Support Vector Machine as a multivariate technique.

Support Vector Machine (To top)

 Machine learning can distinguish 2 categories. One is supervised learning, the other is unsupervised learning. Support Vector Machine (SVM) is a kind of supervised learning method. Basic concept of simple SVM is classifying given data into 2 categories in a hyperspace having dimension with the order of the number of input variables.

 By the way, we use support vector machine in the TMVA tool kit (TMVA v4.0.7 & ROOT v5.27/04)

Training & Testing classifiers (To top)

We prepare for 8 trained classifiers to discriminate signal from backgrounds. Our training strategy is to discriminate signals from dominant background (Drell-Yan plus fake lepton), backgrounds (top pair production) have different kinematics and backgrounds (WZ/ZZ) have similar kinematics backgrounds.

 In lll and llτ cases, we have large contribution from Drell-Yan process (ee,μμ). These cases include Drell-Yan plus one fake lepton, which is mostly making a fake of electron or hadronic tau. In eμτ and lττ cases, there are smaller statistics than lll and llτ cases, and we also have smaller MC statistics. These cases indicate such events that Z boson decays to ττ and jet makes a fake of hadronic tau. In 4 lepton case, WH signal process does not fall into much.

 For lll and llτ cases, we train 3 classifiers for each case, that is "VH vs WZ/ZZ", "VH vs Drell-Yan(ee,μμ)" and "VH vs tt". For eμτ and lττ cases, we train 1 classifier. For 4 lepton case, we also train 1 classifier, which is trained using ZH Monte Carlo sample and all background Monte Carlo samples. About signal process WH/ZH, WH → Lν+ττ (M_H=120GeV/c²) and ZH → LL+ττ (M_H=120GeV/c²) Monte Carlo samples are used to train.

Each classifier has different set of input variables.

Each classifier f returns a response for i th input variables x_i. For example, a classifier f^DY0 which was trained by "VH vs Drell-Yan" in lll case returns a response r^DY0 as

r^DY0_i = f^DY0(x_i)

We prepare for 3 classifiers for lll and llτ, resulted in 3 responses from 3 classifiers for an event. So, we convolute 3 responses into 1 response using a simple function below.

g(x₁, x₂, x₃) = (x₁ · x₂ + x₂ · x₃ + x₃ · x₁)/3.

Then, we get a response for i th event as

r_i = g(r^DY0_i, r^TT0_i, r^DB0_i).

We finally have 5 responses for 5 lepton combination categories.

SVM Output (Control Region: 3 or 4 lepton with Met significance < 1.0) (To top)

SVM Output (Signal Region: 3 or 4 lepton with Met significance ≥ 1.0) (To top)

Results

We do not clearly see any discrepancy between data and our background estimation. Therefore, we extract the expected and observed limit at 95% confidence level

Cross Section Upper Limit by each category (To top)

We define 5 likelihoods (L₀,L₁,L₂,L₃ and L₄) from each response distribution. Then, we extract the expected 95% confidence level limit from binned likelihood by pseudo experiments.

Cross Section Upper Limit (To top)

We simultaneously fit for likelihoods of 5 categories into global likelihood (L_g). We extract the expected 95% confidence level limit from binned likelihood by pseudo experiments.

Conclusion (To top)

This is first challenge to search for the Standard Model Higgs (low mass region) in lν+ττ and ll+ττ final state. To maximize the sensitivity, we used Support Vector Machine. We could not see any discrepancies between data and our background estimation (Counting & Discriminant distribution). Therefore, we extracted the expected and observed cross section limit of 95% confidence level.

In consequence, the expected limit of the Standard Model cross section times branching ratio (σ(SM) × B(H → ττ)) is from 13.3 to 113.8 in search range M_H ∈ [100,150] by 5 GeV/c².

Using about 6.2 fb^-1 data, The observed limit is from 13.9 to 136.6 in as same range as the expected limit.

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