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/c^{2}
which we call lowmass search region because M_{H} = 89^{+35}_{26} GeV/c^{2}
(68% confidence level) as of July 2010, as which top quark mass and W boson mass constrain, indirectly.
In the lowmass 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/c^{2}).
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.
We require event quality, topological condition and kinematical condition. At first, we require vertex quality,
enough distance between leptons in ηφ plane (ΔR>0.2) and leptons come from same
zvertex 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 DrellYan 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.
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).
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/c^{2}, 115 GeV/c^{2}] is expected.
The number of expected signal for different mass at 6.2 fb^{1}
After applying event selection cuts, the expected number of events is shown in below Table.
Dominant background process for all categories is DrellYan process, which includes 2 real
lepton and jet(s) faking leptons. Errors shown in Table include all systematic uncertainties.
Table of Background Estimation @ 6.2fb^{1}
Dilepton mass
Leading 2 leptons mass in control region
Leading 2 leptons mass in signal region
To discriminate signals from backgrounds in candidate events, we use Support Vector Machine as a multivariate technique.
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)
We prepare for 8 trained classifiers to discriminate signal from backgrounds. Our training strategy is to
discriminate signals from dominant background (DrellYan 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 DrellYan process (ee,μμ).
These cases include DrellYan 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 DrellYan(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/c^{2}) and ZH → LL+ττ (M_{H}=120GeV/c^{2})
Monte Carlo samples are used to train.
3 Lepton case  4 L lepton case 
lll  llτ  eμτ, lττ  LLLL 
VH vs DY (f^{DY0}), 12IV  VH vs DY (f^{DY1}), 16IV  VH vs All Bkg (f^{AL0}), 12IV  ZH vs All Bkg (f^{AL1}), 20IV 
VH vs tt (f^{TT0}), 9IV  VH vs tt (f^{TT1}), 16IV     
VH vs WZ/ZZ (f^{DB0}), 16IV  VH vs WZ/ZZ (f^{DB1}), 16IV     
8 classifiers definition and the number of input variables (IV) for each classifiers training
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 DrellYan" 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(x_{1}, x_{2}, x_{3}) = (x_{1} · x_{2} + x_{2} · x_{3} + x_{3} · x_{1})/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.
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
We define 5 likelihoods (L_{0},L_{1},L_{2},L_{3} and L_{4}) from each response distribution. Then,
we extract the expected 95% confidence level limit from binned likelihood by pseudo experiments.


Cross Section Upper Limit by lll case 
Cross Section Upper Limit by llτ case 
 


Cross Section Upper Limit by eμτ case 
Cross Section Upper Limit by lττ case 
 


Cross Section Upper Limit by LLLL case 

Cross Section Upper Limit by each lepton combination
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.
Cross Section Upper Limit
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/c^{2}.
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.