PYTHIA (version 6.4.22) [14] has been used for the purpose of event generation. The corresponding mass spectrum and decay branching fractions are fed to PYTHIA by using the SLHA interface [15]. Subsequent decays of the produced particles, hadroniza- tion and the collider analysis were performed using PYTHIA. We used CTEQ5L parton distribution function (PDF) [16,17] for the analysis. The renormalization/factorization scale Q was chosen to be the parton level center-of-mass energy,√s. We also kept ISR,ˆ FSR and multiple interaction on for the analysis. The production cross-section of h0
via gluon fusion channel for different benchmark points (table 6.1) is shown in table 6.2.
√
s BP-1 BP-2 BP-3 BP-4
7 TeV 6837 7365 6932 6948
14 TeV 23150 25000 23580 23560
Table 6.2: Hard scattering cross-section in fb for the process gg → h0for PDF CTEQ5L
with Q =√s.ˆ
We have used PYCELL, the toy calorimeter simulation provided in PYTHIA, with the following criteria:
I. The calorimeter coverage is |η| < 4.5 and the segmentation is given by ∆η × ∆φ = 0.09× 0.09 which resembles a generic LHC detector.
II. ∆R≡p(∆η)2+ (∆φ)2 = 0.5 has been used in cone algorithm for jet finding.
III. pjetT,min = 10 GeV.
IV. No jet matches with a hard lepton in the event.
In addition, the following set of standard kinematic cuts were incorporated through- out:
1. pℓ
T ≥ 5 GeV and |η|ℓ ≤ 2.5,
2. |η|j ≤ 2.5, ∆Rℓj ≥ 0.4, ∆Rℓℓ ≥ 0.2,
where ∆Rℓj and ∆Rℓℓ measure the lepton-jet and lepton-lepton isolation, respectively.
Events with isolated leptons, having pT ≥ 5 GeV are taken for the final state analysis.
Now depending on the distribution of the transverse decay length it is possible to study the behaviour of this spectacular signal in different regions of a generic LHC detector like CMS or ATLAS. For the purpose of illustration we present a slice like picture of the CMS detector in figure 6.2 to describe this novel signal in more details.
Figure 6.2: Transverse slice from the CMS detector. The maroon square corresponds to the global muons which travel throughout the detector starting from the interaction point. The light green square on the other hand corresponds to the stand-alone muons which leave their imprints only in the muon chamber.
Let us now analyze this rare signal (see eqn.(6.1)) piece wise for the CMS detector as shown by figure 6.2. We choose BP-2 as the sample benchmark point. To start with we divide the entire detector in five different regions on the basis of different transverse decay lengths (LT) and conduct our analysis. The decay length (L) is given by
L = cτ (βγ), (6.2)
where c is the speed of light in vacuum (= 1 in natural unit system), τ is the proper life time and the kinematical factor βγ = |~p|m. Here |~p| is the magnitude of the three
momentum = p|px|2+|py|2+|pz|2 and m is the mass of the decaying particle. Now
it is in general difficult to measure the longitudinal component of the momentum (pz)
which lies along the beam axis, thus we choose to work with the transverse decay length given by LT = cτ (βγ)T, (6.3) where (βγ)T = √ |px|2+|py|2 m .
I. LT ≤ 1 cm ◮ Roughly 10% to 15% of the total number of events appear in this
region. These events are close to the interaction point and may be mimicked by MSSM models with 6Rp. Thus we do not consider these points in our analysis though these are
also free from the SM backgrounds.
II. 1 cm < LT ≤ 50 cm ◮ There exist reasonable number of events (∼ 30% of the
total events) with decay length in between 1 cm and 50 cm. For these events the associated electrons and muons2 will leave charged tracks in the inner silicon tracker
as well as the electrons will deposit their energy at the electronic calorimeter (ECAL). Associated hadronic jets will also deposit their energy at the hadronic calorimeter (HCAL). The associated muons are global in nature and leave their marks throughout, upto the muon chamber starting from few layers on the inner tracker. It is easy for the conventional triggers to work for this kind of signal and a reliable mass reconstruction of these displaced hadronic jets and leptons can lead to a discovery. The number of signal events in this region are shown in table 6.3.
III. 50 cm < LT ≤ 3 m ◮ Almost 40% of the total events appear in this region. The
associated electrons and hadronic jets may or may not get detected in this situation depending on the length of the displaced vertices. However, the associated muons will leave tracks either in the muon chamber only or in the muon chamber along with matching tracks in the inner detector also. The number of signal events in this region are also given in table 6.3.
IV. 3 m < LT ≤ 6 m ◮ There exist some number of events (∼ 10% of the total number
of events) which appear only in the territory of the muon chamber. In this case the associated electrons get absorbed in the thick iron yoke of the muon chamber and thus escape detection. Besides, it is also difficult to identify the hadronic jets as jets in the muon chamber, rather they appear as noise. The muons are, however leave visible tracks in the muon chamber only indicating their stand-alone natures. It is indeed difficult for the conventional triggers to work for this specific signal, rather this asks for
a dedicated special trigger which we believe is a challenging task for experimentalists. The corresponding number of events in this region for BP-2 are shown in table 6.3. V. LT ≥ 7 m ◮ There also exist a small number of events (∼ 4%) where decays occur
outside the detector and yield conventional missing energy signature. No. of events √
s signal LT1 LT2 LT3
≥ 4j+ ≥ 2ℓ+ 6pT ≤ 30 GeV 45 69 17
7 ≥ 4j+ ≥ 2µ+ 6pT ≤ 30 GeV 27 38 11
TeV ≥ 4j+ ≥ 2e+ 6pT ≤ 30 GeV 6 10 2
≥ 4j + 1e + 1µ+ 6pT ≤ 30 GeV 12 21 4
≥ 4j+ ≥ 2ℓ+ 6pT ≤ 30 GeV 234 373 98
14 ≥ 4j+ ≥ 2µ+ 6pT ≤ 30 GeV 128 218 58
TeV ≥ 4j+ ≥ 2e+ 6pT ≤ 30 GeV 37 45 16
≥ 4j + +1e + 1µ+ 6pT ≤ 30 GeV 69 113 24
Table 6.3: Number of signal events for L = 5 fb−1 for √s = 7 and 14 TeV at different ranges of the decay length for BP-2 with 1 cm < LT1 ≤ 50 cm, 50 cm < LT2 ≤ 3 m
and 3 m < LT3 ≤ 6 m. LTis are different transverse decay lengths.
The number of events for different length of displaced vertices as addressed earlier are shown in table 6.3 both for center-of-mass energy 7 and 14 TeV with an integrated luminosity of 5 fb−1. Since this is a background free signal, even with this number of events this spectacular signal can lead to discovery at 14 TeV run of the LHC with L = 5 fb−1. At 7 TeV the situation looks less promising and higher luminosity might
be required for discovering such an event. Distribution of the transverse decay length is shown by figure 6.3.
In summary, this signal can give rise to non-standard activities in the muon chamber with two muons and four hadronic jets. There are, however, number of events which can leave their imprints not only at the muon chamber but also in the inner tracker and calorimeters concurrently. Integrating these two signatures can lead to discovery of an unusual signal of Higgs boson at the 14 TeV run of the LHC. Though with higher luminosity discovery at √s = 7 TeV is also possible. Indubitably, development of new triggers and event reconstruction tools are essential.
It is also important to note that the average decay length for a singlino like LSP is determined by the LSP mass as well as by a set of parameters (λ, κ, vc, Yii
ν , vi′) so that
the constraints on neutrino masses and mixing are satisfied. Here vc and v′
i stand for
0.01 0.1 1 10 100 0 2 4 6 8 10 Number of events
Transverse decay length in m
BP2 √s = 14 TeV√s = 7 TeV
Figure 6.3: Transverse decay length distribution of eχ0
1 for
√
s = 7 and 14 TeV with BP-2 for a typical detector size ∼ 10 m with L = 5 fb−1. Minimum bin size is 10 cm.
The signal is given by eqn.(6.1).