Search for High Energy Electrons from New Neutral Massive Gauge Boson Decay in the CMS Detector at the LHC Using Monte Carlo Simulation

The existence of new heavy neutral massive boson Z′ is a feature of many extensions of Standard Model models as the two-Higgs-doublet model (2HDM), the Hidden Abelian Higgs Model (HAHM), Left-Right Symmetric Model (LRSM), Sequential Standard Model (SSM) and Baryon number minus Lepton number Model (B-L). In the present work we search for two high energy electrons produced from decaying B L Z   heavy neutral massive boson in the events produced in proton-proton collisions at LHC and can be detected by CMS detector. We used the data which is produced from proton-proton collisions by Monte Carlo events generator for different energies at LHC, then we use the angular distribution, invariant mass, combined transverse momentum and combined rapidity distributions for the two high energy electrons produced from B L Z   decay channel to detect the B L Z   signal. B-L extension of the SM model predicts the existence of a B L Z   heavy neutral massive boson at high energies. From our results which we had simulated using MC programs for B L Z   in the B-L extension of standard model, we predict a possible existence of new gauge B L Z   at LHC in the mass range 1 TeV to 1.5 TeV via electrons identification of the two high energy electrons by CMS detector.


Introduction
The Standard Model (SM) of particles physics provides a good explanation for most known particles but there are several points need an answer, dark matter, dark energy, CP violation to explain the baryonic matter-antimatter asymmetry of the universe and finally neutrino oscillations.From that we can say the SM requires an extension.B-L model is an extension for the SM which is based on the gauge group [1][2][3] . The invariance of the Lagrangian under this gauge symmetry implies the existence of a new gauge boson (beyond the SM ones) and the spontaneous symmetry breaking in this model provides a natural explanation for the presence of three right-handed neutrinos in addition to an extra gauge boson and a new scalar Higgs.Therefore, it can lead to a very interesting phenomenology which is different from the SM results and it can be tested at the LHC.
An extra neutral massive gauge boson corresponding to the B-L gauge symmetry is predicted.There are many models which contain extra gauge bosons.These models can be classified into two categories depending on whether or not they arise in a GUT scenario.In some of these models, Z  and SM Z are not true mass due to mixing.This mixing induces the couplings between the extra Z  boson and the SM fermions.
In the B-L extension of the SM model, the extra B L Z   boson and SM fermions are coupled through the nonvanishing B-L quantum numbers.Searching for B L Z   is accessible via a clean dilepton signal at LHC.We will simulate B-L extension of the SM at LHC which is based on the gauge group using MC programs then search for the B L boson in the dielectron events produced in pp collisions at different energies of LHC where the leptonic decay B L

Results
In this section we present our results for production and detection of a B L signal of the B-L extension of SM using MC programs [7,8].We present the production cross section of Z   mass for various g values (where g is the U(1) B-L gauge coupling constant) and for various energies at LHC, branching ratios as a function of B L mass for heavy neutrino mass = 200 GeV which will affect the results of B L due to the fact that it is a heavy particle.We obtained different results in comparison with Ref [9].The analysis in this paper did not take into account the existence of new decay channel for heavy neutrino in B-L model which is one of the important signatures of B-L model and they did not give any branching ratio for heavy neutrino.After that we will present

. Production Cross Section
In Figures 1 and 2 we present the production cross section for B L for the most relevant production mechanisms for different CM energies.Figure 1 gives the cross section for Z   couplings.Two experimental constraints exist on these two parameters, the first comes from direct search for heavy neutral gauge bosons at the CDF experiment which excludes a B L Z   mass less than 600 GeV and the second limit comes from LEP II where: The interactions of B L Z   boson with the SM fermions in B-L model is described by  where Y B-L is the B-L charge associated with the fermions f (see Table 1).The extra neutral gauge boson B L acquires a mass due to the B-L gauge symmetry breaking where g is the U( In Figure 3, the branching ratios of B L to different quarks are equal approximately and for different leptons are higher than those for quarks.Also the branching ratio for heavy neutrino which have mass 200 GeV in our search is less than those for the charged leptons and light neutrinos.In particular, varies between 17% to 17.5% where (l = electron, muon, tau) but for heavy neutrino ) varies from 6% to 8% and for light neutrino varies from  5.5% to 6%.The probabilities that B L can decay into one light and one heavy neutrino are highly suppressed by the corresponding (heavy-light) neutrino mixing and thus they can safely be neglected.Heavy neutrino is the most characteristic for B-L model so it has an effect on different branching ratios because it is rather massive than the SM neutrino.From Figure 3 one can search for Z   at LHC via a clean dilepton signal which can be one of the first new physics signatures to be observed at the LHC.We will study B L Z   in this paper by using the decay channel of B L Z   to electrons pair using PY-THIA8 and turn off all other decay channels for B L Z   where the ratio of dielctron channel is the highest one.

Total Width of
boson decays only to fermions at tree-level and its width is given by the following expression where m f is the mass and C f the number of colors for the fermion type f.In The main switches for Initial State Radiation, Final Sate Radiation and multiple interactions are on. .We note the importance of ta into consid the heavy neutrino since their relative contribution to the total width can be as large as 20% where king eration which includes all dec annels (also decay cha of heavy neutrino ) whereas ) where θ * is the istribution cos(θ angle in the dielectron rest reference frame between the negative electron and the incident incoming quark.PY-THIA8 gives θ only in Lab frame but we use θ * here which is in rest frame so we must convert from lab frame to rest frame to get θ * by using boost vector.We define two additional reference frames: a) the colliding proton CM frame denoted by O (this frame is identical to the laboratory frame) and b) The rest frame of the dilepton system denoted by O * .The dilepton system is boosted along the beam axis.The z-axis is chosen as the direction of one of the beams, and it is then identical for O and O * frames.It should be noted that there is a sign ambiguity in the measurement of cos(θ * ) since for a particular event, there is no information about whether the incoming quark comes from the positive or negative z directions [11].Instead, it is useful to consider the quantity   In the process

ay ch nnel
boson has both vector an uplings t e fermions, these couplings create an asymmetry in the momentum of the electron visible in the polar angle of the lepton pair's center of mass frame.This polar angle which is measured in the center of mass frame of the leptons is typically referred to as the Collins Soper frame.The angular cross section measured in this frame is given by: Here θ * is the emission angle of the electron relati th ve to e quark momentum in the lepton's center of mass frame (see Figure 8).The constants A and B are determined by the weak isospin and charge of the incident quarks as well as the mass of the dilepton pair.From this cross section, it is convenient to define N f as the number of events whose θ * is positive, and N b as the number of events whose θ * is negative.The asymmetry can then be written as: This is the general form of the asymmetry.xists in the det onsidering Collins and Soper noted that an ambiguity e ermination of the emission angle θ * when c This Drell-Yan process is quite simple [12] when the incoming quarks have no transverse momentum.In such a case, the emission angle is determined by the angle the electron makes with the proton beam and thus the incoming quark momentum vector.However, since circular acceleration implies a certain amount of transverse momentum by construction, an ambiguity arises.Since the quark's individual momenta cannot be measured, the momenta boosted into the center of mass frame of the leptons are even more difficult to separate.Consequently, the dependence of the transverse momentum must be minimized.The polar θ * axis is the bisector of the proton beam momentum and the negative (−) of the antiproton beam momentum when the two are boosted into the center of mass frame of the leptons.In so doing, the dependence on the transverse momentum of the incoming quark pair is minimized.
Table 2 shows the numbers of forward and backward electrons produced from B L Z   decay in the range of B L Z   mass 500 GeV to 1500 GeV and also asymmetry calculation.
ure 9 shows the dielectron asymmetry distribution for forward a

. Drell Yan B 2.2.3 ackground Events
The histogram in Figure 10 shows the generated dielc-50 to 700 GeV for tron events for a reconstructed mass of SM Z o .There is a peak centered on the 100 GeV for 6000 events were generated by PHYTHIA8.This peak, or resonant signal corresponds to the production of a Z o with a mass of 91.188 GeV.This process is called the Drell-Yan spectrum and dielectron are produced from Z o decay and they act as SM background for

ming roton and produces a Z which then decays into two
Here q is a quark from an incoming proton and it is annihilated with its antiparticle q from another inco o p dielectron.The reconstructed mass of Z o will be calculated according to the equation:  is reconstructed from the energy and momenta of the selected tron at coupling constant equal 0.1 g  [14].We generated 5000 events for every signal mass where the backgrounds Drell-Yan events and desired signal events are selected by applying a number of s cuts on all events samples (5000 events).
1) Transverse energy of selected electrons E T > 100 GeV.
2) The selected electrons m dielec election ust be in the central or in th e choose the two highest-energy electrons where η is e forward regions of |η| < 1.442 or 1.566 < |η| < 2.5 then w the pseudo rapidity of emitted electrons which describes the angle of a particle relative to beam axis.
θ is the angle between the particle momentum vector P and the beam axis (Figure 11).
From Figure 12 we find a peak at 1 TeV which is the reconstruction mass of B L Z   from the electron-positron invariant masses.This allowed us to compare the signal mbe Table 3.The expected nu r of events, signal events for  B L Z  , background events, and Significance calculation at  g 0.   generated events with the Drell Yan background from Figure 10.

Properties of 
B L Z 

Luminosity
For each generated signal, PYTHIA8 calculated the cross section for each process.This is important becaus nts lum he minosity is the number of events collision per unit area

Significance Calculations
To calculate the significance, each reconstructed mass is fitted by a Gaussian using the ROOFIT package and using the standard deviation with 3σ mass window around the fitted peak for example from Figure 12 at 1000 GeV peak the mass windows is 450 GeV then σ = 75 and µ = 1000.We will integrate the Gaussian from 550 to 1450 to get t action of signal event, then we will multiply this on by the total expected events N exp to get the number of signal N S then he fr fracti event we can calculate the background events N by: The significance formula is: where N S is the number of signal events and N B is the number of background events.Table 3 shows a summary of signal events and background events for different values of B L Z   mass and the corresponding significance.ing of the underlying collision process at low transverse momentum.
The measurements of the rapidity and transverse momentum spectra are based on samples over boson events reconstructed in each dilepton decay mode and collected using high P T single lepton.For the The final result takes into account the bin width and is normalized by the ion.
e determined from the leptons momenta.The measured differential dielectron cross sections are normalized to the inclusive Z cross section.The differential cross section is determined in each y or bin by btracting from the number of detected events in a bin the estimated number of background events.The distri nce and efficiency and for the effects of detector resolution and electromagnetic finalradiation (FSR) using an unfolding technique based on the inversion of a response matrix.

measured total cross sect
The distribution of B L p Z   bosons is symmetric about y = 0 and therefore the a propriate measurement is the distribution as a function of the abs The measurement is normalized to the total cross sectio olute value of rapidity and σ is the total cross section is determined by 2702 events

Conclusion
In this work, we have presented the LHC potential to discover a heavy neutral massive gauge boson B L Z   in B-L extension of SM model via search for two high energy electrons using MC programs where we have simulated the production of B L Z   for different center of mass energies at LHC for various values of coupling constant g and also presented all possible branching ratios of B L  ecay channels to fermions and presented the total width of B L Z   .We have used the two high energy electrons angular distribution and the two high energy electrons invariant mass to detect generator PYTHIA8[4][5][6] and other software tools as CalcHep, MadGraph/Madevent, FeynRules, ROOT data analysis, Physics Analysis Workstation (PAW), ROOFIT package to fit any resulted histogram in order to get P.D.F.(Probability density function) and Mathematica.In this paper, the results are organized into three subsections.Firstly, we present the production of B L Z   at LHC which includes production cross section, different branching ratios and total width.Secondly, the detection of B the dielectron angular distribution, dielectron asymmetry, Drell Yan background events for this channel and dielectron invariant mass.Thirdly, we present the properties of B L Z   which include Luminosity, Significance, Transverse momentum and Rapidity.
width as a function of B L mass for various values of Z   g .Both angular distribution of dielectron and invariant mass of dielectron produced of B L decay are used to detect Z   B L Z   signal at LHC.Finally, we will focus on the properties of B L such as Luminosity, Significance, Transverse momentum and Rapidity.
as a function of B L Z   mass for various g values (where g is the U(1)B.L gauge coupling constant) at CM energy of LHC = 14 TeV. Figure 2 gives cross sections for B L at LHC for CM energies √s = 5, 7, 10, 12, 14 TeV at fixed value of .At the patron level, the Z   0.2 g  B L Z   production cross section depends on two main parameters, the mass of B L Z   and the coupling constant g .Therefore, the B-L model is controlled by two parameters: the mass of the B L Z   and the coupling constant g determining B L

Figure 1 .
Figure 1.Cross section for  B L Z  as a function of  B L Z  mass for various  g values (where  g is the U(1) B-L gauge coupling constant) at fixed CM energy of LHC = 14 TeV.

Figure 2 .
Figure 2. Cross section for  B L Z  as a function of  B L Z  mass for various energies of LHC at √s = 5, 7, 10, 12, 14 TeV at fixed value of  g 0.2  .

Figure 3 .
Figure 3. Branching ratios for  B L Z  as a function of

Figure 4
we present the total decay width of the B L Z   as a function of B L Z   mass for fixed values of g .Figure 5 presents the total decay width of the B L Z   as a function of g for fixed values of B L Z   mass.From Figures 4 and 5 we note that the total width of a B L Z   gauge boson varies from a few hundreds of GeV over a mass range of 0value of g .The decay widths of B L Z ff    in this model are then given by:

Figure 4 .
Figure 4. Total width for B L Z   as a function of mass B L Z   for fixed values of g .

Figure 5 .
Figure 5.Total width for  B L Z  as a function of  g for

Figure 6
Figure 4 presents the total width for B L Z   as a function of mass B L Z   for fixed values of g .H re 5 ere, we used CM enf LHC 14 MeV.Figu presents the total width for ergy o B L Z   as a function of g for fixed values of B L Z   mas note that the total width of swe present the relative variation of the total width as a function of the heavy neutrino mass for different values of includes all decay channels except hannel of heavy neutrino is turn off. decay c 2.2.Detection of B L Z  Signal at LHC gular analy-ibutio 2.2.1.Dielectron An Distribution In addition to the dilepton invariant mass e e M   sis, it has been shown that the angular distr n of the dilepton events [10] can also be used to test the presence of a B L Z   boson by detecting its interference with the SM Z boson.The massive resonance search technique ( e e M   analysis) is extended to include dilepton angular in

Figure 6 .Figure 7 .
Figure 6.Total width for as a function of heavy neutrino mass for fixed values

Figure 8 .
Figure 8.The lepton's center of mass frame and the Collins-Soper frame.qq ll 

Fig nd backward electrons for various values of
Fig nd backward electrons for various values of B L Z   masses.

Figure 9 .
Figure 9. Dielectron asymmetry distribution for forward and backward electrons for various values of  B L Z  masses.

Figure 10 .
Figure 10.The Drell-Yan background electrons produced from Z o boson for quark and antiquark annihilation.

2 . 2 . 4 .
Dielectron Invariant MassNow, we will use the dilepton invariant mass M e e   from the dilepton events[13] to test the presence of a B L Z   boson at LHC through the massive resonance search technique ( e e M   analysis) beside the last m of dilepton angular information to detect -

Figure 11
Figure 11.P e f d el of The s udo rapidity o produce ectrons  B L Z  decay.

Figure 12 .
Figure 12.The reconstruction for  B L Z   mass from produced dilectron invariant masses at B L Z  mass 1 TeV.
N B and σ is the PYTHIA8 cross section nd L i e luminosity and N S is the nts an N B is the number of backure 13 give the required luminosity e it allows us to scale our generated eve to what an actual signal would look like given the inosity [15].T lu in an accelerator.Therefore, the number of expected events N exp can be determined by the formula: N = L where N = of generated events a s th number of signal eve d ground events.Fig for B L Z   observation at LHC for different masses at B L Z   .We note that the value of the luminosity increases by increasing B L Z   mass.

Figure 14
shows the signal significa the ma nce as a function of ss of B L Z

Figure 14 .Figure 15 .Figure 17 .Figure 18 .Figure 19 .
Figure 14.Signal significance as a function of the mass for for  g 0.2  . B L Z 