Left-Right Symmetry and the Charged Higgs Bosons at the LHC

Left-Right Symmetry
and the Charged Higgs Bosons at the LHC

G. Bambhaniya, Theoretical Physics Division, Physical Research Laboratory,
Navarangpura, Ahmedabad - 380009, IndiaDepartment of Physics, Indian Institute of Technology, Kanpur-208016, IndiaInstitute of Physics, University of Silesia, Uniwersytecka 4, PL-40-007 Katowice, PolandDepartment of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
   J. Chakrabortty, Theoretical Physics Division, Physical Research Laboratory,
Navarangpura, Ahmedabad - 380009, IndiaDepartment of Physics, Indian Institute of Technology, Kanpur-208016, IndiaInstitute of Physics, University of Silesia, Uniwersytecka 4, PL-40-007 Katowice, PolandDepartment of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
   J. Gluza, Theoretical Physics Division, Physical Research Laboratory,
Navarangpura, Ahmedabad - 380009, IndiaDepartment of Physics, Indian Institute of Technology, Kanpur-208016, IndiaInstitute of Physics, University of Silesia, Uniwersytecka 4, PL-40-007 Katowice, PolandDepartment of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
   M. Kordiaczyńska Theoretical Physics Division, Physical Research Laboratory,
Navarangpura, Ahmedabad - 380009, IndiaDepartment of Physics, Indian Institute of Technology, Kanpur-208016, IndiaInstitute of Physics, University of Silesia, Uniwersytecka 4, PL-40-007 Katowice, PolandDepartment of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
   and R. Szafron gulab@prl.res.in joydeep@iitk.ac.in gluza@us.edu.pl mkordiaczynska@us.edu.pl szafron@ualberta.ca Theoretical Physics Division, Physical Research Laboratory,
Navarangpura, Ahmedabad - 380009, IndiaDepartment of Physics, Indian Institute of Technology, Kanpur-208016, IndiaInstitute of Physics, University of Silesia, Uniwersytecka 4, PL-40-007 Katowice, PolandDepartment of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
Abstract

The charged Higgs boson sector of the Minimal Manifest Left-Right Symmetric model (MLRSM) is investigated in the context of LHC discovery search for new physics beyond Standard Model. We discuss and summarise the main processes within MLRSM where heavy charged Higgs bosons can be produced at the LHC. We explore the scenarios where the amplified signals due to relatively light charged scalars dominate against heavy neutral and charged gauge as well as heavy neutral Higgs bosons signals which are dumped due to large vacuum expectation value of the right-handed scalar triplet. Consistency with FCNC effects implies masses of two neutral Higgs bosons to be at least of 10 TeV order, which in turn implies that in MLRSM only three of four charged Higgs bosons, namely and , can be simultaneously light. In particular, production processes with one and two doubly charged Higgs bosons are considered. We further incorporate the decays of those scalars leading to multi lepton signals at the LHC. Branching ratios for heavy neutrino , and decay into charged Higgs bosons are calculated. These effects are substantial enough and cannot be neglected. The tri- and four-lepton final states for different benchmark points are analysed. Kinematic cuts are chosen in order to strength the leptonic signals and decrease the Standard Model (SM) background. The results are presented using di-lepton invariant mass and lepton-lepton separation distributions for the same sign (SSDL) and opposite sign (OSDL) di-leptons as well as the charge asymmetry are also discussed. We have found that for considered MLRSM processes tri-lepton and four-lepton signals are most important for their detection when compared to the SM background. Both of the signals can be detected at 14 TeV collisions at the LHC with integrated luminosity at the level of with doubly charged Higgs bosons up to approximately 600 GeV. Finally, possible extra contribution of the charged MLRSM scalar particles to the measured Higgs to di-photon () decay is computed and pointed out.

Keywords:
LHC, Left-Right gauge symmetry, charged Higgs bosons
\preprint

LPN13-089, Alberta Thy 7-13

1 Introduction

The LHC machine is working incredibly well shifting up the discovery limits for all the non-standard masses. For the same reason it is also true for the non-standard couplings and their possible values are shrinking more and more. Good examples are parameters connected with Left-Right (LR) symmetric models. These models enjoy richness of several types of beyond-the-SM particles Mohapatra:1974gc (); Senjanovic:1975rk (). No wonder that these models are interesting for theoretical and phenomenological studies, for some recent works see Nemevsek:2011hz (); Ferrari:2000sp (); Frank:2011rb (); Das:2012ii (); Chakrabortty:2012pp (); Dev:2013oxa (); He:2012zp () and explored also by the LHC collaborations.

The searches at CMS and ATLAS have tightened up the limits on the masses of heavy gauge bosons. Let us mention that before the LHC era the fits to low energy charged and neutral currents were quite modest, e.g. for a charged gauge boson PDG reports GeV Beringer:1900zz (); Czakon:1999ga (). The new LHC analysis pushed the limits already much above 2 TeV CMS:kxa (); CMS:2013qca (); ATLAS:2012qjz (); TheATLAScollaboration:2013iha (); ATLAS:2013jma (); CMS:2012uaa (); salo:1558322 (). All these searches provide robust bounds on the extra gauge bosons, for instance, the present limit for a charged heavy boson coming from the “golden” decay chain is CMS:2012uaa (); salo:1558322 ()

(1.1)

This limit (at 95 % C.L.) is for a genuine left-right symmetric model which we consider here (MLRSM) with and three degenerate generations of heavy neutrinos and it is based on TeV data. Typically, also limits for mass are already beyond 2 TeV.

The combined LEP lower limit on the singly charged Higgs boson mass is about 90 GeV Searches:2001ac (). At the LHC, established limits for singly charged Higgs boson masses are

(1.2)

if Chatrchyan:2012vca () and for higher masses than 160 GeV, see the limits in ATLAS-CONF-2013-090 ().

For doubly charged Higgs bosons the analysis gives lower mass limits in a range

(1.3)

in the 100% branching fraction scenarios CMS:2012kua (); ATLAS:2012hi ().

The mass limit for heavy neutrinos is CMS:2012zv (); Aad:2012dm ()

(1.4)

but it must be kept in mind that bounds on and are not independent from each other CMS:2012uaa (); salo:1558322 (). Neutrinoless double beta decay allows for heavy neutrinos with relatively light masses, see e.g. Mohapatra:1979ia (); Mohapatra:1980yp (); Maiezza:2010ic (); Tello:2010am (); Nemevsek:2011aa (); Chakrabortty:2012mh (); Dev:2013vxa (). Detailed studies which take into account potential signals with TeV at the LHC conclude that heavy gauge bosons and neutrinos can be found with up to 4 and 1 TeV, respectively, for typical LR scenarios Nemevsek:2011hz (); Ferrari:2000sp (). Such a relatively low (TeV) scale of the heavy sector is theoretically possible, even if GUT gauge unification is demanded, for a discussion, see e.g. Shaban:1992he (); Chakrabortty:2009xm ().

In this paper we consider Left-Right symmetric model based on the gauge group Mohapatra:1974gc () in its most restricted form, so-called Minimal Left-Right Symmetric Model (MLRSM). We choose to explore the most popular version of the model with Higgs representations – a bi-doublet and two (left and right) triplets Gunion:1989in (); Duka:1999uc (). We also assume that the vacuum expectation value of the left-handed triplet vanishes, and the CP symmetry can be violated by complex phases in the quark and lepton mixing matrices. Left and right gauge couplings are chosen to be equal, . For reasons discussed in Czakon:2002wm () and more extensively in Gluza:2002vs (), we discuss see-saw diagonal light-heavy neutrino mixings. It means that couples mainly to light neutrinos, while couples to the heavy ones. and turn out to couple to both of them Gluza:1993gf (); Duka:1999uc (). mixing is allowed and is very small, Beringer:1900zz (), the most stringent data comes from astrophysics through the supernova explosion analysis Mohapatra:1988tm (). In our last paper we considered low energy constraints on such a model assuming , i.e., Chakrabortty:2012pp (), we do the same here. Moreover, in MLRSM , which is really negligible for TeV, as dictated by Eq. (1.1), where are the vacuum expectation values of .

We think that it is worth to show how the situation looks like if we stick to the popular and to a large extent conservative version of the model (MLRSM), giving candle-like benchmark numbers for possible signals at the LHC. We should also be aware of the fact, that there are relations between model parameters in the Higgs, gauge and neutrino sectors Czakon:1999ue (); Czakon:1999ga (); Duka:1999uc (); Chakrabortty:2012pp () and it needs further detailed studies. For estimation and discussion of observables which are able to measure final signals in the most efficient way, calculation of dominant tree level signals is sufficient at the moment. Production processes are calculated and relevant diagrams are singled out using CalcHEP Belyaev:2012qa (). For general analysis, multi lepton codes ALPGEN Mangano:2002ea (), PYTHIA Sjostrand:2006za (), Madgraph Alwall:2011uj () are used. Feynman rules are generated with our version of the package using FeynRules Christensen:2008py (); Degrande:2011ua (). The backgrounds for multi lepton signals (3 and 4 leptons) are estimated using ALPGEN-PYTHIA.

In this paper we have grabbed the impact of the relatively light charged scalars in the phenomenology of Left-Right symmetric model. We first discuss how the decay branching ratios of and are affected by the presence of these light charged scalars. Then we note down the possible interesting processes within MLRSM. We study the production and decay modes of the charged scalars. We have provided some benchmark points where we have performed our simulations to make a realistic estimation of the signal events over the SM backgrounds. Our study is based on the reconstruction of the invariant masses of the final state leptons and their mutual separations from where we have shown how we can track the presence of doubly charged scalars. We also note down the impact of the charged scalars in the Higgs to di-photon decay rates. Then we conclude and give an outlook.

2 MLRSM processes with charged Higgs boson particles at the LHC

There are already severe limits on the heavy gauge boson masses, Eq. (1.1), which infer that scale in which the right gauge sector is broken at TeV (for approximate relations between gauge boson masses and , see for example Eq. (2.4) in Chakrabortty:2012pp ()). This is already an interesting situation as for such heavy gauge bosons most of the effects connected with them decouple in physical processes at collider physics. Then there is a potential room to go deeper and estimate more sensitive Higgs boson contributions. Of course, the effects coming from the scalar sector depend crucially also on their masses. Smaller the Higgs boson masses, larger effects are expected. The question is then: how small their masses can be by keeping the right scale large? In the paper we assume light charged scalar masses up to 600 GeV, this choice of masses will be justified when production cross sections are considered.

The point is that all Higgs scalars are naturally of the order of , in addition, neutral Higgs boson scalars and contribute to FCNC effects (see the Appendix) and must be large, above 10 TeV (see however Guadagnoli:2010sd () for alternative solutions). Let us see then if theoretically charged Higgs bosons can have masses below 1 TeV. In the model which we consider in this paper we assume that the Higgs potential is given as in Gunion:1989in (); Duka:1999uc (), we will also use the same notation, for details on the parametrisation of the Higgs scalar mass spectrum, see the Appendix. This model includes a number of parameters: , , . The exact Higgs mass spectrum is calculated numerically. Minimisation conditions are used to get values of dimensionful mass parameters , and which can be arbitrarily large, all other parameters are considered as free, but limited to the perturbative bound111Which is equal to , otherwise proper analysis of the Higgs potential with radiative corrections to determine perturbative regions would be needed., . It is assumed that the lightest neutral Higgs particle is the boson discovered by ATLAS and CMS collaborations. We have taken its mass to lie in the range

(2.1)

An example set of generated mass spectra of Higgs bosons for TeV is presented in Fig. 2.1 (left figure). Mass spectra have been obtained by varying uniformly the Higgs potential parameters in a range (-10,10). We have also taken into account the bounds on neutral Higgs bosons obtained from FCNC constrains assuming TeV by fixing (see Appendix A). The spectra which did not fulfill relation (2.1) were rejected. Altogether we have 6 neutral, 2 singly charged and 2 doubly charged Higgs boson particles in the MLRSM. The figure includes possible spectra of singly and doubly charged as well as neutral Higgs bosons. Some of them can be degenerated or nearly degenerated.

Figure 2.1: On left: an example of 20 Higgs mass spectra obtained by randomly chosen Higgs potential parameters. The constrain on the lowest neutral Higgs mass Eq.(2.1) was imposed and the bounds coming from FCNC were taken into account. On right: cumulative distribution function of the lowest mass of singly and doubly charged and next to lightest neutral scalars. For both figures, TeV.

This study shows that although the Higgs particles naturally tend to have masses of the order of the scale, it is still possible to choose the potential parameters such that some of the scalar particles can have masses much below 1 TeV (spectrum 15). To discuss spectra more quantitatively, the cumulative distribution function of the lowest masses of singly and doubly charged and next to lightest neutral scalar particles are plotted on right Fig. 2.1, again for the same conditions as before and TeV. These results show that for TeV a fraction of the parameter space that gives lightest scalar masses below 1 TeV is at the level of 4%. It means that it is possible to generate the low mass spectra of Higgs boson masses in MLRSM keeping large scale. However, what can not be seen on those plots is that in MLRSM not all four charged Higgs bosons can simultaneously be light. It is a case for , and , for details, see the Appendix. The remaining charged scalar is of the order of the scale, so its effects at LHC is negligible, to make it lighter would require to go beyond MLRSM. For a book keeping, we keep this particle in further discussion. If its mass at some points is assumed to be small (so we go beyond MLRSM), we denote it with a tilde, . Its coupling is kept all the time as in MLRSM (why it can be so is discussed shortly in the Appendix).

In this paper we consider only the processes where charged Higgs particles can be produced directly as shown in the Table 2.1, first column.

Primary production Secondary production Signal
I.
depends on decay modes
depends on decay modes
II.
depends on decay modes
depends on decay modes
III.
See I
See I & II
See II
depends on ’s decay modes
IV.
See II
See I & II
See I
depends on ’s decay modes
V.
VI.
VII. See I & decay modes
VIII. See II & decay modes
IX. See I
X. See II
Table 2.1: Phenomenologically interesting MLRSM processes at the LHC with primarily produced charged scalar particles and possible final signals. Here denotes a photon. are SM-like light massive neutrino states and are heavy neutrino massive states dominated by right-handed weak neutrinos. From now on we will denote . Here represents light charged leptons .
Figure 2.2: Branching ratio for decay with relatively light charged scalars. Here we put TeV, GeV. Symbol on this and next plots stands for a sum of all quark flavours, . Similarly, .
Figure 2.3: Branching ratio for decay with relatively light charged scalars. Here and .
Figure 2.4: Branching ratios for decay with relatively light charged scalars.

The decay branching ratios for heavy neutrino states and heavy gauge bosons in MLRSM which determine both secondary production and final signals in the last column of this table are given in Chakrabortty:2012pp (). However, with assumed light charged Higgs particles, new decay modes are potentially open, and discussion must be repeated. Results are given in Figs. 2.2, 2.3, and 2.4. As can be seen from Fig. 2.2, contribution of charged scalars to the total decay width of is at the percent level. Here more important are heavy neutrino decay modes222Some processes in the Table 2.1 depend strongly on the light-heavy (LH) neutrino mixing scenarios.. Different scenarios for LH neutrino mixings Chakrabortty:2012pp () are discussed, i.e., see-saw mechanisms where and scenarios where LH neutrino mixings are independent of neutrino masses: delAguila:2008pw (). In a case of many heavy neutrino states (as in MLRSM), taking into account constraints coming from neutrinoless double-beta decay experiment, this limit becomes Gluza:1997ts (); Gluza:1995ix (); Gluza:1995ky (). For decays different LH neutrino mixing scenarios affect only light neutrino channel for which BR is small, anyway.

For the decays, Fig. 2.3, four channels with charged Higgs bosons, namely , , , and , contribute to the decay rate in a percentage level. The quark decay modes dominate, and the second important are the heavy neutrino decay modes.

The most interesting situation is for the decays of heavy neutrinos. Here decay mode is the largest in see-saw scenarios. The reason is that in case of Yukawa coupling, say , the change in LH neutrino mixing is compensated by the proportionality of the coupling to the heavy neutrino mass, which is not the case for the gauge and couplings. That is why and decay modes are relevant only in scenarios where LH neutrino mixings are independent of the heavy neutrino masses and are close to the present experimental limits. Large charged Higgs boson decay mode of the heavy neutrino can influence the “golden” process Keung:1983uu (); Ferrari:2000sp (); Nemevsek:2011hz (); Das:2012ii (); Chen:2013foz (); Chakrabortty:2012pp ().

For typical see-saw cases when charged Higgs boson masses are very large, standard model modes dominate: and if whereas if . In scenarios with large LH neutrino mixings the standard modes dominates independently of the heavy neutrino and masses333Relevance of see-saw LH mixings at the LHC has been discussed lately in Chen:2013foz ().. Finally, let us note that in typical Type I see-saw scenarios the TeV scale of heavy neutrino masses implies GeV to accomplish light neutrino masses at the eV level. In this situation nothing happens to the left plots in Figs. 2.2, 2.3, and 2.4 apart from the fact that , and channels will disappear completely there.

In the case of heavy gauge boson decays, quarks dominate and jets will be produced while for SM-like gauge bosons hadronic decay branching is around 70%. That is why typical final signals for reactions I and II in Table 2.1 are two or four jets plus missing energy. There are only two cases without missing energy:

(2.2)

and

(2.3)

However, as we can see from the table, the cleanest signals are connected with doubly charged Higgs particles, that is why we focus on them in this paper. For some related discussions on doubly charged scalars, see e.g. Huitu:1996su (); PhysRevD.40.1521 (); Rizzo:1981xx (); Maalampi:2002vx (); delAguila:2008cj (); Melfo:2011nx (); delAguila:2013yaa (); Babu-Ayon (); delAguila:2013mia (). The processes Eqs. (2.2) and (2.3) with four charged leptons plus jets will be considered elsewhere.

For processes III-X important are charged Higgs boson decay modes. For doubly charged Higgs particles possible decay modes are

(2.4)

where .

Apart from the above decay modes, the other possibilities for the doubly charged scalars can be

(2.5)

when they are not degenerate with the singly charged ones. But for nearly or exact degenerate case, the charged scalars dominantly decay through leptonic modes and here kinematics play a role too.

Figure 2.5: Branching ratios for the decay modes and of the doubly charged scalars as a function of , where . We have kept fixed GeV. Note that the BRs of both the doubly charged scalars ( and ) are the same in scenarios where and .

Fig. 2.5 shows a scenario in which pure leptonic decay modes can be realised. The crucial factor is the Yukawa coupling which depends (indirectly) on heavy right-handed neutrino mass. If heavy neutrino masses are degenerate then democratic scenario is understood where all leptonic channels are the same (i.e. 33%).

Typically, as can be seen from Fig. 2.5, for right-handed neutrino masses to be 1 TeV, 1 TeV and 800 GeV for respectively, the branching ratios are the following

(2.6)

If the first two generations neutrinos () have masses above TeV, decay mode is practically irrelevant. From the discussion it is also clear, that one of the decay modes can dominate if only one of the right-handed neutrino masses is much bigger than remaining two heavy neutrino states. Limits in Eq. (1.3) assume 100% leptonic decays, in our case, taking into account Fig. 2.5, Eq. (2.6) and results given in CMS:2012kua (); ATLAS:2012hi (), mass limits are much weaker, at about 300 GeV, see e.g. Fig. 3 in ATLAS:2012hi ().

For decays of singly charged scalars situation is analogical as for doubly charged scalars (possible decay modes to neutral and scalars are negligible for , as dictated by FCNC constraints).

decays hadronicaly, namely, for GeV

(2.7)

and for GeV.

2.1 Primary production of heavy charged Higgs bosons at the LHC

Below different processes involving solely charged scalar productions are classified. In analysis which follow GeV to respect with a large excess the present exclusion limits on , and masses. SM-Higgs like mass is set to 125 GeV, masses of neutral scalar particles are set at very high limit ( 10 TeV). In this way, as already discussed, scenarios are realised with relatively light (hundreds of GeV) charged Higgs bosons while remaining non-standard particles within MLRSM are much heavier. All cross sections given in this section are without any kinematic cuts, those will be considered with final signals and distributions in section 3.

2.1.1 and

Figure 2.6: Production cross sections for and processes without imposing kinematic cuts.

The cross section for singly charged scalar pair production as a function of their mass is given in Fig. 2.6. This process is dominated by s-channel and t-channel quark exchange diagrams. Contributions coming from s-channel and bosons are negligible for considered MLRSM parameters. For singly charged scalar mass equals to 400 GeV, the cross sections are (as discussed in Section 2, Higgs boson is assumed to be light and we denote it here with a tilde, for TeV the considered cross section is negligible, )

(2.8)
(2.9)

while for singly charged scalar mass equals to 600 GeV are

(2.10)
(2.11)

with TeV.

Increasing center of mass energy from TeV to TeV the cross sections grow by factors , depending on masses of charged Higgs bosons. In general cross sections fall down below for masses of charged scalars above approximately 730(420) GeV for TeV.

2.1.2 and

The dominant contribution to these processes is via neutral s-channel current, i.e., via and . Contributions coming from s-channel and are negligible for considered MLRSM parameters.

To explore the phenomenological aspects of the doubly charged scalars in the MLRSM model we consider two scenarios. when the doubly charged scalars are degenerated in mass, i.e., . This scenario is motivated by analysis of the Higgs potential (a detailed study of the Higgs potential and scalar mass spectrum will be presented elsewhere). In masses are different, i.e., .

Figure 2.7: Scenario I. Cross sections for and processes without imposing kinematic cuts.

Scenario I, degenerate mass spectrum

In our analysis we set our benchmark point with both of the doubly charged scalars at the same mass GeV. In this case, the cross section at the LHC without imposing any cut at is

(2.12)

The contributions to the cross sections from two possible channels are noted for as

(2.13)
(2.14)

where .

For GeV it is

(2.15)

for . The contributions to the cross sections from individual channels for are as following:

(2.16)
(2.17)

The cross sections for pair productions of doubly charged scalars at the LHC with 14 and 8 TeV are given in Fig. 2.7. From the figure we can see that cross sections fall very rapidly as the masses of the doubly charged scalars increase. Also the production cross section for is much larger than that for as shown in the figure. The cross section at TeV for scalar masses above 920(640) GeV is 0.1 .

Figure 2.8: Scenario II. Contour plots for the cross section. TeV, no kinematic cuts imposed.

Scenario II, non-degenerated mass spectrum

Here we choose another set of benchmark points where the doubly charged scalars are non-degenerated. The cross section for the same process with GeV and GeV at TeV is

(2.18)

The contributions to the cross sections from individual channels are given as:

(2.19)
(2.20)

for .

Contour plots for the cross section as a function of doubly charged scalar masses is shown in Fig. 2.8 (left). On the right figure of Fig. 2.8 different projections are used where X and Y axes are for and the cross section, respectively, whereas is projected as a contour. As can be seen from these figures, cross sections at the level of can be obtained for doubly charged scalar masses up to approximately 600 GeV.

2.1.3 and

The production of a doubly charged in association with a singly charged scalar goes through the charged s-channel interaction where gauge bosons are exchanged. Diagrams with s-channel exchanged singly charged scalar is negligible (its coupling to is proportional to which is zero). As is very heavy, the dominant contribution originates from the process via .

To give yet another benchmark, we set TeV and the following charged scalar masses: = 483 GeV, = 527 GeV, = 355 GeV, = 15066 GeV. The choice is for the following Higgs potential parameters (for the mass formulas, see the Appendix): ,, . This example shows that a wide spectrum of charged scalar masses can be easily obtained, still keeping reasonable small potential parameters (important for higher order perturbation analysis). To reduce channel decays, the masses for the heavy right handed neutrinos are set at 4 TeV for the first two generations and 800 GeV for the third generation, see Fig. 2.5. The cross section for the process before any kinematic cuts with centre of mass energy TeV at the LHC is

(2.21)

The contributions to the cross sections from individual channels are noted as:

(2.22)
(2.23)

with .

For the model consistency (i.e. chosen potential parameters), the second singly charged scalar has been chosen with very high mass GeV. Even if it has low mass ( GeV) then also the cross section for the processes is very low compared to as coupling is proportional to and coupling is proportional to . On the other hand, coupling is proportional to and coupling is proportional to . In both cases mediated processes are much less dominant than the mediated processes. But as the charged gauge boson mixing angle is neglected, the vertex is much more suppressed compare to .

Figure 2.9: Production cross sections for and processes at TeV and no kinematic cuts are imposed. Mass of is allowed to be small and denoted with a tilde.
Figure 2.10: Summary of various MLRSM LHC production cross sections considered in the paper is shown with charged scalars at TeV and without kinematic cuts. We have taken degenerate mass for , , and .

It appears that in MLRSM mixed processes, and , vanishes as . In Fig. 2.9 the total cross section for two considered processes are given. The mass of is allowed to be small and because, as discussed before, this is not natural in the MLRSM, its contribution is denoted with a tilde. Anyway, its contribution (keeping a form of its couplings as dictated by MLRSM) is negligible. Final comparison of cross sections of different processes discussed in sections 2.1.1, 2.1.2 and 2.1.3 is given in Fig. 2.10. We can see that the largest cross sections are for a pair production of singly with doubly charged scalars, and the cross sections for production of doubly charged scalar pair is slightly lower, while the smallest cross section is for pair production of singly charged scalars. Contributions from processes where is involved are negligible or at most much smaller than corresponding results where is involved. Keeping in mind the status of the SM background (analysed for our purposes in section 3.3) we look for multi lepton signals for three or more leptons. Thus we focus in the following sections on the processes which involve primary production of at least one doubly charged scalar.

2.2 Primary production of a heavy Higgs and gauge bosons

2.2.1 , and

In our scenarios the production cross sections for these processes are very small and can be ignored. This is because the propagator diagrams are suppressed as they are as heavy as few TeV. For the other light propagators the scalar-gauge boson-gauge boson vertices are proportional to and/or , which are zero here.

3 Simulations and results for final lepton signals

In this paper we are interested in tri- and four-lepton signal events. To enhance such signals, suitable kinematic cuts are applied in order to decrease the SM backgrounds.

3.1 Events selection criteria

The detailed simulation criteria used in our study are following:

  • The Parton Distribution Function (PDF): CTEQ6L1 Pumplin:2002vw ().

  • Initial selection (identification) criteria of a lepton: pseudorapidity and (transverse momentum ) of that lepton should be 10 GeV.

  • Detector efficiency for leptons:

    • For electron (either or ) detector efficiency is 0.7 ();

    • For muon (either or ) detector efficiency is 0.9 ().

  • Smearing of electron energy and muon are considered. All these criteria are implemented in PYTHIA and for details see gb-jd-sg-pk ().

  • Lepton-lepton separation: The separation between any two leptons should be .

  • Lepton-photon separation: with all the photons having GeV.

  • Lepton-jet separation: The separation of a lepton with all the jets should be , otherwise that lepton is not counted as lepton. Jets are constructed from hadrons using PYCELL within the PYTHIA.

  • Hadronic activity cut: This cut is applied to take only pure kind of leptons that have very less hadronic activity around them. Each lepton should have hadronic activity, within the cone of radius 0.2 around the lepton.

  • Hard cuts: GeV, GeV, GeV, GeV.

  • Missing cut: This cut is not applied for four-lepton final states while for three-lepton case due to the presence of neutrino, a missing cut ( GeV) is applied.

  • Z-veto444Same flavoured but opposite sign lepton pair invariant mass must be sufficiently away from mass, such that, typically, GeV gb-jd-sg-pk (). is also applied to suppress the SM background. This has larger impact while reducing the background for four-lepton without missing energy.

3.2 Signal events for doubly charged Higgs particles in MLRSM

Doubly charged scalars decay mainly to either a pair of same sign charged leptons or charged gauge bosons depending on the choice of parameters. As already discussed, we have chosen the parameter space in such a way that the doubly charged scalars decay to charged leptons with almost 100% branching ratio.

This decay is lepton number violating and can also be possibly lepton flavour violating. In our scenarios we assume no lepton flavour violation as the Yukawa couplings are considered to be flavour diagonal. Thus, the four lepton final state contains two pairs of same sign and same flavoured charged leptons where each pair has opposite charges to each other. As there is no neutrino (missing energy) or jet involved it is easy to reconstruct the momentum of the final state particles. We have reconstructed invariant masses555The invariant mass for a lepton pair is defined as , where and are the energy and three momentum of , respectively. for same sign di-leptons (SSDL) and opposite sign di-leptons (OSDL). As the doubly charged scalars are the parents of the di-lepton pairs, invariant mass of the SSDL is expected to give a clean peak around the mass of the doubly charged scalar, which is not necessarily a case for OSDL.

3.2.1 and

Scenario I, degenerated doubly charged mass spectrum

As calculated in Section II, Eq. (2.12), if GeV, the cross section at the LHC with centre of mass energy TeV is , where . After implementing all the cuts, as described in section 3.1, the four lepton events with no missing energy can be estimated. Each pair of SSDL originates from different doubly charged scalars. We have plotted the reconstructed invariant mass distributions for both SSDL and OSDL in Fig. 3.1 with anticipated integrated luminosity . As both the doubly charged scalars are degenerate the invariant mass peaks occur at around 400 GeV. This clean reconstruction of the invariant mass is indeed possible even in the hadronic environment and can be a smoking gun feature indicating the presence of doubly charged scalars.

Figure 3.1: Invariant mass for SSDL and OSDL for with GeV for TeV and . As the doubly charged scalars are degenerate in mass both the invariant mass peaks occur at the same place and thus cannot be distinguished.

We have computed this process also with centre of mass energy 8 TeV. In this case we find that the cross section, with TeV at the LHC, is 1.06 , about 6 times smaller than for TeV. If we take present integrated luminosity to be then total number of the events even before all the cuts, is statistically insignificant to analyse this particular process at the LHC after implementing all the selection criteria. Thus to justify this four lepton signal for this scenario needs more data in future.

To select the doubly charged scalar signal properly and in an independent way, there is another interesting variable which can be used for determination of signals as suggested in Babu-Ayon ()

(3.1)

where and denote pseudorapidity and azimuth of , respectively. amounts the separation between two light charged leptons () in azimuth-pseudorapidity plane. Its physical importance is that in the detector if is smaller than the specified value then one can not distinguish whether the deposited energy is really by one or two leptons. So, one chooses only events for which leptons are well separated. We expect that the leptons originated from a single doubly charged scalar will be less separated than the leptons coming from different charged scalars. In our considered processes and decays the doubly charged scalars decay mainly into pair of same flavoured same sign leptons. Thus in a case of opposite sign di-lepton pair each of them are coming from different doubly charged scalars must be well separated. We have plotted the distribution to address this feature. It is pretty clear from Fig. 3.2 that the distribution peaks at smaller for same sign lepton pair while that for the oppositely charged lepton pair peaks at larger value of , as expected. This implies that most of the leptons in the SSDL pairs are less separated than the leptons which belong to the OSDL pair.

Figure 3.2: Lepton - lepton separations for the same sign lepton pairs () and opposite sign lepton pairs () for within the degenerate scenario with GeV for TeV and .

Scenario II, non degenerated doubly charged mass spectrum

Here we choose another set of benchmark points where the doubly charged scalars are non-degenerate. In Section II, Eq. (2.18), the cross section at TeV has been calculated for the same process with GeV and GeV, . As , the production cross section for is much larger than that for . Thus the four lepton events will be generated mostly from the leptonic decays of the pair than decays. This statement is very distinctively clear from the invariant mass distributions of the same sign di-leptons, as shown in the Fig. 3.3. Maximum number of same di-lepton events are with an invariant mass peak around GeV and that around GeV is much smaller, as expected.

Figure 3.3: Invariant mass for SSDL and OSDL signals in the process in the non-degenerate mass scenario with GeV and GeV for TeV and .

We also performed the distribution for the same benchmark point. For the same reason as explained before our expectation is reflected in Fig. 3.4.

Figure 3.4: Lepton - lepton separations for same sign lepton pairs () and opposite sign lepton pairs () in the process for non-degenerate mass scenario having GeV and GeV with TeV and .

3.2.2 and

These processes lead to the tri-lepton events with missing , see Table 2.1. For chosen MLRSM parameters, Eq. (2.21), the cross section for the process before cuts with centre of mass energy TeV is . The tri-lepton events can be classified into two categories: either or . The first and second types of signals are originated from and mediated processes, respectively. Thus, it is indeed possible to estimate the charge asymmetry, define as the ratio of the number of events of type to the number of events of type at the LHC. This is very similar to the forward-backward asymmetry at Tevatron. This charge asymmetry depends on Parton Distribution Functions (PDF) and thus is a special feature of LHC. We have estimated this ratio () with the above choices of charged scalar masses with TeV and integrated luminosity 300 . We find 554 tri-lepton signal events after all the cuts and that leads to

(3.2)

In SM the corresponding value calculated for the main processes given in the next section in Table 3.1 is . This value is slightly different from the calculated values in Kom:2010mv () where higher order corrections are taken into account and the specific kinematic cuts are different. Nevertheless, MLRSM value given in Eq. (3.2) differs substantially from its SM counterpart to signify its presence.

As discussed in Section II, the vertex is much more suppressed compare to . Thus, in this case most of the tri-lepton events are originated from