Possibility of observing Higgs bosons at the ILC in the lepton-specific 2HDM

The Higgs boson pair production at a linear $e^+e^-$ collider is analyzed in the $4\tau$ final state in the context of lepton-specific or type IV 2HDMs. Both beams are assumed to be unpolarized. The Higgs boson pairs (HA) are produced through off-shell $Z^*$ production and decay to $\tau$-jets which is the main decay channel for neutral Higgs bosons in type IV. Using a simplified detector simulation based on SiD detector at ILC, the 4$\tau$ signal is studied through the $\tau$-jet pair invariant mass reconstruction. Several benchmark scenarios are considered for center of mass energies of 500 and 1000 GeV at integrated luminosity of 500$fb^{-1}$. Among Standard Model (SM) background processes, the main background is $e^+e^- \to ZZ$ followed by $Z \to \tau\tau$. This background is however, well under control. With the luminosity assumed in the analysis, striking signals are obtained beyond the reach of LHC. Such signals would allow for precise determination of masses and cross sections and alredy much lower luminosities are sufficient for discovery.

After the discovery of the Higgs boson at LHC [1,2] which was predicted through a theoretical framework known as the Higgs mechanism [3][4][5][6][7][8], attention has been paid to the question whether the observed particle belongs to a single SU(2) doublet or is part of an extended structure such as two Higgs doublet model (2HDM) [9][10][11]. Since the latter scenario can be made in a way to provide a light Higgs boson which respects the observed particle properties, one may expect an SM like structure consistent with experimental data plus new particles arising from the extended Higgs sector. Such additional Higgs particles can in general be different from the observed particle in terms of their masses and their couplings with SM fermions. Therefore one way to observe such particles would be to benefit from their characteristic features and decay channels which are different from those of the SM Higgs boson.
The additional Higgs bosons of such a model are assumed to be heavier than the observed one. Therefore, a center of mass energy above the threshold of their masses is required to observe them. * majid.hashemi@cern.ch Obviously LHC is able to provide effective center of mass energy required to produce heavy 2HDM Higgs bosons, however, in recent studies we have shown that the ability of linear colliders like ILC is much beyond LHC in observing their signals with a high statistical significance. In [12,13] it was shown that signals from the type I 2HDM Higgs bosons can well be observed at e + e − colliders through H/A → bb. The leptonic decay of the type IV 2HDM Higgs bosons through H/A → µµ was also shown to provide clear signals on top of the background [14,15]. The main reasons for such successful results can be summarized as follows.
First, the e + e − collisions provide a cleaner environment in terms of less particle multiplicity and hadron activity.
Second, some SM processes are simply absent in e + e − colliders because of the electric charge conservation. These processes include single W ± gauge boson production and pair production of W ± and Z bosons.
Third, the SM background processes have a smaller cross section at e + e − colliders. As an example, while the top quark pair production tt acquires a high cross section of 800 pb at LHC, it can appear through Z boson decay at e + e − colliders with a cross section of less than 1 pb at √ s = 500 GeV. The above arguments are not the only ones but can be considered as the main features which discriminate e + e − colliders from LHC.
A general 2HDM may be categorized into four CPconserving types with different scenarios of Higgs-fermion couplings. The ratio of vacuum expectation values of the two Higgs doublets (tan β = v 2 /v 1 ) is the free parameter of the model and leads to enhancement or suppression of Higgs-fermion couplings compared to the corresponding SM couplings [16].
In total five physical Higgs bosons are predicted in 2HDM. The lightest Higgs boson, h, (sometimes denoted as h SM ) is the SM like Higgs boson with the same couplings with fermions as in SM. There are two heavier neutral Higgs bosons, H (CP-even) and A (CP-odd), and two charged Higgs bosons, H ± [17].
The focus in this paper is on 2HDM type IV which allows for the heavy neutral Higgs boson decay to leptons arXiv:1805.10513v1 [hep-ph] 26 May 2018 while suppressing other decay channels at high tan β. Since the τ lepton is the heaviest lepton, decay to a τ pair is the dominant channel and approaches unity because the relevant Higgs-lepton couplings depend on the lepton mass. Therefore below the top quark pair production threshold, H/A → ττ is dominant, while above the threshold there is small reduction in the H/A → τ τ decay allowing H/A → tt to appear marginally. As seen from Fig. 1, H/A → tt reaches 10% at high masses leading to ∼ 10% reduction of H/A → τ τ around m H/A 500 GeV. Since both neutral Higgs bosons (H and A) decay to τ lepton pairs, the signal process has a 4τ signature to be distinguished from SM background processes like e + e − → ZZ → 4τ . The Higgs boson mass range in this analysis is 150−300 GeV to be searched for at a linear collider, operating at √ s = 500 and 1000 GeV. The first scenario can be considered as the first running stage of ILC [18] and the second based on a high energy regime of ILC operation or relevant to a collider with higher energy such as CLIC [19][20][21]. Although the nominal scenarios for CLIC are √ s = 500, 1500 and 3000 GeV, a center of mass energy of 1000 GeV is also expected to be possible. The detector simulation for CLIC detectors are different from ILC, however, overall results obtained for √ s = 1000 GeV based on ILC detectors are expected to remain valid for CLIC environment too.
Several benchmark points are considered for the analysis at √ s = 500 and 1000 GeV separately. The Higgs bosons are assumed to satisfy m A = m H ± to ensure that deviation from SM in terms of ∆ρ is small enough and consistent with experimental value [22].
The 2HDM type IV receives soft limits from flavour physics studies at low tan β [23][24][25]. Therefore the region of study is wide in tan β direction starting from values as low as tan β 1 to 50. The signal process, i.e., e + e − → Z ( * ) → HA is independent of tan β as the ZHA vertex does not depend on Higgs-fermion couplings and the 2HDM type. Therefore the signal process including Higgs bosons decays is effectively independent of tan β. This is a dramatic feature of the signal under study as it makes it independent of any parameter other than the center of mass energy of the collider and the Higgs bosons masses. Therefore only kinematic effects can change the signal cross section and its observation chance.
The strategy of the analysis is to generate signal and backgroud events and apply ILC detector simulation and perform τ identification algorithm using hadronic final state of τ leptons. The invariant mass of the two closest τ jets is then calculated and fills a distribution which serves as the Higgs boson candidate invariant mass. The same approach is applied on background events and a final assessment is made on the possibility of signal observation using statistical techniques. Before going to the details of the analysis, a brief review of the theoretical framework is presented in the next section.

II. THEORETICAL FRAMEWORK
The Higgs-fermion couplings in a general 2HDM appear as a Yukawa Lagrangian as in Eq. 1 [26]. The ρ f parameters depend on the 2HDM type and are proportional to κ f as shown in Tab. I specifically for type IV [27]. The CP-odd Higgs couplings (ρ f A ) are the same as ρ f except for an additional minus sign for f = U . Therefore the neutral CP-even Higgs couplings depend on the values of ρ f which are κ f (as in SM) times a tan β or cot β factor which leads to possible deviations from SM [28]. Consistence with SM couplings and oberved data for the light neutral Higgs is acheived with setting s β−α = 1 which results in SM like Higgs boson behaving the same as the observed one while suppressing the heavy neutral CP-even Higgs coupling with gauge bosons which is proportional to c α−β [17].
The brief form of the Lagrangian takes the form: which is translated into the expanded explicit mode of Eq. 3 when Tab. I is used.
In such a scenario, Higgs boson conversion through A → ZH is also suppressed because at high tan β the leptonic decay dominates over the tan β independent A → ZH decay. Therefore both Higgs bosons decay to τ pairs and the signal (invariant mass distribution of the two τ jets) contains τ jet pairs from both Higgs bosons. However patters of an invariant mass distribution with two peaks showing CP-odd and CP-even Higgs bosons is not well visible due to the missing information from neutrino momenta in τ lepton decays.

III. SIGNAL IDENTIFICATION AND THE SEARCH SCENARIO
The signal process is chosen to be e + e − → Z ( * ) → HA → τ τ τ τ . Only the hadronic decay of the τ lepton is considered to benefit from the unique features of τ jets in the detector. The center of mass energy of the collider should be high enough to produce both Higgs bosons. Here two scenarios of √ s = 500 and 1000 GeV are considered.
The analysis is based on benchmark points in the parameter space of the theoretical model. These points are selected according to the signal cross section.
All benchmark points are consistent with the theoretical requirements including potential stability, perturbativity and unitarity using 2HDMC 1.7.0 [29,30]. The selected points are also consistent with experimental limits according to HiggsBounds [31] and HiggsSignal [32].
For each selected point in the parameter space an LHA file [33] is provided by 2HDMC and is passed to PYTHIA 8.2.15 [34,35] for event generation and cross section calculation.
Tables II and III show the selected points in the physical mass basis for the two center of mass energies of √ s = 500 and 1000 GeV. Table IV shows the corresponding background cross sections at √ s = 500 and 1000 GeV. The whole event generation including multi-particle interaction and showering is performed by PYTHIA. Events generated by PYTHIA are then internally used by DELPHES 3.4 [36] with a detector card specialized for SiD detector at ILC [37]. The jet reconstruction is performed by FASTJET 3.1 [38,39] using anti-k t algorithm with a jet cone size of 0.4.   Table IV. Background processes and their cross sections at √ s = 500 and 1000 GeV.

IV. SIGNAL SELECTION AND ANALYSIS
The DELPHES output is stored in ROOT files [40] which contain reconstructed physical objects like electrons, muons and jets with additional flags for b-tagging and τ -tagging results. The latter is what is used in the current analysis.
The event selection starts from accessing reconstructed jets with a kinematic requirement as E j > 5. GeV, |η| < 5. to reject soft jets or jets close to the beam pipe. The τtagging is in general based on a sophisticated algorithm. The τ -jet should proceed in a narrow cone (isolated jet) accommodating one or three charged tracks associated with one prong or three prong hadronic decay with the hardest track carrying a large fraction of the jet energy.
Events with at least three identified τ -jets are selected for the analysis. Due to the small τ -tagging efficiency, the four τ requirement suppresses the signal. On the other hand requiring two τ -jets allows for a large background from single Z boson production. Therefore events with three τ -jets are selected for finding the τ -jet pair with minimum ∆R which is defined as ∆R = (∆η) 2 + (∆φ) 2 with η = −ln tan(θ/2). The angles θ and φ follow the standard definitions: the polar and azimuthal angles.
Tables V and VI show the signal and background efficiencies in the two scenarios of √ s = 500 and 1000 GeV. As seen from these tables the background (mainly from ZZ) is small at the end and the signal to background ratio is large in all cases. The high signal significance which is due to the small cross section of the background and reasonable selection efficiencies, reveals that the signal can be observed earlier before the nominal integrated luminosity of 500 f b −1 is achieved.
Since both Higgs bosons decay to τ leptons, the τjet pair with minimum ∆R can be associated with the CP-even Higgs or CP-odd Higgs bosons. Therefore an invariant mass distribution should in principle show two peaks related to two bosons. In the current analysis, however, the two bosons are not distinguished because of the ambiguity raised by neutrinos in τ decays and also the near mass selection in the selected benchmark points. Figures 2 and 3 show the signal on top of the background. The error bars have statistical origins but systematic uncertainties from the detector effects have been propagated into the final results. As seen from these figures, the signal is well visible in a clean environment with small background contamination. Signals of the first benchmark points are expected to be visible at lower center of mass energies corresponding to the second and third phases of ILC operation at √ s = 350 and 250 GeV. This expectation can be verifies in detail but what was shown in this analysis is the dramatic potential of linear colliders for the 2HDM Higgs boson observation at moderate masses even though at a specific model type.

V. CONCLUSIONS
Signals of the 2HDM Higgs bosons were analyzed at e + e − collisions at √ s = 500 and 1000 GeV. Different benchmark points were studied for the two scenarios. The 2HDM type IV was assumed as the theoretical framework with the Higgs bosons decaying to τ τ . The hadronic τ decays were assumed for the signal final state. The detector simulation was performed based on parameters from the SiD detector studies at ILC. The signals of the Higgs bosons were shown to be well visible on top of the background at integrated luminosity of 500 f b −1 .

ACKNOWLEDGMENTS
We would like to thank the college of sciences at Shiraz university for providing computational facilities and maintaining the computing cluster during the research program.