Same sign trilepton as signature of charged Higgs in two Higgs doublet model

Extension of the Higgs sector is ubiquitous in physics beyond the Standard Model (BSM), and two Higgs Doublet Model (2HDM) is one of the simplest extensions containing two scalar doublets instead of one for electroweak symmetry breaking. To avoid the dangerous flavour changing neutral current, the Yukawa interactions are restrictedGunion:1989we ; Djouadi:2005gj ; Branco:2011iw and the phenomenology of the BSM scalars vary based on the Yukawa structure. A charged Higgs boson ($H^{\pm}$) would be one of the most striking signals of an extended Higgs sector like 2HDM. The Large Hadron Collider (LHC) has performed several searches for the charged Higgs. For most of the cases the collider studies look for $H^{\pm}$ produced in association with a top quark and decays to jets or $\tau$ leptons ATLAS:2013uxj ; ATLAS:2014otc ; CMS:2015lsf ; CMS:2015yvc ; ATLAS:2016avi ; ATLAS:2018gfm ; ATLAS:2018ntn ; CMS:2018dzl ; CMS:2019bfg ; ATLAS:2020jqj ; ATLAS:2021upq . Production of a charged Higgs via vector boson fusion is also explored in CMS:2017fgp ; ATLAS:2018iui . Discovery prospects of charged Higgs in model independent framework are studied in Coleppa_2020 ; Coleppa:2021wjx .

The LHC searches are motivated by the Yukawa structure of type-II 2HDM and supersymmetry. Thus these searches can not explore an extensive part of $H^{\pm}$ phenomenology where the $H^{\pm}$ is fermiophobic. The type-I 2HDM at the large $\tan\beta$ is one of the simplest realizations of fermiophobic scalars. In this scenario, the typical production of charged Higgs via the top channel becomes very low. As a result, the existing limit on charged Higgs in the type-I 2HDM is essentially non-existent for $\tan\beta$ larger than five Chen:2019pkq ; Kling:2020hmi . Thus, to investigate the vast region with large $\tan\beta$, we need to look for $\tan\beta$ independent channels. Hence, exploration of bosonic decay of the BSM scalars is essential, which is governed by the gauge coupling. Another aspect that determines the signature of a $H^{\pm}$ is the BSM scalar spectrum. If a BSM scalar lighter than $H^{\pm}$ exist, then the signature of the $H^{\pm}$ varies accordingly.

The importance of the bosonic decay model of the $H^{\pm}$ has been identified before. The decay of $H^{\pm}$ to $W^{\pm}$ and a neutral scalar has been studied for both type-II and type-I 2HDM model with $H^{\pm}tb$ associated production of charged Higgs Coleppa:2014cca ; Enberg:2014pua ; Kling:2015uba ; Akeroyd:2016ymd ; Arhrib:2016wpw ; Alves:2017snd ; Arhrib:2019ywg ; Arhrib:2020tqk ; Sanyal:2019xcp and in linear colliders Akeroyd_1999 ; Demirci_2020 . For fermiophobic cases, the $H^{\pm}tb$ coupling is $\tan\beta$ suppressed, and the channel becomes irrelevant for large $\tan\beta$. On the other hand, the electroweak production of $H^{\pm}$ Kanemura:2001hz ; Cao:2003tr ; Belyaev:2006rf ; Chun:2018vsn ; Bahl:2021str in association with a neutral (pseudo)scalar depends on the gauge coupling and dominates over the top associated production at large $\tan\beta$. In type-I 2HDM, the electroweak production of a light charged Higgs can give rise to multi-photon or multi-boson final state Arhrib:2017wmo ; Enberg:2018pye ; Enberg:2018nfv ; Arhrib:2021xmc ; Wang:2021pxc ; Akeroyd:2003bt ; Akeroyd_2004 . However, if the BSM scalars are heavier than the observed Higgs boson, they dominantly decay to a pair of massive gauge bosons, and these analyses can not be applied. Hence it is crucial to consider how to look for a $H^{\pm}$ if it is heavier than the SM Higgs boson to understand the experimental discovery potential of a charged Higgs.

Our goal is to present a complementary search strategy for the charged and neutral Higgses, which are heavier than the SM Higgs boson and display fermiophobic nature. We consider electroweak production of the charged Higgs and its subsequent decay to the heavy CP even neutral scalar $H^{\pm}\to W^{\pm}H$. We found that this channel remains dominant for a wide range of parameter space and give rise to a distinctive $5W$ final state. Although it is possible to explore the $5W$ final state via trilepton signature, the signature will be overwhelmed by the huge background coming from $WZ,t\bar{t}$ and $t\bar{t}V$ channels. Going further to four lepton final state decreases the signal cross-section significantly, and it will compete with another substantial $ZZ/Z\gamma$ background.

In this work, we have shown that the most promising signal is the same sign trilepton (SS3L) final state. Background for this process is rare. We have done a realistic analysis of the SS3L final state for the fermiophobic BSM sector by using the type-I 2HDM as a proxy scenario. We show that the proposed signal will discover or rule out a significant parameter space for BSM scalars even at an integrated luminosity of 300 $fb^{-1}$. The exclusion bounds can be as low as $\tan\beta=2$, and any $\tan\beta$ larger than that will be covered by the high luminosity LHC with an integrated luminosity of 3000 $fb^{-1}$. The proposed signal complement the existing search strategies to expand the reach of LHC searches for charged Higgs. To show robustness of our study, we have studied the scenarios for three different mass gaps between charged Higgs and the heavy CP even neutral scalar. For a mass gap of 120 GeV, all relevant processes apart from $H\to W^{+}W^{-}$ is on-shell and when mass gap is 85 GeV, the process $A\to ZH$ becomes off-shell. It is possible to accommodate even lower mass gap of 60 GeV where all the processes including $H^{\pm}\to W^{\pm}H$ become off-shell.

The paper is organized as follows: In Sec. 2 we briefly discuss the type-I 2HDM model, including the existing theoretical and experimental bounds on the parameter space. Then we motivate towards the possible SS3L signature in Sec. 3 where we also provide the details of the collider analysis. The results are presented in Sec. 4 and we conclude in Sec. 5.

Here we give a brief overview of the type-I 2HDM and discuss possible phenomenology and experimental constraints.

In the previous section, we demonstrated that the existing LHC limit on the BSM scalars in the type-I 2HDM is rather weak. We can improve it by exploring the EW production of $H^{\pm}$ and its decay into gauge bosons. Here we will show that the most promising channel is the same sign trilepton (SS3L) final state. Such signal originates via the following processes¹¹1Another possible source of SS3L is through the charged Higgs pair creation mode: $pp\to H^{+}H^{-}\to(W^{+}H)(W^{-}H)\to(W^{+}W^{+}W^{-})(W^{-}W^{+}W^{-})\to 3\ell^{\pm}\cancel{\it{E}}_{T}+X$. However, the charged Higgs pair production via $Z^{*}/\gamma$ channel is much smaller than the charged current channel and hence does not affect our result.:

Here $X$ is any additional jets and/or leptons. Since the pseudoscalar $A$ is degenerate with $H^{\pm}$, the bottom process will be subdominant compared to the $H^{\pm}H$ channel. Before going into the phenomenological study of the signal, let us first discuss the decay of the BSM Higgs to the gauge bosons. We compute the decay widths and the branching ratios using 2HDMC-1.8.0.

To set the exclusion limits on our signal, we compute the significance ($\sigma_{exc}$) for exclusion using a likelihood ratio method Cowan:2010js given by:

To estimate the discovery reach, we compute the following significance,

For exclusion we demand $\sigma_{exc}\geq 2$ and for discovery we demand $\sigma_{dis}\geq 5$. In Fig 3 we shows the signal cross-sections required for $2\sigma$ exclusion and $5\sigma$ discovery as a function of integrated luminosity.

After applying the selection cuts, the same sign trilepton signal cross-section for different charged Higgs mass is shown in Fig. 4 for a mass gap of 60 GeV(top left), 85 GeV(top right) and 120 GeV (bottom). For all the plots we fix $\sin(\beta-\alpha)=0.995$, and the fermiophobic limit for such $\sin(\beta-\alpha)$ the fermiophobic limit happens at $\tan\beta=10$ as described in Sec. 2.1 and manifest in the top panel of Fig. 2 for $m_{H}=130$ GeV. This is prominent when mass of $H^{\pm}$ and in turn mass of $H$ is the lowest and depicted in blue curve.

As the mass of the BSM heavy Higgs $H$ increases, the $BR(H\to W^{+}W^{-})$ remains large for any $\tan\beta$ and the cross-section remains large beyond the fermiophobic region, which is depicted in red and green curves in Fig. 4. Notice that for the mass gap of 60 GeV, the cross-section shown by yellow curve for $m_{H}^{\pm}=205$ GeV is large at high $\tan\beta$ compared to the blue curve for $m_{H}^{\pm}=190$ GeV. This is because the $BR(H^{\pm}\to HW^{\pm})$ is sizable only for $\tan\beta\gg 10$. When the mass of $H^{\pm}$ and therefore $H$ is least, $BR(H\to W^{+}W^{-})$ peaks at $\tan\beta=10$ where $BR(H^{\pm}\to HW^{\pm})$ is low resulting to a low signal cross-section. This is the case for $m_{H}^{\pm}=190$ GeV as shown in blue curve. When mass of $H^{\pm}$ increases, $BR(H^{\pm}\to HW^{\pm})$ saturates beyond $\tan\beta=10$, and consequently $BR(H^{\pm}\to HW^{\pm})$ becomes large at high $\tan\beta$ which pushes the yellow curve beyond the blue curve. For the mass gap of 120 GeV, the $BR(H^{\pm}(A)\to HW^{\pm}(Z))$ saturates at a lower $\tan\beta$ compared to the mass gaps of 60 GeV and 85 GeV. Hence the signal cross-section also saturates at a lower $\tan\beta$. This is clear from the red, green and brown curves of the three mass gaps. The same argument explains why the width of the blue curve, which corresponds to $m_{H}=130$ GeV is minimum for the mass gap of 120 GeV and maximum for the mass gap of 60 GeV. Finally, when the $H\to hh$ decay comes into play, the signal cross-section decreases rapidly as shown by the black curves for all the mass gaps.

Now we will show our main result of exclusion and discovery region in $m_{H^{\pm}}-\tan\beta$ plane for the different mass gaps. In Fig. 5 we displayed the reach of LHC for three mass gaps where $\sin(\beta-\alpha)=0.995$. The fermiophobic limit corresponds to $\tan\beta=10$ and is shown in the horizontal black dashed line. The exclusion(discovery) contours are depicted by solid(dashed) curves and red(blue) curves corresponds to integrated luminosity of 300(3000)$fb^{-1}$.

For the mass gap of 60 GeV, the low $BR(H^{\pm}\to HW^{\pm})$ at the fermiophobic limit of $\tan\beta=10$ makes the signal cross-section low as mentioned before. Hence the signal is not enough for discovery at 300 $fb^{-1}$ as seen in top left figure. For the mass gaps of 85 GeV and 120 GeV, the discovery regions at 300$fb^{-1}$ are confined only for low $H^{\pm}$ mass where the signal cross-sections are large. We also observe a dip in the discovery regions at 3000$fb^{-1}$ and exclusion regions at 300$fb^{-1}$ and 3000$fb^{-1}$ due to the enhancement to the signal coming from the on-shell $H\to W^{+}W^{-}$ mode. The on-shell effect can also be seen for mass gap of 60 GeV by the presence of a dip in the exclusion region at 3000$fb^{-1}$. From the plots, it is evident that the SS3L signal is capable of excluding a substantial parameter space at the large $\tan\beta$ region. As the mass gap increases, the $H^{\pm}$ decay to $W^{\pm}H$ saturates at a lower value of $\tan\beta$, which pushes the limits to lower $\tan\beta$ region and thus excludes even larger parameter space. This is most evident for the mass gap of 120 GeV as shown in the bottom panel. Also for the mass gap of 120 GeV, when the mass of $H^{\pm}$ is large, we can not exclude the large $\tan\beta$ region as the decay $H\to hh$ dominates at large $\tan\beta$, and our signal becomes irrelevant.

To show how the proposed signal works even closer to the alignment limit, we have performed the phenomenological analysis for $\sin(\beta-\alpha)=0.999$. The limit becomes stronger in this scenario because of the following reasons:

• •

  The $H^{\pm}HW^{\mp}$ coupling is proportional to $\sin(\beta-\alpha)$, the production cross-section and the branching ratio of $H^{\pm}$ increases in this case.

• •

  $H\to W^{+}W^{-}$ remains dominant even with $\cos(\beta-\alpha)$ suppression since the fermionic decay modes of $H$ is $\tan\beta$ suppressed.

• •

  The subdominant signal is enhanced as the $HAZ$ coupling is proportional to $\sin(\beta-\alpha)$.

• •

  $\lambda_{Hhh}$, being proportional to $\cos(\beta-\alpha)$ becomes small and $H\to hh$ decay is suppressed when allowed.

Effectively, the exclusion and discovery limits become stronger for $\sin(\beta-\alpha)=0.999$. This is evident from Fig. 6, specially for the mass gap of 60 GeV the exclusion region at 300 $fb^{-1}$ is much more enhanced. Also the discovery regions at 300 $fb^{-1}$ for the mass gap of 85 GeV and 120 GeV are more enhanced. The discovery region at 300 $fb^{-1}$ for the mass gap of 120 GeV shows a discontinuity as for small $m_{H^{\pm}}$ the cross-section is large and it again reappears when $H$ decay to on-shell $W$ pair is open. Just like the case of $\sin(\beta-\alpha)=0.995$, the limits become most stringent when the on-shell decay of $H\to W^{+}W^{-}$ opens up showing a dip around $m_{H}=165$ GeV. In Fig. 6 the fermiophobic limit corresponds to $\tan\beta\simeq 22$. Since the value of $\tan\beta$ for fermiophobic limit has moved upwards, we expect the exclusion and discovery regions to shift to higher $\tan\beta$, which is quite visible for the discovery regions at 300 $fb^{-1}$ for the mass gaps of 85 GeV and 120 GeV. Similarly the discovery and exclusion regions at 3000 $fb^{-1}$ for the mass gap of 60 GeV are shifted upwards. However, the overall signal cross-sections have increased due to the enhancement of $\sin(\beta-\alpha)$, the shift of the discovery regions at 3000 $fb^{-1}$ and exclusion regions at 300 $fb^{-1}$ and 3000 $fb^{-1}$ for the mass gap of 85 GeV and 120 GeV are negligible.

Observation of a charged Higgs at the LHC will indicate the presence of an extended Higgs sector. The search strategies of looking for a charged Higgs at the LHC dominantly depends on the $H^{\pm}tb$ coupling. However, the $H^{\pm}tb$ coupling can be small for a fermiophobic $H^{\pm}$ scenario like the type-I 2HDM model. As a result, the limit on a charged Higgs is non-existent unless $\tan\beta$ is close to unity. Here we proposed the same sign trilepton signal to complement the existing searches. The SS3L signature appears when a charged Higgs is produced via electroweak interaction in association with $H$ or $A$ and subsequently decays to heavy gauge bosons. By performing a detailed phenomenological analysis, we demonstrate that our proposed signal is capable of extending the reach of LHC up to a very high $\tan\beta$ region for charged Higgs mass of up to 400 GeV. The decay of the BSM scalars $H^{\pm},A$ and $H$ depends on the mass gap among themselves and to cover a large model parameter space we studied three mass gaps between $H^{\pm}$ and $H$, viz. 60 GeV, 85 GeV and 120 GeV, which covers complete off-shell to fully on-shell decay of various BSM scalars. We also showed that the dependency of the signal on mixing angle $\sin(\beta-\alpha)$ is relatively weak, and a slight deviation from the alignment limit is enough to explore the SS3L signature. If the deviation from the alignment limit is significant, then the proposed signal will not work efficiently as both the couplings $H^{\pm}HW^{\mp}$ and $HAZ$ couplings are proportional to $\sin(\beta-\alpha)$. Also, the exact fermiophobic limit will move towards the low $\tan\beta$ region, which is already constrained via the $H^{\pm}$ search in association with the top quark.

The authors would like to thank Ravindra Kumar Verma for some useful comments and discussions. T.M. was supported by a KIAS Individual Grant PG073502 at Korea Institute for Advanced Study. P.S. was supported by the appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government. This was also supported by the Korean Local Governments - Gyeongsangbuk-do Province and Pohang City.