The discovery of the 125 GeV Higgs boson [1,2] has been a remarkable achievement of the Large Hadron Collider (LHC). This has provided us a closure regarding the predictions of the Standard Model (SM). While our quest toward understanding the physics beyond the Standard Model (BSM) continues, the 13 TeV run of the LHC is expected to make a big impact in terms of both higher energy reach and better precision by accumulating a huge amount of data at large luminosity. The enigma of the nonzero neutrino mass has pushed the theorists as well as experimentalists to develop new theories and experimental techniques in order to establish the right theoretical pathway toward unveiling the true nature of neutrino mass generation. The neutrino oscillation experiments have established the fact that at least two of the three light neutrinos are massive, and that they have sizable mixing among themselves (for a review, see [3]). The SM, lacking any right-handed neutrinos, is unable to account for these phenomena. This has led to a plethora of scenarios leading to neutrino mass generation [4–12]. As the resulting neutrino mass eigenstates may be either Dirac or Majorana type, both scenarios have potentially unique signatures [13–23] in the collider experiments. The LHC Collaborations have put forth significant effort to extract any possible information about such scenarios from the accumulated data, and the null results so far have only been able to constrain the parameter space of various neutrino mass models [24–29].

In the post-Higgs discovery LHC era, the true nature of the scalar sector remains another vital area of interest. The natural question that arises is whether the 125 GeV Higgs is the only scalar as predicted by the SM or other exotic scalars exist alongside, as predicted by various BSM theories including some of the neutrino mass models [10,30]. The measurements of couplings of the 125 GeV Higgs with known SM particles have so far been consistent with the SM predictions [31]. Thus, even if this Higgs boson were indeed part of a larger scalar sector, its mixing with the other states would be small. There are still enough uncertainties in these measurements to allow new exotic scalar multiplets. Unless the LHC observes some hint of a new scalar, our only hope lies in the precision measurements of the Higgs couplings in order to constrain the BSM physics scenarios. Meanwhile, there has been a long term interest in the simplest two-Higgs doublet models (2HDM) (for a review, see [32]) which are also strongly motivated by supersymmetric scenarios. A two-Higgs doublet model predicts the presence of two CP-even, one CP-odd and two charged Higgses, one of the CP-even Higgs states being the 125 GeV Higgs boson. Despite the presence of these additional scalar states, the mixing between the two doublets can be arranged so that the other scalars are practically decoupled from the SM Higgs. In such cases, the interaction of the SM-like Higgs with the exotic scalars may be so suppressed that any hint of such interactions can be very hard to pick up even with the precision measurements at the LHC. The hope of finding these scalars, therefore, lies in their direct search. While the increasing center-of-mass energy at the LHC can probe heavier exotic particles, extracting any new physics information from the tremendous amount of collected data also faces the increasing challenge of tackling the QCD background. Hence looking for lepton-enriched final states is understandably efficient in suppressing the SM background contributions and probing new physics scenarios which can potentially give rise to lepton-rich final states.

In this work, we consider a 2HDM where the additional Higgs doublet has an odd Z2 symmetry charge opposite to all the SM particles, preventing it from interacting directly with the leptons and quarks. One can additionally incorporate right-handed neutrinos in the model with similar transformation property under Z2 symmetry as the new Higgs doublet. One can thus generate Dirac neutrino mass terms when the Z2 breaks spontaneously and the new Higgs doublet gets a vacuum expectation value (VEV). This class of models, known as neutrinophilic Higgs doublet models (νHDM), has been proposed long ago [33–35] and the relevant phenomenology has been studied quite extensively [36–44]. In principle, one can also generate Majorana neutrino mass terms in such a scenario, since a Majorana mass term for the additional right-handed neutrinos does not break the Z2 symmetry but breaks the accidental lepton number symmetry by two units (ΔL=2). Such a neutrino mass generation mechanism looks very similar to the Type-I seesaw [4–7] case, save for the fact that one uses the neutrinophilic Higgs VEV instead of electroweak VEV in order to generate the light-heavy neutrino mixing. The advantage of having the additional Higgs doublet to generate nonzero neutrino masses is that the additional VEV can be very small¹

This is also preferred from the naturalness argument [45].

Depending on whether the nonzero neutrinos are Dirac or Majorana type, the collider signals of a νHDM scenario can be very different. When Majorana neutrinos exist, a smoking gun signal would be lepton number violating final states. In this work, instead of looking for direct heavy neutrino production, we have considered the production of the neutrinophilic charged Higgs (H±) and explored its various possible decay modes. There are some earlier studies on the charged Higgs in similar scenarios emphasizing its decay into a charged lepton and a heavy neutrino in the process [44]. We show that even cleaner signals can be obtained using this decay mode with higher lepton multiplicity where the SM background is practically nonexistent. We also show that sizable signal event rates can be obtained with other possible decay modes of the H±, which can serve as complementary channels in probing a νHDM-like scenario. We perform our analysis using the 13 TeV LHC as well as an e+e- collider with 1 TeV center-of-mass energy. In the process, one can extract information on the neutrino sector parameters also. We show that a very clean indication of the neutrino mass hierarchy can be obtained from the multiplicity of the charged leptons in the final state even after a rigorous collider simulation. Such information can be very useful in complementing the neutrino oscillation experiments.

In the νHDM model, the particle content of the SM is extended by one additional Higgs doublet (ϕν) and three generations of SM gauge singlet right-handed neutrinos (N). A discrete Z2 symmetry is introduced, under which both ϕν and Ni, i=1, 2, 3, are odd while all the SM fields are even. The most general scalar potential involving the two Higgs doublets is given by Vsc=-m12ϕ†ϕ+m22ϕν†ϕν-m32(ϕ†ϕν+ϕν†ϕ)+λ12(ϕ†ϕ)2+λ22(ϕν†ϕν)2+λ3(ϕ†ϕ)(ϕν†ϕν)+λ4(ϕ†ϕν)(ϕν†ϕ)+λ52[(ϕ†ϕν)2+(ϕν†ϕ)2],(1)where a nonzero m3 explicitly breaks the Z2 symmetry in the model. In the absence of this term, the Z2 symmetry can be broken spontaneously by VEV vν of the field ϕν, while the standard electroweak symmetry is broken when ϕ acquires a VEV, vϕ.

Let us first discuss a framework, where m3=0, i.e. Z2 symmetry is broken only spontaneously in order to generate light neutrino masses and mixing. The model is constrained by sterile neutrino searches, effective number of neutrinos and amount of He4 required in big bang nucleosynthesis (BBN), observed temperature anisotropies of cosmic microwave background (CMB) and astrophysical limits.

Because of an instability of right-handed neutrinos Ni induced by their mixing to left-handed neutrinos, the mixing strength between νℓ, ℓ=e, μ, τ, and Ni, that is, |Uℓi|, can be probed by sterile neutrino searches. In semileptonic meson decays, Ni are produced and can subsequently decay to charged leptons and mesons. Present constraints on |Uei|2 and |Uμi|2 allow a region where their magnitude is of order 10-10 to 10-6, assuming MNi<2  GeV [29]. For tau-sterile mixing, |Uτi|2≲10-4, assuming MNi<0.3  GeV.

In νHDM, however, we found the model favoring even lower values of active-sterile mixing, of order |Uℓi|2∼10-18 to 10-12, at MNi=1  GeV, and even lower for higher Majorana neutrino masses (see Fig. 1). The largest and smallest active-sterile mixings are driven by Uτ3 and Uτ1 elements. Therefore all the active-sterile mixing elements fall between them: |Uτ1|<|Uℓi|<|Uτ3|. The matrix elements are proportional to MN-1/2; therefore C11MN<|Uℓi|<C21MN with some constants C1 and C2. They are deduced from Fig. 1, having values C1=4.34×10-9  MeV1/2 and C2=2.34×10-6  MeV1/2. The matrix elements then belong to the following interval: 1.4×10-10GeVMNi≲|Uℓi|≲7.4×10-8GeVMNi.(2)In addition, the constraints for |Uℓi| were derived from assumption that the branching ratios for Ni decay are dominant. This is not applicable for νHDM, since then the decay modes of right-handed neutrinos are dominated by decays to invisible particles.

As the model is unconstrained by semileptonic and leptonic decay modes, the lower bound for MNi arises from BBN. In the early universe the right-handed neutrinos must be heavy enough to fall off from the thermal equilibrium before BBN. This is due to the latest results for the effective number of neutrinos (Nν=3.15±0.23) by PLANCK [46], which forbids large interference from right-handed neutrinos. This leads to a constraint MNi≳100  MeV.

In addition neutrinophilic VEV vν is constrained from both above and below. Ultralight VEV is forbidden by astrophysical constraints: vν≳O (eV) [47,48]. On the other hand, the surface energy density associated with the domain wall arising from discrete Z2 symmetry breaking is η∼vν3 [49]. The effect of these domain walls to the temperature anisotropies of CMB is ΔTT≈GηH0,(3)where G is Newton’s gravitational constant, H0 is the Hubble constant, and we have assumed λi<1 [50]. Since the observed temperature anisotropies by PLANCK are ∼10-5, the birth of a domain wall will not contradict cosmological data if the VEV is small. If we require the contribution to CMB temperature anisotropies not to exceed the experimental limit, together with the astrophysical constraints, we get O(eV)≲vν≲O(MeV).(4)In order to apply perturbative theory to νHDM, the absolute values of the elements of the light neutrino Yukawa coupling matrices must be 4π at most. We performed a global fit to available neutrino oscillation data to calculate the matrix elements, assuming normal neutrino mass ordering, higher θ23 octant, and no CP violation. We found the dependence of the largest Yukawa coupling of vν and MN to be max|Y(vν,MN)|≈0.629×100  keVvν×MN100  GeV.(5)The dependence is illustrated in Fig. 2.

The breaking of Z2 symmetry is necessary in order to generate light neutrino masses within the framework of this model by means of their mixing with heavy right-handed neutrinos. One can add the following Yukawa interaction and Majorana neutrino mass terms to the Lagrangian while keeping the Z2 parity unbroken, Ladd=yνijL¯iϕνNj+12mRijNicNj+H.c.,(6)where mRij represents the Majorana mass terms corresponding to the right-handed neutrinos. Once ϕν acquires a VEV, the Yukawa term gives rise to Dirac neutrino mass terms, mDij=vν×yνij.

The physical Higgs sector now consists of two neutral CP-even (h, Hν), one neutral CP-odd (Aν), and the charged Higgs (Hν±)²

We have assumed the scalar potential to be CP invariant.

Constraints on the charged Higgs mass and its couplings may arise from direct collider search results, neutrino oscillation data, and lepton flavor violating decay branching ratios. The LHC Collaborations have looked for signatures of exotic scalars in various channels and put bounds on the charged Higgs mass in the range 300–1000 GeV provided it can decay only into a top and a bottom quark [59–62]. However, in our present scenario, the charged Higgs, being a neutrinophilic one, does not couple to the quarks. In such scenarios, there are no direct search constraints on mHν±. In principle, the constraints derived from slepton searches at the LHC can be reinterpreted to put bounds on the neutrinophilic charged Higgs masses although only in the massless limit of the lightest neutralino. Two body decay of the sleptons into a charged lepton and lightest neutralino gives rise to a dilepton signal which can be relevant for the present scenario. Existing data exclude slepton masses up to 450 GeV in the presence of a massless neutralino [63,64]. However, one always obtains same-flavor-opposite-sign (SFOS) lepton pairs from such slepton pair production processes. The signal requirement also demands a jet veto in the central region alongside the SFOS lepton pair for such analyses. In the present scenario, the largest event rate in such a signal region can be obtained when Hν± decays into a charged lepton and a heavy neutrino. A heavy neutrino further decays into a light neutrino and Z-boson which further decays invisibly. Clearly, the resulting signal cross section is rendered small due to branching suppressions. The demand of SFOS lepton pairs makes this cross section even smaller.³

The obtained signal cross section for our lightest benchmark point even before the detector simulation is less than the observed number as quoted in [63,64].

Charged Higgs in our benchmark scenarios can give rise to novel signatures in lepton enriched final states. Majorana neutrinos, if produced via cascade from the charged Higgs can further decay resulting in same-sign leptonic final states, which are characteristic to seesaw models and also have much less SM background. The gauge bosons resulting from the decays of the neutrinophilic Higgs and heavy neutrinos may also decay leptonically, and thus one can easily obtain a multilepton final state associated with missing energy. Leptonic branching ratios of the gauge bosons being small, one would expect smaller event rates in the final state with increasing lepton multiplicity. However, it also means less SM background to deal with resulting in cleaner signals. In this section we explore the different possible multilepton final states with or without the presence of additional jets along with detailed signal to background simulation in order to ascertain the discovery potential of the charged Higgs for our chosen benchmark points in the context of 13 TeV LHC as well as future lepton colliders.

We have considered a simple extension of the SM with one additional scalar doublet and three generations of singlet right-handed Majorana neutrinos, where the additional Higgs states interact with the SM sector only via the right-handed neutrinos. The model, known as the neutrinophilic Higgs doublet model, is a well-motivated framework from the viewpoint of neutrino mass generation. The light neutrinos gain tiny nonzero masses via the Type-I seesaw mechanism when the neutrinophilic Higgs obtains a VEV to break the Z2 symmetry. We have discussed in brief why the spontaneous breaking of the Z2 symmetry is disfavored, if one imposes the constraints derived from the CMB temperature anisotropies induced by domain walls as well as LFV decay branching ratios. We have, therefore, considered a scenario where the Z2 parity is broken explicitly and thus is devoid of the domain wall problem. In such a scenario, the charged Higgs can have interesting collider phenomenology, explored in this work. Depending on the different decay modes of the neutrinophilic charged Higgs, we have identified some particularly clean signal regions likely to provide a hint of νHDM scenarios at the collider experiments.

We have also highlighted the interesting role play of the light neutrino mass hierarchy. Whether the neutrinos follow normal or inverted hierarchy is likely to be manifested via multiplicity of different flavored leptons in the final state. Thus such a finding at the collider experiments can complement the neutrino oscillation experiments which are yet to ascertain the correct mass hierarchy of the three light neutrinos.

The fact that the charged Higgs pair production cross section falls quite rapidly at the LHC with increasing mass led us to perform a comparative study between the LHC and a future e+e- machine in order to probe such scenarios. We observed that although LHC is quite efficient to probe light charged Higgs masses, an e+e- collider will be able to probe a much larger parameter space with heavier states.