Triplet Scalars and Dark Matter at the LHC
Abstract
We investigate the predictions of a simple extension of the Standard Model where the Higgs sector is composed of one doublet and one real triplet. We discuss the general features of the model, including its vacuum structure, theoretical and phenomenological constraints, and expectations for Higgs collider studies. The model predicts the existence of a pair of light charged scalars and, for vanishing triplet vacuum expectation value, contains a cold dark matter candidate. When the latter possibility occurs, the charged scalars are longlived, leading to a prediction of distinctive single charged track with missing transverse energy or double charged track events at the LHC. The model predicts a significant excess of twophoton events compared to SM expectations due to the presence of a light charged scalar.
pacs:
NPAC0820
MADPH081517
IPMU080091
I Introduction
Uncovering the mechanism for electroweak symmetrybreaking (EWSB) is one of the primary goals of the Large Hadron Collider (LHC). Despite the tremendous successes of the Standard Model (SM), the scalar sector of the theory that purports to be responsible for EWSB has yet to be confirmed experimentally. It is possible that the mechanism of EWSB is more complicated than in the SM and that the lowenergy scalar sector contains more degrees of freedom than a single SU(2) doublet. A variety of extensions of the SM scalar sector have been proposed over the years, and many of these introduce additional TeVscale particles in order to address other issues that cannot be resolved in the SM: the gauge hierarchy problem, the abundance of matter in the universe (both luminous and dark), gauge coupling unification, and the tiny but nonvanishing neutrino masses. In addition, the tension between electroweak precision observables (EWPOs) that favor a relatively light SM Higgs boson ( GeV EWPO ; Kile ; LEP ) and the LEP II direct search lower bound GeV LEP2 point toward the possibility of an augmented scalar sector with additional light degrees of freedom.
The imminent operation of the LHC – together with the recent establishment of nonvanishing neutrino masses and heightened interest in the origin of visible and dark matter – make a detailed analysis of various scalar sector extensions an important study. In this paper, we focus on the possibility that the SM Higgs doublet is accompanied by a light real triplet that transforms as under SU(3SU(2U(1. This possibility was first discussed by Ross and Veltman in Ref. Veltman and subsequently by the authors of Refs. triplet1 ; triplet2 ; triplet3 ; triplet4 ; triplet5 ; triplet6 ; Chivukula:2007gi . In Ref. Cirelli:2005uq , it was noted that the neutral component of could be a viable cold dark matter (CDM) candidate if it has no vacuum expectation value. In that work, it was shown that the could saturate the observed relic density, Komatsu:2008hk , if TeV. Since is reduced for smaller due to the larger annihilation rate, a lighter triplet would comprise one part of a multicomponent dark matter scenario.
Recently, it was also observed in Refs. GUT1 ; GUT2 ; GUT3 that in several nonsupersymmetric grand unified models that avoid rapid proton decay and achieve coupling unification in agreement with experimental data, a light real triplet emerges. In particular, as noted in Ref. GUT1 , if the real triplet living in the adjoint representation of is light, it can help to achieve unification. From this standpoint, the model studied by Ross and Veltman in Ref. Veltman has a well defined UV completion, thereby providing extra motivation to study its phenomenological aspects in detail.
In exploring the model’s phenomenology, we will attempt to identify the main features that distinguish it from other simple extensions of the SM scalar sector, such as those with multiple SU(2 doublets, , an extra real singlet, , or a complex triplet Veltman . In brief:

Models containing either a SM singlet or a second doublet can lead to neutral scalar mass eigenstates that involve mixtures of the weak states. The presence of this mixing can modify the tension between EWPO and direct searches by allowing for lighter scalars to contribute to the renormalized SM gauge boson propagators while reducing the Higgstrahlung production cross section in annihilation. Typically, the branching ratios for the decay of the SMlike neutral mass eigenstate () are unchanged from those of the SM Higgs, while the heavier neutral scalar () decays can be different due to the presence of the “Higgs splitting” decay mode: . Under some circumstances one has , leading to a reduction in Br(. In addition, models with two Higgs doublets lead to an additional CPodd scalar () and physical charged Higgses () and one could have exotic Higgs properties such as vanishing couplings to matter (“fermiophobia”).
In contrast, for models containing both an SU(2 doublet and triplet, mixing between neutral flavor states is generally suppressed due to constraints arising from the parameter. Consequently, the effect on EWPO is typically less pronounced than in the singlet or multiple doublet models, and the modification of SMlike Higgs production is not sufficiently large to allow one to evade the LEP II bounds. On the other hand, the can be stable, as noted above. In this case, one can expect a relatively longlived charged scalar, leading to the possibility of distinctive charged track events at colliders. When the neutral tripletlike scalar is not stable, its branching ratios can differ significantly from those of the heavier neutral scalar in the singlet or two Higgs doublet scenarios, due to differences in the couplings to gauge bosons.

The complex and real triplet scenarios lead to distinctive features in both production and decay. For example, a complex triplet (as in leftright symmetric models LR ), , couples to SM leptons leading to the TypeII seesaw mechanism TypeII for neutrino masses. In this case one has the possibility of observing lepton number violation through the decays and using the associated production one can distinguish this model easily Tao .
In what follows, we focus on the extension of the SM with a real triplet, which we denote the “SM”, and explore all features in detail. The model predicts the existence of light charged Higgses that can be considered as pseudoGoldstone bosons. We find that in the SM the predictions for the decay of the SMlike Higgs into two photons can differ substantially from the predictions in the Standard Model due to contributions from the light charged scalar to the oneloop decay amplitude. In the case when one assumes that the neutral tripletlike Higgs has a vanishing vev and is responsible for a fraction of the cold dark matter density in the Universe, one expects the charged scalars to be longlived, leading to distinctive single or double charged track plus events at the LHC. For nonvanishing triplet vev, the twophoton decays of the tripletlike neutral scalar can lead to a substantial rate for and final states in DrellYan production of tripletlike scalar pairs. It may also be possible to discover the SM by searching for events associated with the hadronic decays of the tau lepton.
This article is organized as follows: In section II we discuss the basic structure of the model that underlies these expectations, including the various possibilities it provides for symmetrybreaking. Section II.3 gives the model’s phenomenological constraints, including those arising from EWPO and cosmology. In sections III and IV, respectively, we analyze the features of Higgs decays and production relevant to both the LHC and Tevatron, including the dependence of these features on the key parameters of the model as well as a detailed study of the SM backgrounds. In particular, we discuss the prominent signatures of the SM noted above. In the last section we summarize the distinctive features of the model in comparison with other scenarios for EWSB. A few technical details appear in the Appendices.
Ii A Triplet Extension of the Standard Model
In this section we study the main properties of the triplet extension of the Standard Model, wherein the scalar sector is composed of the SM Higgs, , and a real triplet, . The Lagrangian of the scalar sector is given by
(1) 
where is the SM Higgs and the real triplet can be written as
(2) 
with being real, and
(3) 
Here and are the gauge bosons and the generators of the group. The most general renormalizable scalar potential is
(4)  
where all parameters are real. Notice that Tr , with odd. We present a more compact form of the potential,
(5) 
where we have made the abbreviation , with
(6) 
We emphasize that in the limit (in the absence of the last term in the potential in Eq. (4)) the scalar potential of the theory possesses a global symmetry and the discrete symmetry . These symmetries protect the dimensionful parameter , and the case of small corresponds to a soft breaking of this symmetry. We take advantage of the final term in the potential in Eq. (4) to establish the convention that by absorbing the sign into the definition of .
ii.1 Mass Spectrum and Vacuum Structure
In general, the neutral components of both scalars, and , can have a nonzero vacuum expectation value. Defining
(7) 
where and are the SM Higgs and triplet scalar vevs, respectively, we find that the minimization conditions for the treelevel potential are
(8)  
(9) 
and
(10) 
where the last expression follows from the condition of a local minimum, i.e. the determinant of the matrix containing the second derivatives must be positive in each minimum. These conditions will, of course, require modification when the full oneloop effective potential is considered. For purposes of analyzing the basic phenomenological features of the model, however, it suffices to consider the treelevel potential.
The minimization conditions of Eqs. (8) and (9) allow for
four possible cases:
(1) and
(2) and
(3) and
(4) and
The last two possibilities are clearly not viable phenomenologically,
whereas either of the first two are, in principle, consistent with experiment.
The parameters in the potential must be chosen so that the global
minimum of the potential yields solutions (1)
and (2)^{1}^{1}1It is possible that the vacua with are longlived metastable minimaBarger:2003rs ; Kusenko:1996xt , a possibility we do not consider here..
In addition, from Eq. (9) we see that if , solution (2)
is forbidden. Thus, a necessary (but not sufficient) condition
for a minimum with but is that the model possesses
the global symmetry and symmetry.
The potential in Eq. (4) is bounded from below
when and are nonnegative and when the
following relation holds for negative :
(11) 
In addition, before imposing the constraints coming from the mass spectrum, the conditions , , and must be satisfied in order to keep perturbativity. In what follows, we analyze the spectrum associated with different phenomenologically viable vacua assuming each is the global minimum.
ii.1.1 Mass Spectrum
Case (1a): and with
Upon electroweak symmetry breaking, the mass matrices of the neutral ( and ) and charged ( and ) scalars, defined in Eq. (7), are
(12) 
respectively, where the minimization conditions have been used to eliminate and in favor of the vacuum expectation values, and . The eigenvalues of these matrices are the treelevel masses of the physical scalars (, , ) of the theory, and are given by
(13)  
(14)  
(15) 
where is a mixing angle defined below, in Eq (II.1.1) and csc stands for cosecant. The mass parameters of the field and the second eigenvalue of are vanishing, and are associated with the wouldbe Goldstone bosons, and respectively. The physical mass eigenstates and the unphysical electroweak eigenstates are related by rotations through two new mixing angles – one for the neutral scalars, , and the other for charged scalars :
(17) 
In terms of parameters in the Lagrangian, the mixing angles are
(18) 
The neutral mixing angle can, in turn, be expressed in terms of the physical masses:
(19) 
We note that the masssquared of the charged Higgs, Eq. (15), is linearly proportional to . Since, as we previously mentioned that, in the limit , the theory enjoys a global symmetry, we identify these charged scalars, , as the associated pseudoGoldstone bosons for small .
We will elaborate in more detail in Section II.3 that constraints
coming from measurements on the parameter place an upper bound on the
triplet vev, , which we take to be . Since
the neutral mixing angle, , is proportional to , it
remains small throughout the parameter space, except when . For this reason,
we refer to as the SMlike scalar and as the like scalar. Using the condition in Eq. (11)
and the approximation that we find that . Therefore,
.
Case 1b): and with
After EWSB that leads to , the SM retains an global symmetry as well the discrete . The breaking of the global implies the existence of massless Goldstone bosons^{2}^{2}2These are the same Goldstone bosons of the model proposed by GeorgiGlashow in 1972 GG72 . – in this case, the – in addition to the SM would be Goldstone bosons. From Eq. (12) and the vanishing of with , we see the appearance of this second massless mode explicitly. The presence of these massless charged scalars with unsuppressed gauge coupling to the is precluded by LEP studies, so that this case is ruled out by experiment. Given these considerations, we do not consider this case further, and we will avoid any choice of the parameters in the potential implying a global minimum for and with . When and , the charged scalars are massless at treelevel as indicated by Eqs. (12) and (15).
Case (2): and
For this scenario, wherein and both vanish, and do not mix and the treelevel masses are given by
(20) 
and
(21) 
Radiative corrections break the degeneracy between the charged and neutral components of the triplet. The mass splitting has been computed in Ref. Cirelli:2005uq
(22) 
where () gives the sine (cosine) of the weak mixing angle,
(23) 
and contains the U.V. regulator. Note that when the treelevel relation is used, the dependence of the mass splitting on vanishes. The resulting value for the splitting is
(24) 
in the limit .
ii.1.2 Vacuum Structure
Having identified the four possibilities for symmetry breaking and the corresponding scalar mass spectrum for those that remain phenomenologically viable, we discuss in Appendix A the conditions under which the specified values of the doublet and triplet vevs yield the absolute minimum vacuum energy (we always require that specified vevs correspond at least to a local minimum). These considerations will place restrictions on the remaining independent model parameters for the two phenomenologically viable cases:

For this case, for which both vevs are nonvanishing, we eliminate and as independent parameters in favor of , and the remaining four independent parameters: , , , and . In the discussion of the lowenergy phenomenology, we will trade three of the latter in terms of the physical masses, choosing as the six independent parameters: , , , , , and with GeV.

In this scenario with vanishing triplet vev and corresponding to triplet dark matter, we begin with five independent parameters since must vanish. Noting that at treelevel, we choose , , , , and as independent parameters.
When discussing the lowenergy phenomenology, we will give the dependence of branching ratios and collider production rates on , , , , and without imposing the requirement of absolute vacuum energy minimum. It is possible that the chosen minimum is not the absolute minimum but rather a longlived metastable minimum Barger:2003rs ; Kusenko:1996xt . Requiring that the lifetime of the metastable vacuum is much larger than the age of the universe will lead to restrictions on the model parameters, but these restrictions may be less severe than those following from the requirement that the chosen vacuum is the absolute minimum. In the case of the minimal supersymmetric Standard Model (MSSM) for example, it has been shown in Ref. Kusenko:1996jn that the conditions on the third generation triscalar couplings that follow from metastability of the electroweak minimum with respect to a charge and color breaking minimum are considerably less restrictive than those implied by taking the electroweak vacuum to be the absolute minimum. A detailed analysis of the metastability conditions for the SM involves a substantial numerical investigation, which we defer to future work. Instead, we outline in Appendix A the conditions that are likely to be sufficient but not necessary for the universe to have evolved into the specified vacuum.
ii.2 Interactions: Main Features
The full set of interactions involving , , and gauge bosons follow from Eqs. (15) and the mixing matrices in Eqs. (II.1.1) and (17). The Feynman rules relevant to our analysis of the production and decay phenomenology appear in the Appendix. Here we highlight a few key features of these interactions and their implications for phenomenology.

HiggsHiggs Interactions: The terms in proportional to and provide for socalled “Higgs splitting” decay modes such as when kinematically allowed. Note that the amplitude for the Higgs splitting decay of the neutral tripletlike scalar, , is proportional to and is thus suppressed.

GaugeHiggs Interactions: As usual, one has couplings of the type and where . The former are responsible for the dominant production mode of the and through the pair production process. Both couplings also contribute to the weak vector boson fusion (VBF) production process. Couplings of the type where denotes or will be suppressed either by or the small mixing between the SMlike and tripletlike scalars. For this reason, associated production of a single tripletlike scalar, , , and , will be strongly suppressed compared to the corresponding production of a SMlike scalar.
From the standpoint of decay profiles, the (or mixing factor) suppression is generally not relevant, since it cancels from branching ratios. However, an exception occurs in the case of the singly charged scalar, , which has three relevant couplings involving gauge bosons: , , and . The first two couplings are proportional to , while the latter contains a component that is free from this suppression factor and that is generated by the underlying interaction. Given the small mass splitting, Eq. (24), this interaction allows for the decay that occurs via the emission of a virtual . In the limit of tiny , this decay channel becomes the dominant one. In the case of the extra neutral Higgs, , one finds that there are two relevant couplings to gauge bosons and , both of which proportional to . As we discuss below, these couplings contain distinct dependences on the quantity defined in Eq. (19). In particular, the vertex is
(25) while the and couplings are all proportional to (see below) since they occur only in the presence of  mixing. The independent term in Eq. (25) is generated by the term in the Lagrangian after the obtains a vev. In contrast, there is no term or coupling of the to matter fields in the Lagrangian, so the and vertices must be proportional to the mixing parameter . As we discuss below, one may in principle exploit these different dependences on to study the dependence of various tripletlike scalar branching ratios.

Yukawa Interactions: When the mixing angles are nonzero, both the SMlike and tripletlike scalars couple to fermions through Yukawa interactions. The relevant part of the Lagrangian describing interactions between the physical scalars and the SM fermions is
(26) where stands for any charged SM fermion and is the CabibboKobayaskiMaskawa matrix. Since , and the Yukawa couplings of and are always suppressed compared to those of the doubletlike neutral scalar. As discussed above, this suppression will not affect the decay branching ratios but does govern those of the which can decay to –even for zero .
We emphasize that the presence of gauge interactions involving the implies that the branching ratios are generally different from those in other extended Higgs sector models that lead to a second, CPeven neutral scalar. For example, in extensions involving a single real scalar singlet, , the and branching ratios will be identical when since the can decay only due to  mixing. Modifications only occur when the Higgs splitting mode becomes kinematically allowed. In the SM, on the other hand, the coupling to and can only occur at treelevel through  mixing, while the existence of its coupling to does not require such mixing. Below the threshold, this difference will affect Br( which is dominated by boson loops, while above the threshold, it will imply a difference between Br() and Br(), even in the absence of a kinematically allowed Higgs splitting mode.
ii.3 Phenomenological Constraints
Electroweak precision observables (EWPO) and direct searches place important constraints on the parameters of the model. Here we review the phenomenological constraints that have the most significant impact on the prospects for discovering the SM and distinguishing it from other possibilities.

The parameter. In this theory does not contribute to the mass, since there is no interaction. It does, however contribute to through a interaction. Consequently, the gauge boson masses are given at treelevel by
(27) leading to a wellknown treelevel correction to the parameter:
(28) where
(29) gives the weak mixing angle in the scheme (indicated by the hatted quantities), gives the effect of SM electroweak radiative corrections, denotes contributions from new physics. In the present case, we have
(30) From a global fit to EWPO one obtains the result
(31) Consequently, in what follows we will adopt the bound
(32) The bound in Eq. (32) could be relaxed by requiring a higher level of confidence, but the magnitude would not change by more than a factor of two. Such a change would be inconsequential for the phenomenology of the SM, so we will retain the bound of Eq. (32).

Corrections to the and boson propagators. Because the couples to electroweak gauge bosons, it will generate one loop contributions to the corresponding propagators. These contributions have been studied extensively in Refs. triplet3 ; triplet4 ; triplet5 ; triplet6 . In light of the parameter constraints on it is instructive to consider these effects in the limit of vanishing mixing angle. As discussed above, this limit can arise when either: and both vanish, or vanishes but not . When and both differ from zero, we may consider this limit as the first term of an expansion in the small mixing angles. To that end, we will consider the combinations of the gauge boson propagators that appear in the oblique parameters , , and . To zeroth order in the mixing angles, , the triplet contribution to vanishes since triplet3 . The effects of on can only arise through mixing with , which carries unit hypercharge. At lowest order in gauge interactions and zeroth order in mixing angles, , the triplet contribution to the parameter is small since it is protected by the custodial SU(2 symmetry. In this limit, the treelevel relation between the masses and is given by
(33) The parameter is given by
(34) We find that in the limit of zero mixing, , while
(35) where we have neglected terms of . From the bound in Eq. (32) and the expression in Eq. (33) we observe that . Using the relation we obtain
(36) A global fit to all EWPO gives Kile
(37) or
(38) at 68 % confidence. The corresponding range for the mass splitting is
(39) The constraints on that follow from the parameter are clearly consistent with this result. Oneloop gauge boson contributions to are much smaller than and do not affect our general conclusions^{3}^{3}3One should not interpret the 68% C.L. lower bound in Eq. (39) as implying a minimum mass splitting; the range, for example, is consistent with .. It is possible that the mixing angle is not small when [see Eq. (19)]. This scenario could lead to substantial effects on the gauge boson propagators and may help alleviate the tension between EWPO that favor a light SMlike Higgs and the lower bound from direct searches. We will explore this possibility more extensively in a subsequent study and concentrate in this work on the small mixing scenario. See Ref. Chen for a recent study of these constraints.

Collider Constraints. LEP searches for both charged and neutral scalars place severe constraints on the possible existence of light scalars. The neutral scalar Higgs is SMlike, and one has to impose the lower bound from LEP2, GeV. In the case of the singly charged Higgses, , one should assume a conservative lower bound GeV due to the absence of nonSM events at LEP LEP . Since one has to use the same bound for the extra neutral scalar Higgs.

Big Bang Nucleosynthesis. In principle, considerations of primordial nucleosynthesis could have important implications for the SM. In particular, it has been pointed out in Ref. BBN that the existence of a charged scalar with lifetime s can reduce the relative abundance of Li produced during big bang nucleosynthesis, thereby exacerbating the present tension with the H and He abundances and the value of the baryon asymmetry derived from the cosmic microwave background. This bound is irrelevant for the SM, however, since the decay is very fast (see Fig. 5 below).
Iii Properties of the Higgs Decays
As discussed above, there are four physical scalars in this theory: two neutral scalars and (SMlike and tripletlike, respectively), and two singly charged scalars with small couplings to fermions. In this section we discuss the main features of the Higgs decays in all possible scenarios.
iii.1 Cold Dark Matter and Higgs Decays
In the case when the real triplet does not acquire a vev, the neutral component can be a viable cold dark matter candidate. We previously mentioned that, in this case, the scalar potential has a global symmetry and a , discrete symmetry. In Ref. Cirelli:2005uq this CDM candidate has been studied in detail. Under the assumption that this candidate is responsible for the CDM relic density in the Universe, the mass should be TeV. However, as we will show in the next section the production cross section is very small in this case. In this scenario the main decay channel of the singly charged Higgs is due to the small mass splitting coming from radiative corrections. In order to test this scenario at the LHC, we must assume that TeV so that the is only one component of the CDM density. In this case the pair production and weak vectorboson fusion cross sections for and are large enough to generate observable effect. Since the is stable one should only expect to see missing energy and a charged track. In Ref. Cirelli:2005uq the authors pointed out that if the mass of is approximately GeV, its relic density makes up about of the total DM density. We will restrict our attention to the scenarios where is light in order think about the possibility to test the model at the LHC.
The existence of the charged scalars in SM can modify predictions for the decay of the SMlike Higgs, , into two photons since, in general, the parameter can be large. This effect arises from the quartic term in the potential, proportional to , that generates a coupling after EWSB. Note that this interaction is not suppressed by the triplet vev (see Appendix C for the Feynman rules). For a sufficiently light charged Higgs, , and large , the charged scalar loop contributions to the amplitude can yield nonnegligible changes in Br(). In order to analyze the impact of the charged Higgs in this mode, we define the relative change in the decay partial width by
(40) 
where and are the decay widths with and without the contribution of the charged Higgs, respectively. In Fig. 1 we show for and different values of the parameter and charged Higgs mass. Notice that predictions for the decays into two photons can be modified appreciably when the charged Higgs mass is below GeV. When the parameter is negative we find a large enhancement in the decay width. Since, when where the DM candidate, , and the charged Higgs, , are approxiately degenerate, we expect large modifications of the decay mode only when is responsible for a fraction of the Dark Matter density in the Universe.
iii.2 SMLike Higgs Boson Decays: General Case of
Since the mixing between the SM Higgs and the real triplet is typically small, the scalar is SMlike. The decays of are similar to the decays of the SM Higgs except for the decays into two photons. As we have discussed before, the presence of the charged Higgs can dramatically modify the decay width for this channel. Since this channel is important for the discovery of the scalars at the LHC we discuss the predictions here in detail. The expected accuracy for the branching ratio at the LHC for this channel is about EWPO .
In Fig. 2 we show the values for the difference between the predictions in the SM and in our model for when GeV and GeV. When GeV, is small since the mixing angle is large and in this case the coupling between and is suppressed when is negative. Apart from this particular region of parameter space, we expect a large modification of the decay width of the SMlike Higgs decay into two photons when . More generally, for light , the relative change in the can be larger in magnitude than the expected LHC precision for this channelEWPO , allowing one to use this channel to gain indication of the sign of the coupling over a limited range of the parameter space. As we discuss below, one may in principle determine by studying its branching ratios. Looking further to the future, a more precise study of Br() at an collider could be carried out ILC .
iii.3 Charged Higgs Boson Decays
As indicated earlier, the is never stable since in all cases. In the dark matter scenario, the decay is the only twobody mode. The relative importance of this channel to other twobody modes depends critically on the value of that governs the strength of the Yukawa interaction via the mixing angle . In Fig. 3, we give the branching ratios as a function of for two illustrative values of . For just below the threshold (left panel), Br() dominates for . For larger values of the triplet vev, the and channels are the largest, although the modes are also appreciable. For heavier (right panel), the , and channels are leading when .
The relative importance of the various final states for a given depends strongly on , as illustrated in Fig. 4. When the charged Higgs is light – well below the gaugeHiggs threshold – the main decay channels for near the upper end of its allowed range are and (see the left panel of Fig. 4). As is increased, the , , and become dominant, with the relative importance of each depending on the specific range of under consideration. On the other hand, for very small , the final state dominates even for heavy (see the right panel of Fig. 4). These features of the decays can, in principle, be used both to distinguish the SM from other scenarios as well as to determine the parameters and . For the case of an unstable , for example, (see Eq. (15)), while the branching ratios depend strongly on both and . Thus, knowledge of both and the branching ratios could be used to identify the a range of values for these parameters.
We emphasize that when the vev is very small, the charged Higgs is longlived since the total decay width is quite small. This feature can lead to the presence of a charged track that can be used for identification. We illustrate this point in Fig. 5, where we show the decay length as a function of for different values of . For the decays above the green line (horizontal line), one may observe a charged track associated with the . It is important to mention that the existence of the coupling is due to the breaking of the custodial symmetry once acquires a vev. Recall that in a two Higgs doublet model this coupling is absent. Therefore, one can use this decay in order to distinguish the model at future colliders.
iii.4 TripletLike Neutral CPeven Higgs Boson Decays
The new extra neutral CPeven Higgs in this theory, , is tripletlike since the mixing in the neutral sector is typically small due to the small allowed values of the triplet vev, GeV. At the same time, all the relevant couplings of for the decays are suppressed by, . The total decay width will be proportional to , and when , becomes stable and we recover the dark matter scenario. However, the branching ratios will be independent of the triplet vev. The specific branching ratios will differ from those for the SMlike Higgs due to the absence of a term in the Lagrangian and the dependence on in its coupling to . These features imply a change in the relative importance of the partial widths that depend on the coupling compared to the corresponding SMlike Higgs decays. Moreover, the branching ratios will depend strongly on the value of the quartic coupling due to its presence in .
Figures 67 illustrate the branching ratios as a function of for different values of . In each case, we see that when is light the most relevant decay channels are and . The branching ratios for these channels are similar to those for the SM Higgs, except for the and channels. As discussed above, both depend on the coupling that does not require  mixing to be nonvanishing. Consequently, the relative importance of these two branching ratios depends on the quartic coupling . In particular, a relatively large, positive value for this parameter suppresses these branching ratios. In what follows, we will exploit the channel in the strategy for discovery and identification of the SM. Once the massive gauge boson channels are open the relevant decays are and and again the branching ratios are independent of . As Figs. 67 indicate, the branching ratios can vary strongly with and can differ significantly from those for a pure SM Higgs. For example, when , the branching ratio can be substantially larger than that for a final state, a situation that does not occur for the SMlike Higgs.
In Figs. 8 and 9 we show the decay length for the CPeven neutral tripletlike versus the triple vacuum expectation value for different Higgs masses, where the green line (horizontal line) corresponds to a decay length equal to 10 m. Above this line one has a different scenarios with a longlived neutral Higgs and when one recovers the dark matter scenario.
iii.5 Heavy Higgs Scenario
When the mass of the Tripletlike Higgs is above the gauge boson pair threshold one could in principle observe unique features of the SM at an linear collider by studying the ratios of different neutral and charged scalar decays. To illustrate this possibility, Fig. 10 shows the predictions for the ratios and . The ratio is always larger than one when the Higgs mass is above 400 GeV, while only when the parameter is positive.
Iv Production Mechanisms at the LHC and Tevatron
In this section we study the production mechanisms for and at the LHC. The leading production channels for these scalars are the DrellYan (DY) pair production processes:
Here and are the momenta for the quarks and Higgses, respectively. In terms of the variable in the parton centerofmass frame with energy , the parton level cross sections for these processes are
(41)  
(42) 
where