Exotic Higgs decay via charged Higgs

The most common search channel for heavy neutral Higgses in models with an extension of the Standard Model Higgs sector is A/H0 → ττ , which becomes ineffective when new decay modes of A/H0 open. In this paper, we analyzed two such channels involving charged Higgses in the final states: A/H0 → W±H∓ and H0 → H+H−. With the consequent decay of H± → τν, we found that the limits for σ × BR(gg → A/H0 → W±H∓) × BR(H± → τν) vary from 30 to 10fb for mA/H0 between 300 and 1000GeV for 95% C.L. exclusion, and about 80 to 30 fb for 5σ discovery. For H+H− mode, 95% C.L. limits on σ × BR(gg → H0 → H+H−) × BR2(H± → τν) vary from 9 to 4 fb for mH0 between 400 and 1000 GeV, while the 5σ reach is about 20 to 10 fb. We further interpret the cross section limits in the Type II 2HDM parameter space. While A → W±H∓ offers great sensitivity in both sin(β − α) versus tan β and mA versus tan β parameter space, H0 → H+H− can cover most of the parameter space for H0. Reach in H0 → W±H∓ is more limited, especially for mH0> 2mH± . It is, however, complementary to H0 → H+H− when BR(H0 → H+H−) is accidentally suppressed.


Introduction
The discovery of the SM-like Higgs boson at the LHC is the greatest triumph in particle physics [1][2][3][4]. The stabilization of the observed Higgs mass of 126 GeV, however, provides strong motivation of physics beyond the Standard Model (SM). In addition, there are puzzles facing particle physics which cannot be explained in the SM, for example, the particle candidate for dark matter and the generation of neutrino mass. Solutions to those problems typically lead to models with an extended Higgs sector. Well known examples include the Minimal Supersymmetric Standard Model (MSSM) [5][6][7], Next-to-Minimal Supersymmetric Standard Model (NMSSM) [8,9], and Two Higgs Doublet Models (2HDM) [10][11][12][13]. In addition to a SM-like Higgs boson in these models, the low energy spectrum typically includes extra CP-even Higgses, CP-odd Higgses, as well as charged ones.
The discovery of beyond the SM Higgses is an unambiguous evidence for new physics beyond the SM. The search for those extra Higgses, however, is typically challenging. For the extra neutral Higgses at the LHC, most of the current searches focus on the conventional Higgs search channels of W W , ZZ, γγ, τ τ and bb [14][15][16][17][18][19][20]. The production of the extra Higgses is typically suppressed compared to the SM Higgs, either due to their larger masses or their suppressed couplings to the SM particles. The decays of beyond the SM Higgses to the W W and ZZ is absent for the CP-odd Higgs, and could be highly suppressed for the non-SM like CP-even Higgses. The τ τ or bb decay modes suffer from either suppressed signal or large SM backgrounds, therefore are only relevant for regions of the parameter space with an enhanced bb or τ τ coupling. The search for the charged Higgs is even more difficult. For m H ± > m t , the cross section for the dominant production channel of tbH ± is typically small. The dominant decay mode H ± → tb is hard to identify given the large tt and ttbb backgrounds [21], while the subdominant decay of H ± → τ ν has suppressed JHEP11(2015)068 charged Higgs. In section 4, we present the details of our collider analyses. In section 5, we study the implication of the cross section limits on the parameter space of the Type II 2HDM models. Finally in section 6 we summarize our main results and conclude.

2HDM and exotic Higgs decay
There are two SU(2) L Higgs doublets in the 2HDM: The neutral component of each Higgs doublet obtains a vacuum expectation value (vev) v 1 and v 2 with v = v 2 1 + v 2 2 = 246 GeV after electroweak symmetry breaking. Three degrees of freedom are eaten by the SM W and Z boson, with the remaining Higgses being two CP even Higgses h 0 and H 0 , one CP odd Higgs A and a pair of charged Higgses H ± : (2. 2) The most general Higgs potential has eight free parameters with the assumption of a discrete Z 2 symmetry that can only be softly broken. Two of these parameters are replaced by v and tan β = v 2 /v 1 , with the remaining five can be chosen as the CP-even Higgs mixing angle α, physical Higgs masses (m h 0 , m H 0 , m A , m H ± ) and the Z 2 soft breaking parameter m 2 12 . The couplings that are relevant for with g being the SM SU(2) L coupling. While the coupling of the charged Higgs to the heavy CP-even Higgs H 0 is proportional to sin(β − α), the coupling of the charged Higgs to the CP-odd Higgs A is independent of the mixing angle. Note that if H 0 is non-SM like with h 0 being the observed 126 GeV SM-like Higgs, | sin(β − α)| ∼ 1, which maximizes the W ∓ H ± H 0 coupling. Given the strong limits on the light charged Higgs search either from the LEP [50] or from the LHC [19,20], i.e. m H ± > 155 GeV, we consider m H 0 ,A > 250 GeV in the h 0 -126 GeV case in our analyses. The above couplings of gauge boson to a pair of Higgses are universal for different types of 2HDM. The Higgs couplings to the fermions, however, is highly model dependent. For the rest of paper, we will work in the framework of the Type II 2HDM, in which H 1 couples to the down-type quarks and leptons, while H 2 couples to the up-type quarks. For a review of different types of 2HDM, please see ref. [10]. Figure 1 shows the branching fractions of A as a function of tan β. Once A → W ± H ∓ is kinematically open, in general, it quickly dominates over the usual fermionic decay mode A → bb, τ τ for tan β 20. For large tan β, branching fractions for A → bb, τ τ increase due to enhanced bottom and tau Yukawa couplings. For small tan β, the branching fraction for A → W ± H ∓ decreases slightly since loop induced processes A → γγ, Zγ rise due to JHEP11(2015)068 enhanced top quark contributions. The left panel of figure 1 shows the branching fractions of A when H 0 decouples. Once m A > m H 0 + m Z , A → ZH 0 opens and gives a significant contribution in A decay, as shown in the right panel of figure 1 for m H 0 = 150 GeV.
A → H ± W ∓ , however, still dominates, with branching fraction around 60% in a large range of tan β.
For the heavy CP-even Higgs H 0 , in addition to the decay to W ± H ∓ as the CP-odd Higgs A, it can also decay into a pair of charged Higgs once kinematically open: H 0 → H + H − . The relevant coupling receives contributions from all Higgs quartic couplings. In general, it depends on tan β, sin(β − α), m H 0 , m H ± as well as m 2 12 . Note that there is no AH + H − vertex because of the CP conservation assumption.

Current collider limits
The main search mode for the non-SM like neutral Higgses is through τ τ channel, which has been performed at both the ATLAS and CMS experiments [14,15] with 7+8 TeV data set of about 20 fb −1 integrated luminosity. For the gluon fusion production, the cross section limits of gg → φ → τ τ from ATLAS vary between 30 pb to 8 fb for m φ between 100 to 1000 GeV. Interpreting the cross section limits in the MSSM m max h scenario, a sizable portion of the MSSM parameter space has been ruled out, extending from tan β ∼ 10 for m A ∼ 100 GeV, to tan β ≈ 60 for m A = 1000 GeV [14]. Limits from CMS are similar [15].
In figure 3, we recast the current 95% C.L. limit of pp → φ → τ τ in the (m H 0 , tan β) (left panel) and (m A , tan β) (right panel) planes of the Type II 2HDM. The solid black curves correspond to the limits in the MSSM, when m A ≈ m H 0 with both A and H 0 contributing to the signal. The solid red curves correspond to the limits in the type II 2HDM, when only contribution from H 0 or A is included and other non-SM Higgses decouple. The reach is considerably weaker: the current exclusion is about tan β ∼ 12 at m H 0 = 200 GeV, and tan β ∼ 50 for m H 0 = 600 GeV, and similar for the CP-odd GeV, the limits are much more relaxed, as shown by the red dashed curves. In particular, no limit on m H 0 above H + H − threshold can be derived given the strong suppression of H 0 → τ τ branching fraction.
Searches with bb, W W , h 0 Z and h 0 h 0 for the non-SM Higgses have also been performed at both the ATLAS and CMS [16-18, 38, 39]. No evidence for a neutral non-SM like Higgs was found and the limits are considerably weaker than the τ τ channel.
In our analyses, we consider A/H 0 → W ± H ∓ and H 0 → H + H − , with a benchmark point of m H ± = 170 GeV. Both ATLAS and CMS have searched for a charged Higgs in H ± → τ ν, cs mode [19,20]. For the low mass region of m H ± < m t , the charged Higgs is produced via top decay, while for the high mass region of m H ± > m t , tbH ± associated JHEP11(2015)068 production is considered. While most of the low mass region has been excluded for charged Higgs mass less than about 155 GeV, there is no limit for 160 GeV < m H ± < m t given the suppressed BR(t → bH ± ) near the threshold. The reach for high mass region only extends down to m H ± > 180 GeV, due to the overwhelming SM tt background at the low mass region.
In addition, there are strong constraints on the non-SM Higgs sector from flavor constraints [40,41] and precision measurements [43][44][45][46][47][48]. In particular, the latest analyses on Br(B → X s γ) with updated NNLO QCD predictions have constrained the charged Higgs to be heavier than 480 GeV at 95% C.L. [42]. Precision observables, in particular, S and T oblique parameters, also impose correlations between the charged Higgs mass with the neutral ones: m H ± ∼ m A or m H ± ∼ m H 0 . These limits, however, could be relaxed with additional contributions to the flavor or precision observables from other sectors in the new physics models [49]. In this paper, since we focused on the collider aspect of the Higgs exotic decay, we did not apply those constraints explicitly. We chose the mass spectrum of the non-SM Higgses to be characteristic of the exotic decay channels that we analyze. One should, however, keep those potentially dangerous indirect constraints in mind when considering a specific new physics model with an extended Higgs sector.

Collider analyses
In this section we analyzed gg → A/H 0 → W ± H ∓ and gg → H 0 → H + H − , with the subsequent decay of H ± → τ ν. Due to the spin correlation in τ decay, the charged product from tau decay is typically harder for the ones from the signal process with tau coming from JHEP11(2015)068 H ± decay comparing to the ones from the SM backgrounds with τ mostly from W decay. Both signal and background processes are generated by MadGraph/MadEvent [52] and then passed to TAUOLA to simulate tau lepton decay [53]. We present model independent limits on σ × BR for both the 95% C.L. exclusion as well as 5σ discovery at the 14 TeV LHC with 300 fb −1 integrated luminosity.
We studied the gluon fusion production of A/H 0 , followed by A/H 0 → W ± H ∓ with H ± → τ ν and W → ν: The τ hadronic decays are adopted to take advantage of spin correlation for the final state hadrons. We consider the two leading hadronic decay modes of tau lepton: τ ± → π ± ν τ and τ ± → ρ ± ν τ with BR(τ ± → π ± ν τ ) = 0.11 and BR(τ ± → ρ ± ν τ ) = 0.25. For simplicity, we only display the results of the π channel below. The contributions from both π and ρ channels are combined for the model independent σ × BR limits. The leading SM backgrounds are with leading-order (LO) cross section σ 1 (W W ) = 3.64 pb, σ 2 (W W ) = 0.91 pb and σ(ZZ) = 0.3 pb, including subsequent W and Z decay. The latter two are followed by one tau decaying leptonic and the other tau decaying hadronically. The reducible backgrounds are with cross section σ 1 (W Z) = σ 2 (W Z) = 0.21 pb including subsequent decay. These processes have additional e/µ or τ lepton and can thus be reduced by vetoing the extra lepton. We apply the K-factors of 1.5, 1.3 and 1.7 to the channels W W , ZZ and W Z, respectively [54,55]. We select events with one lepton and one hadronically decaying tau satisfying the basic cuts: where h τ = π, ρ. We veto events with extra leptons or hadronically decaying taus satisfying To simulate the detector effects, we smear the hadronic/leptonic energy by a Gaussian distribution whose width is parameterized as [56,57]  With the above basic cuts and smearing, the distributions of p T (π) and E T for the signal (black curve) and SM backgrounds are shown in figure 4. We note that the signal has a harder p T (π) spectrum compared to the backgrounds. This is a well-known result of spin correlation in the τ decay. For the H + signal, the left-handed τ + decays to a right-handed ν τ , causing the π + to preferentially move along the τ + momentum direction [58,59]. In contrast, the τ + coming from a W + decay is right-handed which has the opposite effect on the π + . The distribution for p T (ρ) is similar for τ ± → ρ ± ν. Signal also has E T distribution peaked at higher value. We thus tighten the selection cuts by imposing E T > 50 GeV, p T (π, ρ) > 50 GeV. (4.7) We show the σ × BRs of signal and backgrounds before and after cuts, as well as cut efficiencies (with respect to last level of cuts) for m H 0 /A = 300 GeV and m H ± = 170 GeV in table 1 for τ ± → π ± ν. We choose nominal value of 10 fb for the signal cross section. 2 The dominant background after cuts is the irreducible backgrounds W W with one W decaying leptonically and the other decaying to tau. Utilizing the E T cut and p T cut, all the backgrounds could be suppressed sufficiently.
The left panel of figure 5 shows the 95% C.L. exclusion limit (red lines) and 5σ discovery reach (black lines) for σ × BR(gg → A/H 0 → W ∓ H ± ) × BR(H + → τ + ν) as a function of m H 0 /A at the 14 TeV LHC with 300 fb −1 luminosity, combining both π and ρ channels. We have fixed m H ± = 170 GeV. The solid, dashed and dotted lines are for the limits with no systematic error, 5% and 10% systematic errors, respectively. For the neutral Higgs mass between 300 to 1000 GeV, the cross section limits vary between 30 to 10 fb for 95% C.L. exclusion and about 80 to 30 fb for 5σ discovery. The cross section limits with 5% or 10% systematic error included are about a factor of 7 or 10 worse.

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Cuts  Table 1. The cross sections (row 2 and 6) and cut efficiencies (row 3-5) of signal gg → A/H 0 → W ∓ H ± → τ νν and SM backgrounds after various cuts with τ ± → π ± ν at the 14 TeV LHC. We assume a nominal signal cross section of 10 fb. For the background processes, the K-factors have been included. (W Z) 2 and (W Z) 2 * refer to W Z → ± τ + τ − ν with both taus decay to pions for (W Z) 2 and one tau to pion and one tau to lepton for (W Z) 2 * . The significance S/ √ B is given for 300 fb −1 luminosity. We assume m H 0 /A = 300 GeV and m H ± = 170 GeV.

Another interesting search channel with the charged Higgs in the final states is
with both taus decaying hadronically. The leading SM backgrounds are The W ± Z background can be reduced by lepton veto.
Adopting the same basic cuts as in eqs.   Table 2. The cross sections and cut efficiencies of the signal gg → H 0 → H + H − → τ + τ − νν and the SM backgrounds after various cuts for τ ± → π ± ν channel at the 14 TeV LHC. We assume L = 300 fb −1 and a nominal cross section for the signal to be 1 fb. We fix m H 0 = 400 GeV and m H ± = 170 GeV. The K-factors for backgrounds are included.
p T (π) distribution is very similar to that of figure 4. Both E T and p T (π, ρ) peak at higher value, similar to the W ± H ∓ channel. In addition to the p T (π, ρ) and E T cuts the same as in eq. (4.7), we impose m ππ,ρρ cuts to reduce the ZZ and W Z backgrounds with τ τ pair coming from Z boson: m ππ,ρρ < 50 GeV or m ππ,ρρ > 90 GeV. (4.10) In table 2, we show cut efficiencies as well as the signal and the SM background cross sections before and after cuts, for gg → H 0 → H + H − with H ± → τ ν for τ ± → π ± ν final states. The dominant SM background is W W , which can be suppressed sufficiently to achieve good signal significance.
In the right panel of figure 5, the 95% C.L. exclusion limit (red lines) and 5σ discovery reach (black lines) for σ × BR(gg → H 0 → H + H − ) × BR 2 (H + → τ + ν) are shown as a JHEP11 (2015)068 Table 3. Benchmark points shown for illustrating the discovery and exclusion limits of gg → A/H 0 → W ± H ∓ and gg → H 0 → H + H − in the context of the Type II 2HDM. We assume m H ± = 170 GeV and m h 0 = 126 GeV. The checkmarks indicate kinematically allowed channels. The "−" means the parent particle being too heavy to be of interesting.
function of m H 0 at the 14 TeV LHC with 300 fb −1 luminosity, combining both π and ρ channels. We have fixed m H ± = 170 GeV. For the neutral Higgs mass between 400 to 1000 GeV, the cross section limits vary between 9 to 4 fb for 95% C.L. exclusion and about 20 to 10 fb for 5σ discovery. The cross section limits with 5% or 10% systematic error included are about a factor of 2 or 4 worse.

Implication for the Type II 2HDM
To interpret the 95% C.L. exclusion and 5σ reach limits in the type II 2HDM, we choose three benchmark points as listed in The production of gg → A only depends on tan β while gg → H 0 depends on both tan β and sin(β −α) [24]. In figure 7, the branching fractions of A/H 0 → W ± H ∓ are shown for BP1 (left panel) and BP2 (right panel), respectively. The suppression of the BR(A → W ± H ∓ ) at sin(β − α) ∼ 0 is due to the competing A → h 0 Z mode. BR(A → W ± H ∓ ) gets smaller at both large and small tan β due to the competing A decays to fermions or loop induced processes. For H 0 → W ± H ∓ , the branching fraction is larger than 50% only for | sin(β − α)| 0.8, since H 0 W ± H ∓ coupling is proportional to sin(β − α).
In figure 8, the branching fractions of H 0 → W ± H ∓ and H 0 → H + H − are shown in the left and right panel, respectively, for BP3. Comparing to BP2 with m H 0 = 300 GeV, BR(H 0 → W ± H ∓ ) receives stronger suppression at both small and large tan β due to the opened H 0 → H + H − and H 0 → tt. It is only significant around a small region near tan β ∼ 1.
The branching fraction of H 0 → H + H − exhibits more complicated dependence on sin(β − α) and tan β due to the H 0 H + H − coupling. The branching fraction is more than 50% at tan β 2 or tan β 0.5 for | sin(β − α)| close to 1.
In the left panel of figure 9, we show the reach in sin(β − α) versus tan β plane for A → W ± H ∓ (BP1). For BP1 with m A = 300 GeV, regions above the red (black) curves can be excluded at 95% C.L. (discovered at 5σ) at the 14 TeV with 300 fb −1 luminosity, JHEP11(2015)068  except the region enclosed by the black ellipse around tan β ∼ 10, which can not be covered by 5σ discovery due to the suppression of the production cross section. The region with tan β 0.2 can be covered by exclusion for all values of sin(β − α) and tan β 0.3 can be covered by discovery except the region with tan β ∼ 10, | sin(β − α)| < 0.5. The loss of sensitivity at small tan β is mainly due to the reduction of H ± → τ ν branching fraction. Reach gets slightly worse for sin(β − α) close to zero due to the competition of A → Zh 0 , which suppresses the branching fraction of A → W ± H ∓ correspondingly (see the left panel of figure 7). Reach with 10% systematic error are shown in pink and grey curves JHEP11(2015)068 for 95% C.L. exclusion and 5σ discovery, respectively. The regions shrink considerably comparing to the 0 systematic error case. Only 0.6 < tan β < 5 and tan β > 20 can be excluded and the discovery reach is further reduced to 1 < tan β < 3 or tan β > 30.
In the right panel of figure 9, we show the reach in sin(β − α) versus tan β plane for H 0 → W ± H ∓ (BP2), indicated by regions to the left (right) of the curves for negative (positive) sin(β − α). Regions with sin(β − α) < −0.2 or sin(β − α) > 0.3 can be covered by gg → H 0 → W ± H ∓ with 95% C.L. exclusion. This channel is insensible to region around sin(β − α) ∼ 0 since H 0 → W ± H ∓ is highly suppressed. This channel is sensitive to intermediate tan β between 1 to 10, while the reach for tan β is enhanced for | sin(β−α)| ∼ 1, which is the preferred region for h 0 being the SM-like 126 GeV Higgs. The decrease in the sensitivity in the thin slice region for sin(β −α) between 0.6 to 0.9 is due to the reduction of gg → H 0 production cross section. The reach for 5σ discovery is slightly worse. Introducing 10% systematic error (regions enclosed by the pink and grey curves) reduces the exclusion and discovery reach further.
The reach of H 0 → W ± H ∓ for BP3 with m H 0 = 400 GeV is similar to that of BP2. There is no reach in regions of tan β 10 and tan β 0.4, due to the competing H 0 → H + H − , tt modes. Figure 10 shows the exclusion (region to the left of red/pink curve) and discovery (region to the left of black/grey curve) reach in m A/H 0 versus tan β plane for A (left panel) and H 0 (right panel) with gg → A/H 0 → W ± H ∓ channel. For low m A of 300 GeV, tan β as low as 0.2 can be probed, while tan β > 1 can be excluded for m A = 1000 GeV. Reach is reduced for tan β around 10 due to the suppression of the production cross section. Also shown in blue curve is the reduced exclusion by H 0 /A → τ + τ − [14] due to the opening JHEP11(2015)068 Regions to the left of the red/pink (black/grey) curve can be excluded (discovered) assuming 0 and 10% systematic errors, respectively. We assume m H ± = 170 GeV and sin(β − α) = 1.
of A → W ± H ∓ . The reach for the exotic decay of A → W ± H ∓ can cover most of the parameter region in m A versus tan β plane while the conventional search mode of A → τ τ mode being highly suppressed. For results with 10% systematic error included (regions to the left of pink/grey curves), the mass reach is about 350 GeV less. The reach for H 0 → W ± H ∓ is much more limited, in particular for m H 0 > 400 GeV since H 0 → W ± H ∓ is suppressed once H 0 → H + H − opens for m H 0 > 2m H ± . Regions around tan β ∼ 1, however, can still be excluded (discovered) for m H 0 up to 900 (800) GeV due to the suppression of H 0 → H + H − in that region. Given the insensitivity of conventional search channel H 0 → τ τ for tan β ∼ 1, H 0 → W ± H ∓ could be an alternative discovery channel for the neutral CP-even Higgs. For results with 10% systematic error included, the reach is about 400 GeV less.
In the left panel of figure 11, we show the 95% C.L. exclusion (red/pink) and 5σ discovery (black/grey) reach (regions above the curves) in sin(β − α) versus tan β plane for H 0 → H + H − for BP3. This channel is sensitive to large region of the parameter space for tan β > 1. The thin slice of insensitive region at negative sin(β − α) is due to the suppression of H 0 → H + H − , while the thin slice of insensitive region at positive sin(β − α) is due to the suppression of gg → H 0 .
The right panel of figure 11 shows the reach in m H 0 versus tan β plane with gg → H 0 → H + H − channel. Regions with tan β 1-2 can be excluded at 95% C.L. for m H 0 between 400 to 1000 GeV. For results with 10% systematic error included, the mass reach is about 150 GeV less. The reach around tan β ∼ 10 is reduced due to the reduction in the production cross section. Combing both H 0 → W ± H ∓ and H 0 → H + H − channels, most regions of tan β 0.3 can be covered, while the conventional search channel of H 0 → τ τ gets highly suppressed.

Conclusion
The conventional search mode for the extra neutral Higgses in models with an extension of the SM Higgs sector is A/H 0 → τ τ , which is only sensitive to the large tan β region. Furthermore, the opening of the exotic Higgs decay modes, for example A/H 0 → W ± H ∓ and H 0 → H + H − , greatly reduces the sensitivity of the τ τ mode. These new decay channels, however, can be used to probe the heavy neutral Higgses, which is discussed in detail in this paper. One feature of the taus from light H ± decay is that the decay products of tau, for example, pions and rhos, tend to be more energetic comparing to the SM background taus from W decay. This can be used to suppress the SM backgrounds in both channels that we analysed: gg → A/H 0 → W ± H ∓ → τ + E T and gg → H 0 → H + H − → τ τ + E T . For m A/H 0 between 300 and 1000 GeV, we found that the σ × BR(gg → A/H 0 → W ± H ∓ ) × BR(H ± → τ ν) varies from 30 fb to 10 fb for 95% exclusion, and about 80 to 30 fb for 5σ discovery. For H + H − mode, 95% C.L. limits on σ ×BR(gg → H 0 → H + H − )×BR 2 (H + → τ + ν) vary from 9 to 4 fb for m H 0 between 400 and 1000 GeV, while the 5σ reach is from 20 to 10 fb. The cross section limits including 5% or 10% systematic error is considerably worse.
We further interpret the cross section limits in the Type II 2HDM parameter space. For A → W ± H ∓ , we found that almost all regions of the parameter space in sin(β − α) versus tan β plane can be covered, except for very small tan β for a benchmark point of m A = 300 GeV. It is also sensitive to most regions in m A versus tan β plane with m A up to about 1000 GeV, and tan β as low as 1. It provides an alternative channel to search for the CP-odd Higgs when the conventional mode of A → τ τ becomes ineffective.

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For the CP-even Higgs H 0 , the most sensitive channel is H 0 → H + H − , which covers all regions of the parameter space in sin(β − α) versus tan β plane except for tan β < 1 for a benchmark point of m H 0 = 400 GeV. In m H 0 versus tan β plane, m H 0 up to about 1 TeV can be excluded at 95% C.L., while m H 0 up to about 950 GeV can be discovered at 5σ significant level. While the reach in H 0 → W ± H ∓ is more limited, especially for m H 0 > 2m H ± , it is complementary to H 0 → H + H − mode for regions of tan β 1. If 10% systematic error is assumed, the mass reach is typically about 150-400 GeV less.
The discovery of extra Higgses besides the SM-like one would certainly be an unambiguous evidence for new physics beyond the SM. The exotic decay modes of heavy Higgs decaying to two light Higgses, or one Higgs with one SM gauge boson provide alternative search channels, which could greatly enhance the discovery potential for heavy Higgses at current and future colliders. Once those non-SM Higgses are discovered, kinematic reconstruction would provide important information about their mass spectrum. A cross check with the indirect flavor and precision constraints would be complementary and lead to new hints towards new physics beyond the SM.