$pp\to A\to Zh$ and the wrong-sign limit of the Two-Higgs-Doublet Model

We point out the importance of the decay channels $A\to Zh$ and $H\to VV$ in the wrong-sign limit of the Two-Higgs-Doublet Model (2HDM) of type II. They can be the dominant decay modes at moderate values of $\tan\beta$, even if the (pseudo)scalar mass is above the threshold where the decay into a pair of top quarks is kinematically open. Accordingly, large cross sections $pp\to A\to Zh$ and $pp\to H\to VV$ are obtained and currently probed by the LHC experiments, yielding conclusive statements about the remaining parameter space of the wrong-sign limit. In addition, mild excesses - as recently found in the ATLAS analysis $b\bar b \to A\to Zh$ - could be explained. The wrong-sign limit makes other important testable predictions for the light Higgs boson couplings.


Introduction
After the discovery of a Standard Model (SM)-like Higgs boson with a mass of 125 GeV at the LHC [1,2] the experimental collaborations put a large effort on the precise determination of its mass [3] and its couplings to the other SM fermions and gauge bosons [4]. Even though no significant deviations from the SM predictions were observed, there is plenty of room for the SM-like Higgs boson to be part of an extended Higgs sector. Accordingly, apart from the precise determination of the SM-like Higgs boson's properties, the search for additional Higgs bosons is ongoing. A well-motivated, simple extension of the SM Higgs sector is the class of Two-Higgs-Doublet Models (2HDMs), which were introduced by Lee in 1973 [5] to explain the observed matter-antimatter asymmetry as arising from a spontaneous breaking of CP. The field content of the SM is complemented with an extra SU (2) doublet, which even in the CPconserving case results in a richer scalar spectrum: two CP-even scalars, the lightest h and the heavier Higgs boson H, a pseudoscalar A and two charged scalars H ± . In the 2HDM a softly broken Z 2 symmetry is commonly extended to the Yukawa sector to prevent the appearance of tree-level flavor changing neutral currents [6,7]. This procedure results in four distinct 2HDM Electronic addresses: pmmferreira@fc.ul.pt, stefan.liebler@kit.edu, jonas.wittbrodt@desy.de. types, some of which include a peculiar and interesting region of parameter space called the wrong-sign limit [8][9][10][11][12][13][14]. In this region, there is a relative sign between the couplings of the SMlike Higgs boson to down-type quarks and to gauge bosons with far-reaching phenomenological consequences. This sign change -the down-type quark couplings to the SM-like Higgs boson in the 2HDM acquire the opposite sign as in the SM -is a physical quantity, as it has physical consequences which cannot be removed by some field redefinition.
Standard searches for additional Higgs bosons focus on the decays into fermions and gauge bosons. In particular in some 2HDM types, where the coupling to down-type fermions is enhanced through large values of tan β, searches in the τ + τ − final state [15,16] are very powerful in setting limits on the 2HDM parameter space. On the other hand, for low values of tan β, the 2HDM parameter space is probed by heavy Higgs decays into a pair of top quarks [17] or gauge bosons [18][19][20][21][22][23][24][25]. Searches in the di-photon channel are especially useful to constrain pseudoscalars below m A < 350 GeV [26,27]. Since the discovery of a light Higgs h at 125 GeV the search for pseudoscalars decaying into a gauge boson Z and the light Higgs h has been deserving special attention and was carried out at 8 TeV [28, 29] and 13 TeV [30,31]. If the mass splitting between the pseudoscalar and the heavy CP-even Higgs boson is large enough, also H → ZA and A → HZ constrain parts of the parameter space [32,33]. Lastly, CP-even Higgs decays into a pair of light Higgs bosons probe corners of the parameter space [34-41]. Ref. [42] provides a recent overview of excluded parameter regions from the various mentioned decays in the 2HDM. In this paper, we emphasize that in the wrong-sign limit of the 2HDM of types II/F both A → Zh and H → V V can be dominant, even if the decay into a pair of top quarks is kinematically open. Therefore the small deviation in the search bb → A → Zh with h → bb at masses of the pseudoscalar around ∼ 440 GeV observed by the ATLAS collaboration, see Ref.
[31], with 0.1 − 0.3 pb above the SM background, can be explained in the wrong-sign limit. The search assumed leptonic decays of the Z boson as hadronic decays of the Z boson only become useful at higher invariant masses of the pseudoscalar [43]. We note that the region of interest was also probed by the 8 TeV ATLAS and CMS analysis [28,29], which already set bounds on cross sections of similar size. The initial 13 TeV analysis [30] carried out by the ATLAS collaboration with an integrated luminosity of 3.2fb −1 also shows upward fluctuations, though at larger cross sections. If the small excess is confirmed, a signal in the gluon-fusion induced production mode is likely to be seen as well, at least at intermediate values of 5 < tan β < 7.5. On the other hand, if not confirmed, the upcoming data accumulated in the searches for heavy Higgs bosons, both in A → Zh and H → V V , will conclusively probe the remaining parameter space of the wrong-sign limit. In contrast, the decay of the CP-even Higgs boson into two light SM-like Higgs bosons is not yet sensitive to the parameter region under discussion.
The wrong-sign limit also makes testable predictions for the light Higgs boson couplings, most prominently it enhances the gluon-fusion cross section and simultaneously reduces the partial width into two photons. These deviations from the SM Higgs properties of the light Higgs boson do not decouple and therefore also limit the parameter space of the wrong-sign limit. We base our numerical analysis on a data set that does not only take into account the light Higgs boson data and the searches for heavy Higgs bosons, but also theoretical considerations like boundedness from below, stability and perturbativity of the scalar potential. It also respects bounds from B-physics and electroweak precision measurements.
Our paper is organized as follows: In Section 2 we provide an introduction to the Two-Higgs-Doublet Model including the four different types and define the wrong-sign limit. Based on an extensive data set generated for the 2HDM of type II, Section 3 explains the enhancement of pp → A → Zh in the wrong-sign limit. We discuss other phenomenological consequences of the wrong-sign limit in Section 4. In particular, we address the enhancement of pp → H → V V , which is also under current experimental investigation and present the deviations in the light Higgs boson signal strengths induced by the wrong-sign limit. We conclude in Section 5.
2 The 2HDM and the wrong-sign limit As we argued in the introduction, the Two-Higgs-Doublet Model (2HDM) is one of the simplest extensions of the SM Higgs sector. Despite its simplicity, the model boasts a rich phenomenology. Spontaneous CP breaking is possible, some versions of the model provide natural candidates for dark matter or tree-level flavor changing neutral currents (FCNC) whose magnitude can be made naturally small via appropriate symmetries (for a recent review, see [44]). In the most used versions of the model, a global Z 2 symmetry is imposed on the Lagrangian, softly broken by a dimension two term. This symmetry is introduced to eliminate tree-level flavor changing neutral currents in the Yukawa sector [6,7]. The scalar potential for this version of the model may be written as with all 8 parameters real. The quartic couplings of the model must obey well-known bounded from below conditions [45][46][47][48] and other constraints to ensure perturbative unitarity [49,50]. After spontaneous symmetry breaking the doublets Φ 1 and Φ 2 acquire real vacuum expectation values (vevs), v 1 and v 2 . To ensure that the electroweak gauge bosons have their known masses the relation v 2 1 + v 2 2 = v 2 with v = 246 GeV, has to hold. The model's scalar sector is usually described in terms of the following set of parameters: the vev v; the four physical scalar masses (those of h, H, A and H ± ); the angle β, defined such that tan β = v 2 /v 1 ; the angle α, which is the diagonalization angle for the (2 × 2) CP-even mass matrix; and the soft-breaking term in the scalar potential, m 2 12 . Without loss of generality, we may take the interval of variation of α to be −π/2 ≤ α ≤ π/2. Notice both possible signs for this parameter. In all that follows, we will assume that the light CP-even Higgs boson h is the one that has been observed at the LHC. Thus we fix m h = 125 GeV.
As for the Yukawa sector, it can be shown that for the Z 2 symmetry to eliminate treelevel FCNC, each set of same-charge fermions should couple to a single scalar doublet. This leaves four possibilities for the scalar-fermion couplings, summarized in Tab. 1. In what regards the quark sector, models I and Lepton Specific (LS) have almost identical phenomenologies, u-type d-type leptons as do models II and Flipped (F). There are significant constraints on the models' parameter space, stemming from B-physics, in particular from b → sγ measurements [51][52][53][54][55]. Roughly, these constraints translate into a lower bound on tan β (we will take 1 ≤ tan β ≤ 35) and, for Model II and the Flipped model, a lower bound on the mass of the charged scalar (we will take m H ± ≥ 480 GeV). Please notice that the latest results from Ref. [55] already put this bound at about 580 GeV, a point to which we shall return. The mixing between the two Higgs doublet alters the couplings of h vis a vis what one would expect if the lightest CP-even was exactly the SM Higgs. It is customary to define for each SM decay state X. At tree-level, this ratio is simply the square of the ratio of the couplings κ X = g 2HDM X /g SM X . For the ZZ and W W couplings to h, one obtains for all 2HDM model types. Given the ranges allowed for both α and β and LHC results indicating SM-like behavior for h, one finds that κ V V > 0, so the coupling of h to the electroweak gauge bosons in the 2HDM always has the same sign as in the SM. As for the couplings of h to up-type quarks, they are such that for all Yukawa models, since Φ 2 always couples to up-type quarks. For down-type quarks, one has for models I and LS and for models II and F, Given that tan β > 0 and the angle α ranges from −π/2 to π/2, it is easy to see that κ U > 0. However, though for models I and LS κ D > 0, for models II and F that is no longer true -the coupling of the light Higgs boson h to down-type quarks in the 2HDM of type II/F can have the opposite sign to the respective SM coupling and to κ V V . This wrong-sign limit [8][9][10][11][12][13][14] is realized if α > 0. More useful information can be gathered if one rewrites Eq. (5) as Since the light Higgs boson h should behave like the SM Higgs boson [4] one must have sin(β − α) 1. Thus the only possibility to have a negative sign in κ D is if cos(β − α) tan β 2, which points to higher values of tan β and cos(β − α) > 0. In fact, current LHC results still allow for sizeable values of cos(β − α) (∼ 0.3 − 0.4).
The wrong-sign limit is not merely a strange corner of parameter space. It has, in fact, phenomenological consequences observable at the LHC. The change in sign of the bottomquark coupling affects both the gluon-fusion production cross section -enhancing it -and the di-photon branching ratio of the light Higgs boson h -suppressing it. 1 As a consequence, the wrong-sign limit is an example of a nondecoupling regime within the 2HDM, as it cannot lead to light Higgs boson properties exactly equal to ones of the SM Higgs boson [8], a point which we will address again in Section 4. We note that the wrong-sign limit is also under tension from requesting validity of the model up to just a few TeV [56]. We will now consider the effect of the wrong-sign limit on other observables, in particular the production of a pseudoscalar and its subsequent decay to Zh. In the 2HDM of type II the couplings A − Z − h and H − V − V are proportional to cos(β − α) and therefore lead to sensitivity to the wrong-sign limit in searches for heavy scalars in Zh and V V final states. Lastly, the coupling H − h − h also increases with cos(β − α) yielding a potential sensitivity in future di-Higgs searches.

pp → A → Zh in the wrong-sign limit
Recently, in Ref.
[31], the ATLAS collaboration reported a small deviation on the search channel pp → A → Zh: an excess, relative to background expectations, of 0.1 − 0.3 pb for σ(pp → A → Zh)BR(h → bb), for a potential pseudoscalar mass of about 440 GeV. The significance is larger in case the pseudoscalar A is produced through bottom-quark annihilation rather than gluon fusion, but both production processes show a deviation. The statistical significance of this excess is (yet) too low to indicate anything meaningful, but it does raise the question: would it be possible to account for such an excess within the framework of the 2HDM? Common wisdom suggests that for that mass range both the production cross sections and the branching ratios into Zh would be too small for an excess to occur. In fact, for such masses, one is above the tt 1 The enhancement of the gluon fusion cross section can be understood by expanding it in terms of the dominant top-and bottom-quark amplitudes, A t and A b . The cross section is proportional to The second term changes sign upon flipping the sign of the bottom-quark Yukawa coupling. Since this term is negative in the SM this leads to an enhancement of the cross section in the wrongsign limit (see also footnote 3). A similar argument holds for the di-photon branching ratio with additional W boson and charged Higgs boson in the loop, where the effect of the negative bottom quark Yukawa is however much less pronounced. The dominant negative interference for the di-photon branching ratio is induced through the additional charged Higgs boson, see the discussion of Fig. 6. threshold and the cross section for gluon fusion is expected to decrease rapidly. Furthermore, since the pseudoscalar can decay to a pair of top quarks, that decay channel would be expected to dominate over all others.
However, several details of the 2HDM allow to overcome those initial difficulties. To wit: • The gluon-fusion production cross section is expected to be larger for a pseudoscalar A (of a 2HDM with tan β = 1) than for a SM scalar H. At leading order, both processes occur due to a triangle fermion loop diagram. To illustrate the enhancement for a pseudoscalar, we compare the top-triangle contribution to the production cross section for a pseudoscalar mass of m A = 440 GeV with the analogous contribution for a scalar of the same mass. We conclude that the pseudoscalar cross section is .36 times larger than the scalar cross section, with x φ = m 2 φ /4m 2 t . The functions a φ q can e.g. be found in Ref. [57]. The ratio is also hardly affected by higher-order contributions. At next-to-next-to-leading order (NNLO) QCD [58][59][60][61][62] it yields σ(gg → A)/σ(gg → H) = 17.03 pb/7.16 pb ∼ 2.38 at a center-of-mass energy of 13 TeV even including bottom-and charm-quark effects at next-to-leading (NLO) QCD [63]. The numbers are produced with SusHi 1.6.0 [57,64].
• In the 2HDM of type II, the coupling of the pseudoscalar to the top quark is proportional to 1/ tan β, but the coupling to bottom quarks grows with tan β. Therefore, with increasing tan β bottom-quark annihilation bb → A is a sizeable contribution to pseudoscalar Higgs production pp → A. Traditionally, it can be described at NNLO QCD in the five-flavor scheme [65] or at NLO QCD in the four-flavor scheme [66,67] and theory predictions were based on cross sections matching qualitatively between the two schemes [68]. Since recently theoretically clean matching procedures are also available [69][70][71][72], which are numerically very close to the five-flavor scheme. We thus proceed with bottom-quark annihilation described in the five-flavor scheme as implemented in SusHi 1.6.0. We compare the gluon-fusion and the bottom-quark annihilation cross sections in the fiveflavor scheme for a pseudoscalar of m A = 440 GeV at 13 TeV as a function of tan β in Fig. 1. Around tan β = 7.5 both gluon fusion and bottom-quark annihilation are of a similar size, namely 0.3 pb each. For slightly larger values of tan β bb → A is a bit larger than gg → A, which appears to be the case for the mild excess in Ref. [31].
• The coupling of the pseudoscalar to Zh is proportional to cos(β − α) which, in the wrong-sign limit, can have values of the order of 0.2 − 0.6. Though the branching ratio BR(A → Zh) will be proportional to the square of this number, the magnitude of it is sufficient to make this the preferred decay channel of A for certain regions of the parameter space, namely those which include the wrong-sign limit. In that case, for intermediate values of tan β, the decay mode into Zh also dominates over the decay modes into quark pairs, both tt and bb.
We emphasize that within the Minimal Supersymmetric Standard Model (MSSM) such large values of cos(β − α) are hard to obtain, in particular since in the decoupling limit with m A m Z cos(β − α) → 0 is quickly reached. The alignment limit usually occurs at larger values of tan β [73], if not large values for the soft-breaking parameters or µ are chosen. To illustrate the above statements we use a data set generated by ScannerS [9,[74][75][76]. We imposed the tree-level theoretical constraints of boundedness from below [44,46] and perturbative unitarity [44]. We additionally required the electroweak vacuum to be the global minimum of the tree-level Higgs potential [77]. These constraints were imposed only at the electroweak scale. We did not consider the issue of requiring validity of the model up to higher scales, which would further constrain the theory's parameter space (see, for instance, Refs. [56,78,79]). We checked experimental bounds from B-physics, of which the aforementioned constraint on b → sγ is the most important one. Electroweak precision measurements were taken into account through bounds on the oblique parameters S, T and U [80]. The branching ratios, decay widths and production cross sections of all Higgs bosons were calculated using HDECAY 6.511 [81,82] and SusHi 1.6.0 [57,64] 2 . Thus, the bottom-quark annihilation cross section is based on the five-flavor scheme description. This information was passed to HiggsBounds 4.3.1 [86][87][88][89] to check exclusion bounds from searches for additional Higgs bosons. We finally required that the 125 GeV scalar is very much SM-like. We achieve this by demanding that the rates are within at most 20% of their expected SM values (i.e. 1). This ensures a very good compliance with current LHC bounds [4]. As already stated, we allow −π/2 ≤ α ≤ π/2 and 1 ≤ tan β ≤ 35. The masses of the non-SM-like Higgs bosons are constrained to 30 GeV ≤ m A ≤ 1 TeV, 130 GeV ≤ m H ≤ 1 TeV and 480 GeV ≤ m H ± ≤ 1 TeV and the soft Z 2 breaking parameter to 1 GeV 2 ≤ m 2 12 ≤ 5 × 10 5 GeV 2 . Before we explain the details of our results, we emphasize that for our purposes the usage of the narrow-width approximation is still allowed and interference effects among Higgs bosons and/or the SM background can be neglected: in the 2HDM Ref. [90] pointed out the importance of interference effects in gg(→ H) → V V among the heavy Higgs boson, the light Higgs boson and the SM background. Three reference points include a heavy Higgs mass of 400 GeV, very close to the mass region discussed here. For those points large interference occurs in parameter regions where the signal contribution gg → H → V V has a cross section below ∼ 10 −2 pb for moderate values of tan β, i.e. beyond the interesting parameter regions discussed here. The same conclusion can be derived for bb(→ H) → V V . A similar statement holds for pp(→ A) → Zh, for which both gg → A → Zh and bb → A → Zh including the interferences with the background were discussed in Ref. [91]. A new version of vh@nnlo [92] will soon allow to study such interferences, at least at leading order in perturbation theory. Therefore, for all relevant processes in this paper, gg/bb → H → V V and gg/bb → A → Zh, we can rely on the narrow-width approximation. This allows to take into account higher-order contributions both in production and decay separately.
We first show the branching ratio of A → Zh in Fig. 2 as a function of the pseudoscalar mass m A and tan β. We highlighted, in red, the regions of parameter space corresponding to the wrong-sign limit. It is clear from the figures that in the wrong-sign limit the decay A → Zh can indeed become the dominant one, even when the 2HDM parameter space is constrained by the LHC requirement that the lightest CP-even Higgs boson h is SM-like. Fig. 2 (a) demonstrates that large branching ratios are also obtained above the threshold where the decay into a topquark pair is kinematically open. Fig. 2 (b) shows that the largest branching ratios are obtained for tan β within 3 to 7. On the one hand, for moderate values of tan β the decay into a top-quark pair is suppressed and the decay into a bottom-quark pair is not yet sufficiently enhanced. The minimum of the sum of the partial decay widths to tt and bb is at tan β ∼ 7.5 for m A = 440 GeV. On the other hand, the wrong-sign limit can accommodate smaller values of cos(β − α) with increasing tan β, which explains why BR(A → Zh) is reduced with increasing tan β.
The reduction of cos(β − α) with increasing tan β is also apparent in Fig. 3 (a). The blue points are, as before, those for which the light Higgs boson rates are within 20% of the expected SM values. In contrast to the previous figures the red points correspond to the subset of the blue points for which 400 ≤ m A ≤ 500 GeV and σ(pp → A → Zh → Zbb) ≥ 0.1 pb. Here we sum up both gluon fusion and bottom-quark annihilation to obtain σ(pp → A). As explained in Ref. [8], the curved band on the right of the plot corresponds to the wrong-sign limit -and indeed we see all red points lie along this band. Thus we confirm that an excess observed in pp → A → Zh is associated with larger positive values of cos(β − α) and thus the wrong-sign limit. Finally, Fig. 3 (b) depicts the production cross section σ(pp → A) in pb as a function of tan β, again summing up both gluon fusion and bottom-quark annihilation. Notice how the red points, for which the cross section of pp → A → Zh is sizeable, seem to follow a descending line up to tan β 7.5, and increase from that point on. This inflexion marks the value of tan β for which the bottom-quark initiated production process becomes as important as gluon fusion, as we illustrated in Fig. 1. Finally, we split the cross section into gluon fusion and bottom-quark annihilation and combine it with the branching ratios A → Zh and h → bb in Fig. 4 (a) and (b). In those figures we also indicate the measured bounds from the ATLAS analysis [31] as black lines. For the wrong-sign limit we distinguish different regions of tan β, namely 1 < tan β < 5, 5 < tan β < 7.5 and tan β > 7.5 with red, yellow and green points, respectively. It is apparent that in most of the wrong-sign limit parameter space larger cross sections are obtained for the gluon-fusion process, which can be understood from the fact that points with tan β < 5 are favoured in our data set, see Fig. 2 (b). Still the wrong-sign limit allows for sufficient room to also have σ(bb → A)BR(A → Zh → Zbb) > 0.1 pb at values of tan β > 5. Such values of tan β are on the other hand not yet excluded by the gluon-fusion induced process, see Fig. 4 (b). Please note that a much larger cross section observed in the bottom-quark initiated production process is hard to achieve theoretically. Thus if the excess in σ(bb → A)BR(A → Zh → Zbb) rises to a significantly larger cross section, the wrong-sign limit of the 2HDM of type II cannot provide an explanation. It is also clear that the investigation of both production processes separately allows for a conclusive probe of the wrong-sign limit of the 2HDM of type II. Ref. [42] shows that at low tan β the process gg → A → Zh rules out a large parameter region of the wrong-sign limit, see e.g. their Fig. 4. This is in full accordance with our observations, where only values of tan β > 5 are not yet excluded by gg → A → Zh.
An interesting feature of the exclusion through the process pp → A → Zh → Zbb is the fact that h → bb vanishes for cos(β − α) · tan β ≈ 1. As indicated in the caption of Fig. 6 of Ref.
[31] this causes a nonexcluded parameter region for low tan β far away from cos(β −α) = 0. Obviously, this region can however be excluded through the measurement of the light Higgs boson couplings to bottom quarks and does not correspond to the wrong-sign limit, which occurs at values of cos(β − α) tan β being twice as large.

Observable consequences of an excess in pp → A → Zh
Since the 2HDM is such a tightly constrained model, having an excess on a particular channel usually has consequences for other ones. In the case we are studying, the region of parameter space which explains an eventual excess in σ(pp → A → Zh → Zbb) is in the wrong-sign limit, the coupling of the lightest Higgs boson to down-type quarks being of an opposite sign to the corresponding SM quantity. Furthermore, the relevant range of tan β values implies that, for the pseudoscalar, the bb production mechanism is as important as the gluon-fusion process. We will now show what such an excess would imply for the two other non-SM-like scalars of the theory -H and H ± .
We first consider Fig. 5 (a). We show the allowed values of the charged scalar mass m H ± and the heavy CP-even Higgs mass, m H . Clearly an excess in the channel pp → A → Zh → Zbb would require the two remaining scalars to have masses below about 700 GeV -as was to be expected, since the wrong-sign limit cannot occur for very large masses [8]. The lower limit on m H ± observed in this figure was imposed from the start, and pertains, as explained above, to bounds on b → sγ. In fact, the most recent results from B-physics calculations [55] already set this lower bound at 580 GeV -which, we observe, could already be in conflict with further constrained points, i.e. those for which the lightest CP-even scalar does not deviate from SM behavior by more than 10%. Nonetheless, if the pp → A → Zh → Zbb excess were confirmed, this figure would give us the mass range upon which the remaining 2HDM scalars would have to be found, their masses at most ∼ (150 − 300) GeV apart.
As we argued previously the coupling of the heavy CP-even Higgs boson to two heavy gauge bosons is proportional to cos(β − α), and similarly the decay into two light CP-even Higgs bosons increases with cos(β − α). It is thus not surprising that such decays are very sensitive to -the CMS results would not be significantly different -and therefore gives us an idea where the current experimental sensitivity to this process is. What is clear from the displayed figure is that the points corresponding to the wrong-sign limit lie very closely to the black line. Therefore, the 2HDM explanation for an excess in pp → A → Zh would imply a signal in the channel pp → H → ZZ of a magnitude that can surely be probed in the next years. At larger values of tan β the constraints originating from the gluon-induced channel are also weaker. It is worth mentioning that in type II models the coupling of H to bottom quarks is proportional to cos α/ cos β. Since SM-like behavior for the light Higgs boson h implies β − α π/2, this coupling is essentially growing as tan β. As such, the bb production process for H will have a significant contribution, as it did for A production, and can thus constrain the regions with larger values of tan β. Finally, let us remember that the wrong-sign limit is a nondecoupling regime. There are "irreducible" contributions to the gluon-fusion cross section and the di-photon decay width which make it so that the light Higgs boson h can never have production and decay rates exactly like those of the SM Higgs. For the di-photon width, this stems from a destructive contribution to the amplitude from the charged scalar, essentially independent of m H ± for masses up to ∼ 700 GeV, see Ref. [8]. As such the wrong-sign limit can be ruled out if measurements of sufficient precision are performed on the lightest Higgs rates. To illustrate this, consider Fig. 6, where we present the signal strength µ γγ versus µ ZZ for the lightest Higgs boson.
The lower band of points in this figure corresponds to the wrong-sign limit, and it is clear it does not include the point (1, 1) corresponding to the SM expected values. Further, we see that the yellow points, corresponding to an excess in σ(pp → A → Zh → Zbb) of at least 0.1 pb and SM-like signal strengths within 10%, would imply a di-photon rate for h at least 5% smaller than its SM expectation, and a ZZ rate at least 7% larger than the SM value. Similar enhancements are predicted for the W W , ττ and bb channels, all of them arising from a positive interference in the wrong-sign limit between the top and bottom quark contributions to the gluon-fusion cross section 3 . Figure 6: Di-photon decay rate µ γγ versus ZZ production and decay rate µ ZZ for the lightest CP-even Higgs boson in the 2HDM of type II. It applies the same colour code as in Fig. 3, highlighting in yellow points where the rates of the lightest CP-even Higgs-boson deviate from the SM values by at most 10%.

Conclusions
We conclude that the wrong-sign limit in the 2HDM of type II leads to enhanced and often dominant branching ratios of A → Zh and H → V V , due to sizeable values of cos(β − α). It is thus possible to produce an excess in the current searches of heavy Higgs bosons decaying into Higgs and/or gauge bosons at the LHC. We demonstrated this enhancement for pp → Zbb, stemming from the production of a pseudoscalar A with mass above the tt threshold and its subsequent decay to Zh, the SM-like Higgs then decaying further to a pair of bottom quarks. This statement applies to moderate values of tan β -below 15, above roughly 3 -which are experimentally not yet excluded by searches for heavy Higgs bosons decaying into fermions. At intermediate values of tan β between ∼ 5 and ∼ 7.5 the signal in the bottom-quark induced process is likely to be accompanied by a signal in the gluon-fusion process. The wrong-sign limit makes testable predictions also for the lightest CP-even Higgs boson couplings, namely enhancing the gluon fusion cross section and lowering the decay rate into two photons. The mild excess currently seen by the ATLAS collaboration in pp → Zbb is entirely in agreement with the current precision achieved for the couplings of the lightest Higgs boson.