Mapping $pp\to A\to ZH\to l^+l^-b\bar b$ and $pp\to H\to ZA\to l^+l^-b\bar b$ Current and Future Searches onto 2HDM Parameter Spaces

By borrowing the results from a Large Hadron Collider (LHC) analysis performed with $36.1~\text{fb}^{-1}$ of Run 2 data intended to search for $A$ production followed by $ZH$ decay in turn yielding $l^+l^-b\bar b$ ($l=e,\mu$) final states in the context of the standard four Yukawa types of the 2-Higgs Doublet Model (2HDM), we recast it in terms of sensitivity reaches for the similar process $pp\to H\to ZA\to l^+l^-b\bar b$. This simple exercise across the two processes, which is possible because the only kinematic difference between these are different widths for the Higgs bosons, in turn affecting minimally the efficiency of an experimental selection, enables us to expand the region of parameter space that can be tested to the case when $m_H\ge m_A+m_Z$. Furthermore, we extrapolate our results to full Run 3 data samples. We conclude that, while the high energy and luminosity stage of the LHC can afford one with increased sensitivity to the 2HDM in general, the recast analysis does not add anything to what already probed through the actual one.


I. INTRODUCTION
Following the discovery of a 125 GeV Higgs boson at the Large Hadron Collider (LHC), several studies of its properties have been carried out over the years. The situation at present is that the measured Higgs signal rates in all accessed production and decay channels agree with the Standard Model (SM) predictions. Although the current LHC Higgs data are generally consistent with the SM, the possibility that the observed Higgs state could be part of a model with an extended Higgs dynamics, one that includes an extra doublet, still exists. Therefore, since the discovered Higgs state belongs to a doublet, one is induced to consider a generic 2-Higgs Doublet Model (2HDM) [1].
This Beyond the SM (BSM) scenario contains two Higgs doublets used to give mass to all gauge bosons and fermions of the SM. The Higgs particle spectrum of the 2HDM is as follows: two CP even (h and H, with, conventionally, m h < m H ), one CP odd (A) and a pair of charged (H ± ) Higgs bosons. Amongst the many signals that these additional Higgs states could produce, of particular relevance are those involving their cascade decays, wherein a heavier Higgs state decays in a pair of lighter ones or else into a light Higgs state and a gauge boson. This is the case as the former process gives access to the shape of the Higgs potential of the enlarged Higgs sector while the latter channel is intimately related to the underlying gauge structure, which may well be larger than the SM one.
We concern ourselves here with the second kind of processes, specifically involving only the neutral Higgs states in addition to the discovered SM-like one, which in our 2HDM is identified with the h state. In short, we intend to study A → ZH and H → ZA decays 1 .
The pattern of Branching Ratios (BRs) of the two decays A → ZH and H → ZA was first discussed in Refs. [3] and [4] (albeit in a Supersymmetric version of the 2HDM) and more recently implemented in Refs. [5,6] in the 2HDM. As for production channels, the by far most relevant one is gluon-gluon fusion, i.e., gg → A or H, with an occasional competing contribution from bb → A or H, respectively.
LHC searches for the complete channels gg, bb → A → ZH and gg, bb → H → ZA have been carried out at both ATLAS [7] and CMS [8,9], by exploiting leptonic decays of the gauge boson, Z → l + l − (l = e, µ), and hadronic decays of the accompanying neutral Higgs state, in particular, H or A → bb or τ + τ − . Based on this approach, current experimental data exclude heavy neutral Higgses with masses up to about 600-700 GeV, depending on the BSM Higgs spectrum and the value of tan(β), the ratio of the Vacuum Expectation Values (VEVs) of the aforementioned two Higgs doublets. These findings are broadly in line with previous phenomenological results obtained in Ref. [10], which had forecast the LHC scope in accessing both A → ZH and H → ZA decays in a variety of final states. Far away from the alignment limit, sin(β − α) = 1, searches have been carried out at the LHC Run 2 looking for additional Higgs bosons decaying to A → hZ or/and H → hh leading to l + l − bb [11,12] or/and τ + τ − bb [13]. While in the exact alignment limit, A → hZ and H → hh will be suppressed, There are additional reasons for studying A → ZH and H → ZA decays. For a start, Ref. [14] emphasised the importance of using the pp → A → Zh process to test the wrongsign limit of the so-called 2HDM Type-II (see below). Furthermore, Ref. [15] highlighted the fact that this very same process echoes the dynamics of the EW Phase Transition (EWPT).
It is the scope of this paper to revisit these two decay chains, in particular, we intend to use a synergetic approach that recasts the results of experimental searches in one mode, interpreted in terms of 2HDM constraints, into the scope of the other in the same respect. This is possible because they can have the same final state. Here, we consider the final state l + l − bb and start from the results of [7] for the A → ZH decay in order to obtain the corresponding ones for the complementary channel H → ZA, altogether showing that such a recasting can afford one with a much stronger sensitivity that either channel alone can offer.
The plan of the paper is as follows. In the next section, we introduce the 2HDM. We then scan its parameter space in order to establish the sensitivity of LHC data analyses to such a BSM scenario and map the findings of one channel into the other. We then conclude.

A. The Model
Unlike the SM, the 2HDM contains two complex scalar doublets Φ 1,2 from SU (2) L with the most general gauge invariant renormalisable scalar potential of the 2HDM given by: Following the hermiticity of the scalar potential, m 2 11 , m 2 22 and λ 1,...4 are real parameters whereas m 2 12 , λ 5,6,7 can be complex. Assuming the CP-conserving version of the 2HDM, m 2 12 , λ 5,6,7 and the VEVs of the fields Φ i are real parameters. As a consequence of extending the discrete Z 2 symmetry to the Yukawa sector in order to avoid Flavour Changing Neutral Currents (FCNCs) at tree level, λ 6,7 = 0, whereas the mass term m The Yukawa Lagrangian can be written in the form where m f is the relevant fermion mass, P L,R = (1 ± γ 5 )/2 and V denotes the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Thus, in the absence of FCNCs, the Higgs-fermion couplings are flavour diagonal in the fermion mass basis and depend only on the mixing angle, β, in the alignment limit. where the coefficients ξ f h i are interpreted as the ratio of the Higgs boson couplings to the fermions with respect to the SM values, which are defined in the alignment limit in Tab. I, limitedly to the case of the H and A states, which are of interest here.
Since we are interested in the two decays processes A → ZH and H → ZA, recall that the coupling of the heavy neutral Higgs scalar with the pseudoscalar and the gauge boson Z in the 2HDM is given by: Couplings Type-I Type-II Type-X Type-Y

B. Theoretical and Experimental Constraints
There are several theoretical and experimental constraints for the parameter points of the 2HDM to pass, discussed below.
• Unitarity: various scattering processes require that unitarity is conserved at the treelevel at high energy. The unitarity requirements in the 2HDM have been studied in [16][17][18]. Sets of eigenvalues e i (i − 1, ...12) for the scattering matrix of all Higgs and Goldstone bosons of the 2HDM are obtained as follows: We require all e i 's to be less than 16π for each i = 1, ...12.
• Vacuum stability requires the scalar potential to be bounded from below [19] by satisfying the following inequalities: • EW Precision Observables (EWPOs) [20], such as the oblique parameters S and T [21,22], require a level of degeneracy between the charged Higgs boson state and one of the heavier neutral Higgs bosons. Here, we assume m H ± = m A or m H , as appropriate (see below), so that the T parameter exactly vanishes in the alignment limit.
• Exclusion limits at 95% Confidence Level (CL) from Higgs searches at colliders (LEP, Tevatron and LHC) via HiggsBounds, version 5.3.2 [23][24][25] are enforced. Furthermore, the ATLAS Collaboration has set an upper limit at 95% CL on the production cross section σ of the A state times its decay BR into ZH → l + l − bb, i.e., σ(A) × BR(A → ZH → l + l − bb) [7], that is not included in this tool, hence we have accounted for it separately.
• Constraints from the Higgs boson signal strength measurements are automatically satisfied as we assume sin(β − α) = 1.

A. The Scan
A scan is performed over the parameter space of the 2HDM. In doing so, we use the program 2HDMC [26], firstly, to check the theoretical constraints as well as the EWPOs with an integrated luminosity of 300 fb −1 , by calculating the so called 'upgrade factor' for both signals and backgrounds, while retaining the acceptance and selection efficiencies of the analysis at the lower √ s value. The change in energy will naturally affect signals and backgrounds differently. We treat the former by using SusHi (as intimated) and the latter by using MadGraph5, version 2.6.4 [31]. (For completeness, the background is considered to be any reducible or irreducible SM process that creates a pair of b-jets plus a pair of electrons or muons, as in Ref. [7].)

B. Numerical results
In this study, we identify the lightest CP-even Higgs boson of the 2HDM as the observed Higgs state at the LHC, with m h = 125 GeV, and assume sin(β − α) = 1.
We scan over the following parameter range: The set of values chosen for tan(β), and the masses, align with the choices in [7].
•   prediction of the model with the observed and expected limits given in Ref. [7]. If the prediction exceeds the observed limit, then the parameter combination is excluded. When the prediction exceeds the expected limit, we anticipate that the signal would be visible above background given the energies and luminosities available, hence, the experiment is sensitive to these parameters.
The choice of m 2 12 = m 2 A tan(β)/(1+tan(β)) 2 enables us to reconstruct the exclusion limits at 95% CL given in Ref [7]. However, this choice does not actually allow to satisfy theoretical constraints in all four types of 2HDM. Therefore, we have dismissed it in our analysis. where m A > m H + 100 GeV, the decay A → ZH is considered while in the bottom right of each plot, where m H > m A + 100 GeV, the decay H → ZA is considered. The corridor along the diagonal between these regions is coloured grey to indicate that neither decay is accessible. If a combination of parameters is forbidden by theory, HiggsBounds or flavour constraints then the corresponding area is filled with solid colour, conversely, white areas pass all these checks and so are of interest. The hatching over the solid colour is used to indicate which of the checks causes the corresponding parameter combination to fail. There are three boundary lines drawn over the plots: these are the observed and expected 95% tan(β)   2 We neglect here to consider the case of √ s = 13 TeV and L ≈ 140 fb −1 , as it only improves marginally the present situation yet it would be make the plots far too crowded. even more possible parameter space than seen at tan(β) = 5. Finally, in the lower right frame of Fig. 1, the parameter space for tan(β) = 20 is shown. The state of H → ZA is unchanged, but now A → ZH has no expected or observed exclusion at 13 TeV, i.e., these parameters are harder to probe. With the upgrade to 14 TeV and 300 fb −1 there is some sensitivity to A → ZH at tan(β) = 20.
As might be expected, the behaviour of Type-II, shown in Fig. 2  is shown to be excluded for almost all mass choices, by multiple constraints.
In Fig. 4 the behaviour of the Type-X 2HDM is shown, at a set of tan(β) values that differs from those previously considered. For these Yukawa couplings and tan(β) choices HiggsBounds excludes all areas inside the expected limits. This remains true even after the end of Run 3.
Finally, Tab. II summarises our findings, highlighting that sensitivity only really exists for 5 < tan(β) < 10 and limitedly to the 2HDM Type-I, both at Run 2 and 3, and -II and -Y (or Flipped), but only at Run 3. The case of Type-X (or Lepton specific) is never accessible.

IV. CONCLUSIONS
In summary, we have revisited an experimental analysis of the ATLAS Collaboration of the production and decay process gg, bb → A → ZH → l + l − bb performed at Run 2 with