Prospects for charged Higgs bosons in natural SUSY models at the high-luminosity LHC

We continue our examination of prospects for discovery of heavy Higgs bosons of natural SUSY (natSUSY) models at the high luminosity LHC (HL-LHC), this time focussing on charged Higgs bosons. In natSUSY, higgsinos are expected at the few hundred GeV scale whilst electroweak gauginos inhabit the TeV scale and the heavy Higgs bosons, H, A and H^\pm could range up tens of TeV without jeopardizing naturalness. For TeV-scale heavy SUSY Higgs bosons H, A and H^\pm, as currently required by LHC searches, SUSY decays into gaugino plus higgsino can dominate H^\pm decays provided these decays are kinematically accessible. The visible decay products of higgsinos are soft making them largely invisible, whilst the gauginos decay to W, Z or h plus missing transverse energy (MET). Charged Higgs bosons are dominantly produced at LHC14 via the parton subprocess, gb->H^\pm t. In this paper, we examine the viability of observing signtures from H^\pm ->\tau\nu, H^\pm ->tb and H^\pm ->W, Z, h + MET events produced in association with a top quark at the HL-LHC over large Standard Model (SM) backgrounds from (mainly) t\bar{t}, t\bar{t}V and t\bar{t}h production (where V=W, Z). We find that the greatest reach is found via the SM H^\pm(->\tau\nu) +t channel with a subdominant contribution from the H^\pm(->tb) +t channel. Unlike for neutral Higgs searches, the SUSY decay modes appear to be unimportant for H^\pm searches at the HL-LHC. We delineate regions of the m_A vs. \tan\beta plane, mostly around m_A \sim 1-2 TeV, where signals from charged Higgs bosons would serve to confirm signals of a heavy, neutral Higgs boson at the 5\sigma level or, alternatively, to exclude heavy Higgs bosons at the 95% confidence level at the high luminosity LHC.


Introduction
There are two routes to discovery of supersymmetry (SUSY) at hadron colliders such as the CERN Large Hadron Collider (LHC): one is via direct pair production of R-parity odd states and the other is via single (or pair) production of new R-parity even states such as the additional heavy Higgs bosons present in the Minimal Supersymmetric Standard Model (MSSM) [1].Of course, strictly speaking, the production of the heavy Higgs boson states is not necessarily a signal for supersymmetry (unless these are seen via their decays into supersymmetric particles) since such states are also possible in non-supersymmetric models with an extended Higgs sector.In the present paper, we continue our work on the second approach: prospects for SUSY discovery via the required additional SUSY Higgs bosons.While much work has been done in this field, our focus is on LHC signals of the heavy Higgs bosons of natural SUSY models, wherein no large fine-tunings are required in order to gain a weak scale characterized by m W,Z,h ≃ 100 GeV.In previous work, we examined prospects for SUSY Higgs discovery in natural SUSY via resonance production of heavy neutral Higgs bosons H and A, followed by 1. decays into Standard Models modes with H, A → τ + τ − being most promising [2], and 2. decays into pairs of SUSY particles [3] which offer qualitatively new channels for SUSY Higgs boson discovery.Within natural SUSY, once the heavy Higgs boson decay channels to gaug-ino+higgsino become open, these may rapidly dominate the branching fractions.This leads to two effects: 1. the new SUSY decay modes diminish the branching fractions into SM modes, thus diminishing the expected LHC reach via these decay channels, and 2. the new SUSY decay modes open up new avenues for SUSY Higgs detection, where these new channels would signal the presence of the expected SUSY particles.In the present paper, we extend our earlier analyses to include production of charged SUSY Higgs bosons H ± .Discovery of charged SUSY Higgs bosons is expected to be more challenging than discovery of the neutral bosons.This is due to typically smaller production cross sections (for a given Higgs boson mass) but also to less distinctive discovery signatures.We investigate here whether this situation still maintains under the rubric of natural SUSY.
Here, we take the measured value of the Z-boson mass as representative of the magnitude of weak scale, where in the MSSM the Z mass is related to the weak scale Lagrangian parameters via the electroweak minimization condition where m 2 Hu and m 2 H d are the Higgs soft breaking masses, µ is the (SUSY preserving) superpotential higgsino mass parameter and the Σ d d and Σ u u terms contain a large assortment of loop corrections (see Appendices of Ref. [4] and [5] and also [6] for leading two-loop corrections).We adopt the notion of practical naturalness [7,8], wherein the value of an observable O is natural if all independent contributions to O are comparable to (within a factor of few), or smaller than O.For natural SUSY models, we use the naturalness measure [4,9] ∆ EW ≡ |maximal term on the right − hand − side of Eq. (1)|/(m 2 Z /2) , and take ∆ EW ≲ 30 (3) to be natural.For most SUSY benchmark models, the superpotential µ parameter is tuned to cancel against large contributions to the weak scale from SUSY breaking.Since the µ parameter typically arises from very different physics than SUSY breaking, e.g. from whatever solution to the SUSY µ problem that is assumed,1 then such a "just-so" cancellation is highly implausible [11] (though logically possible) compared to the case where all contributions to the weak scale are ∼ m weak , so that µ (or other parameters) need not be tuned.Several important implications of Eq. ( 3) for heavy SUSY Higgs searches include the following.
• The superpotential µ parameter enters ∆ EW directly, leading to |µ| ≲ 350 GeV.This implies that for heavy Higgs searches with m H ± ≳ 2|µ|, then SUSY decay modes of H ± should typically be open.If these additional decay widths to SUSY particles are large, then the branching fractions to the (usually assumed) SM search modes would be correspondingly reduced.
For tan β ∼ 10 with ∆ EW ≲ 30, then m H ± can range up to ∼ 5 TeV.For tan β ∼ 40, then m H ± stays natural up to ∼ 20 TeV (although for large tan β ≳ 20, then bottom squark contributions to Σ u u become large and provide much stronger upper limits on natural SUSY spectra [7]).In Sec. 2, we first present a natural SUSY benchmark point which then leads to a natural SUSY Higgs scenario which we previously dubbed m 125 H (nat).The m 125 h (nat) scenario is promoted as a template for SUSY Higgs searches in that [2] 1. it leads to a value of m h ≃ 125 GeV throughout almost the entire m A vs. tan β search plane and 2. the value of ∆ EW is also low (though sometimes exceeding a value of 30 at higher tan β values) thoughout the search plane.In Sec. 3, we list the dominant charged SUSY Higgs boson production cross sections at LHC14 (LHC with √ s = 14 TeV).It is well-known that the gb → tH ± subprocesses is the dominant H ± production mechanism at the LHC [13][14][15].In Sec. 4, we present charged Higgs boson branching fractions from the m 125 h (nat) scenario in the m A vs. tan β plane, and find that indeed SUSY decay modes do become rapidly dominant once these are kinematic accessible.In Sec. 5, we examine pp → tH ± + X followed by H ± → τ ± ν τ and map out distributions which help obtain signal over SM background levels.In Sec. 6, we examine pp → tH ± + X followed by H ± → tb decay.In Sec. 7, we study the impact of the SUSY decays of H ± bosons: unfortunately, we find that the relevant cross-sections are mostly in the sub-fb range for mass values where the branching fractions for these modes become substantial, and (contrary to what we found for H and A bosons) SUSY decays of H ± do not offer a viable search strategy.In Sec. 8, we plot out the reach of high-luminosity LHC for charged Higgs bosons of natural SUSY.Our summary and conclusions are contained in Sec. 9.

A review of some previous related work
Here, we present a brief (and likely incomplete) review of some related work on charged Higgs bosons from SUSY.In Ref. [16], it was already emphasized that detection of a top quark signal in accord with SM expectations would preclude the decay t → bH + and thus require m H ± ≳ m t − m b .In light of present t t signal results, this implies m H ± ≳ 168 GeV.This result was already used by Kunszt and Zwirner in Ref. [17] to form the low m A limit of the proposed m A vs. tan β heavy SUSY Higgs search plane.Decays of heavy SUSY Higgs boson to SUSY decay modes were originally explored in Ref. [18][19][20][21] and the complete set of H ± decay widths may be found in Appendix C of [1].In Ref. [12], these decay modes were examined in the context of natural SUSY.In that work, it was noted that for H, A, H ± → wino + higgsino channels, the higgsino decays led to mainly soft, quasi-visible decay debris whilst the winos decayed dominantly via two-body modes into W + higgsino, Z + higgsino and h + higgsinos.
In Ref. [13][14][15], it was found that the dominant production process for charged Higgs bosons at LHC was the reaction gb → tH − + c.c.. NLO corrections to this production process were calculated in Ref. [22,23] and [24].Signals from the final state tH ± (→ τ ν τ ) were examined in Ref. [25] and [26].The decay channel H + → hW + (which is highly suppressed in natSUSY) was examined in Ref. [27].The use of three [28] and four [29] b-quark tags in gg → tbH ± was examined.Corrections to the tbH ± vertex were examined in Ref. [30].Initial projections of the LHC reach for (charged) SUSY Higgs bosons were given by Denegri et al. [31] and by Assamagan et al. [32].Search limits from LHC for the H ± → τ ν τ decay mode were presented based on ∼ 36 fb −1 of integrated luminosity by ATLAS [33] and by CMS [34].An ATLAS search for charged Higgs bosons in the H ± tb mode based on 139 fb −1 was given in Ref. [35].A guidebook for LHC searches for SUSY and non-SUSY charged Higgs bosons was provided in Ref. [36] and a review of non-SUSY charged Higgs is available in Ref. [37].

A natural SUSY benchmark point and the m 125 h (nat) scenario
Following our previous work, we here adopt the same natural SUSY benchmark point as in Ref. [3], which was dubbed m 125 h (nat) since the value of m h is very close to its measured value throughout the entire m A vs. tan β plane.We use the two-extra-parameter non-universal Higgs model (NUHM2) [38] with parameter space m 0 , m 1/2 , A 0 , tan β, µ, m A which is convenient for naturalness studies since µ can be set to its natural range of µ ∼ 100 − 350 GeV whilst both m A and tan β are free parameters. 2 We adopt the following natural SUSY benchmark Higgs search scenario: A similar m 125 h (nat) benchmark model spectrum, but with µ = 250 GeV and m 1/2 = 1.2 TeV, was shown in Table 1 of Ref. [2] for tan β = 10 and m A = 2 TeV and so for brevity 2 The NUHM2 framework allows for independent soft SUSY breaking mass parameters for the scalar fields H u and H d in the Higgs sector, but leaves the matter scalar mass parameters universal to avoid flavour problems.The parameters m 2 Hu and m 2 H d are then traded for µ and m A in the parameter set shown in (5).
we do not show the revised spectrum here.We adopt the computer code Isajet [39] featuring Isasugra [40] for spectrum generation.The SUSY Higgs boson masses are computed using renormalization-group (RG) improved third generation fermion/sfermion loop corrections [41].
The RG improved Yukawa couplings include full threshold corrections [42] which account for leading two-loop effects [43].For tan β = 10 and m A = 2 TeV, we note that ∆ EW = 16 so the model is indeed EW natural.Also, with m h = 124.6GeV, m g = 2.4 TeV and m t1 = 1.6 TeV, it is consistent with LHC Run 2 SUSY search constraints.Most important for our purpose, the two lightest neutralinos, χ0 1 and χ0 2 , and the lighter chargino, χ± 1 , are higgsino-like with masses ∼ 200 GeV while the neutralino χ0 3 is bino-like with a mass of 450 GeV and the heaviest neutralino and the heavier chargino have masses ∼ 0.86 TeV.Thus, the H, A, H ± → wino + higgsino decay modes turn on for m H,A,H ± ≳ 1.1 TeV (although H, A, H ± → bino + higgsino turns on at somewhat lower m A values).It is important to note that while the value of ∆ EW may change somewhat for small variations of the parameters that are held fixed in Eq. ( 5), we expect that the Higgs sector phenomenology is relatively insensitive to our specific choice (as long as µ ≲ 300 GeV to maintain naturalness).

H ± production cross sections at LHC14
In Fig. 1, we show leading order total cross sections for production of charged SUSY Higgs bosons at LHC14, as generated using Pythia [44] for two values of tan β = 10 (solid) and 40 (dashed).We show cross sections for charged Higgs boson production at the LHC via tH ± production (blue), resonant H ± production (light green), H + H − production (light blue), and hH ± (magenta), AH ± (green) and HH ± (red) production.
We see from Fig. 1 that the dominant production mechanism at LHC14 is via the gb → tH ± subprocess [13][14][15].For tan β = 40, the cross section varies from ∼ 10 3 fb at low m H ± to ∼ 10 −2 fb at m H ± ∼ 3 TeV.These dominant cross sections are enhanced by large tan β.If we compare tH ± production to the rate for b b, gg → A, H production [2] for tan β = 10 and m A ∼ 1.5 TeV, we find that charged Higgs production rates are suppressed compared to resonance production of A by a factor ∼ 5.And since σ(b b, gg → A) ∼ σ(b b, gg → H), charged Higgs production compared to resonance H, A production is suppressed by about an order of magnitude.This seems reasonable since charged Higgs production occurs in association with a (spectator) top quark in contrast to the resonantly produced neutral H or A boson.
The next largest cross section is direct resonance production of H ± via (Yukawa suppressed) u d fusion or via (parton distribution function suppressed) cs fusion.Note that this is suppressed relative to neutral H/A resonance production from b b fusion by the smaller Yukawa couplings (of the first two generation of quarks) and/or small Kobayashi Maskawa mixing elements.These light green curves show a tan β enhancement due to the Yukawa couplings involved in the production mechanism.The resonance production cross section is typically about two orders of magnitude below tH ± associated production.
The next largest production cross sections are HH ± and AH ± which are produced via W * exchange followed closely by H + H − pair production which takes place via s-channel γ * and Z * exchange.All these production vertices involve gauge interactions and so are tan β independent.As a result, the tan β = 10 and 40 curves lie on top of one another.These three cross sections are kinematically suppressed because they involve the production of a pair of heavy bosons, and are ∼ 1.5 − 3 orders of magnitude below the dominant tH ± cross sections.
In magenta, we show hH ± associated production which occurs dominantly via s-channel W * exchange where the production vertex includes a factor g cos(α + β) (see Eq. (8.110) of Ref. [1])3 which vanishes in the decoupling limit.As a result, these cross sections are suppressed from the dominant tH ± cross section by ∼ 3 − 5 orders of magnitude depending on m H ± and tan β.They also feature a dip at certain values of m H ± which occurs when the Higgs mixing angle α is such that cos(α + β) → 0. An additional cross section σ(pp → W ± H ∓ + X) occurs at the loop level, and so is highly suppressed and we do not include it here: see Ref. [45].
In light of our discussion of the various production cross sections, for our HL-LHC SUSY charged Higgs reach analysis we will restrict ourselves to the dominant tH ± production process.In Fig. 2 we show the values of σ(pp → tH ± + X) at LHC14 in the m A vs. tan β plane for our m 125 h (nat) scenario.The largest cross sections ∼ 10 3 fb are denoted by dark red whilst the lowest cross sections ∼ 10 −3 fb are denoted dark blue.We also show the latest ATLAS 95% CL exclusion limit from their search for H, A → τ + τ − events using LHC13 with 139 fb −1 in several non-natural Higgs scenarios which nonetheless maintain m h ∼ 125 GeV [46].Thus, to uncover new physics at HL-LHC in the SUSY Higgs sector, we will mainly focus our attention on m H ± values in the TeV range.

H ± branching fractions in natSUSY
The LHC signal from charged Higgs boson production will clearly depend on how H ± decays.For TeV scale values of m H ± , the dominant SM decays are via H ± → tb and H ± → τ ν τ .Decays to h, W and Z bosons are dynamically suppressed.Charged Higgs boson decays via the gaugino plus higgsino modes can also be important if these are not kinematically suppressed.With this in mind, in Fig. 3, we show some select H ± branching fractions (BFs) in the m A vs. tan β plane for the model plane (Eq.5).The branching fractions are color-coded, with the larger ones denoted by red whilst the smallest ones are denoted by dark blue.The branching fractions are extracted from the Isasugra code [39].
In Fig. 3a) we show the BF for H + → t b.This decay mode to SM particles is indeed dominant for m A ≲ 1 TeV and for larger values of tan β ≳ 20 − 30.In frame b), we show the BF(H + → τ + ν τ ).Like H + → t b, this mode is enhanced at large tan β and has provided the best avenue for SUSY charged Higgs discovery/exclusion plots so far.
While SUSY decay modes of H ± to higgsino pairs are also open in these regions, these decay modes are suppressed by mixing angles for reasons discussed below.Supersymmetry requires that there is a direct gauge coupling [1] where S i labels various matter and Higgs scalar fields of the MSSM, ψ i is the fermionic superpartner of S i and λ A is the gaugino with gauge index A. Also, g is the corresponding gauge coupling for the gauge group in question and the t A are the corresponding gauge group matrices.Letting S i be the Higgs scalar fields, we see there is an unsuppressed coupling of the Higgs scalars to a gaugino and a higgsino as mentioned earlier.This coupling can lead to dominant SUSY Higgs boson decays to SUSY particles when the gaugino-plus-higgsino decay channel is kinematically unsuppressed.But it also shows why the heavy Higgs decay to higgsino pairs is suppressed by mixing angles for |µ| ≪ |M 1,2 |, once we recognize that a Higgs boson-higgsino-higgsino coupling is forbidden by gauge invariance.
In frame c), we show BF(H + → χ0 , where χ0 1 is dominantly higgsino-like and χ+ 2 is dominantly wino-like for natural SUSY models like the m 125 h (nat) scenario.Here, we see that for larger values of m A ≃ m H + ≳ 1.2 TeV, then this mode turns on, and at least for moderate tan β ∼ 10 − 20 (which is favored by naturalness [12]), rapidly comes to dominate the H + decay modes along with the neutral wino+higgsino channels H → χ+ (frame e)).In our analysis we have assumed that the gaugino mass parameters unify at the high scale, so that at the weak scale M 1 ≃ 1 2 M 2 : as a result, χ 0 3 is dominantly bino-like, χ 0 4 and χ ± 2 are dominantly wino-like, while χ0 1,2 and χ ± 1 are mainly higgsino-like.The sum of these three wino+higgsino decay channels thus dominate the H + decay branching fractions for m H,A ≳ 1.2 TeV and low-to-moderate values of tan β.For high values of tan β, the b and τ Yukawa couplings become large, and SM decays to fermions once again dominate SUSY decays.Decays of H + to gauge boson pairs and to h are unimportant in the decoupling limit as mentioned above.For completeness, we also show in frame f) the decay mode H → χ+  3 which is to higgsino+bino.This mode is large only in a small region of m H ∼ 1 TeV and modest tan β where the mode H → bino + higgsino decay has turned on, but where H → wino + higgsino has yet to become kinematically open.Decays to winos dominate decays to binos because the SU (2) gauge coupling g is larger than the hypercharge gauge coupling g ′ .5 Search for H ± → τ ν τ Next, we turn to the examination of the prospects for discovering the charged Higgs boson produced at the HL-LHC via pp → H ± t + X, followed by H ± → τ ν τ decay.For signal and 2 → 2 background processes listed below, we use the Pythia event generator [44].For 2 → 3 BG processes such as W b b, Zb b and ht t production, we adopt Madgraph [47] for the subprocess calculation but then interface with Pythia for parton showers, hadronization and underlying event.Our final state particles are then fed into the Delphes [48] detector simulation program which includes a jet-finding algorithm and routines for identifying both b-jets and hadronic tau jets (labelled as τ h ).
In Delphes, a jet object is reconstructed using an anti-k algorithm with p T (min) > 25 GeV and ∆R < 0.4.For a baseline jet we require: 3 from Isajet 7.88 [39] for the model line introduced in the text.
For a baseline b-jet, besides the requirement for a baseline jet, we further require • the jet to be tagged as a b-jet by Delphes.
For a signal τ h -jet, besides the requirement of baseline jet, we further require • the jet must be a tagged hadronic tau-jet τ h by Delphes with For the baseline lepton isolation requirement, we require For a signal lepton, besides the requirement for baseline lepton isolation, we further require • |η e,(µ) | < 2.47 (2.5) and • p T (e(µ)) > 20 (25) GeV.

H
In this channel, we search for H ± → τ h + ̸E T along with the presence of a spectator t-jet which is signalled by the presence of a tagged b-jet.We include SM BGs from t t, single top, W b b, Zb b, W W , W Z, ZZ, Zh, W h and ht t production.We first require: • exactly one signal τ h -jet with no baseline leptons; the no baseline lepton requirement targets events where the spectator top decays hadronically, though of course events with a semileptonic decaying top could contribute if the lepton evades detection; • n(b − jet) ≥ 1, where b here (and in the rest of Sec. 5) refers to baseline b-jets, and • a neutrino reconstruction method4 is employed here.If the invariant mass of the reconstructed neutrino, the signal τ h -jet and any of the tagged baseline b-jets in the event reconstructs to m = m t ± 50 GeV, then the event is vetoed.
This latter requirement is imposed to veto a portion of the very large pp → t t background.With these remaining events, an examination of various distributions of signal and background (that we do not show for brevity) leads us to impose the following analysis cuts: , where b 1 is the leading baseline b-jet, and • min(∆R(b, τ h )) > 0.9, where the b loops over all tagged baseline b-jets in the event.
After these cuts, the resulting transverse mass distribution m T (τ h , ̸E T ) is shown in Fig. 4. As expected, the signal histograms peak around the value of m H ± , while the backgrounds yield falling distributions.Our goal in each signal channel is to look for an excess above the SM backgrounds in the largest transverse mass bins which are most sensitive to TeV-scale charged Higgs decay.From the distribution, the solid colored histograms represent the various BGs, of which the dominant is light yellow: t t.The signal distributions, labelled as dotted curves for several benchmark scenarios as listed, can emerge from BG at large values of m T , provided the signal is large enough.E T ) from pp → H ± (→ τ ν) + t + X followed by the decay τ → hadrons+ ̸E T .We also show dominant SM backgrounds.
• n(b − jet) ≥ 1 and • the neutrino reconstruction method described above is employed here.If the invariant mass of the reconstructed neutrino, the signal lepton plus any of the baseline b-jets in the event is within m = m t ± 50 GeV, then event is vetoed.
Standard Model backgrounds from t t, single top, W b b, W W , W Z, W h, ht t and Zh can also lead to the same event topology as the signal.
Examination of various distributions leads us to impose the following analysis cuts: )) > 150 GeV, where ∆ϕ is the azimuthal angle between the ⃗ ̸E T and the closest lepton or jet with p T > 25 GeV.The resultant m T (ℓ, ̸ E T ) distribution is displayed in Fig. 5.The dominant BG at low m T comes from t t production (light-yellow histogram) while the dominant BG at high m T comes from W W production.We also show several signal benchmark distributions (dotted curves) which may cause an excess of events over background expectations at high m T (ℓ, ̸E T ).In this case, the signal distributions shown will only cause a slight excess above background at high m T .But combined with the other channels, this signal channel can slightly increase the overall significance.

H ± → τ ν τ with t → bℓν ℓ channel
In this channel, we attempt to extract the signal from pp → tH ± production followed by H ± → τ h + ̸ E T but where the spectator t-quark decays semi-leptonically: t → bℓν ℓ .SM backgrounds from t t, single top, W W , W Z, W h, Zh and ht t production are included in our analysis.
We require: • exactly one signal lepton and no other baseline leptons, • exactly one signal τ h -jet, • the charges of the signal lepton and the τ h -jet must be OS (opposite-sign) and • n(b − jet) ≥ 1.
Examination of the resultant signal and background distributions leads us to the following additional analysis cuts: The resultant m T (τ h , ̸ E T ) distribution is shown in Fig. 6.The dominant BG at low m T again comes from t t production.At high m T , then the various signal histograms can cause a noticeable increase in the expected m T distribution beyond SM expectations, albeit with a rather low event rate.Figure 6: Distribution in m T (τ h , ̸E T ) from pp → H ± t + X followed by H ± → τ h + ̸E T decay and also t → bℓν ℓ decay.We also show dominant SM backgrounds.

LHC reach in H ± → τ ν τ channel
Using the analysis cuts for the various signal channels delineated above, we can now create reach plots to show the LHC14 discovery sensitivity or exclusion limits for pp → H ± t production in the m A vs. tan β plane.We use the 5σ level to claim discovery of a charged Higgs boson and assume the true distribution one observes experimentally corresponds to signal-plus-background.We then test this against the background-only distribution in order to see if the background-only hypothesis can be rejected at the 5σ level.Specifically, we use the binned transverse mass distributions (bin width of 25 GeV) from each signal channel as displayed above to obtain the discovery/exclusion limits.
In the case of the exclusion plane, the upper limits for exclusion of a signal are set at 95% CL; one assumes the true distribution one observes in experiment corresponds to backgroundonly.The limits are then computed using a modified frequentist CL s method [49] where the profile likelihood ratio is the test statistic.In both the exclusion and discovery planes, the asymptotic approximation for obtaining the median significance is employed [50].
In Fig. 7, we plot our result for the discovery/exclusion regions via the H ± → τ ν channel for the HL-LHC with √ s = 14 TeV and 3000 fb −1 of integrated luminosity in the m A vs.
tan β plane using our m 125 h (nat) benchmark scenario (which is quite typical for natural SUSY models [51]).In frame a), we plot the 5σ discovery reach using the combined three channels discussed previously.Above the dashed black line, experiments at the HL-LHC should be able to discover H ± at the LHC operating at √ s = 14 TeV, assuming an integrated luminosity of 3000 fb −1 .The green and yellow bands display the ±1σ and ±2σ uncertainties in our mapping of the discovery region.The region above the dashed blue line is excluded by ATLAS searches for H/A → τ τ events, albeit in a scenario with decoupled superpartners [46].From the plot, we see that a discovery region does indeed emerge, starting around m A ∼ 500 GeV and tan β ∼ 18 and extends out to m A ∼ 3 TeV for tan β ∼ 50 where both the σ(pp → tH ± + X) and the branching fraction for H + → τ ν τ decays are both enhanced.The discovery region pinches off below tan β ∼ 15 where the H ± → τ ν τ branching ratio becomes too small.
In frame b), we plot the 95% CL exclusion limit for HL-LHC for our combined three signal channels.The exclusion limit now extends out to beyond m A ∼ 3 TeV for large tan β ∼ 50.We also see that the exclusion contour extends to about tan β ∼ 10 for relatively light m H + ; however, this part of the plane is already excluded by ATLAS searches.

Search for H ± → tb
In this section, we examine the capability of HL-LHC to discover charged Higgs bosons in the H ± → tb decay channel.Recent limits have been placed within this search channel by the ATLAS collaboration using 139 fb −1 of data [35].Our analysis proceeds similarly to Sec. 5 except now we place an emphasis on the presence of high-p T top-jets in the final state.
In the following, we will use lower case letter such as j (b) to denote the small radius jets (tagged b-jets) while upper case letter such as J (T ) denote large radius jets (top-jets).
For a tagged baseline b-jet: • satisfy the above small radius jet requirements, • tagged b-jet by Delphes.
Also, for candidate events with an isolated lepton or a signal b-jet, we further require The analysis is then separated into four orthogonal channels depending on whether or not the final state does or does not contain a tagged T -jet, and whether or not it contains an isolated lepton.
In all cases, the small radius b-jet (denoted as b 1 below) arising directly from the H ± decay is determined by the following procedure.
• we require p T (b 1 ) > 350 GeV, • R(b 1 , J 1 ) > 1.5 (so this means b 1 must be outside the cone of the fat jet top candidate).
• m(j, j ′ , b 1 ) cannot be in the top mass range [125,225] GeV, where j, j ′ are any small radius jet pairs in the event.
• If multiple candidates satisfying these conditions are found, the one with the hardest p T is taken as b 1 .
• Events are vetoed if no b-jets satisfy these conditions.
Then, m(T 1 , b 1 ) is used to reconstruct the mass of the H ± in all cases.Note that in the channels where the HEPTopTagger2 has positively tagged a top-jet, i.e. the 1t, 1t1l channels, it is the four vector reconstructed by the algorithm that is taken as T 1 .But in the channels where HEPTopTagger2 fails to identify a top-jet, then it is the fat jet itself that is taken as the T 1 .
The m(T 1 , b 1 ) distributions are then shown as the final results for each signal channel.The background samples being considered for the hadronic channels [1t, 1t(no tag)] are t t (with ≥ 3 truth b's removed to avoid double counting with t tb b events that are separately simulated), single top, t tb b and tttt.The backgrounds for the semileptonic channels [1t1l, 1t(no tag)1l] are t t (again with ≥ 3 truth bs removed), t tb b and t tt t.We have not simulated t tV events as we require at least three b-jets which has been shown to be very small [55].

Single tagged top channel without signal leptons
In this channel, we search for pp → tH ± + X with H ± → tb decay.The primary t-quark in the tH ± final state tends to be non-central, and so rarely produces a tagged top-jet, but does more often produce a tagged b-jet.So for this channel, we focus on reconstructing the decay-produced top jet from H ± → tb, where TeV-scale charged Higgs decay gives rise to a well-collimated T -jet.Thus, • The HEPTopTagger2 algorithm that we use has tagged exactly one top from the large radius boosted (R < 1.5, p T (J) > 300 GeV) jet n T = 1.(This fat jet is denoted as J 1 below).
The top-jet four vector reconstructed by the HEPTopTagger2 is used as T 1 .The four vector for the subjet b reconstructed by the tagger is denoted as b 2 .We further require the following.
• At least 3 b-jets: n b ≥ 3, of which at least two of them must satisfy the signal b-jet requirements listed above.
Based on examination of various signal/background distributions, we also require • m(b, b ′ ) > 215 GeV, where the b and b ′ are the b-jet pair with the max p T in the events, • max(R(b ′ , H ± )) > 1.5, where the b ′ are any b-jets in events that are not b 1 and b 2 .The , where b ′ are any b-jets in the events.
At this point, we are able to construct the distribution m(tb) ≡ m(T 1 , b 1 ) shown in Fig. 8.The dominant background distributions are shown as solid colored histograms whilst several signal benchmark models are shown as dashed histograms.From the plot, we see that the signal distributions roughly reconstruct m(H ± ) while background is dominated by t tb b production at low mass, and by t t at high invariant mass.The goal then is to search for resonant signal bumps against the continuum of expected backgrounds.If this bump is buried under the SM background, this channel will make a negligible contribution to the significance when combined with other channels.

Single top (no tag) channel without signal leptons
In this channel, the HEPTopTagger2 fails to tag any tops.However, • there is at least one large radius boosted (R < 1.5, p T > 300 GeV) jet n J >= 1 with trimmed mass [56] 115 GeV < m J < 190 GeV, and at least one small radius (R < 0.4) b-jet within the cone of the large radius jet J.Then, the fat Jet with the hardest p T is taken as the top candidate arising directly from the charged Higgs decay (denoted as J 1 /T 1 ).The hardest b within J 1 /T 1 cone is taken as b 2 .
Figure 8: Distribution in m(tb) from pp → H ± t + X followed by H ± → tb decay.These events include a top-jet tagged by HEPTopTagger2.We also show dominant SM backgrounds.
• At least 3 b jets: n b ≥ 3, of which at least two of them must satisfy the signal b-jet requirements listed above.
We then require: The distribution m(tb), reconstructed from T 1 and b 1 , is shown in Fig. 9 where again the m(tb) roughly reconstructs m(H ± ) and where again the t t and t tb b are the dominant backgrounds.
Figure 9: Distribution in m(tb) from pp → H ± t + X followed by H ± → tb decay, but no fat jet tagged as top by HEPTopTagger2.We also show dominant SM backgrounds.

Single top (tagged) plus lepton channel
In this signal channel, we again require tagged top-jet, but now also require the presence of an isolated lepton arising from semileptonic decay of one of the tops.
We require • The HEPTopTagger2 has tagged exactly one top from the large radius boosted (R < 1.5, p T > 300 GeV) jet n T = 1.
As before the top four vector reconstructed by the HEPTopTagger2 is denoted as T 1 .The four vector for the subjet b reconstructed by the tagger is denoted as b 2 .
• At least 3 b-jets: n b ≥ 3, of which at least two of them must satisfy the signal b-jet requirements listed above.
We further require Figure 10: Distribution in m(tb) from pp → H ± t + X followed by H ± → tb decay, a fat jat tagged as a top-jet by HEPTopTagger2, and an isolated lepton from the decay of one of the top quarks.We also show dominant SM backgrounds.

Single top (no tag) plus lepton channel
In this channel, we examine events where the HEPTopTagger2 fails to tag any top jets but there is a lepton from the decay of one of the tops.We require, • there is at least one large radius boosted (R < 1.5, p T > 300 GeV) jet n J ≥ 1 with trimmed mass [56] 115 GeV < m J < 190 GeV, and at least one small radius (R < 0.4) b-jet within the cone of the large radius jet J.Then, the fat Jet is taken as the hardest p T top candidate directly from the charged Higgs decay (denoted as J 1 /T 1 ).The hardest b-jet within J 1 /T 1 is taken as b 2 .
• At least 3 b-jets: n b ≥ 3, of which at least two of them must satisfy the signal b-jet requirements listed above.
We also require The m(tb) distribution (again constructed by combining T 1 and b 1 ) for signal and background events with non-tagged top-jets and an isolated lepton is shown in Fig. 11.

LHC reach in H ± → tb channel
As in the H ± → τ ν τ analysis, after adopting the above cuts for the various signal channels, we can now create reach plots in terms of discovery sensitivity or exclusion limits for pp → H ± t+X followed by H ± → tb in the m A vs. tan β plane.In this case, we use the binned m(tb) distributions (bin width of 25 GeV) from each signal channel as displayed above to obtain the discovery/exclusion limits.
In Fig. 12, we show our results for the discovery/exclusion regions via the H ± → tb channel for the HL-LHC with √ s = 14 TeV and 3000 fb −1 of integrated luminosity in the m A vs. tan β plane using our m 125 h (nat) benchmark scenario.In frame a), we plot the 5σ discovery reach using the combined four H ± → tb signal channels listed above.The dashed black line denotes the computed reach while the green and yellow bands display the ±1σ and ±2σ uncertainty.From the plot, we see that a discovery region is indeed found, starting around m A ∼ 500 GeV and tan β ∼ 18.For these combined H ± → tb signal channels, the discovery region extends Figure 11: Distribution in m(tb) from pp → H ± t + X followed by H ± → tb decay.We also require that there is no fat jet tagged as a top-jet by HEPTopTagger2 but that there is an isolated lepton from the decay of one of the top quarks.We also show dominant SM backgrounds.out to m A ∼ 1.6 TeV for tan β ∼ 50.The discovery region pinches off below tan β ∼ 25 where the signal, after analysis cuts, becomes too small relative to the standard model background.Unfortunately, the entire discovery region lies within the portion of the plane that already appears to be excluded by the ATLAS search for H/A → τ τ decays [46].
In frame b), we plot the 95% CL exclusion limit for HL-LHC for our combined four signal channels.The exclusion limit now extends out to m A ∼ 2.1 TeV for large tan β ∼ 50, and well outside the ATLAS excluded region denoted by the dashed blue line.We also see that the exclusion contour extends somewhat below tan β ∼ 20 for lighter m H + ∼ 1 TeV.Also, a small exclusion region has now appeared at low tan β ∼ 3, which has also appeared in the ATLAS analysis [35].
Figure 12: In a), we plot the 5σ discovery region of the m A vs. tan β plane for pp → H ± t + X followed by H ± → tb decay for HL-LHC with 3000 fb −1 .In b), we plot the corresponding 95% CL exclusion region.The dashed blue line shows the boundary of the region excluded at the 95% confidence level in Ref. [46].
7 Search for H ± → SUSY at HL-LHC In Ref. [3], we examined s-channel production of heavy neutral SUSY Higgs bosons followed by decays to SUSY particles, where in natural SUSY H, A → gaugino+higgsino was the dominant decay mode (when kinematically open) except where tan β was very large.The heavier higgsinos decay to soft visible particles plus ̸E T whilst the gauginos decay via W, Z, h+ ̸E T .This led to discovery channels of H, A → W, Z, h+ ̸E T at HL-LHC, with accessible parameter regions mapped out in the m A vs. tan β plane for natSUSY in Ref. [3].The number of signal events after cuts were typically in the range of tens of events at best at HL-LHC with 3000 fb −1 of integrated luminosity.
The question here is then: are there lucrative charged Higgs H ± → SU SY decay channels available for HL-LHC?We saw in Fig. 3 that for moderate tan β and m H ± > m(gaugino) + m(higgsino) that the SUSY decay modes also become the dominant decay channels for charged Higgs bosons.And like their neutral Higgs counterparts, the final state configurations for H ± → SU SY end up being H ± → W, Z, h+ ̸E T according to the various charged Higgs and sparticle branching fractions from Isajet [39].
Thus, we have also examined the prospects for pp → tH ± → t+SU SY → t+(W, Z, h)+ ̸E T at HL-LHC.An essential difference of pp → tH ± + X compared to pp → H, A + X at LHC is that for a given heavy Higgs mass, the top-quark plus charged Higgs cross section is typically suppressed by an order of magnitude or more from s-channel neutral heavy Higgs production.A plot of charged Higgs production cross section times BF (H ± → SU SY ) in fb in the m A vs. tan β plane is shown in Fig. 13 for the m 125 h (nat) scenario.From the plot, for m A ≳ 1T eV where decays to SUSY particles begin to become important, the cross sections lie in the sub-fb regime.In addition, one typically tries to tag the spectator t-or b-jet in tH ± production which also leads to a reduction in signal level.Then one must factor in further SUSY decay branching fractions to W, Z, h+ ̸E T along with W, Z, h branching fractions into observable final states.The upshot is: the reduced signal channels compared to SM backgrounds t t, t tb b, t tW , t tZ, t th etc. did not lead to any compelling discovery channels that we could find.
8 Regions of the m A vs. tan β plane accessible to HL-LHC via charged and neutral Higgs boson searches in natSUSY We have found so far that a charged Higgs boson signal should be accessible to the HL-LHC in two different channels: H ± → τ ν τ and, to a lesser degree, via H ± → tb.The regions of the m A vs. tan β plane which are available to HL-LHC via 5σ discovery and 95% CL exclusion have been mapped out.At this point, it is worthwhile to compare the reach of HL-LHC via charged Higgs boson searches to the reach which can be achieved via s-channel H and A signals as delineated for natSUSY in Ref. [2] and [3].In Fig. 14, we plot out the 5σ reach of HL-LHC with 3000 fb −1 in the m A vs. tan β plane for heavy charged and neutral Higgs boson signals in the natSUSY scenario.The red dashed contour shows the computed 5σ discovery reach via the H, A → τ τ channel.Of all channels assessed so far, this provides the maximal discovery reach due to higher production cross sections pp → H, A+X, lower backgrounds in the ditau decay channel and the capability to reconstruct the ditau invariant mass m(τ τ ) using the ability to roughly reconstruct the missing neutrino momentum.The discovery region lies above the contour whch extends from tan β ∼ 8 for m A = 1 TeV to tan β ∼ 35 for m A = 2.4 TeV.The decay branching fraction for A → τ τ is of course enhanced by the well-known factor tan 2 β.Next most important is the yellow-dashed contour for pp → H, A with H, A → SU SY → (W, Z, h)+ ̸E T .These combined channels determine the ultimate reach and only turn on for m A ≳ 1 TeV where H, A → SU SY becomes kinematically accessible in the natSUSY scenario.The reach via SUSY decays is comparable with the H, A → τ τ reach for m A ∼ 1.2 TeV, but for m A ≳ 1.5 TeV, the reach via SUSY decays drops off more quickly for larger tan β values mainly because the H and A decays to SM fermions are enhanced by large Yukawa couplings, suppressing the branching fractions for decays to SUSY particles.The green-dashed contour denotes the HL-LHC 5σ discovery reach via pp → tH ± + X followed by H ± → τ ν τ decay.For a given m A , the pp → tH ± + X cross section is well below the resonantly enhanced pp → H, A and furthermore one cannot reconstruct a charged Higgs invariant mass via the H ± → τ ν channel: as a result, the reach via the charged Higgs channel is substantially less than the the reach via pp → H, A → τ τ .The blue dashed contour denotes the 5σ discovery reach for pp → tH ± + X with H ± → tb.This discovery region is mainly applicable at large tan β.Within the model, a substantial region of parameter space is accessible to HL-LHC via several discovery channels, but we should keep in mind that portions of this plane is excluded by the ATLAS search, albeit in a model with decoupled superpartners [46].
In Fig. 15, we show all four contours, but now as 95% CL exclusion limits, should no

Conclusions
In this paper we have investigated the ability of HL-LHC to discover the charged Higgs bosons of supersymmetric theories in the natural SUSY scenario.We believe that the natSUSY scenario is strongly motivated in that it naturally explains the measured magnitude of the weak scale which arises from a conspiracy of the weak scale soft terms: µ ∼ 100 − 400 GeV while m 2 Hu is radiatively driven to rather small negative values at the weak scale (EW symmetry is barely broken).Other sparticle masses can be much larger, lying in the TeV or beyond region since their contributions to the weak scale are suppressed (at least) by loop factors.Unnatural SUSY models which predict much higher values for m weak are regarded as rather implausible since they will require an unnatural conspiracy/finetuning of parameters in order to gain m weak ∼ 100 GeV.
The charged Higgs boson masses can range from their present lower limits from LHC searches up into the multi-TeV range (depending on tan β) with little cost to EW naturalness.Furthermore, once their masses exceed m(higgsino) + m(gaugino), then the decay to SUSY particles can become dominant.This reduces heavy Higgs decay to SM particle signals as expected in unnatural scenarios such as 2HDMs, but also opens up possible new avenues for heavy Higgs discovery.In this paper, we have delineated search strategies for charged Higgs bosons in both the H ± → τ ν τ and H ± → tb channels and have also computed the regions of m A vs. tan β parameter space which are accessible to HL-LHC as the 5σ and 95% CL contours.The HL-LHC reach for charged Higgs bosons is typically contained within the stronger reach via s-channel production of heavy neutrals H and A. For searches at the HL-LHC, decays of the charged Higgs boson to superpartners appear to be unimportant.Nonetheless, there do exist regions where all of H ± , H and A may be discovered.

Figure 2 :
Figure 2: The dominant pp → tH ± + X cross section at √ s = 14 TeV in the m A vs. tan β plane.The region to the left of the dashed blue line, is currently excluded at the 95% confidence level by limits from ATLAS searches for pp → H, A → τ + τ − [46].

where b 1
is the leading baseline b-jet and • min(∆R(b, ℓ)) > 1.2, where the b loops over all tagged baseline b-jets in the event.

where b 1
is the leading baseline b-jet and • min(∆R(b, τ h )) > 1.2, where the b loops over all baseline b-jets in the event.

Figure 7 :
Figure 7: In a), we show the 5σ discovery region of the m A vs. tan β plane for pp → H ± t + X followed by τ → ℓ+ ̸E T decay for HL-LHC with 3000 fb −1 .In b), we plot the corresponding 95% CL exclusion region.The region above the dashed blue curve is excluded by ATLAS searches for H/A → τ τ events.
where the b b ′ are the b-jet pairs with the max p T in the events,• max(R(b ′ , H ± )) > 2.4, where the b ′ are any b-jets in events that are not b 1 and b 2 .The H ± is reconstructed from T 1 , b 1 , • 0.8 < min(R(b ′ , b 1 )) < 2.8, where the b ′ are any b-jets in the events.
where the b, b ′ are the b pairs with the max p T in the events, • max(R(b ′ , H ± )) > 1.5, where b ′ are any b-jets in the events that are not b 1 and b 2 .The H ± is reconstructed from T 1 and b 1 .• min(R(b ′ , b 1 )) > 1, where the b ′ are any b-jets in the events, and • R(b 1 , l) > 0.9.The m(tb) invariant mass distribution from the signal BM models and backgrounds, again constructed by combining T 1 and b 1 , are shown in Fig. 10.In this case, the t tb b background is dominant in the range where m(tb) reconstructs m(H ± ).
where the b, b ′ are the b pairs with the max p T in the events, • max(R(b ′ , H ± )) > 1.1, where b ′ are any b-jets in the events that are not b 1 and b 2 .H ± is reconstructed from T 1 and b 1 , • min(R(b ′ , b 1 )) > 1, where b ′ are any b-jets in the events and • R(b 1 , l) > 0.9.

Figure 13 :
Figure 13: Plot of charged Higgs production cross section times BF (H ± → SU SY ) in fb in the m A vs. tan β plane for the m 125 h (nat) scenario.

Figure 14 :
Figure 14: Plot of 5σ discovery projections for heavy SUSY Higgs boson searches at HL-LHC in the m A vs. tan β plane for the m 125 h (nat) scenario.

Figure 15 :
Figure 15: Plot of 95% CL exclusion projections for heavy SUSY Higgs boson searches at HL-LHC in the m A vs. tan β plane for the m 125 h (nat) scenario.

•
[12]|m 2 H d | ≫ |m 2 Hu | or µ 2 , then |m H d | sets the heavy Higgs mass scale (m A,H,H ± ∼ |m H d |) while |m Hu | sets the mass scale for m W,Z,h .Then, assuming that m H ± ≫ M W , naturalness requires[12]