1. 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 the 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 performed in this field (for numerous references, see
Section 1.1), 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
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
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 gaugino+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
. 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 is still maintained under the rubric of natural SUSY.
We take the experimental value of the
Z-boson mass to represent the magnitude of weak scale. In the MSSM, the
is related to the weak scale Lagrangian parameters via the electroweak minimization condition
where
and
are the Higgs soft SUSY breaking mass parameters,
is the (SUSY preserving) superpotential higgsino mass parameter and the
and
terms contain various loop corrections (detailed in the Appendix of Ref. [
4] and see also [
5] for leading two-loop corrections). We consider the value of an observable
is natural if all
independent contributions to
are comparable to (within a factor of few), or smaller than
. For natural SUSY models, we use the naturalness measure [
4,
6].
and take
to be natural. In many SUSY models, the
-parameter is adjusted to precisely balance large SUSY breaking contributions in Equation (
1). Since the
parameter typically arises from very different physics than SUSY breaking, this “just-so” cancellation, though logically possible, seems rather implausible compared to the case where all the terms in Equation (
1) are
, so that
does not need not be tuned.
Implications of Equation (
3) relevant to heavy SUSY Higgs searches at the LHC include:
The superpotential higgsino mass parameter directly enters , leading to GeV. This, in turn, implies that for heavy Higgs searches with the SUSY decay modes of should typically be kinematically allowed. If these additional decay widths to SUSY particles are significant, the branching fractions to the SM search modes (typically used for LHC searches for bosons) would be correspondingly reduced.
For
or
, then
sets the heavy Higgs mass scale (
) while
sets the mass scale for
. Then, assuming that
, naturalness requires [
7]
For
with
, the value of
can be as large as
TeV, while maintaining naturalness. For
,
stays natural up to
TeV (although for large
, bottom squark contributions to
become large and provide stronger upper limits on natural SUSY spectra [
8]).
In
Section 2, we first present a natural SUSY benchmark point which then leads to a natural SUSY Higgs scenario, which we previously dubbed
. The
scenario is promoted as a template for SUSY Higgs searches in that [
2] (1) it leads to a value of
GeV throughout almost the entire
vs.
search plane and (2) the value of
is also low (though sometimes exceeding a value of 30 at higher
values) throughout the search plane. In
Section 3, we list the dominant charged SUSY Higgs boson production cross-sections at LHC14 (LHC with
center-of-mass energy
TeV). It is well-known that the
subprocesses is the dominant
production mechanism at the LHC [
9,
10,
11]. In
Section 4, we present charged Higgs boson branching fractions from the
scenario in the
vs.
plane, and find that indeed SUSY decay modes do become rapidly dominant once these are kinematic accessible. In
Section 5, we examine
followed by
and map out distributions that help obtain signals over SM background levels. In
Section 6, we examine
followed by
decay. In
Section 7, we study the impact of the SUSY decays of
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
do not offer a viable search strategy. In
Section 8, we plot out the reach of high-luminosity LHC for charged Higgs bosons of natural SUSY. Our summary and conclusions are contained in
Section 9.
1.1. A Synopsis of Related Work
Here, we present a brief synopsis of related studies on charged Higgs bosons from SUSY. In Ref. [
12], it was already emphasized that the detection of a top quark signal in accord with SM expectations would preclude the decay
and thus require
. In light of present
signal results, this implies
GeV. This result was already used by Kunszt and Zwirner in Ref. [
13] to form the low
limit of the proposed
vs.
heavy SUSY Higgs search plane. Decays of heavy SUSY Higgs boson to SUSY decay modes were originally explored in Refs. [
14,
15,
16,
17] and the complete set of
decay widths may be found in Appendix C of [
1]. In Ref. [
7], these decay modes were examined in the natural SUSY framework. In this study, it was observed that for
channels, the light higgsinos are essentially invisible because their decays mainly yield soft, quasi-visible SM particles (soft leptons from higgsino decays are a notable exception), whilst the winos dominantly decay via two-body modes into
,
and
, where the
and
h typically have large transverse momentum.
In Refs. [
9,
10,
11], it was found that the dominant production process for charged Higgs bosons at LHC was the reaction
NLO corrections to this production process were calculated in Refs. [
18,
19,
20]. Signals from the final state
were examined in Refs. [
21,
22]. The decay channel
(which is highly suppressed in natSUSY) was examined in Ref. [
23]. The use of three [
24] and four [
25]
b-quark tags in
was examined. Corrections to the
vertex were examined in Ref. [
26]. Initial projections of the LHC reach for (charged) SUSY Higgs bosons were given by Denegri et al. [
27] and by Assamagan et al. [
28]. Search limits from LHC for the
decay mode were presented based on
fb
of integrated luminosity by ATLAS [
29] and by CMS [
30]. An ATLAS search for charged Higgs bosons in the
mode based on 139 fb
was given in Ref. [
31]. A guidebook for LHC searches for SUSY and non-SUSY charged Higgs bosons was provided in Ref. [
32] and a review of non-SUSY charged Higgs is available in Ref. [
33].
2. A Natural SUSY Benchmark Point and the Scenario
Following our previous work, we here adopt the same natural SUSY benchmark point as in Ref. [
3], which was labeled
because the value of
is naturally very close to its measured value throughout the entire
vs.
plane. We use the non-universal Higgs model (NUHM2) [
34], which has two additional parameters relative to the much-studied mSUGRA/CMSSM framework. The six parameters,
then completely specify the NUHM2 model. Notice that
now appears as an independent parameter. The fact that it can be set to be within the natural range,
100–350 GeV, greatly facilitates the phenomenological examination of natural SUSY models (The NUHM2 framework really accommodates independent soft SUSY breaking mass parameters for the scalar fields
and
in the Higgs sector, but leaves the matter scalar mass parameters universal to avoid flavor problems. The parameters
and
are then traded for
and
in the parameter set shown in (
5)). We adopt the following natural SUSY benchmark Higgs search scenario:
A similar
benchmark model spectrum, but with
GeV and
TeV, was shown in Table 1 of Ref. [
2] for
and
TeV and so for brevity we do not show the revised spectrum here. We adopt the computer code Isajet [
35] featuring Isasugra for spectrum generation. The SUSY Higgs boson masses are computed using renormalization-group (RG) improved third generation fermion/sfermion loop corrections [
36]. The RG improved Yukawa couplings include full threshold corrections [
37] which account for leading two-loop effects [
38]. For
and
TeV, we note that 1)
so the model is indeed EW natural, and 2) the resulting superpartner and the light Higgs boson masses are all consistent with LHC Run 2 SUSY search constraints; specifically,
GeV,
TeV and
TeV, with other squark and all slepton masses
TeV. Most important for our purpose, the two lightest neutralinos,
and
, and the lighter chargino,
, are higgsino-like with masses
GeV while the neutralino
is bino-like with a mass of 450 GeV and the heaviest neutralino and the heavier chargino have masses
TeV. Thus, the
decay modes turn on for
TeV (although
turns on at somewhat lower
values). It is important to note that while the value of
may change somewhat for small variations of the parameters that are held fixed in Equation (
5), we expect that the Higgs sector phenomenology is relatively insensitive to our specific choice (as long as
GeV to maintain naturalness).
Although not directly related to the main subject of this paper, we note that the lightest higgsino of natSUSY models can constitute only a fraction of the observed dark matter if it is a
thermal relic of standard Big Bang cosmology. The remainder of the dark matter could, e.g., be axions, or something else. One would also need to ensure that the spin-independent neutralino–nucleon cross-section is not in conflict with experimental bounds [
39]. We are not greatly concerned about this because the neutralino relic density can be further diluted by late decays of saxions or moduli [
40] into standard model particles. The bottom line is that dark matter physics is a model-dependent issue only tenuously connected to LHC signals for heavy Higgs bosons [
41].
3. Production Cross-Sections at LHC14
In
Figure 1, we show leading order total cross-sections for the production of charged SUSY Higgs bosons at LHC14, as generated using Pythia [
42] for two values of
(solid) and 40 (dashed). We show cross sections for charged Higgs boson production at the LHC via
production (blue), resonant
production (light green),
production (light blue), and
(magenta),
(green) and
(red) production.
We see from
Figure 1 that the dominant production mechanism at LHC14 is via the
subprocess [
9,
10,
11]. For
, the cross section varies from
fb at low
to
fb at
TeV. These dominant cross-sections are enhanced by large
. If we compare
production to the rate for
production [
2] for
and
TeV, we find that charged Higgs production rates are suppressed compared to resonance production of
A by a factor
. And since
, charged Higgs production compared to resonance
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 via (Yukawa suppressed) fusion or via (parton distribution function suppressed) fusion. Note that this is suppressed relative to neutral resonance production from 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 enhancement due to the Yukawa couplings involved in the production mechanism. The resonance production cross-section is typically about two orders of magnitude below associated production.
The next largest production cross-sections are and which are produced via exchange followed closely by pair production, which takes place via s-channel and exchange. All these production vertices involve gauge interactions and so are independent. As a result, the 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 cross-sections.
In magenta, we show
-associated production, which occurs dominantly via
s-channel
exchange where the production vertex includes a factor
(see Equation (8.110) of Ref. [
1]) (The convention for Higgs mixing angle
in Ref. [
1] differs from often-used conventions, which result in the mixing angle factor
), which vanishes in the decoupling limit. As a result, these cross-sections are suppressed from the dominant
cross section by ∼3–5 orders of magnitude depending on
and
. They also feature a dip at certain values of
, which occurs when the Higgs mixing angle
is such that
. An additional cross-section
occurs at the loop level, and so is highly suppressed and we do not include it here: see Ref. [
43].
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
production process. In
Figure 2, we show the values of
at LHC14 in the
vs.
plane for our
scenario. The largest cross-sections
fb are denoted by dark red whilst the lowest cross-sections
fb are denoted dark blue. We also show the latest ATLAS 95% CL exclusion limit from their search for
events using LHC13 with 139 fb
in several non-natural Higgs scenarios, which nonetheless maintain
GeV [
44]. Thus, to uncover new physics at HL-LHC in the SUSY Higgs sector, we will mainly focus our attention on
values in the TeV range.
4. Branching Fractions in natSUSY
The LHC signal from charged Higgs boson production will clearly depend on how
decays. For TeV scale values of
, the dominant SM decays are via
and
. 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
Figure 3, we show the most relevant
branching fractions (BFs) in the
vs.
plane for the model plane (Equation (
5)). The various ranges of branching fractions are shown by different colors, with the larger ones denoted by red and orange, turning to shades of green and blue culminating in the smallest branching fractions denoted by dark blue. The branching fractions are extracted from the Isasugra code [
35].
In
Figure 3a, we show the BF for
. This decay mode to SM particles is indeed dominant for
TeV and for larger values of
20–30. In frame (b), we show the BF(
). Like
, this mode is enhanced at large
and has provided the best avenue for SUSY charged Higgs discovery/exclusion plots so far.
While SUSY decay modes of
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
labels various matter and Higgs scalar fields of the MSSM,
is the fermionic superpartner of
and
is the gaugino with gauge index
A (and the bar indicates Dirac-conjugate). Also,
g is the corresponding gauge coupling for the gauge group in question and the
are the corresponding gauge group matrices. Choosing
be the Higgs scalar fields, it is clear that there is a full-strength coupling, unsuppressed by small mixing angles, of the Higgs scalars to a gaugino and a higgsino. This interaction term results in Higgs boson decays to SUSY particles as long as the gaugino-plus-higgsino decay channel is kinematically unsuppressed. Note that the same reasoning also shows why the heavy Higgs decay to higgsino pairs is suppressed by mixing angles for
, once we recognize that a Higgs boson–higgsino-higgsino coupling is forbidden by gauge invariance.
In frame (c), we show BF(
), where
is dominantly higgsino-like and
is dominantly wino-like for natural SUSY models like the
scenario. Here, we see that for larger values of
TeV, this mode turns on, and at least for moderate
10–20 (which is favored by naturalness [
7]), rapidly comes to dominate the
decay modes along with the neutral wino+higgsino channels
(frame (d)) and
(frame (e)). In our analysis, we have assumed that the gaugino mass parameters unify at the high scale, so that at the weak scale
: as a result,
is dominantly bino-like,
and
are dominantly wino-like, while
and
are mainly higgsino-like. The sum of the three wino+higgsino decay channels dominates the
decay branching fractions for
TeV and low-to-moderate values of
. For high values of
, the
b and
Yukawa couplings become large, and SM decays to fermions once again dominate SUSY decays. Decays of
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
, which is to higgsino+bino. This mode is large only in a small region of
TeV and modest
where the mode
decay has turned on, but where
has yet to become kinematically open. Decays to winos dominate decays to binos because the
gauge coupling
g is larger than the hypercharge gauge coupling
.
5. Search for
Next, we turn to the examination of the prospects for discovering the charged Higgs boson produced at the HL-LHC via
, followed by
decay. For signal and
background processes listed below, we use the Pythia event generator [
42]. For
BG processes such as
,
and
production, we adopt Madgraph [
45] 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 [
46] detector simulation program, which includes a jet-finding algorithm and routines for identifying both
b-jets and hadronic tau jets (labeled as
) (we use the default Delphes configuration card, Delphes-card-HLLHC, for our simulation of events at the high luminosity LHC).
In Delphes, a jet object is reconstructed using an anti-k algorithm with GeV and . For a baseline jet, we require:
For a baseline b-jet, besides the requirement for a baseline jet, we further require
For a signal -jet, besides the requirement of a baseline jet, we further require
For the baseline lepton isolation requirement, we require
For a signal lepton, besides the requirement for baseline lepton isolation, we further require
5.1. E/T Channel
In this channel, we search for E/T along with the presence of a spectator t-jet, which is signaled by the presence of a tagged b-jet. We include SM BGs from , single top, , , , , , , and production. We first require:
Exactly one signal -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;
, where
b here (and in the rest of
Section 5) refers to baseline
b-jets,
A neutrino reconstruction method (in events where one of the tops decays hadronically, and the other leptonically, so that the E/T comes only from the (massless) neutrino; i.e., , one can construct assuming that the W boson from top decay is on-shell. This vetoes about half the potentially enormous background with a loss of less than 10% of the signal) is employed here. If the invariant mass of the reconstructed neutrino, the signal -jet and any of the tagged baseline b-jets in the event reconstructs to GeV, then the event is vetoed.
This latter requirement is imposed to veto a portion of the very large 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:
GeV,
,
, where is the leading baseline b-jet,
, where the b loops over all tagged baseline b-jets in the event.
After these cuts, the resulting transverse mass distribution
is shown in
Figure 4. As expected, the signal histograms peak around the value of
, 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:
. The signal distributions, labeled as dotted curves for several benchmark scenarios as listed, can emerge from BG at large values of
, provided the signal is large enough.
5.2. Channel
In this subsection, we examine the production reaction where followed by the channel, where or . For this signal channel, we require:
Exactly one signal lepton and no other baseline leptons,
No jets have been -tagged (-veto); here, we are again targeting events where the top decays hadronically, and the tau decays leptonically.
,
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 GeV, then the event is vetoed.
Standard model backgrounds from , single top, , , , , and can also lead to the same event topology as the signal.
Examination of various distributions leads us to impose the following analysis cuts:
GeV,
GeV, where is the azimuthal angle between the and the closest lepton or jet with GeV.
,
, where is the leading baseline b-jet and
, where the b loops over all tagged baseline b-jets in the event.
The resultant
distribution is displayed in
Figure 5. The dominant BG at low
comes from
production (light-yellow histogram) while the dominant BG at high
comes from
production. We also show several signal benchmark distributions (dotted curves) which may cause an excess of events over background expectations at high
. In this case, the signal distributions shown will only cause a slight excess above background at high
. But combined with the other channels, this signal channel can slightly increase the overall significance.
5.3. with Channel
In this channel, we attempt to extract the signal from production followed by , but where the spectator t-quark decays semi-leptonically: . SM backgrounds from , single top, , , , and production are included in our analysis.
We require:
Exactly one signal lepton and no other baseline leptons,
Exactly one signal -jet,
The charges of the signal lepton and the -jet must be OS (opposite-sign),
.
Examination of the resultant signal and background distributions leads us to the following additional analysis cuts:
GeV,
GeV,
,
,
, where is the leading baseline b-jet,
, where the b loops over all baseline b-jets in the event.
The resultant
distribution is shown in
Figure 6. The dominant BG at low
again comes from
production. At high
, then the various signal histograms can cause a noticeable increase in the expected
distribution beyond SM expectations, albeit with a rather low event rate.
5.4. LHC Reach in Channel
Using the analysis cuts for the various signal channels delineated above, we can now make plots to illustrate the LHC14 discovery sensitivity or exclusion limits for production in the vs. plane. We use the level to claim the discovery of a charged Higgs boson, assuming that the true distribution one observes experimentally corresponds to signal-plus-background. Our aim here is to compare this distribution against the background-only distribution in order to see if the background-only hypothesis can be rejected at the 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 (and also exclusion) limits.
For our studies of what experiments at the LHC might rule out should they not see a significant signal above the standard model backgrounds, we adopt 95% CL as the limit for exclusion, assuming that the true distribution in experiment corresponds to background-only. We then compute the limits using a modified frequentist
method [
47] where the profile likelihood ratio is the test statistic. For both the exclusion and discovery planes, we use the asymptotic approximation for obtaining the median significance [
48].
In
Figure 7, we plot our result for the discovery/exclusion regions via the
channel for the HL-LHC with
TeV and 3000 fb
of integrated luminosity in the
vs.
plane using our
benchmark scenario. In frame (a), we plot the
discovery reach using the combined three channels discussed previously. The
channel discussed in
Section 5.1 is by far the largest contributor to the significance that yields this reach, with the
channel of
Section 5.3 making up most of the remainder. The
channel of
Section 5.2 constributes only a tiny amount to the significance. Above the dashed black line, experiments at the HL-LHC should be able to discover
at the LHC operating at
TeV, assuming an integrated luminosity of 3000 fb
. The green and yellow bands display the
and
uncertainties in our mapping of the discovery region. The region above the dashed blue line is excluded by ATLAS searches for
events, albeit in a scenario with decoupled superpartners [
44]. From the plot, we see that a discovery region does indeed emerge, starting around
GeV and
and extends out to
TeV for
where both the
and the branching fraction for
decays are enhanced. The discovery region pinches off below
where the
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 TeV for large . We also see that the exclusion contour extends to about for relatively light ; however, this part of the plane is already excluded by ATLAS searches.
6. Search for
In this section, we examine the capability of HL-LHC to discover charged Higgs bosons in the
decay channel. Recent limits have been placed within this search channel by the ATLAS collaboration using 139 fb
of data [
31]. Our analysis proceeds similarly to
Section 5 except now we place an emphasis on the presence of high-
top-jets in the final state.
In the following, we will use lower case letters such as j (b) to denote the small radius jets (tagged b-jets) while upper case letters such as J (T) denote large radius jets (top-jets).
The parameters for baseline reconstructed particles are, for charged lepton l:
For small radius jet j:
For a tagged baseline b-jet:
For a large radius jet J:
Jet reconstruction using the Cambridge/Aachen algorithm (CA) [
49,
50],
Cone size ,
GeV,
.
For a tagged top-jet T:
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 below) arising directly from the decay is determined by the following procedure.
We require GeV,
,
(so this means must be outside the cone of the fat jet top candidate).
cannot be in the top mass range GeV, where j, are any small radius jet pairs in the event.
If multiple candidates satisfying these conditions are found, the one with the hardest is taken as .
Events are vetoed if no b-jets satisfy these conditions.
Then, is used to reconstruct the mass of the in all cases. Note that in the channels where the HEPTopTagger2 has positively tagged a top-jet, i.e., the channels, it is the four vector reconstructed by the algorithm that is taken as . But in the channels where HEPTopTagger2 fails to identify a top-jet, then it is the fat jet itself that is taken as the . The distributions are then shown as the final results for each signal channel.
The background samples being considered for the hadronic channels
are
(with
truth
bs removed to avoid double counting with
events that are separately simulated), single top,
and
. The backgrounds for the semileptonic channels
are
(again with
truth
bs removed),
and
. We have not simulated
events as we require at least three
b-jets, which have been shown to be very small [
52].
6.1. Single Tagged Top Channel without Signal Leptons
In this channel, we search for with decay. The primary t-quark in the 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 , where TeV-scale charged Higgs decay gives rise to a well-collimated T-jet. Thus,
The top-jet four vector reconstructed by the HEPTopTagger2 is used as . The four vector for the subject b reconstructed by the tagger is denoted as . We further require the following.
At least 3 b-jets: , of which at least two of them must satisfy the signal b-jet requirements listed above.
At least 6 jets: .
No isolated leptons: .
Based on examination of various signal/background distributions, we also require
GeV,
GeV, where the b and are the b-jet pair with the max in the events,
, where the are any b-jets in events that are not and . The is reconstructed from , ,
, where are any b-jets in the events.
At this point, we are able to construct the distribution
shown in
Figure 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
while the background is dominated by
production at low mass, and by
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.
6.2. 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 (
,
GeV) jet
with trimmed mass [
53]
GeV, and at least one small radius (
)
b-jet within the cone of the large radius jet
J. Then, the fat Jet with the hardest
is taken as the top candidate arising directly from the charged Higgs decay (denoted as
). The hardest
b within
cone is taken as
.
At least 3 b jets: , of which at least two of them must satisfy the signal b-jet requirements listed above.
At least 6 jets: ,
No isolated leptons: .
We then require:
GeV,
GeV, where the b are the b-jet pairs with the max in the events,
, where the are any b-jets in events that are not and . The is reconstructed from , ,
, where the are any b-jets in the events.
The distribution
, reconstructed from
and
, is shown in
Figure 9 where again the
roughly reconstructs
and where again the
and
are the dominant backgrounds.
6.3. Single Top (Tagged) Plus Lepton Channel
In this signal channel, we again require a tagged top-jet, but now also require the presence of an isolated lepton arising from the semileptonic decay of one of the tops.
We require
The HEPTopTagger2 has tagged exactly one top from the large radius boosted (, GeV) jet .
As before, the top four vectors reconstructed by the HEPTopTagger2 are denoted as . The four vectors for the sub-jet b reconstructed by the tagger are denoted as .
At least 3 b-jets: , of which at least two of them must satisfy the signal b-jet requirements listed above.
At least 4 jets: .
Exactly one signal isolated leptons: .
We further require
GeV,
GeV, where the b, are the b pairs with the max in the events,
, where are any b-jets in the events that are not and . The is reconstructed from and .
, where the are any b-jets in the events, and
.
The
invariant mass distribution from the signal BM models and backgrounds, again constructed by combining
and
, are shown in
Figure 10. In this case, the
background is dominant in the range where
reconstructs
.
6.4. 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 (
,
GeV) jet
with trimmed mass [
53]
GeV, and at least one small radius (
)
b-jet within the cone of the large radius jet
J. Then, the fat jet is taken as the hardest
top candidate directly from the charged Higgs decay (denoted as
). The hardest
b-jet within
is taken as
.
At least 3 b-jets: , of which at least two of them must satisfy the signal b-jet requirements listed above.
At least 6 jets: .
Exactly one signal isolated lepton: .
We also require
GeV,
GeV, where the b, are the b pairs with the max in the events,
, where are any b-jets in the events that are not and . is reconstructed from and ,
, where are any b-jets in the events and
.
The
distribution (again constructed by combining
and
) for signal and background events with non-tagged top-jets and an isolated lepton is shown in
Figure 11.
6.5. LHC Reach in Channel
As in the analysis, after adopting the cuts listed above for the various signal channels, we can now create reach plots for the LHC discovery sensitivity or exclusion limits from followed by in the vs. plane. In this case, we use the binned distributions (bin width of 25 GeV) from each signal channel as displayed above to obtain the discovery/exclusion limits.
In
Figure 12, we show our results for the discovery/exclusion regions via the
channel for the HL-LHC with
TeV and 3000 fb
of integrated luminosity in the
vs.
plane using our
benchmark scenario. In frame (a), we plot the
discovery reach using the combined four
signal channels listed above. The dashed black line denotes the computed reach while the green and yellow bands display the
and
uncertainty. From the plot, we see that a discovery region is indeed found, starting around
GeV and
. For these combined
signal channels, the discovery region extends out to
TeV for
. The discovery region pinches off below
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
decays [
44].
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
TeV for large
, and well outside the ATLAS excluded region denoted by the dashed blue line. We also see that the exclusion contour extends somewhat below
for lighter
TeV. Also, a small exclusion region has now appeared at low
, which has also appeared in the ATLAS analysis [
31].
7. Search for 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
was the dominant decay mode (when kinematically open) except where
was very large. The heavier higgsinos decay to soft visible particles plus
whilst the gauginos decay via
. This led to the discovery channels of
at HL-LHC, with accessible parameter regions mapped out in the
vs.
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
of integrated luminosity.
The question here is then: are there lucrative
charged Higgs
decay channels available for HL-LHC? We saw in
Figure 3 that for moderate
and
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
end up being
according to the various charged Higgs and sparticle branching fractions from Isajet [
35].
Thus, we have also examined the prospects for
at HL-LHC. An essential difference of
compared to
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
in fb in the
vs.
plane is shown in
Figure 13 for the
scenario. From the plot, for
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
production which also leads to a reduction in signal level. Then one must factor in further SUSY decay branching fractions to
along with
branching fractions into observable final states. The upshot is: the reduced signal channels compared to SM backgrounds
,
,
,
,
etc. did not lead to any compelling discovery channels that we could find.
8. Regions of the vs. 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:
and, to a lesser degree, via
. The regions of the
vs.
plane, which are available to HL-LHC via
discovery and
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 Refs. [
2,
3].
In
Figure 14, we plot out the
reach of HL-LHC with 3000 fb
in the
vs.
plane for heavy charged and neutral Higgs boson signals in the natSUSY scenario. The red dashed contour shows the computed
discovery reach via the
channel. Of all channels assessed so far, this provides the maximal discovery reach due to higher production cross-sections
, lower backgrounds in the ditau decay channel and the capability to reconstruct the ditau invariant mass
using the ability to roughly reconstruct the missing neutrino momentum. The discovery region lies above the contour which extends from
for
TeV to
for
TeV. The decay branching fraction for
is of course enhanced by the well-known factor
.
Next most important is the yellow-dashed contour for
with
. These combined channels determine the ultimate reach and only turn on for
TeV where
becomes kinematically accessible in the natSUSY scenario. The reach via SUSY decays is comparable with the
reach for
TeV, but for
TeV, the reach via SUSY decays drops off more quickly for larger
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
discovery reach via
followed by
decay. For a given
, the
cross section is well below the resonantly enhanced
and furthermore one cannot reconstruct a charged Higgs invariant mass via the
channel: as a result, the reach via the charged Higgs channel is substantially less than the the reach via
. The blue dashed contour denotes the
discovery reach for
with
. This discovery region is mainly applicable at large
. 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 [
44].
In
Figure 15, we show all four contours, but now as 95% CL exclusion limits, should no signal appear at the HL-LHC. For
TeV, the main exclusion would come from not discovering
while for lower
TeV the main exclusion come from not discovering
, where the exclusion contour dips to very low
(where
becomes lighter than 125 GeV). The charged Higgs exclusion contours are contained within the
exclusion contour.
9. 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: 100–400 GeV while 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 that predict much higher values for are regarded as rather implausible since they will require an unnatural conspiracy/finetuning of parameters in order to gain GeV.
The charged Higgs boson masses can range from their present lower limits from LHC searches up into the multi-TeV range (depending on ) with little cost to EW naturalness. Furthermore, once their masses exceed , 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 and channels and have also computed the regions of vs. parameter space, which are accessible to HL-LHC as the 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 and A may be discovered.