Signal versus Background Interference in $H^+\to t\bar b$ Signals for MSSM Benchmark Scenarios

In this paper, we investigate sizeable interference effects between a heavy charged Higgs boson signal produced via $gg\to t\bar b H^-$ (+ c.c.) followed by the decay $H^-\to b\bar t$ (+ c.c.) and the irreducible background given by $gg\to t\bar t b \bar b$ topologies at the Large Hadron Collider (LHC). We show how such effects could spoil current $H^\pm$ searches where signal and background are normally treated separately. The reason for this is that a heavy charged Higgs boson can have a large total width, in turn enabling such interferences, altogether leading to very significant alterations, both at the inclusive and exclusive level, of the yield induced by the signal alone. This therefore implies that currently established LHC searches for such wide charged Higgs bosons require modifications. We show such effects quantitatively using two different benchmark configurations of the minimal realisation of Supersymmetry, wherein such $H^\pm$ states naturally exist.


Introduction
After the discovery of a Higgs-like particle at Large Hadron Colliders (LHC) a few years ago [1,2], a significant amount of both theoretical and experimental activities have taken place trying to identify the nature of this object.The mass of such a particle and its couplings to some Standard Model (SM) particles are now measured with a good precision [3,4].Their values indicate that such a Higgs-like particle is light and its properties (spin, CP quantum numbers and interactions) are consistent with those of the SM Higgs boson.
However, there are many theoretical and experimental indications that show that the SM can only be an effective theory of a more fundamental one that still needs to be discovered.Many Beyond the SM (BSM) scenarios have been put forward over the years and it is fair to say that one stems as the most appealing one -Supersymmetry (SUSY).This is because it solves the well-known hierarchy problem of the SM by protecting the Higgs mass from unstable higher order corrections thanks to the new symmetry between fermions and bosons that it predicts [5].Furthermore, SUSY also has the capability to address the Dark Matter (DM) and gauge unification problems of the SM, indeed, without any proliferation of fundamental parameters if one assumes that SUSY can in turn be viewed as an effective realisation of some Grand Unified Theory (GUT), like Supergravity [6,7].The Minimal Supersymmetric Standard Model (MSSM) is the simplest realisation of SUSY that predicts a light Higgs boson that can be identified as the observed 125 GeV Higgs-like particle and can be as successful as the SM when confronted with experimental data, yet it can surpass it in all the above respects.
The Superpotential of the MSSM has to be holomorphic, thus one needs to introduce at least two Higgs doublets fields, one more than in the SM.One of these generates masses for up quarks and the other one generate masses for down quarks and charged leptons.From the 8 degrees of freedom present in such a 2-Higgs Doublet Model (2HDM), 3 are acquired by the longitudinal components of the gauge bosons W ± and Z 0 , so that the latter get a mass too, and the remaining 5 appears as new Higgs particles: 2 CP-even h and H (with m h < m H ), one CP-odd A and a pair of charged ones H ± .Discovery of any such new states would be unmistakable evidence of BSM physics, yet, only charged Higgs states would be a clear hint towards a 2HDM structure, as required by the MSSM, as additional neutral Higgs states could be attributed to singlet structures entering an extended Higgs sector.
At a hadron collider, production of charged Higgs bosons proceeds through many channels.If the charged Higgs boson is light (i.e., m H ± < m t + m b ), it can be produced from top or anti-top decay: i.e., gg, q q → t t followed by, e.g., t → bH − (+ c.c.).Given the fact that the t t cross section is very large, this mechanism would give an important source of light charged Higgs states.After the top-bottom threshold (i.e., m H ± > m t +m b ), a charged Higgs boson can be produced in association with top-bottom pairs, i.e., bg → tH − [8].In fact, these two channels are captured at once by the gg → H − t b (+ c.c.) 'complete' process, as explained in [9,10].There exist other production mechanisms too, such as pp → H + H − , pp → A 0 H ± , pp → H ± W ∓ , etc. which are however subleading compared to the previous ones1 .
At the LHC, a light charged Higgs boson, with m H ± < m t + m b , can be detected from t t production followed by top or anti-top quark decay t → bH + if the H − state decays dominantly to τ ν.ATLAS and CMS have already set a limit on BR(t → bH + ) × BR(H + → τ ν) [12,13], which can be translated into a limit on the (m H ± , tan β) plane, where tan β is the ratio of the two Higgs doublet vaccuum expectation values (VEVs).In the MSSM, charged Higgses with mass less than about 160 GeV are ruled out for almost any value of tan β (only a small area for tan β ≈ m t /m b remains open).However, heavy charged Higgs states, with m H ± > m t + m b , would decay dominantly into t b, which is a rather difficult final state to extract due to large reducible and irreducible backgrounds associated with jets emerging from H − → tb decays.Even then, one could still get a moderate signal from such a channel for small tan β ≤ 1.5 or large tan β ≥ 40 [14,15].Another possibility for detecting heavy charged Higgs states would be the search for H + → τ ν τ (i.e., like the preferred one for a light state), which enjoys a smaller background in comparison.At the LHC Run 2, both channels have been searched for and no excess over the background only hypothesis have been reported.Therefore, limits are set on σ(pp → tH − ) × BR(H − → tb/τ ντ ) (+ c.c.) [16][17][18].In the MSSM, one can have additional SUSY channels that can contribute to H ± production and/or decay, e.g., production from squark/gluino cascades [33,34] and/or decays into chargino-neutralino states [35,36], though these require drastic MSSM configuration assumptions, hence they are not currently pursued by ATLAS and CMS.
The current highest priority, in relation to charged Higgs boson searches at the LHC, is to further establish the H + → t b decay channel in the heavy mass regions.With this in mind, using the framework of a generic 2HDM [37], we have investigated the possibility of having large interference effects between signals from a heavy charged Higgs boson via bg → tH − → tW − A → tW − b b (and similarly for h and H) and the irreducible background from bg → tW − b b processes.Therein, it was shown that such interference effects can modify any dedicated charged Higgs boson searches where signal and background are treated separately, which is the case for all aforementioned experimental analyses.
The purpose of this paper is to address similar issues for the MSSM, i.e., to quantify the impact of interference effects between the 'complete' signal gg → t bH − and the irreducible background in the H − → b t decay channel.We will show that such effects are indeed large for heavy H ± masses for two MSSM benchmark scenarios, both for inclusive cross section calculations and after a full detector analysis.The plan of the paper is as follows.In the forthcoming section we describe the MSSM configurations used.Sect. 3 dwells on the MSSM spectra conducive to generate such large interference phenomena.Sect. 4 presents our numerical results.Finally, we conclude in Sect. 5.

Definition of the benchmark scenarios
At tree level, the MSSM Higgs sector is completely fixed by 2 parameters: tan β and a Higgs boson mass, e.g., the CP-odd one (M A ).One of the major predictions of SUSY is the presence of a light CP-even Higgs (lighter than Z boson at the lowest order) in the spectrum.However, high order corrections can shift such a mass to reach 125 GeV and above and make it possible for the MSSM to fit the observed Higgs-like particle mass [19][20][21].The MSSM spectrum, masses and couplings is computed here with the help of the public code FeynHiggs [22,23].The latter includes the full one-loop and a large part of the dominant two-loop radiative corrections to the Higgs masses.Given the fact that the theoretical uncertainty on the Higgs mass calculation in the FeynHiggs code has been estimated to be of the order of 3 GeV, all MSSM parameters that predicts a light CP-even in the range 125.5 ± 3 GeV are considered as viable points and will be kept for our analyses.
In the MSSM, the most important parameters relevant for the prediction of the masses, couplings and, hence, production cross sections and decay probabilities of the Higgs bosons are: tan β, M A , the soft SUSYbreaking masses for the stop and sbottom squarks (which, for simplicity, we assume all equal to a common mass parameter M S ), the soft SUSY-breaking gluino mass m g , the Superpotential Higgs-mass parameter µ and the left-right mixing terms in the stop and sbottom mass matrices, i.e., We also use the SusHi public code [24,25] to compute charged Higgs production cross sections which include Next-to-Leading Order (NLO) corrections.Both SusHi and FeynHiggs use the same on-shell renormalisation scheme, therefore, the input values of the MSSM parameters can be passed seamlessly from the Higgs spectrum to the cross section calculations.The MSSM parameter space is already highly constrained by asking that one of the CP-even neutral scalar states should mimic the properties of the SM-like Higgs boson observed at LHC while the additional Higgs bosons should satisfy the existing constraints obtained from ATLAS and CMS from different channels.For this purpose, FeynHiggs code is linked to HiggsBounds [28][29][30][31] and HiggsSignals [32] allowing us to check the consistency of our parameter space against various MSSM Scenarios Table 1: MSSM input parameters for two benchmark scenarios.
LHC, as well as Tevatron and LEP constraints.Additionally, a variety of lower energy constraints have been enforced, as detailed in [26].
All of the MSSM benchmark scenarios adopted in our analysis are characterised by relatively large values of the ratio X t /M S .This ensures that the mass of the SM-like Higgs state falls within the required range without the need for an extremely heavy stop.In addition, the gaugino mass parameters, M 2 and M 1 , are usually assumed to be related via the GUT relation We set the Higgs-sfermion interaction terms A f to zero for the first and second generation fermions: f = u, d, c, s, e, µ.Moreover, the masses of the gluino and first two generation squarks are set to 1.5 TeV, large enough to evade the current ATLAS and CMS limits from SUSY searches.In Tab. 1 we list the MSSM parameters needed for the evaluation of the spectrum.We now move on to a detailed description of the MSSM benchmark scenarios to be used here, known as hMSSM and m mod+ h (see [27] for details).

Higgs-boson masses and branching ratios
For every benchmark scenario, we show the ∆χ 2 behavior, the best fit point, the charged Higgs total width, the typical branching fractions for charged Higgs decays into various final states and the charged Higgs production cross section.

hMSSM scenario
In Fig. 1, we present ∆χ 2 (top-left) and the charged Higgs total width (top-right) in the (M A 0 , tan β) plane.The best fit point is located at M A ≈ 1 TeV and tan β ≈ 2. The green lines show the exclusion limits from HiggSignals at 1σ (solid) and 2σ (dashed) while the gray area is ruled out by the various LHC searches implemented in HiggsBounds.As one can see, the charged Higgs in the hMSSM scenario is rather heavy ≥ 550 GeV and the total width is large for small tan β and gets reduced for high tan β values.In the bottom-panel we show the ratio Γ H ± /M H ± as a function of the charged Higgs mass (left), as well as a function of charged Higgs production cross section (right).The latter can be slightly above 1 pb.It is also visible from lower panel that the charged Higgs total width can be about 4% of the charged Higgs mass at low tan β.
In the hMSSM scenario, the charged Higgs decays mainly into top-bottom with more than 90% branching fraction for tan β ≤ 8 (see Fig. 2, left) which decreases for larger tan β values.For small tan β, the branching ratio BR(H + → t b) is very close to 100 %.In this scenario, the τ ν channel has a rather small branching ratio, less than 10%, in most of the cases as depicted in Fig. 2(right) and becomes negligible for low tan β.

m mod+ h scenario
In the m mod+ h scenario, the allowed parameter region is shown in Fig. 3 (top-left).The best fit point is located at M H ± ≈ 1 TeV and tan β = 20.In order to have a low ∆χ 2 and simultaneously a light CP-even Higgs, close to 125 GeV, a value of tan β > 10 is required.The latter requirement leads to a suppression of the total width of charged Higgs because the branching ratio to top-bottom is proportional to m t / tan β.The same argument holds for the charged Higgs production cross section which becomes smaller than in the previous scenario.The total charged Higgs width is shown in the allowed parameter region in the top-right panel of Fig. 3 .Again, we need heavy charged Higgs to have sizeable total widths but contrary to the previous scenario we now need quite large values of tan β.In the two bottom panels of Fig. 3, we present tan β as a function of Γ H ± /M H ± with the colour code showing the charged Higgs mass (left) and the charged Higgs production cross section (right).Clearly, a compromise has to be reached between the values chosen for the charged Higgs mass while having non-negligible values for the production cross section.
In Fig. 4, we again show the allowed region and the colour code illustrates the charged Higgs branching fractions.In the top panels, we show BR(H + → tb) and BR(H + → τ ν) where it can be seen that the tb branching ratio is larger than the τ ν one.In the bottom panels, we only illustrate the dominant charginoneutralino channels, namely: BR(H + → χ 0 1 χ + 1 ) and BR(H + → χ 0 2 χ + 2 ).   3 in the (M A 0 , tan β) plane.We present the branching ratio

Benchmark Points (BPs)
This section briefly outlines the benchmarks points found via the methodology outlined in the previous section.
In Tab. 2 we display the details of the two benchmark points which we provide numerical results for.The hMSSM benchmark in this table is chosen as it has a high charged Higgs width to mass ratio and thus is expected to have a high interference relative to the signal cross section.The m mod+ h benchmark was chosen as it has a much smaller charged Higgs width to mass ratio.The two benchmarks then provide insights to the effects of interference on both high and low width scenarios.The cross sections are calculated at 13 TeV at the NLO.
In Tab. 3, we illustrate additional information on the input masses as well as tan β with the dominant decay modes and production of charged Higgs boson in the hMSSM approach, for low-tan β and intermediate values of M A .In Tab. 4, we provide, similar information but for m mod+ h scenario with large tan β and heavy charged Higgs mass.In both tables the cross sections are calculated at 13 TeV at the NLO.Let us define scattering interference as I = T − S − B where 'T' is the full scattering amplitude including all signal and background Feynman diagrams and the interference of these diagrams.'S' is the signal scattering amplitude including only the signal diagrams and 'B' is the background scattering amplitude including only the background diagrams.As the same phase space is shared by all of these terms, we can perform the calculation of these terms independently and evaluate the interference via the equation presented above.
To explore the effects of interference on the search for a charged Higgs, we utilise the two BPs outlined in Tab. 2 for the hMSSM and m mod+ h cases.These two points provide two kinematically distinct scenarios, one of which -the hMSSM -has a high width to mass ratio for the charged Higgs of 4.4%, while the other has a much lower ratio with 0.31%.
Signal cross sections are significantly smaller than background cross sections before cuts.Hence the simulation of the T and B terms outlined above must have low uncertainty, which requires very large Monte Carlo (MC) samples.This mandates a prudent use of computing resources and thus an extremely large sample of events was generated for T, B and S at parton level only to obtain a value for the cross section of these processes with very low error.After this was done, smaller detector level samples were generated for the purpose of applying cuts and obtaining efficiencies.The parton level cross sections and the detector level efficiencies are then used together to form the cutflow that will be presented in this section.The parton level results for both benchmark points can be found in Tab. 5.The parton level sample for both samples contained 20,000,000 events both generated in MadGraph5 [40] with a Centre-of-Mass (CoM) energy of 13 TeV, while the detector level samples for both benchmarks contained 500,000 events comprised of 50 independent samples of 10,000 events generated in MadGraph5 at the same CoM energy, sent to Pythia8 [41] for hadronisation/fragmentation and finally passed to Delphes [42] for detector smearing.

Model
Typical detector acceptances were utilised, namely electrons and muons must have their transverse momentum p T > 7 GeV and pseudo-rapidity |η| < 2.5 and jets must have p T > 20 and |η| < 2.5.We also demand exactly one lepton in the final state, so that the longitudinal momentum of missing energy can be solved for via where, Reconstruction was then undertaken via the simultaneous minimisation of the following equations by permuting through all combinations of jets in the process, and The results of this reconstruction can be found in Figs. 5 and 7, normalised to unit area.This reconstruction requires one to use the model dependent width of the particles.Additionally in the aforementioned figures, we present the same reconstruction methodology but without the use of model dependent widths to highlight the difference in these methodologies.
We apply a simple set of acceptance cuts to illustrate the sensitivity of the interference term, these cuts include a final state definition of 1 lepton, 5 or more jets, more than 2 or 3 b-jets, greater than 20 GeV missing transverse energy and, finally, the transverse mass of missing energy and the lepton must be higher than 60 GeV.Specifically, m W T = ( / E x + x ) 2 + ( / E y + y ) 2 > 60 GeV.This cutflow, applied to each of the BPs, can be found in Tabs.6 and 7.

hMSSM scenario
It can be seen in Fig. 5 that all particles appear to be reconstructed very well.The model-dependent reconstruction and the model-independent cases perform equally well for the signal.However, for the background and total samples the reconstruction is quite different.The model-dependent assumption provides a much better separation from the signal, this is especially apparent in both the leptonic and hadronic charged Higgs invariant mass distributions.
The ratio of signal cross section to interference cross section before cuts is 86.4%.This alone is an alarmingly high level of interference that a traditional experimental study would not account for correctly.The ratio after cuts in the 2b-tag scenario is 8.8%, showing a significant reduction via a small set of cuts.
The effect of stricter b-tagging in this scenario was to significantly increase the magnitude of the inclusive cross section of the interference.However both the signal and interference cross sections are extremely small and are below the order of the error associated with these values, thus this should be kept in mind when interpreting the ≥ 3 b-tag results.This being said, the signal to interference ratio increases from 8.8% after a ≥ 2 b-tag cut to 500% with a negative value after a ≥ 3 b-tag cut.It is also important to note that a negative value of interference does not simply mean a cancellation with the signal, as the true effect of the interference is predicated on the overall shape of the interference distribution relative to the signal distribution.In general there are three cases: 1.The interference takes the same shape as the signal and is positive, here we can expect a boosting of our new physics effects.
2. The interference takes the same shape as the signal and is negative, here we expect a cancellation of our new physics effects.
3. The interference takes a different shape and is either positive or negative, here we can expect a boosting and cancellation of new physics effects in different regions of phase space, manifesting as a "peak-dip" structure in the expected distributions.
In Fig. 6, an exploration of this shape can be seen undertaken at parton level, due to the large sample size required to reduce the per bin error to an acceptable level.It can be seen that the interference shape is not smooth and has large effects in both the positive and negative directions.However, its impact in the region of the peak of the charged Higgs invariant mass is minimal.Perhaps a delicate set of cuts guided around particular variables, such as invariant mass peaks, can be used to ensure the minimisation of interference effects. of the t and b-quark masses is far smaller in this scenario it appears that the reconstruction is performed very similarly for the signal and background.This can be further seen in the lack of difference between the model-dependent and model-independent reconstructions.Thus, extraction of the signal would be far more difficult in this case.

m mod+
As the ratio of the charged Higgs mass to charged Higgs width is smaller than in the hMSSM benchmark, we expect the interference effects to be smaller.However, the interference may become much larger relative to the signal after a cutflow.Tab.7 displays the cutflow results for this BP and one can see that the pre-cut ratio of interference cross section to signal cross section is 15.3%, while the ratio after cuts is 44.2% with a positive value of interference.This displays that even in scenarios where the width is small, a non-refined choice of cuts can cause the interference to grow large relative to the signal, thus potentially damaging the performance of an analysis.In this scenario the more strict use of b-tagging increased the ratio of the interference cross section to the signal cross section to 120.7%.

Cut
The interference shape at parton level in this scenario can be found in Fig 8 .The shape is once again not smooth and has large effects in both the positive and negative directions.

Conclusions
By borrowing the MSSM as a theoretical template that contains charged Higgs bosons, we have shown how experimental searches for these states cannot be made immune from large interference effects between signal and background whenever they have a large mass and a width of just a few percent of the mass and upwards.We have illustrated this for the case of the H + → t b decay channel, which is onset by gg → b tH + production.In this case, the (irreducible) background intervening in such interference effects is gg → t tb b, which can see both QCD and EW interactions.(Notice that we have ignored the corresponding q q induced production  channels, as they are largely subleading.)This study's goal was to show that signal and background are wrongly treated as separate in current LHC approaches.
In order to realistically assess the above phenomenon, we have decayed the t t pair semi-leptonically and carried out a full parton shower, hadronisation and detector analysis.In doing so, we have first prepared the MSSM parameter space regions amenable to phenomenological investigation by enforcing both theoretical (i.e., unitarity, perturbativity, vacuum stability, triviality) and experimental (i.e., from flavour physics, void and successful Higgs boson searches at the Tevatron and LHC, EW precisions observables from LEP and SLC) constraints, assuming two benchmark configurations of the MSSM, the so-called hMSSM and m mod+ h scenarios.
After performing a sophisticated MC simulation, allowing for both model-independent and model-dependent  selections, we have seen that such interference effects can be very large, even of O(100%), both before and after H ± detection cuts are enforced.This appears to be the case for the masses tested, approximately 300 and 700 GeV, in the MSSM scenarios adopted, though interference effects will manifest themselves at different LHC stages, depending on the overall cross sections, which vary significantly from one benchmark to another.Crucially, after all cuts are applied, the shapes of the signal and its interference (with the aforementioned irreducible background) are different so that it is not actually possible to proceed to a rescaling of the event yields due solely to the signal.In turn, in experimental analyses, one should account for such interference effects at the event generation level.We have proven this to be the case for a standard cut flow, while deferring the study of similar effects in the case of a machine learning framework to a future publication.

Figure 1 :
Figure 1: ∆χ 2 (top-left) and the charged Higgs total width (top-right) in the (M A 0 , tan β) plane.The best fit point is located at M A ≈ 1 TeV and tan β ≈ 2. The green lines show the exclusion limits from HiggSignals at 1σ (solid) and 2σ (dashed) while the gray area is ruled out by the various LHC searches implemented in HiggsBounds.The ratio Γ H ± /M H ± as a function of the charged Higgs mass is shown in bottom-left panel while in the bottom-right it is presented as a function of charged Higgs production cross section.

Figure 3 :
Figure 3: Allowed parameter region in the m mod+ h scenario and in the (M A 0 , tan β) plane with a colour code showing ∆χ 2 (top-left) and the charged Higgs boson mass (top-right).The LHC Higgs searches constraints are included.The light green contours are HiggsSignals exclusion limits at 1σ (solid) and 2σ (dashed).The light gray area is excluded by HiggsBounds at 2σ.The solid black lines are contours for the lighter CP-even scalar h 0 mass.The best fit point is located at M H ± ≈ 1 TeV and tan β = 20.In the two bottom panels of Fig. 3 we present tan β as a function of Γ H ± /M H ± with the colour code showing the charged Higgs mass (left) and the charged Higgs production cross section (right).

hscenarioFigure 5 :
Figure 5: Invariant Mass distributions for reconstructed particles in the hMSSM benchmark.Top: Model independent.Bottom: Model dependent.

Figure 6 :
Figure 6: The charged Higgs invariant mass distribution of the signal, background as well as total (left) plus the interference and signal (right) at parton level in the hMSSM scenario.

Figure 7 :
Figure 7: Invariant Mass distributions for reconstructed particles in the mod+ h benchmark.Top: Model independent.Bottom: Model dependent.

Figure 8 :
Figure 8: The charged Higgs invariant mass distribution of the signal, background as well as total (left) plus the interference and signal (right) at parton level in the m mod+ h

Table 2 :
Benchmarks points for the two scenarios

Table 4 :
Benchmarks points for m mod+

Table 5 :
Parton level results for the hMSSM and m mod+ h benchmarks.

Table 6 :
Cut flow results presented in cross sections for the hMSSM benchmark.

Table 7 :
Cut flow results presented in cross sections for the m mod+