Searching for Charged Higgs Bosons in the $B-L$ Supersymmetric Standard Model at the High Luminosity Large Hadron Collider

Upon assuming the $B-L$ Supersymmetric Standard Model (BLSSM) as theoretical framework accommodating a multi-Higgs sector, we assess the scope of the High Luminosity Large Hadron Collider (HL-LHC) in accessing charged Higgs bosons ($H^\pm$) produced in pairs from $Z'$ decays. We show that, by pursuing both di-jet and tau-neutrino decays, several signals can be established for $H^\pm$ masses ranging from about $M_{W}$ to above $m_t$ and $Z'$ masses between 2.5 TeV and 3.5 TeV. The discovery can be attained, even in a background free environment in some cases, owing to the fact that the very massive resonating $Z'$ ejects the charged Higgs bosons at very high transverse momentum, a kinematic region where any SM noise is hugely depleted.

Searches for light charged Higgs bosons (H ± ) in the decay of top quarks, t → H ± b, are presently being carried out at the Large Hadron Collider (LHC), with the assumption that their decay channels are dominated by H ± → τ ν τ or H ± → jj, where j represents a jet and the possible partonic combinations are cs and cb. For heavy H ± states, with M H ± > m t , one resorts instead to the H ± → tb channel, via associated production of a charged Higgs boson with a top quark. (See [1,2] for recent reviews by ATLAS and CMS.) In both cases then, H ± states are produced in single mode. The scope for testing charged Higgs boson pair production at the LHC is instead much limited, whichever the channel to be pursued [3], primarily owing to the small cross sections involved. The experimental analyses are carried out model independently. The results though can be interpreted in a variety of Beyond the SM (BSM) scenarios (see [4] for a recent review). A popular framework in this respect is the Minimal Supersymmetric Standard Model (MSSM), which is the most economical realization of Supersymmetry (SUSY) containing H ± states. However, this SUSY incarnation is plagued by innumerable problems, both theoretical and experimental, so that non-minimal models of SUSY are being explored [5].
Amongst these, an intriguing one is the B − L Supersymmetric Standard Model (BLSSM), which, while inheriting the beneficial aspects of SUSY from the MSSM, it surpasses it as it naturally predicts massive neutrinos (as required by experiment), an enlarged Higgs sector (which allows for a SM limit) and an expanded gauge symmetry (potentially a remnant of a Grand Unification Theory (GUT)) [5,6] as well as a Dark Matter (DM) candidate (the SUSY counterpart of a neutrino, i.e., a sneutrino) that, thanks to its interactions with richer Higgs and gauge spectra, complies with both direct and indirect constraints better than the MSSM candidate [7][8][9][10].
The BLSSM is also an example of New Physics (NP) that predicts the existence of charged Higgs bosons. While single H ± production here is not dissimilar from the MSSM case, a notable difference emerges in the case of double H ± production. The reason why MSSM cross sections at the LHC for pp → H + H − X processes are small is that charged Higgs boson pairs are never produced resonantly. This is unlike the BLSSM, where the condition M Z > 2M H ± is naturally realized, given the constraints on the Z mass, around 3.5 TeV presently [7,9]. Hence, within the BLSSM, once can resort to the pp → Z * , γ * , Z → H + H − mode, see Z (resonant) component, together with its interference with the SM, is the actual signal and the γ * , Z * ones are the (irreducible) background ones, which are nonresonant given that the current lowest mass limit on H ± states is essentially the W ± mass [4]. Such a signal is best searched for via the aforementioned τ ν τ and jj channels, even when M H ± > m t , as efficiency of other decay modes is much poorer in comparison. In the light of this, there are also reducible backgrounds to be dealt with, primarily tt, gauge boson pair production (W + W − and ZZ) and W ± , Z + jets. The Branching Ratios (BRs) of the charged Higgs boson of the BLSSM can be seen in Fig. 2, wherein the BLSSM points have been generated over the following intervals of its fundamental parameters: 0.5 ≤ µ ≤ 3 TeV, 50 ≤ M A ≤ 10 3 TeV, 10 ≤ tan β ≤ 30, 0. At this point, it is also worth mentioning that other H + H − production modes exist in the BLSSM that could play a role at the LHC in the context we are address- ing, specifically, induced by gluon-gluon induced channels. These can be neglected though for our purposes, as the box component does not benefit from any BLSSM specific enhancement while the triangle one (which would indeed include a Z boson in s-channel) is suppressed owing to the Landau-Yang mechanism [11]. Further, also BLSSM intrinsic backgrounds, such as Z → W + W − and Z → W ± H ∓ decays are negligible, as they are proportional to (the sine of) the Z-Z mixing angle, sin θ , which is constrained by LEP data to be less than 10 −3 [12,13].
Another aspect that renders H + H − production at the LHC within the BLSSM more interesting than in the MSSM is the fact that, while in the latter the γH + H − and ZH + H − vertices are fixed by the SM gauge symmetries, in the former one has some freedom to find a sizable range of parameters that can make the Z H + H − coupling sufficiently large to offset the phase space suppression coming with the fact that the Z is bound to be rather heavy, as discussed. In the BLSSM, the coupling of charged Higgs bosons to the Z is generated through the possible mixing in the mass matrix of the Z and Z gauge bosons and/or the kinetic mixing between U (1) Y and U (1) B−L , which is ∼g (see Ref. [14] for further details). Over the above volume of BLSSM parameter space, we find cross sections σ(pp → γ * , Z * , Z → H + H − ), i.e., prior to any H ± decay restricted to the kinematic range Fig. 3 (left frame) over the (M Z , M H ± ) plane for the fixed value ofg = −0.29. It is important to notice here that, in the definition of the BLSSM signal, a key role is played by the interference between the Z and γ * , Z * components of the process, which turns out to be constructive over the relevant parameter range, as can be seen from Fig. 3 From those in this plot, we now select five Benchmark Points (BPs), which differ in the Z and H ± masses but have common gauge couplings g B−L andg, see Tab. I, to be used in the forthcoming phenomenological analysis. In defining these, we have made sure that, on the one hand, they do not fall foul of the aforementioned LEP (indirect) constraints and, on the other hand, the ensuing Z will not have been discovered via LHC (direct) searches in Drell-Yan (DY) mode already (i.e., by the time the analysis that we advocate will be pursued), which is demonstrated by Fig. 4 for the illustrative case of BP3 (it is the same for the other BPs as well) [15]. In fact, the top frame herein shows the line-shape of the differential cross section mapped in invariant mass of the final state M ll ≡ √ŝ (l = e, µ) near the Z resonance, here of 2576 GeV, wherein the Z effect and that of its interference with the irreducible SM background are clearly visible against the latter, yet, the significance of these two contributions over the SM noise after, e.g., 300 fb −1 of luminosity is about 1.5 at best, see the bottom frame. Even for a tenfold increase in collider luminosity, as expected at the High Luminosity LHC (HL-LHC) [16], corresponding to an increase of a factor √ 10 in significance, the latter should remain below 5.  This beneficial effect of such an interference is also seen in the differential distributions, e.g., in the where / E T represents the missing transverse energy due to neutrinos escaping detection. This is illustrated in Fig. 5. In the plots, we show the spectra of the total missing transverse energy (top frame) and transverse momentum of the ττ system (bottom frame). From here, it is clear that the contribution of a very massive Z , combined with its interference with γ and Z, has a twofold effect. On the one hand, the total cross section for pp → Z → H + H − → ττ + / E T at 14 TeV, which is already a significant 2.5 × 10 −3 pb, through the effect of the interference is enhanced by more than one order of magnitude. On the other hand, the presence of the Z pushes the final state particles to the high end of these distributions, which is not the case for the MSSM wherein the final state particles cannot be extracted from the huge irreducible background existing at low values of these kinematic observables. Hence, by imposing a minimum requirement on / E T and/or p T (ττ ) of several hundreds of GeV, one should be able to extract a BLSSM signal, so long that reducible backgrounds are also controlled at the same time (which we will show being the case later on). The drawback of this approach is that event rates for the signal might turn out be rather small in the end (notice the normalization of the curves in Fig. 5), so that event samples generated by the HL-LHC may indeed be needed to pursue this analysis. Indeed, in this case, the tenfold increase in all event rates will enable us to probe at the same time not only the fully tauonic signature of charged Higgs bosons, i.e., pp → γ * , Z * , Z → H + H − → τν ττ ν τ , but also the semihadronic one, i.e., pp → γ * , Z * , Z → H + H − → jjτ ν τ .
But let us now proceed to the signal-to-background analysis. Both signal and backgrounds are computed with MadGraph5 [17] that is used to estimate multiparton amplitudes and to generate events for the calculation of the cross sections as well as for their subsequent processing. PYTHIA6 [18] has been used for showering, Events/ 10 GeV 200 400 600 800 Events/ 10 GeV hadronisation, heavy flavour decays and for adding the soft underlying event. The simulation of the response of the ATLAS and CMS detectors was done with the DELPHES package [19], wherein reconstructed objects are simulated from the parametrized detector response and includes tracks, calorimeter deposits and high level objects such as isolated electrons, jets, taus and missing transverse momentum. Finally, for event reconstruction, we have used MadAnalysis5 [20].
First, we study the fully tauonic decays of the charged Higgs boson pair. As for the τ 's, we use the τ -tagging algorithm included in MadAnalysis5 so that both leptons and jets are identified as originating from a τ if they can be matched to it when lying within a cone of radius ∆R = 0.4 around a parton-level τ , as well matching the charged tracks from the τ decays, this yielding an overall efficiency of about 40%. Further, the missing transverse energy / E T in the event is defined as the negative sum of the transverse momentum of all reconstructed objects, so that the quality of the reconstruction of all charged particles, especially jets and electrons, has strong bearings on the unwanted amount of missing energy. Notice that the presence of two neutrinos associated with the final state τ 's makes it impossible to reconstruct the H ± mass, however, one can instead reconstruct a Jacobian peak which should be correlated to the Z mass, e.g., through a transverse mass distribution, M T , defined by using all  The cut flow for the full process pp → γ * , Z * , Z → H + H − → ττ + / E T for our 5 BPs at √ s = 14 TeV and an integrated luminosity of 300 fb −1 . The last three columns correspond to the relevant reducible backgrounds: the first column for W + W − , the second column for tt and the third column for the Drell-Yan (DY) process. For all 5 BPs, in the last line, the yield of the full process is shown alongside that of the signal rate only (in paratheses), as defined in the text.
visible objects in the detector and the / E T . Fig. 6 shows both the / E T and M T observables, prior to any cut, illustrating that they correlate equally to the actual value of M Z . The cut flow we have exploited is found in Tab. II, wherein l = e, µ and τ , η and p T refer to pseudorapidity and transverse momentum, respectively, and the b-jet veto is enforced by rejecting events that contain at least one b-tagged jet. The dominant (reducible) background processes are tt with leptonic decays (which can in particular be reduced by the aforementioned veto against the existence of a high p T bottom-quark jet, tagged as such), SM di-boson production and the DY channels (all proceeding via τ 's), while Z+jets and W +jets can be neglected. The complete pp → γ * , Z * , Z → H + H − process can be established and, as illustrated in the last line of the table, the pure S component in it is extractable as a clear excess above the intrinsic (irreducible) B yield. A cut in / E T , based on the top frame of Fig. 6, is crucial to achieve this outcome. Finally, the value of M Z can be fit to the surviving M T distribution upon subtracting all backgrounds, including the intrinsic (irreducible) one.
Then, we probe the signature τ ν τ jj out of full di-charged Higgs boson production and decay pp → γ * , Z * , Z → H + H − → jjτ ν τ . The dominant (reducible) SM background arises from events with W ± and Z bosons produced in association with jets. Additional sources of SM background come from di-boson V V and tt production and semileptonic decays via τ s. For signal isolation we have chosen the essential cuts first introduced by Ref. [21], with |η(l)| < 2.4, |η(j)| < 2.5, p T (l) > 30 GeV and p T (j) > 30 GeV. Further, other than (a somewhat returned) / E T cut, here, also additional cuts on the di-jet invariant mass, ∆R separation between τ and jet as well as τ transverse momentum are necessary to establish the full pp → γ * , Z * , Z → H + H − process, indeed, in a (reducible) background free environment, see Tab. III. Again, the last line of the table makes evident the pure S component above the intrinsic (irreducible) B yield. In this case, one of the two H ± masses is reconstructible, from the di-jet system. This is illustrated in Fig. 7, where the M jj variable (here plotted after all cuts) is defined by choosing the two highest transverse momentum jets. The charged Higgs peaks are most evident around the generated H ± mass. Their normalization, upon subtraction of the intrinsic (irreducible) background, would represent the BLSSM specific signal, due to Z mediation, though this will require a very large luminosity, typical of the HL-LHC [16].

Conclusions
The LHC at CERN will enable during Run 2 and 3 to establish a specific BLSSM signal, mediated by on-shell production of a heavy Z state and yielding a charged Higgs boson pair, eventually decaying into two τ 's and / E T . Its HL-LHC version, benefiting from a tenfold increase in instantaneous luminosity, will further allow one to access the final state in which one H ± decays hadronically into two jets, the other again going into a τ ν τ pair. As H + H − production in the MSSM is only mediated by an off-shell γ * , Z * current, such a hallmark BLSSM  (2) 8 (5) 9 (6) 11 (7) 17 (12) 0 0 0 0 TABLE III: The cut flow for the full process pp → γ * , Z * , Z → H + H − → jjτ + / E T for our 5 BPs at √ s = 14 TeV and an integrated luminosity of 300 fb −1 . The last four columns correspond to the relevant reducible backgrounds: the first column for W ± +jets, the second column for tt, the third column for V V (V = W ± , Z) and the fourth column for Z+jets. For all 5 BPs, in the last line, the yield of the full process is shown alongside that of the signal rate only (in paratheses), as defined in the text. signature clearly requires sampling the H ± decay products at large / E T values, which is indeed possible via a judicious choice of experimental cuts.