Searching for a Heavy Neutral CP-Even Higgs Boson in the BLSSM at the LHC Run 3 and HL-LHC

The detection of a heavy neutral CP-even Higgs boson of the $B-L$ Supersymmetric Standard Model (BLSSM), $h'$, with $m_{h'}\simeq 400~\text{GeV}$, at the Large Hadron Collider (LHC) for a center-of-mass energy of $\sqrt{s}=14~\text{TeV}$, is investigated. The following production and decay channels are considered: $gg\to h'\to{ZZ}\to4\ell$ and $gg\to h'\to{W^+W^-}\to2\ell+\slashed{E}_T$ (with $\slashed{E}_T$ being the Missing~Transverse~Energy~(MET)), where $\ell=e,\mu$, with integrated luminosity $L_{\text{int}}=300~{\text{fb}}^{-1}$ (Run 3). Furthermore, we also look into the di-Higgs channel $gg\to h'\to{hh}\to{b\bar{b}\gamma\gamma}$ at the High-Luminosity LHC (HL-LHC) with an integrated luminosity of $L_{\text{int}}=3000~{\text{fb}}^{-1}$. We demonstrate that promising signals with high statistical significance can be obtained through the three aforementioned channels.


I. INTRODUCTION
The search for a heavy neutral CP-even Higgs boson at the current Run 3 of the LHC and a future HL-LHC is an active area of research [1][2][3][4][5][6][7][8][9].This is so because virtually any extension of the Higgs sector beyond the single doublet structure of the Standard Model (SM), in which the only neutral CP-even state of it is identified with the particle that was discovered in 2012 at the LHC by the ATLAS and CMS experiments [10,11], contains it.As a result, currently, probing such a heavy Higgs boson is one of the main goals of the LHC experiments, as it could well provide the first hint for physics Beyond the SM (BSM).Both ATLAS and CMS have searched for a heavy Higgs boson and the corresponding analyses typically involve looking for events in which the heavy Higgs boson is produced and then decays into SM particles, such as W ± or Z bosons, in turn decaying into leptons or jets [1], or into the SM Higgs boson itself [12], which then decays into, e.g., photons, b-quarks or τ leptons.Supersymmetric extensions of the SM are one of the BSM frameworks that consistently predict the existence of several Higgs bosons, including a heavy neutral CP-even one.Such a Higgs boson mass can be significantly larger than the one of the SM Higgs state, potentially reaching several hundred GeV.For example, the Minimal Supersymmetric Standard Model (MSSM) contains five a mustafa@sci.cu.edu.egb skhalil@zewailcity.edu.egc s.moretti@soton.ac.uk; stefano.moretti@physics.uu.seHiggs bosons: two CP-even (h and H, with m h < m H ), one CP-odd (A) and two charged states (H + and H − ): for reviews, see, e.g., [13].This is the simplest construct implementing supersymmetry, where the lightest CP-even Higgs boson, h, is designated as the SM Higgs boson, with a mass of 125 GeV, which, however, imposes a strenuous configuration on the MSSM parameter space, forcing the other CP-even Higgs boson, H, to be rather heavy and significantly decoupled.However, if supersymmetry is non-minimal, in either its gauge or Higgs sector or both, then the mass of additional CP-even Higgs states can become rather less constrained [14].An example of this is the so-called BLSSM, which indeed offers the possibility of LHC signals for a CP-even Higgs state not only above the SM Higgs mass, e.g., in the range up to 500 GeV [9], but also afford one with a lighter mass spectrum, in turn able to explain past [15,16] and present data anomalies [17].
The BLSSM is a theoretical extension of the MSSM that includes an additional U (1) gauge symmetry known as B − L (baryon number minus lepton number) [18][19][20][21] as well as an extended Higgs sector.The B − L symmetry is motivated by the observation that the difference between baryon and lepton number is conserved in many particle physics processes.In the BLSSM, the B − L symmetry may be broken at the few TeV scale, giving rise to new particles such as two new extra neutral CP-even Higgs bosons.One of them, labeled h ′ , can have energies in the hundreds of GeV range.It is indeed the presence of such a h ′ state that causes the aforementioned new phenomenology to emerge in collider experiments, which can then be used to test the BLSSM hypothesis.
We emphasize that the SM-like Higgs state, henceforth labeled by h, is derived from the real parts of the neutral components of the Electro-Weak (EW) scalar doublets H u and H d whereas the (typically) next-to-lightest Higgs boson, h ′ , stems from the real parts of the neutral components of the B − L scalar singlets χ 1 and χ 2 .Despite the fact that the mass mixing between these two types of Higgs bosons is negligible, a non-vanishing kinetic mixing allows for relevant couplings between h ′ and the SM particles, resulting in a total cross section of h ′ production and decay into W + W − , ZZ or hh of O(1) fb.These signals are typically smaller than the associated backgrounds but, by using appropriate selection strategies, they can be probed with a reasonably high sensitivity.However, given that current experimental limits have significantly constrained also the BLSSM parameter space above and beyond what allowed for in Ref. [9], which targeted Run 2 sensitivities, we revisit here the scope of Run 3 and the HL-LHC in accessing the heavy neutral CP-even Higgs boson of the BLSSM, h ′ , in the mass region of 400 GeV or so.It is also worth mentioning that heavy Higgs boson searches have been conducted in many supersymmetric (and non-supersymmetric) extensions of the SM.Indeed, the BLSSM itself has been phenomenologyically investigated rather widely in relation to Higgs, dark matter and heavy gauge boson physics due to its many degrees of freedom and its wide parameter space [9,[15][16][17][22][23][24][25][26][27][28][29][30][31][32].Specifically, for heavy Higgs bosons, the situation in the BLSSM is significantly different from that of the MSSM, where the SM-like Higgs boson mass and couplings constrain the heavy Higgs boson phenomenology greatly.In contrast, in the BLSSM, while the Higgs bosons of MSSM origin are just as restricted as in the actual minimal model, the constraints on the other Higgs bosons from the B − L sector are much relaxed in comparison.
The paper is organized as follows.We briefly review the BLSSM particle content, superpotential and gauge structure in Sec.II, where we also discuss at some length its Higgs sector.Studies of h ′ signals at the LHC are then carried out in Sec.III, wherein a detailed Monte Carlo (MC) analysis for h ′ production via (mostly) gluon-gluon fusion (ggF) and decay via and hh → b bγγ is performed.Our conclusions and final remarks are given in Sec.IV.

II. THE BLSSM
The BLSSM is based on the gauge symmetry group where g is the gauge kinetic mixing, as discussed below, with V µ and V ′ µ are the U (1) Y being the U (1) B−L gauge fields, respectively.
Superfield Spin-0 Spin- The BLSSM superpotential is given by The relevant soft supersymmetry-breaking terms, adopting the usual universality assumptions at the Grand Unification Theory (GUT) scale, are given by where the sum in the first term runs over the scalar fields ϕ = Q, Ũ , D, L, Ẽ, Ñ , H u,d , χ 1,2 and , ν, N ) are the trilinear scalar interaction couplings associated with the fermion Yukawa couplings.The B − L symmetry can be radiatively broken by the following non-vanishing Vacuum Expectation Values (VEVs): ⟨χ 1 ⟩ = v 1 and ⟨χ 2 ⟩ = v 2 .We define tan β ′ as the ratio of these VEVs (tan [18,33]. After B −L Spontaneous Symmetry Breaking (SSB), the new gauge boson, Z ′ , acquires its mass from the kinetic term of the B − L Higgs fields, χ 1,2 .Namely, we have where g is the gauge coupling mixing between U (1) Y and U (1 Furthermore, the mixing angle between the (SM) Z and (BLSSM) Z ′ states is given by which should be < ∼ 10 −3 .
We now turn to the neutral CP-even Higgs bosons in the BLSSM.The Higgs potential is where g 2 = g 2 1 + g 2 2 + g2 .We expand the neutral components around their VEVs: The Higgs bosons (symmetric) mass matrix in the basis (σ u , σ d , σ 1 , σ 2 ) is given in block form by where the off-diagonal block mixing of both the MSSM and B − L sectors is where we have used the shorthand notations s X ≡ sin X and c X ≡ cos X.The MSSM Higgs mass matrix M 2 HH in the basis (σ u , σ d ) is given by where we have used the shorthand notation t X ≡ tan X and the B − L Higgs mass matrix M 2 χχ in the basis (σ 1 , σ 2 ) is given by where the tree-level tadpole equations solutions give where m 2 u,d , m 2 1,2 are the soft supersymmetry breaking Higgs H u,d , χ 1,2 mass parameters at the SSB scale(s).
The heavy Higgs boson tree-level mass eigenvalues are given in terms of the lightest SM-like Higgs boson h ≡ h 1 mass, which is fixed at m h = 125 GeV, and the lightest B − L Higgs boson h ′ ≡ h 2 mass, which we take to be m h ′ = 400 GeV, as follows For In Fig. 1, we display the mixing Z H 2i versus the gauge kinetic mixing g.As it can be seen from this plot, h ′ is essentially generated from σ 1,2 with smaller contributions from the real components of σ d which, however, connect it to the SM sector.The MSSM gauginos (bino, wino and gluino) soft masses are fixed to M B ∼ 7.74 × 10 2 GeV, M W ∼ 8.52 × 10 2 GeV and M g ∼ 6.38 × 10 2 GeV at the SSB scale(s), respectively, while the B − L gaugino (bino ′ ) soft mass M B′ , and the bino-bino ′ gauginos mixing soft mass M B B′ are given in Table IIa.
The second lightest Higgs boson h ′ interaction couplings to quarks are given in terms of quark masses M u,d by while its couplings to the SM gauge and Higgs bosons are given by where θ w and θ w ′ are the weak and Z − Z ′ mixing angles, respectively.For , the trilinear Higgs boson coupling h ′ hh (relevant to our forthcoming analysis) is approximated by

III. SEARCH FOR A HEAVY NEUTRAL CP-EVEN HIGGS BOSON AT THE LHC
Many computational tools are used throughout this work, from building the model analytically to performing the numerical simulations at detector level.The BLSSM was first implemented into the Sarah package for Mathematica and the output was then passed to SPheno [34,35] for numerical calculations of the particle spectrum.After that, the ensuing UFO model was used in MadGraph [36] for MC event generation and Matrix Element (ME) calculations.After that, Pythia was used to simulate initial and final state radiation (through the Parton Shower (PS) formalism) as well as fragmentation/hadronization effects [37].For detector simulation, the Pythia output was passed to Delphes [38].Finally, for data analysis, we used MadAnalysis [39].As for the BP used, we made sure that it was consistent with HiggsBounds and HiggsSignals [40,41] limits, as obtained from the latest LHC data.The Feynman diagrams associated to the h ′ production and decay mechanisms discussed here are found in Fig. 2, wherein the • symbol is meant to signify the exact loop function allowing for both b and t quark contributions.The Higgs production and decay rates are computed by factorising the h ′ propagator, so that the overall event yield can be broken down into the h ′ production cross section and decay Branching Ratios (BRs).The MC event generation is done at Leading Order (LO) for both Signal (S) and Background (B), however, we include Next-to-Next-to-LO (NNLO) inclusive k-factors from Quantum Chromo-Dynamics (QCD) in computing our significances, specifically, we use 2.2 for the ggF signal and 1.2 for the Vector Boson Fusion (VBF) one (see below) as well as the (EW) backgrounds [42][43][44][45][46].
In Fig. 3 (left), we fix the SM-like Higgs boson mass to its measured value, i.e., m h ∼ 125 GeV, and show the change of m h ′ with the gauge kinetic mixing parameter g.However, one should be 2: Feynman diagrams for h ′ production via ggF and decays via (from left to right) Also, in Fig. 3 (right) we show the h ′ decay BRs, again, as functions of g.In all three plots, the symbol • refers to the BP adopted here, for which the corresponding σ and BR values are found in Table III.The production cross section of h ′ depends significantly on g, which is (as mentioned) the only source of mixing between the BLSSM Higgs χ 1,2 singlets and the MSSM Higgs doublets H u,d that enables h ′ couplings with SM particles.However, the h ′ decay BRs are not significantly affected by it because both the partial and total decay widths of h ′ in each channel receive nearly the same contribution from g, which cancels out from the BRs.It is noteworthy that the three most significant decay channels are the bosonic ones in W + W − , ZZ and hh.In contrast, the fermionic decay channels into t t and b b are relatively less significant.Therefore, in the forthcoming MC analysis, we will concentrate on the former three decay channels.
For each channel, there are many corresponding background processes and all can be reduced by applying the cut-flows of Tables IVa In Tables IVa, IVb and IVc, the kinematical variables are defined such that M eff is the effective mass being obtained as the sum of the transverse momentum of all final state objects and the transverse energy, while E T is the scalar sum of the transverse energy of all (visible) final state objects in the plane transverse to the beam [39].Furthermore, M ab... is an invariant mass and ∆R ab is the separation between final state objects.(Note that an (opposite-sign) di-lepton mass reconstruction around one M Z value in the 4ℓ channel is not useful, as the irreducible background is here dominated by pp → ZZ, Zγ * → 4ℓ.) TABLE III: Production cross section σ (at √ s = 14 TeV) and decay BRs into W + W − , ZZ and hh for the h ′ state (with m h ′ = 400 GeV) of our BP, including the overall rates in the three final states 2ℓ + / E T , 4ℓ and b bγγ.Normalization is to LO for all σ's.
Table IVa provides the cut-flow for the h ′ production and decay analysis via the 2ℓ + / E T signature, while event shapes and rates (the latter in correspondence to Run 3 luminosity) for are presented in Fig. 4. Herein, we also present the contributions of an additional signal channel, induced by (W + W − dominated) VBF with two additional (untagged) forward/backward jets, as it contributes not negligibly to the same ggF signal regions (so that it has been taken into account in extracting our final sensitivities).In this figure, the normalized (to 1) distributions used for the ℓℓ , and ⃗ / E T is the negative vector sum of the transverse momenta of the reconstructed objects, including muons, electrons, photons, jets) of the final state (i.e., using both leptons in its definition), the latter integrating to the actual event numbers for Run 3 and also in presence of the background contribution.Altogether, from this last spectrum, it is clear that a high signal significance can be reached, however, it also shows that the shape does not promptly correlate to the h ′ mass value.Yet, the significant excess seen in this channel will clearly motivate a parallel search in the 4ℓ final state, which we are illustrating in the next subsection.However, before doing so, let us dwell more on the noise composition.
The dominant backgrounds in this channel are non-resonant W + W − , t t, and W ± t production, all of which have real W + W − pairs in the final state.Other important backgrounds include Drell-Yan (DY) events (pp → Z/γ ( * ) → ℓ + ℓ − ) with / E T that may arise from mis-measurements, W ± + jets events in which a jet produces an object reconstructed as the second electron and W ± γ events in which the photon undergoes a conversion.Boson pair production W ± γ * / W ± Z ( * ) / W h ( * ) and ZZ ( * ) can also produce opposite-charge lepton pairs with additional leptons that are not detected.
Demanding the following set of identification cuts (ID) with the number of b-jets N (b) < 1, the number of charged lepton pairs N (ℓ + ℓ − ) ≤ 2 and the number of jets N (j) ≤ 4 in the kinematical (Kin) regions 1. for the leading lepton P T ℓ ≥ 25, 2. for the subleading lepton P T ℓ ≥ 15 and 3. for the two lepton |η| ℓ < 2.5 increases the S to B significance by a factor of about 2.5.The final analysis is included in Table IVa.
After ID and Kin cuts, the DY, W ± + jets, W ± γ ( * ) /Z ( * ) , ZZ ( * ) noises were eliminated so that in the end we kept only the irreducible backgrounds from W + W − , t t and pp → 2ℓ + / E T events, which we stacked on top of each other in Fig. 4.  Table IVb provides the cut-flow for h ′ production and decay via the 4ℓ channel, while some relevant kinematics, in terms of event shapes and rates (the latter, again, in correspondence to Run 3 luminosity) for is presented in Fig. 5. Here, we concentrate on the normalized (to 1) distributions in transverse energy of all leptons (E T ) and opposite-sign di-lepton invariant mass (M ℓ + ℓ − ), both of which are used in our cut-flow.(Regarding the latter, notice that the loss of significance in applying the cut in invariant mass against the dominant irreducible background pp → ZZ, Zγ * → 4ℓ is rather insignificant against the benefits of rejecting the irreducible one, e.g., from top-antitop quark production and fully leptonic W + W − decays (which has typically a harder distribution in this variable), so that the whole of the latter can be neglected.)In the end, the spectrum from which to extract the h ′ resonance, i.e., the final state invariant mass, M 4ℓ , clearly reveals a broad excess over a 400 GeV or so mass interval, altogether yielding significances in the discovery range.
In fact, also a noticeable peak appear for M 4ℓ ≈ 400 GeV (which, as mentioned, can be correlated with the M ℓ + ℓ − T distribution in the 2ℓ+ / E T final state), so that one can improve further the potential for h ′ discovery in the 4ℓ channel by optimizing a cut in this variable.In all cases we show only the ggF contribution to the 4ℓ signal for our BP while for the last spectrum we also show the (stacked) distribution.
Table IVc provides the cut-flow for the h ′ production and decay analysis of the last channel we study, wherein we use HL-LHC luminosity, as this channel is not accessible during Run 3. The distributions used to inform our cut-flow herein (normalized to 1) are found in Fig.

D. Historical Significances
Before closing this section, we describe the patterns of significances in the three channels that we have studied, as they would evolve with luminosity, assuming fixed energy at √ s = 14 TeV.
These are shown in Fig. 7. lt is evident that a full characterization of the h ′ state, involving its coupling to SM (massive) gauge and Higgs bosons is only possible through a combined effort of analyses to be entertained at both Run 3 of the LHC and HL-LHC.

IV. CONCLUSIONS
In summary, we have shown that a theoretically well-motivated realization of supersymmetry, the so-called BLSSM, may yield detectable signals of a heavy neutral CP-even Higgs boson at the LHC, both during Run 3 and the HL-LHC phase.These emerge from the lightest (neutral) Higgs state of this scenario with prevalent B − L composition, h ′ , while the lightest (neutral) Higgs state with predominant MSSM nature is identified with the discovered one, h (with m h = 125 GeV).The subprocesses pursued to this effect, assuming a BP with an illustrative mass m h ′ = 400 GeV, have The first one would be accessible during the early stages of Run 3 and the study of mass distributions would allow one to extract an indication of the h ′ mass.This information can then be used to optimize the selection of the second signal, which would reveal a clear pick centered around m h ′ by the end of Run 3.With the latter information available, one would then be able to establish the third signal at the HL-LHC.All this will therefore enable one to fully characterize the h ′ state, not only through its mass, but also in terms of its couplings, as the W + W − , ZZ and hh decays are the dominant ones given before the cut-flow and normalized to 1 while the latter one given after it and normalized to the total event rate for the integrated luminosity L int = 3000 fb −1 .In all cases we show only the ggF contribution to the b bγγ signal for our BP while for the last spectrum we also show the (stacked) distribution.
in the BLSSM while those to t t and b b pairs may be accessible at production level through the ggF channel.This finally opens up the possibility of eventually separating the BLSSM hypothesis from alternative ones also based on supersymmetry, since -thanks to the peculiar feature of (gauge) We have come to these conclusions by performing a full MC analysis in presence of ME, PS, fragmentation/hadronization effects as well as detector modeling and upon devising dedicated cutand-count cut-flows for each signature pursued.We are therefore confident that ATLAS and CMS would have sensitivity to this specific non-minimal realization of supersymmetry and advocate dedicate searches for the aforementioned signals.

FIG. 3 :
FIG. 3: The dependence of (left) m h ′ , (middle) the h ′ production cross section via ggF at √ s = 14 TeV and (right) h ′ decay BRs (right) upon the gauge kinetic mixing coupling g.The values corresponding to the BP ofTable IIa are labeled by •.

(
c) pp → h ′ → hh → b bγγ cut-flow at L int = 3000 fb −1 .TABLE IV: S vs B rates for the three signals pursued in our analysis in correspondence of our BP: the 2ℓ + / E T (a), 4ℓ and b bγγ (c) final state.We adopt here √ s = 14 TeV and integrated luminosity of Run 3 and HL-LHC.Inclusive NNLO k-factors from QCD are used here throughout.cut-flow (i.e., E T , M eff and ∆R ℓ + ℓ − ) are presented, alongside the full transverse mass (M ℓ + ℓ − T

FIG. 4 :
FIG.4: S and B distributions in E T normalized to 1 before applying the cut-flow (left), and stacked normalized to the total event rate M ℓ + ℓ − T

FIG. 5 :
FIG.5: S and B distributions in E T (top-left), M ℓ + ℓ − (top-right) and M 4ℓ (bottom), as defined in the text, the former two given before the cut-flow and normalized to 1 while the latter one given after it and normalized to the total event rate for the integrated luminosity L int = 300 fb −1 .

6 .
These are the spectra in the transverse energy of the b bγγ final state (E T ), γγ and b b invariant masses (M γγ and M b b, respectively) and separations (∆R γγ and ∆R b b, respectively).Such a figure also presents the invariant mass of the final state (M γγb b), normalized to the HL-LHC luminosity.As seen from the signal and background responses to the cut-flow, it is clear that knowledge of the m h ′ value, gained during Run 3 of the LHC by exploiting the two previous signatures, is crucial in accessing this signal, which can ultimately be done at the 5σ level, despite the initially overwhelming background.

FIG. 6 :
FIG. 6: S and B distributions in E T (top-left), M γγ (top-right), M b b (middle-left), ∆R γγ (middle-right) ∆R b b (bottom-left) and M γγb b (bottom-right), as defined in the text, the former 5

FIG. 7 :
FIG. 7: Significance of the h ′ → W + W − , ZZ and hh signals that we have studied versus L int for our BP.Data are produced at a center-of-mass energy of √ s = 14 TeV.The rates are computed after applying the relevant kinematical analyses described in the text.The three • points indicate the luminosity choices used in the MC simulations performed.
SM = SU (3) C ⊗ SU (2) L ⊗ U (1) Y ) and the U (1) B−L one are summarized in Table I, where the U (1) Y,B−L charges generators are given by

TABLE I :
Chiral superfields and their quantum numbers in the BLSSM.
) FIG. 1: The Higgs mixing Z H 2i (i = 1, . .., 4) versus the gauge kinetic mixing coupling g.The values corresponding to the Benchmark Point (BP) of (forthcoming)Table IIa are labeled by •.

TABLE II :
BP and relevant outputs.