Phenomenology of supersymmetric Z' decays at the Large Hadron Collider

I study the phenomenology of heavy neutral bosons Z', predicted in GUT-inspired U(1)' models, at the Large Hadron Collider. In particular, I investigate possible signatures due to Z' decays into superymmetric particles, such as chargino, neutralino and sneutrino pairs, leading to final states with charged leptons and missing energy. The analysis is carried out at sqrt{s}=14 TeV, for a few representative points of the parameter space of the Minimal Supersymmetric Standard Model, suitably modified to accommodate the extra Z' boson and consistent with the discovery of a Higgs-like boson with mass around 125 GeV. Results are presented for several observables and compared with those obtained for direct Z' decays into lepton pairs, as well as direct production of supersymmetric particles. For the sake of comparison, Z' phenomenology in an effective supersymmetric extension of the Sequential Standard Model is also discussed.


Introduction
Searching for heavy neutral gauge bosons Z ′ is one of the challenging goals of the experiments performed at the Large Hadron Collider (LHC). In fact, such bosons are predicted in extensions of the Standard Model involving an extra U(1) ′ gauge group, inspired by Grand Unification Theories (GUTs) (see. e.g., [1,2] for a review). Furthermore, Z ′ bosons are also present in the so-called Sequential Standard Model (SSM), where the Z ′ has the same couplings to fermions as the Standard Model (SM) Z boson. Though not being theoretically motivated, the SSM is often used as a benchmark for the experimental searches.
The LHC experiments have so far searched for high-mass neutral gauge bosons Z ′ and have set exclusion limits on its mass m Z ′ . In detail, the ATLAS Collaboration [3] set the limits in the range m Z ′ > 2.22−2.90 TeV for a SSM Z ′ and m Z ′ > 2.51−2.62 TeV for GUT-inspired U(1) ′ models. The same numbers for CMS [4] are instead m Z ′ > 2.59 GeV for the SSM and m Z ′ > 2.26 GeV in U(1) ′ models. However, such analyses were carried out looking for high-mass dilepton pairs (e + e − or µ + µ − ) and assuming that the Z ′ has only Standard Model decay modes. Possible decays beyond the Standard Model (BSM), e.g. in supersymmetric particles, were investigated first in [5] and lately reconsidered in [6][7][8] within the Minimal Supersymmetric Standard Model [9,10]. Although SM decays are still dominant and the most promising for the searches, the opening of new decay channels decreases the branching ratios into electron and muon pairs and therefore the mass exclusion limits. Ref. [11], using a representative point of the MSSM parameter space as in [8], found that the LHC exclusion limits decrease by an amount ∆m Z ′ ≃ 150-300 GeV, once accounting for BSM decay modes at √ s = 8 TeV.
From the viewpoint of supersymmetry the lack of evidence of new supersymmetric particles in the LHC runs at 7 and 8 TeV, together with the discovery of a boson with mass m h = 125.7±0.4 GeV [12] and properties consistent with the Standard Model Higgs boson [13], sets some tight constraints on the mass spectra and couplings of possible supersymmetric models. While awaiting the collisions at 13 and ultimately 14 TeV, it is therefore worthwhile thinking of scenarios, not yet excluded by the current searches and compatible with the Higgs discovery, which may deserve some specific analyses at high luminosity and energy. Extending the MSSM via a U(1) ′ group presents some features, which makes it a pretty interesting scenario, so that novel analyses, looking for signals of supersymmetric Z ′ decays by using current and future data, may be well justified. Unlike direct sparticle production in qq or gg annihilation, the Z ′ is a colourless particle and its mass sets a constraint on the invariant mass of the sparticle pair. Therefore, if one had to discover a Z ′ , its decay modes would be an ideal environment to look for supersymmetry, as they would yield a somewhat cleaner signal, with respect to direct production. Supersymmetric Z ′ decays would also be an excellent framework to study electroweak interactions in regions of the phase space which would not be accessible through other processes, such as Drell-Yan interactions. Moreover, possible decays into pairs of the lightest neutralinos of the MSSM will lead to mono-photon or mono-jet final states, like those which are investigated when looking for Dark Matter candidates.
The reference point of the parameter space chosen in Refs. [8,11] yielded substantial decay rates into supersymmetric particles and was consistent with the present exclusion limits, but did not take into account for the recent discovery of a Higgs-like boson. In this paper I shall extend the work in [8] giving some useful benchmarks for possible Z ′ searches within supersymmetry. First, it will be chosen a set of points in the parameter space yielding a SM-like Higgs boson with a mass around 125 GeV. Then, thanks to the Monte Carlo implementation of the U(1) ′ model and of the SSM, as well as of the MSSM, a phenomenological analysis will be performed and a few final-state distributions in events with supersymmetric Z ′ decays will be presented. On the contrary, Ref. [8] only calculated total production cross sections and branching ratios and left the investigation of differential distributions as an open issue.
In detail, in Section 2 I will shortly review the theoretical framework of the investigation here undertaken, paying special attention to the new features of the MSSM once a Z ′ boson is included. In Section 3 I shall discuss the practical implementation of supersymmetric Z ′ decays in a few computing codes and Monte Carlo event generators. Sections 4, 5 and 6 will deal with the phenomenology of the Z ′ in three scenarios, namely the Z ′ ψ and Z ′ η models, within U(1) ′ gauge theories, and the SSM, respectively. Section 7 will contain some final remarks and comments on possible further developments of this work.

U(1) ′ gauge groups and Minimal Supersymmetric Standard Model
The theoretical framework of supersymmetric Z ′ decays was thoroughly reviewed in [5] and, more recently, in [8]. Hereafter, for the sake of brevity, I shall just point out the essential aspects of the models, taking particular care about the new properties of the MSSM due to the extra Z ′ .
As discussed in [1,2], U(1) ′ groups typically arise from the breaking of a Grand Unification gauge group E 6 of rank 6. The neutral boson Z ′ ψ is associated with the group U(1) ′ ψ , coming from the breaking into SO(10) as follows: The Z ′ χ is instead related to the subsequent breaking of SO(10) according to: The Z ′ ψ and Z ′ χ mix into a generic Z ′ (θ) depending on the mixing angle θ: The Z ′ ψ and Z ′ χ models correspond to θ = 0 and θ = −π/2, respectively. Another scenario, which is often investigated from both theoretical and experimental viewpoints, is the one, characteristic of superstring theories, where E 6 breaks in the Standard Model (SU(2) L × U(1) Y ) and an extra U(1) ′ , labelled as U(1) ′ η : Eq. (4) leads to a Z ′ η boson, with a mixing angle θ = arccos 5/8 in Eq. (3). One can anticipate that the following analysis will be performed for the Z ′ ψ and Z ′ η models, since other models like those leading to the Z ′ χ , as well as the Z I , Z ′ S and Z ′ N , corresponding to the mixing angle θ described in [8], are less interesting, as the Z ′ branching ratios into supersymmetric final states are rather low.
As far as the MSSM is concerned, a few relevant features are inherited by the presence of the extra Z ′ boson. In the Higgs sector, besides the two Higgs doublets of the MSSM, an extra singlet is necessary to break the U(1) ′ group and give mass to the Z ′ . After electroweak symmetry breaking, one is then left with a novel scalar, named H ′ in [8], whose mass is typically larger than m Z ′ . Furthermore, two extra neutralinos are present, associated with the supersymmetric partners of the Z ′ and of the extra Higgs bosons, for a total of six neutralinos: in [8] it was nevertheless argued that these new neutralinos are too heavy to be significant in Z ′ phenomenology. For the purpose of the sfermions, as debated in [5], their masses get an extra D-term correction depending on the sfermion U(1) ′ charges and on the Higgs vacuum expectation values. This contribution to the D-term is not positive definite and therefore it may even drive to unphysical scenarios, where the sfermion squared mass gets negative (see few examples in Ref. [8]).
Besides GUT-inspired models, I will also account for the Sequential Standard Model; unlike the U(1) ′ gauge groups, the SSM is not a real model, but nonetheless it is used by the experimental collaborations as a benchmark for the searches. In fact, if the Z ′ has the same couplings to the fermions as the Z, the production cross section can be straightforwardly computed as a function of the Z ′ mass. Following [7,8] I will assume that even the couplings to sfermions and gauginos are the same as the Z in the MSSM. In principle, a consistent SSM should be built up along the lines of [14], wherein it was explained that any sequential Z ′ must be accompanied by another Z ′ and a longitudinal W ′ . However, employing this improved formulation of the SSM goes beyond the goals of this paper and therefore I shall stick to the approximations in [7,8], with a Z ′ SSM coupled to SM and BSM particles like the Standard Model Z.

Framework for Z ′ supersymmetric decays
Hereafter, I will present a phenomenological analysis of Z ′ production and decay at the LHC, paying special attention to supersymmetric decay modes and comparing the results with those obtained in standard analyses, where only Standard Model channels are allowed. As discussed before, the investigation will be concentrated on the Z ′ ψ , Z ′ η and Z ′ SSM models and, for each scenario, it will be chosen a point in the parameter space not yet excluded by the LHC searches and leading to an interesting Z ′ phenomenology within supersymmetry. In all cases, I will set the Z ′ mass to the value and will use the following relation between U(1) ′ and U(1) Y coupling constants g ′ and g 1 , typical of GUTs: When dealing with the SSM, the Z ′ coupling constant to fermions will be the same as the Z: where g 2 is the SU(2) coupling and θ W the Weinberg mixing angle.
In [8] the authors fixed the Z ′ mass and the MSSM parameters and calculated, either analytically or numerically, particle masses and Z ′ branching ratios into SM and MSSM final states. However, the computation was carried out at leading order (LO) in the couplings g 1 , g 2 and g ′ and therefore the mass of the lightest MSSM neutral Higgs boson, which roughly plays the role of the Standard Model Higgs, was around the value of the Z mass, i.e. about 90 GeV. In this paper, I shall include higher-order corrections, especially top and stop loops, in such a way to recover a light Higgs mass about 125 GeV. For this purpose, I will make use of the Mathematica package SARAH [15] which calculates the mass matrices by using renormalization group equations at one loop 1 . Among the implemented models, SARAH includes the so-called UMSSM, namely the extension of the MSSM through a U(1) ′ gauge group: the output of SARAH is used as a source code for SPheno [17] to create a precision spectrum generator for the given scenario. Model files in the Universal FeynRules Output (UFO) format [18] are then used by the MadGraph code [19] to generate the hard scattering process, with both Z ′ production, i.e. qq → Z ′ , and decay according to the chosen mode. The events are thus written in the Les Houches format and the HERWIG Monte Carlo event generator [20] can provide them with parton showers and hadronization, eventually leading to exclusive final states. The analysis within the SSM is somewhat different, since SARAH and SPheno do not contain this benchmark model. A straightforward implementation can nevertheless be achieved within the package FeynRules itself [18], by simply adding to the MSSM code a Z ′ boson, coupled to SM and BSM particles as the Z in the Standard Model. FeynRules then constructs the UFO model files which can be read by MadGraph and HERWIG to simulate full hadron-level events.
In order to perform a consistent investigation and comparison with previous work in [5,7,8], few further changes were implemented into SARAH and FeynRules. In SARAH, I added Dirac right-handed neutrinos and sneutrinos, not present in its default version, in order to allow Z ′ decays into both left-and right-handed neutrino and sneutrino pairs. When modifying SARAH, the mass of the right-handed neutrino is set to zero by default. In the FeynRules implementation of the SSM, the Z ′ W W coupling was suppressed: in fact, if one naively assumed that the Z ′ couples to W W pairs like the Z, on the one hand the decay Z ′ → W W would largely dominate, on the other the unitarity of the theory would be in trouble, because of the enhancement of W W scattering mediated by a Z ′ . A consistent SSM, possibly built up along the lines of [14], would not suffer from this drawback. 2 In the choice of the working reference point for this investigation, I will make use of the results in [21,22], wherein the authors determined the regions of the supersymmetric phase space which are not yet excluded by the direct searches and are consistent with a Higgs of 125 GeV, taking care of the limits from flavour physics and Dark Matter searches. Stricly speaking, the results of [21,22] are obtained for the so-called phenomenological MSSM (pMSSM), which makes a few simplifying assumptions in order to reduce the number of parameters. In detail, the pMSSM assumes that the soft supersymmetry-breaking terms are real, there is no new source of CP violation, diagonal matrices for the sfermion masses and trilinear couplings, i.e. no flavour change at tree-level, same soft masses and trilinear couplings at least for the first two generations of squarks and sleptons at the electroweak scale. The leftover parameters are then the ratio of the MSSM neutral Higgs vacuum expectation values tan β = v 2 /v 1 , the Higgs (higgsino) mass parameter µ, the soft masses of bino and wino M 1 and M 2 , the sfermion masses and the trilinear couplings. As in [5,8], because of the Z ′ , one has an extra gauginoB ′ , whose soft mass parameter is named M ′ .
For all the scenarios which will be studied, M 1 , M ′ , tan β and µ will be set as follows: Given M 1 , the wino mass M 2 can be obtained by using the relation Furthermore, in the Standard Model it is well known that bottom and especially top quarks play a fundamental role in Higgs phenomenology: in fact, top loops give the highest corrections to the Higgs mass and the largest contribution to the Higgs production cross section in gluon fusion. It is therefore obvious that in the MSSM stops and sbottoms, the supersymmetric partners of top and bottom quarks, will deserve special attention and, although they have not been observed, the measured mass of the Higgs boson sets some constraints on their masses. In fact, they can be be very heavy, i.e. their mass in the TeV range, but even quite light, say of the order of a few hundreds GeV, provided that the mixing is large, i.e. the mixing parameter A t is about a few TeV (see, e.g., the discussion in [23]). The latter case is often chosen in the supersymmetry studies, namely the first two squark generations heavier than sbottoms and stops. In this paper, I shall consider both possibilities: all three squark generations heavy and generate, as well as the option of a lighter third generation. The authors of [21] define the mixing parameter: which runs in the range 0 < x t < √ 6 M S , M S being the geometrical average of the stop masses, i.e. M S = √ mt 1 mt 2 , where mt 1 and mt 2 are obtained after adding to the soft mass m 0 t the D-term (see [5]) and diagonalizing the stop mixing matrix. In Eq. (9), A t is a dimensionful quantity related to the dimensionless trilinear cou- where m t is the top quark mass, which will be fixed to m t = 173 GeV. For x t = 4 TeV, one obtains that, using the numbers in (8), A t ≃ 4 TeV and A t,0 ≃ 23.2. Later on, all the trilinear couplings, as well as A λ , contained in the scalar-potential term involving the neutral components of the three Higgs bosons In the following sections, I shall present the results yielded at the LHC by the models U(1) ′ ψ , U(1) ′ η and, for the sake of comparison, by the SSM. In [8], a few decay chains where taken into account: they all started with a primary supersymmetric decay, i.e. into pairs of charged sleptons, sneutrinos, charginos or neutralinos, and eventually yielded final states with two or four charged leptons and missing transverse energy (MET), associated with neutrinos or light neutralinos. For each model, I will consider a specific point in the parameter space, with the goal of maximizing the branching ratio in at least one of the supersymmetric modes, eventually leading to leptons and missing energy. Then, I shall present some leptonic final-state distribution, in the scenario which maximizes the BSM Z ′ decay rate. Whenever the comparison is consistent, the results will be confronted with those from the standard search strategy, where the Z ′ directly decays into a SM charged-lepton pair and has no BSM decay width. 3 Note that SARAH requires A λ / √ 2 ≃ 2.8 TeV as an input, rather than A λ in Eq. (10).

Phenomenology -U(1) ′ ψ model
The model U(1) ′ ψ leads to a heavy boson Z ′ ψ , corresponding to a mixing angle θ = 0 in Eq. (3). In [8], it was found that, in a reference point of the parameter space and for a Z ′ ψ mass between 1 and 5 TeV, about 35% of the Z ′ ψ width is due to the supersymmetric modes. However, as discussed above, that scenario was not consistent with a Higgs mass of 125 GeV and the supersymmetric mass spectrum was computed only at tree level.
Hereafter, the representative points of the parameter space will be chosen in order to satisfy the Higgs mass constraint and the supersymmetry exclusion limits. The quantities M 1 , M ′ , µ and tan β are fixed as in Eq. (8); as for sfermions, I assume that sleptons, as well as the first two generations of squarks, are degenerate at the Z ′ ψ mass scale and have mass 4 : where ℓ = e, µ, τ , ν = ν e , ν µ , ν τ and q = u, d, c, s. The soft masses of stops and sbottoms are instead fixed as follows: The sfermion masses at the Z ′ ψ mass scale are obtained after summing to the numbers in (11) and (12) the D-terms due to U(1) ′ and electroweak symmetry breaking. The equations for the D-term correction to the masses of up-and down-type squarks and sleptons are given in [5] and will not be reported here for the sake of brevity; at leading order the masses yielded by the SARAH code agree with those computed by using the expressions in [5]. For m Z ′ = 2 TeV, the sfermion masses are quoted in Tables 1 and  2, for squarks and sleptons, respectively. The notationq 1,2 ,l 1,2 andν 1,2 refers to the mass eigenstates, which differ from the gauge onesq L,R ,l L,R andν L,R because of the mixing; the mixing terms are proportional to the fermion squared masses, and therefore they are mostly relevant in the case of the stops. From such tables, one can learn that the impact of the D-term is about 100 GeV on squarks and even larger than 200 GeV on sleptons; also, in the chosen reference point, the D-term can be either positive or negative.
In the Higgs sector, there will be three neutral scalars (h, H and H ′ ), where h and H are the usual MSSM ones and H ′ is the extra U(1) ′ -inherited one, a pseudoscalar A and a pair of charged H ± ; The Higgs masses, computed by SARAH at one loop, are reported in Table 3. The lightest scalar h has roughly the mass of the SM-like Higgs boson, H is approximately as heavy as the Z ′ ψ , whereas H ′ , A and the charged H ± are above 4 TeV, and therefore too heavy to be significant for Z ′ ψ phenomenology. The λ parameter, contained in the trilinear potential V λ , is related to µ and the vacuum expectation value v 3 of the extra Higgs boson Table 4 contains the masses of the two charginos (χ ± 1,2 ) and of the six neutralinos (χ 0 1 , . . .χ 0 6 ): in principle, with the exception ofχ 0 6 , whose mass is even above 6 TeV, several Z ′ ψ decay modes into pairs of charginos and neutralinos are kinematically permitted.
Given the numbers in Tables 1-4, one can calculate, by means of the SPheno program, the branching ratios of the Z ′ ψ into Standard Model and supersymmetric final states. At leading order in g ′ , i.e. O(g ′2 ), the main Z ′ ψ branching ratios are quoted in Table 5, for m Z ′ = 2 TeV and omitting decay rates which are below 0.1%. The Standard Model decays are still the dominant ones, but one has an overall 28.3% branching ratio into supersymmetric final states, which deserves further investigation. In particular, the decay into chargino pairsχ + Since the highest BSM rate is the one into chargino pairs, it is worthwhile carrying out the phenomenological analysis for final states originated from a Z ′ ψ →χ + 1χ − 1 process. As discussed in [8], primary decays into chargino pairs can lead to a chain yielding charged leptons and missing energy in the final states. To gauge the rates of the different final states, one must compute the branching ratios of the 2-and 3-body decays of the charginosχ ± 1 . These numbers, calculated by means of SPheno, are quoted in Table 6. As hadronic final states are likely affected by large QCD backgrounds, I shall focus on the modes with neutralinos and leptons, which will eventually lead to the following decay chain: with ℓ = µ, e. The neutrinos and neutralinos in (13) will give rise to some missing Table 1: Masses of squarks in the MSSM, for the chosen reference point and accounting for the U(1) ′ ψ modifications. The masses ofq 1,2 differ from those of the gauge eigenstates q L,R because of the mixing contribution, relevant especially in the stop case. All numbers are expressed in GeV.
energy; the diagram of such a process is presented in Fig. 1. The U(1) ′ ψ /MSSM model, in the UFO format, can be used by MadGraph to generate parton-level events and then by HERWIG to simulate showers and hadronization. The cross section for the process pp → Z ′ ψ , computed by MadGraph at LO, by using the CTEQL1 set [24] for the initial-state parton distributions and m Z ′ = 2 TeV, is σ(pp → Z ′ ) ≃ 0.13 pb. The cross section for the decay chain (13) is then given by: σ(pp → Z ′ ψ → ℓ + ℓ − + MET) ≃ 7.9 × 10 −4 pb at 14 TeV. This means that such events can be, e.g., about 80 for a luminosity L ≃ 100 fb −1 , almost 240 at 300 fb −1 and so on. Though being less likely than SM channels, supersymmetric decays lead to pretty different final states which, if the Z ′ mass is known, have a fixed invariant mass.
In the following, I will present some relevant leptonic distributions and, whenever the comparison makes sense, the results will be shown for both direct decays Z ′ → ℓ + ℓ − and the cascade (13). Fig. 2 presents the transverse momentum spectrum of leptons produced in both processes: as the production of ℓ + and ℓ − is symmetric, the histograms contain the p T of both leptons. For direct production, the p T distribution starts to be non-negligible for p T > 200 GeV, i.e. about m Z ′ /10, then increases and reaches a peak about p T ≃ 1 TeV = m Z ′ /2; above 1 TeV the spectrum rapidly decreases. On the contrary, in the case of the decay chain (13), the lepton transverse momentum has a completely different behaviour: it increases in the low range and reaches its peak at p T ≃ 15 GeV, then it smooothly decreases, in such a way that there are nearly no Figure 1: Final state with two charged leptons and missing energy, due to neutrinos and neutralinos, through a primary decay of the Z ′ into a chargino pair. events with leptons with p T > 60 GeV. The observed spectra can be easily understood, since in one case the two leptons get the full initial-state transverse momentum, whereas, in the case of the cascade, a consistent (missing) p T is lent to neutrinos and neutralinos, which significantly decreases the p T of ℓ + and ℓ − .  1 decay. Right: angle between the two leptons ℓ ± and in the laboratory frame for direct Z ′ ψ → ℓ + ℓ − production (dashes) and after the decay chain in Eq. (13) (solid histogram).
In Fig. 3 one can instead find the invariant mass m ℓℓ (left) and the angle θ between the two charged leptons in the laboratory frame (right). The invariant mass is plotted  only for the cascade (13), since, for direct Z ′ ψ → ℓ + ℓ − , it would just be a narrow resonance with the same mass and width as the Z ′ ψ . When the leptons come from the process in Eq. (13), their invariant mass does not have to reproduce the Z ′ ; it varies essentially in the range 20 GeV < m ℓℓ < 100 GeV and has its maximum value about m ℓℓ ≃ 45 GeV. The θ spectrum, in the case of direct production, exhibits a maximum about θ ≃ 3, a value close to back-to-back production, i.e. θ = π. When the leptons are accompanied by missing energy, the θ distribution is broader, lies above the directproduction spectrum at small and middle angles, below at high θ, and is peaked at a lower θ ≃ 2.75. Fig. 4 presents the ℓ ± rapidity distributions: the η spectrum for leptons originated from a supersymmetric cascade presents more events at η = 0, corresponding to production perpendicular to the beam axis, whereas one has a higher probability of leptons at small angle with respect to the beam, i.e. large values of |η|, when they come from a primary Z ′ ψ → ℓ + ℓ − process. Fig. 5 presents the differential distributions of two observables which are typically studied in supersymmetry searches: the sum of the transverse momenta of 'invisible' particles like neutrinos and neutralinos, also called MET (missing transverse energy), and the transverse mass m T of all final-state particles (neutrinos, neutralinos and charged leptons) in (13). They are defined as follows: The MET spectrum is significant essentially in the low range: it is sharply peaked at MET≃ 15 GeV and smoothly decreases so that for MET> 300 GeV there are nearly no events. The transverse mass distribution exhibits instead an opposite behaviour: it is relevant in the range m Z ′ /2 < m T < m Z ′ and presents a sharp peak at m T ≃ 1.8 TeV, just below the Z ′ ψ mass threshold.
Since the Z ′ ψ branching ratio into neutralino pairsχ 0 1χ 0 1 in almost 5%, even the process has a non-negligible cross section, i.e. σ(pp → Z ′ ψ → MET) ≃ 6.4 × 10 −3 pb, which yields about 640 events at L = 100 fb −1 and up to almost 2 × 10 3 at 300 fb −1 . In fact, unlike charginos, the lightest neutralinos are stable particles in the MSSM, and therefore the cross section of the process (15) does not get any further branching fraction which possibly decreases the event rate. Therefore, the U(1) ′ ψ extension of the MSSM could be an interesting scenario to search for Dark Matter candidates in the 14 TeV run of the LHC. The typical signature is given by mono-photon or mono-jet final states, with the photon and jet being associated to the initial-state radiation from the ncoming quarks. The actual implementation of photon isolation criteria or jet-clustering algorithms goes beyond the scopes of this paper and will not debated here. Nevertheless, Fig. 6 displays the missing transverse energy (MET) due to the neutralinos in the final state in (15). The neutralino MET distribution is peaked at MET ≃ 10 GeV and smoothly decreases, up to the point of being quite negligible for MET > 300 GeV.

Phenomenology -U(1) ′ η model
The model U(1) ′ η corresponds to a mixing angle θ = arccos 5/8 and, even in the reference point considered in [8], gives rise to an interesting Z ′ η phenomenology within supersymmetry, accounting for about 1/4 of the total width. In the following, though keeping the constraints due to the Higgs mass and direct supersymmetry searches, I shall choose a slightly different representative point of the parameter space, with respect to the previous U(1) ′ ψ model, in order to possibly enhance supersymmetric Z ′ η decays. In particular, the Z ′ η will still have mass m Z ′ = 2 TeV, M 1 , M 2 , M ′ , tan β, µ, A q , A ℓ and A λ will be set to the values in Eqs. (8) and (10), like in the Z ′ ψ scenario, whereas all three generations of squarks and sleptons will be degenerate at the Z ′ η scale, with masses equal to the following values: where q = u, d, c, s, t, b and ℓ = e, µ, τ . After adding the D-term, the masses of squarks and sleptons are those quoted in Tables 7 and 8, exhibiting a substantial impact of the D-term. The squark masses increase or decrease by few hundreds GeV, whereasl 2 andν 1 get slightly heavier, ml 2 a bit lower andν 2 considerably lighter, by about 850 GeV. This is therefore an example of negative D-term; in the scenarios investigated in [8], negative and large D-terms have even led to the exclusion of a few Z ′ models, as some sfermion squared masses had become negative, and therefore unphysical. Table 9 contains the masses of the Higgs bosons, which are rather similar to those obtained for the Z ′ ψ case: m h ≃ 125 GeV, m H ≃ m Z ′ and the masses of H ′ , A and H + are above 4 TeV. With those numbers for the Higgs boson, the λ parameter in the trilinear potential V λ is now equal to λ = √ 2µ/v 3 ≃ 4.3 × 10 −2 . Chargino and neutralino masses are reported in Table 10: the two charginos (χ ± 1 andχ ± 2 ) and the first four neutralinos (χ 0 1 . . .χ 0 4 ) are roughly as heavy as those in the Z ′ ψ model previously considered;χ 0 5 andχ 0 6 have masses above 1.5 and 2.5 TeV, respectively, and, being so heavy, are quite negligible for Z ′ η phenomenology.  Table 8: Masses of sleptons in the Z ′ η scenario, with a soft term m 0 ℓ = mν = 1.3 TeV. All numbers are in GeV and ℓ = e, µ.  Table 11 presents the branching ratios of the Z ′ η into the most significant decay channels: the Standard Model modes are still the most relevant ones, with the supersymmetric channels accounting for about 21% of the total width. Among the supersymmetric channels the one into sneutrino pairsν 2ν * 2 exhibits the highest rate, slightly below 10% after adding up all three flavours, , whereas the decay intoχ + 1χ − 1 accounts for about 6% and those into neutralino pairs for another 5%. As done for the purpose of the previous model, the phenomenological analysis will be undertaken for the supersymmetric mode with the highest branching ratio, i.e. Z ′ η →ν 2ν * 2 . In the notation used in this paper,ν 2 is the supersymmetric partner of the ν 2 , which, after the mixing, is mostly a right-handed neutrino. The sneutrinos decay into neutrinos and neutralinos, with branching ratios given in Table 12: according to whether the neutralino is aχ 0 3 ,χ 0 2 or aχ 0 1 , the decay rate varies from 4% to almost 60%. Following [8], an interesting cascade, leading to a final state with leptons and missing energy, is the one driven by the decayν 2 →χ 0 2 ν 2 , followed by a decay ofχ 0 2 into the lightestχ 0 1 and a pair of charged leptons, through an intermediate charged sleptonl ± , as in Fig. 5. In other words, I shall investigate the following decay chain:   The final state of the cascade (17) is then made of four charged leptons and missing energy, because of two light neutralinos and two neutrinos. The main branching fractions ofχ 0 2 are quoted in Table 13: the rate in final states with the lightest neutralinoχ 0 1 and a charged-lepton pair, interesting to recover the event in Fig. 17, is about 13%, with a fraction 2/3, i.e. nearly 9%, leading to final-state electrons or muons. The cross section for Z ′ η production in the above scenario at 14 TeV, computed by MadGraph, is σ(pp → Z ′ η ) ≃ 0.18 pb. Given the numbers in Tables 12 and 13, and accounting only for e ± and µ ± , the cross section of the cascade (17) is thus σ(pp → Z ′ η → 4ℓ + MET) ≃ 1.90 × 10 −4 pb, which yields about 20 events at L = 100 fb −1 and 60 at 300 fb −1 .
In Fig. 8 the lepton transverse momenta in the decay chain (17) and in direct decays Z ′ η → ℓ + ℓ − are plotted: unlike the Z ′ ψ case, where we had final states with two charged leptons, with roughly the same kinematic properties, the decay chain (17) presents four leptons, with different kinematics. Therefore, in Fig. 8, on the left-hand side we have the spectra in p T of the hardest (solid) and softest (dashes) lepton in the cascade (17), on the right-hand side the p T of ℓ ± in Z ′ η → ℓ + ℓ − . In the cascade, the hardest lepton has a broad spectrum, relevant in the 10 GeV< p T < 50 GeV range and maximum around p T ≃ 20-25 GeV; the p T of the softest ℓ ± is instead a narrow distribution, substantial only for 8 GeV< p T < 20 GeV and sharply peaked at p T ≃ 11 GeV. The spectrum in direct production Z ′ η → ℓ + ℓ − is roughly the same as in the Z ′ ψ case: in fact, using normalized distributions like (1/σ) dσ/dp T minimizes the impact of the value of the coupling. In Fig. 9, I have instead included two invariant-mass spectra: m 4ℓ , the invariant mass of the four charged leptons in (17), and m ℓℓ , invariant mass of of the ℓ + ℓ − pairs in secondary χ 0 2 → χ 0 1 ℓ + ℓ − processes, assuming that one is ideally able to identify and reconstruct the leptons coming from eachχ 0 2 decay.
The m ℓℓ spectrum is significant only in the range 4 GeV < m ℓℓ < 13 GeV and peaked around m ℓℓ ≃ 9 GeV; m 4ℓ is relevant between 40 and 150 GeV and is maximum at m 4ℓ ≃ 70 GeV. Finally, Fig. 10 presents the spectrum of the missing transverse energy and transverse mass of the final states in the process in Fig. 5, defined as in Eq. (14). The MET distribution is similar to the Z ′ ψ one, peaked at 20 GeV and decreasing quite rapidly for larger MET values; the transverse mass is relevant in the range m Z ′ /2 < m T < m Z ′ and is overall a broader and smoother distribution with respect to the previous model, with a peak still around m T ≃ 1.8 TeV.

Phenomenology -Sequential Standard Model
The Sequential Standard Model (SSM) is the simplest extension of the Standard Model, since it just contains Z ′ and possibly W ′ bosons, with the same couplings to fermions as the Standard Model Z and W . Although it does not have any strong theoretical motivation, as happens for GUT-inspired gauge symmetries, the SSM turns out to be very useful as a benchmark model, since, once the coupling to quarks is fixed, the production cross section can be computed. Extending the SSM to supersymmetry will imply, in the simplest formulation, that the couplings of the Z ′ SSM to MSSM sfermions and gauginos are the same as the Z. As discussed in Section 2, the Z ′ SSM coupling to W W pairs must be suppressed, otherwise the W W scattering cross section, mediated by a Z ′ SSM , would diverge. In the representative point of Ref. [8], the Z ′ SSM had substantial branching fractions in supersymmetric channels, yielding an overall contribution around 40% to the total decay width.
As in the U(1) ′ -based analyses, I shall set the Z ′ SSM mass to the value m Z ′ = 2 TeV and choose a reference point where M 1 , tan β and µ, as well as the trilinear couplings A q , A ℓ and A λ are still the same as in Eqs. (8) and (10). For the sake of obtaining a light Higgs mass of 125 GeV and an interesting phenomenology in supersymmetry, the  Left: missing transverse energy due to neutrinos and neutralinos soft sfermion masses at the Z ′ SSM mass scale will be chosen as: where m 0 q is the soft mass of the first two squark generations, i.e. q = u, d, c, s, while sbottoms and stops are lighter, as was done in the U(1) ′ ψ model.
After adding to the quantities in Eq. (18) the D-term correction, one will get the squark and slepton masses quoted in Tables 14 and 15: unlike the cases analyzed before, the impact of the D-term for the chosen SSM point is small and not larger than 5%. In fact, in the SSM the D-term only contains the contribution due to electroweak symmetry breaking, whereas the additional U(1) ′ term is clearly absent. In the Higgs sector, there is no extra H ′ , which was instead necessary in the breaking of the U(1) ′ symmetry, but the particle content is the same as in the MSSM. Their masses are quoted in Table 16: the light h has always mass around 125 GeV and the other three bosons between 630 and 640 GeV.    The masses of charginos and neutralinos are given in Table 17: unlike the U(1) ′ models, in the SSM the neutralino sector is the same as in the MSSM, i.e. fourχ 0 1 . . .χ 0 4 . With the exception ofχ ± 2 andχ 0 4 , the gaugino masses are of the order of a few hundreds GeV and therefore they are light enough to be capable of contributing to the width of a 2 TeV Z ′ SSM . The branching ratios of the Z ′ SSM into Standard Model and supersymmetric channels are given in Table 18. The total rate into BSM final states is 27%, with the highest fraction being the one into charginosχ + 1χ − 1 , about 17%; decays into neutralinos and sneutrinos account for about 10%, whereas SM modes are the remaining 73%.
As done for the U(1) ′ models, the analysis will be carried out for the supersymmetric channel with the highest rate, i.e. the one into chargino pairs, possibly leading to final states with leptons and missing energy, like in Fig. 1. The main chargino branching ratios are quoted in Table 19: the Cabibbo-favoured decays intoχ 0 1 ud andχ 0 1 cs are largely dominant, but even those into electrons and muons, i.e. e + ν e and µ + ν µ pairs, are quite relevant, accounting for about 1/4 of the total Z ′ SSM rate.
As done previously, the analysis will be undertaken for chargino decays into leptons and light neutralinos, then leading to final states with two charged leptons and missing energy: with ℓ = e, µ. At √ s = 14 TeV, the inclusive cross section reads σ(pp → Z ′ SSM ) ≃ 0.63 pb and the one of the chain (19) iσ(pp → Z ′ SSM → ℓ + ℓ − + MET) ≃ 6.18 × 10 −3 pb, implying about 600 final states with e + e − or µ + µ − and missing energy in the phase L = 100 fb −1 and even few thousands at 300 fb −1 . It is thus confirmed the finding of Ref. [8], where it was observed that the SSM is the scenario which enhances both production cross section and rates into supersymmetric final states.
In Fig. 11 the lepton transverse momentum is presented for primary and secondary lepton production in Z ′ SSM decays, ehibiting features rather similar to the Z ′ ψ case. In Z ′ SSM → ℓ + ℓ − events, the normalized differential cross section 1/σ(dσ/dp T ) increases with p T , is sharply peaked around p T ≃ m Z ′ /2 and rapidly decreases, so that there are nearly no events for p T > 1.3 TeV. On the contrary, when the leptons are produced through a primary Z ′ SSM →χ + 1χ − 1 process, the distribution is sharply peaked in the low p T range, about p T ≃ 11 GeV, rapidly goes down, being completely negligible for p T > 40 GeV.
The rapidity distribution, presented in Fig. 12 (left) is comparable with Z ′ ψ decays, with a higher fraction of events around η = 0 when the lepton comes from the cascade and at large |η| for ℓ ± yielded by a direct Z ′ SSM → ℓ + ℓ − . Even the spectrum of θ (right-      hand side of Fig. 12), the opening angle between ℓ + and ℓ − , qualitatively exhibits the same features as the U(1) ′ ψ case: the decay chain (19) yields a broader distribution, with more events for middle θ values and less at small and very high θ. The invariant mass distribution m ℓℓ , displayed in Fig. 13, is relevant in the range 20 GeV < m ℓℓ < 80 GeV and reaches its maximum value at m ℓℓ ≃ 37 GeV. Of course, the ℓ + ℓ − invariant-mass distribution in Z ′ SSM → ℓ + ℓ − processes is a Breit-Wigner function, peaked at m ℓℓ ≃ m Z ′ , which is instead omitted. The MET spectrum is peaked around 20 GeV and rapidly decreases at larger values, whereas the m T distribution is broader than in the Z ′ ψ scenario, is substantial for 1 TeV< m T < 2.5 TeV and maximum around the Z ′ SSM mass, i.e. m T ≃ 2 TeV.

Conclusions
I presented a phenomenological analysis of supersymmetric Z ′ decays at the LHC, for √ s = 14 TeV and a few models, based on GUT-inspired U(1) ′ symmetries and on the Sequential Standard Model. The MSSM was suitably extended, in order to accommodate the new features due to the U(1) ′ group and the extra Z ′ boson, and the reference points in the parameter space were chosen in such a way to recover a light Higgs with mass of 125 GeV and obtain relevant Z ′ branching ratios in the supersymmetric channels.
Within the GUT-driven models, the analysis was carried out for the so-called U(1) ′ ψ and U(1) ′ η groups, since, even in previous work on supersymmetric Z ′ decays, they were the theoretical scenarios where the supersymmetric signals were enhanced. When fixing the soft squark masses, two options were considered, namely degenerate squarks for all three generations as well as lighter stops and sbottoms with respect to the first two generations. It was found that, in both U(1) ′ models, for the chosen parameters and m Z ′ = 2 TeV, supersymmetric modes account for about 25-30% of the Z ′ width, with the decays into chargino and sneutrino pairs yielding the highest supersymmetric branching ratios for the Z ′ ψ and Z ′ η models, respectively. The Z ′ ψ scenario had also a visible rate into the lightest neutralinosχ 0 1 , which could be a useful channel to search for Dark Matter candidates.
In the Z ′ ψ case, it was then considered a decay chain, initiated by a Z ′ ψ →χ + 1χ − 1 process, leading to a final state with two charged leptons and missing transverse energy, due to the production of neutrinos and neutralinos. About O(100) of such events for luminosities of 100 or 300 fb −1 , as expected in the 14 TeV LHC run. The decay into neutralinos (χ 0 1χ 0 1 ) yields an even larger number of events, about O(10 3 ) at 14 TeV, and therefore the U(1) ′ ψ extension of the MSSM may be worth to be investigated when looking for Dark Matter particles at the LHC. In the Z ′ η scenario, the Z ′ η →ν 2ν * 2 process, whereν 2 is mostly a right-handed sneutrino, can give rise to a chain yielding four charged leptons and again missing energy. The expected rate of such events is lower than the Z ′ ψ scenario, but still a few dozens of events are expected for pp collisions at 14 TeV. In both U(1) ′ models, observables like lepton trasverse momentum, rapidity, opening angle and invariant mass, as well as missing transverse energy and transverse mass, are peculiar of supersymmetric decays; the spectra are rather different from those obtained in direct Z ′ → ℓ + ℓ − processes and, because of the Z ′ -mass constraint, from other supersymmetry searches.
For the sake of comparison, even the Sequential Standard Model was investigated: in the chosen point of the parameter space, it is still the decay into charginos, leading to final states with two charged leptons and missing transverse energy, the most promising supersymmetric channel. Several hundreds of events are in fact foreseen in the high-energy LHC run, and even O(10 3 ) for a luminosity of 300 fb −1 . The final-state distributions for the Z ′ SSM are similar to those obtained for the Z ′ ψ , as in both cases one has two charged leptons, neutrinos and neutralinos, but nevertheless some peculiar features, due to the different couplings, are still visible.
In summary, the expected rates and final-state observables would make supersymmetric Z ′ decays a rather interesting investigation to search for supersymmetry, once the Z ′ mass were to be known. For the time being, opening the supersymmetric decay channels up will result in lowering the Z ′ mass exclusion limits, since the expected rates in dilepton pairs decrease. Therefore, although the presented analysis will be useful to search for supersymmetry only after the possible discovery of the Z ′ , it should be possibly taken into account when determining the Z ′ mass exclusion limits. Once the data on high-mass leptons are available even at √ s = 14 TeV, it will be very interesting comparing the data with the theory results on the product σ(pp → Z ′ ) × BR(Z ′ → ℓ + ℓ − ), as done in [11] for the analysis at 8 TeV, and determine the exclusion limits accounting for supersymmetric decays. However, a complete analysis should necessarily compare possible supersymmetric signals in Z ′ decays with the backgrounds coming from the Standard Model processes as well as non-supersymmetric Z ′ decays and include the detector simulation. The computation of the backgrounds and the implementation of detector effects is presently in progress.
Furthermore, beyond the models here investigated, which are among those accounted for in the experimental analyses, it may be worthwhile studying in the near future other scenarios, such as the leptophobic models (see, e.g., the pioneering work in [25] or late studies in [26]), wherein the Z ′ does couple to quarks, thus allowing production via qq → Z ′ , but the coupling to leptons is suppressed. Within supersymmetry, the very fact that the Z ′ is leptophobic necessarily decreases the SM rate and enhances the branching ratios in supersymmetric particles. As Z ′ decays into charginos and neutralinos played a major role in the analysis here presented, a possible application of this work is in the context of split supersymmetry [27], wherein the scalar particles are much heavier than the gauginos, which are therefore the only supersymmetric particles accessible at colliders. Investigations of leptophobic Z ′ models as well as of Z ′ bosons in the framework of split supersymmetry are in progress as well.