Predictions of the Constrained Exceptional Supersymmetric Standard Model

We discuss the predictions of a constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m_0, soft trilinear coupling A_0 and soft gaugino mass M_1/2. We predict a supersymmetry (SUSY) spectrum containing a light gluino, a light wino-like neutralino and chargino pair and a light bino-like neutralino, with other sparticle masses except the lighter stop being much heavier. In addition, the cE6SSM allows the possibility of light exotic colour triplet charge 1/3 fermions and scalars, leading to early exotic physics signals at the LHC. We focus on the possibility of a Z' gauge boson with mass close to 1 TeV, and low values of (m0,M_1/2), which would correspond to an LHC discovery using"first data", and propose a set of benchmark points to illustrate this.


Introduction
The minimal supersymmetric standard model (MSSM) [1] provides a very attractive supersymmetric extension of the standard model (SM) in which the superpotential contains the bilinear term µH d H u , where H d,u are the two Higgs doublets which develop vacuum expectation values (VEVs) at the weak scale and µ is the supersymmetric Higgs mass parameter which can be present before SUSY is broken. However, despite its attractiveness, the MSSM suffers from the µ problem: one would naturally expect µ to be either zero or of the order of the Planck scale, while, in order to get the correct pattern of electroweak symmetry breaking (EWSB), µ is required to be in the TeV range.
It is well known that the µ term of the MSSM can be generated effectively by the low energy VEV of a singlet field S via the interaction λSH d H u . However, although an extra singlet superfield S 1 seems like a minor modification to the MSSM, which does no harm to either gauge coupling unification or neutralino dark matter, there are further costs involved in this scenario since the introduction of the singlet superfield S leads to an additional accidental global U(1) (Peccei-Quinn (PQ) [2]) symmetry which will result in a weak scale massless axion when it is spontaneously broken by S [3]. Since such an axion has not been observed experimentally, it must be removed somehow. This can be done in several ways resulting in different non-minimal SUSY models, each involving additional fields and/or parameters [4,5]. For example, the classic solution to this problem is to introduce a singlet term S 3 , as in the next-to-minimal supersymmetric standard model (NMSSM) [4], which reduces the PQ symmetry to the discrete symmetry Z 3 . However the subsequent breaking of a discrete symmetry at the weak scale can lead to cosmological domain walls which would overclose the Universe.
A cosmologically safe solution to the axion problem of singlet models, which we follow in this paper, is to promote the PQ symmetry to an Abelian U(1) ′ gauge symmetry [6].
The idea is that the extra gauge boson will eat the troublesome axion via the Higgs mechanism resulting in a massive Z ′ at the TeV scale. The necessary U(1) ′ gauge group could be a relic of the breaking of some unified gauge group at high energies. Recall that the unification of gauge couplings in SUSY models allows one to embed the gauge group of the SM into Grand Unified Theories (GUTs) based on simple gauge groups such as SU (5), SO(10) or E 6 . In particular the E 6 symmetry can be broken to the rank-5 subgroup SU(3) C × SU(2) L × U(1) Y × U(1) ′ where in general U(1) ′ = U(1) χ cos θ + U(1) ψ sin θ [7], where the two anomaly-free U(1) ψ and U(1) χ symmetries originate from the following breakings: E 6 → SO(10) × U(1) ψ , SO(10) → SU(5)× U(1) χ .
Within the class of E 6 models there is a unique choice of Abelian gauge group which 1 Note that we drop hats on the superfields. allows zero charges for right-handed neutrinos and thus large Majorana masses and a high scale see-saw mechanism, namely the U(1) N gauge symmetry given by θ = arctan √ 15.
This defines the so-called exceptional supersymmetric standard model (E 6 SSM) [8] In this Letter we discuss some of the predictions of particular relevance to the LHC from a constrained version of the E 6 SSM (cE 6 SSM), based on a universal high energy soft scalar mass m 0 , soft trilinear coupling A 0 and soft gaugino mass M 1/2 . Our primary focus is on the most urgent regions of parameter space which involve low values of (m 0 , M 1/2 ) and low Z ′ gauge boson masses which would correspond to an early LHC discovery using "first data". To illustrate these features we propose and discuss a set of "early discovery" benchmark points, each associated with a Z ′ gauge boson mass around 1 TeV and (m 0 , M 1/2 ) below 1 TeV, which would lead to an early indication of the cE 6 SSM at the LHC. We find a SUSY spectrum consisting of a light gluino of mass ∼ M 3 , a light winolike neutralino and chargino pair of mass ∼ M 2 , and a light bino-like neutralino of mass ∼ M 1 , where M i are the low energy gaugino masses, which are typically driven small by renormalisation group (RG) running. Sfermions are generally heavier, but there can be an observable top squark. There may also be light exotic colour triplet charge 1/3 fermions and scalars, whose masses are controlled by independent Yukawa couplings. Some first results have already been trailed at conferences [9] and a longer paper containing full details of the analysis is in preparation [10].
In section 2 we briefly review the E 6 SSM, then in section 3 we introduce the cE 6 SSM.
Section 4 describes the experimental and theoretical constraints and section 5 discusses the aforementioned predictions of the cE 6 SSM elucidated by five "early discovery" benchmark points. Section 6 concludes the paper.

The E 6 SSM
One of the most important issues in models with additional Abelian gauge symmetries is the cancellation of anomalies. In E 6 theories, if the surviving Abelian gauge group factor is a subgroup of E 6 , and the low energy spectrum constitutes a complete 27 representation of E 6 , then the anomalies are cancelled automatically. The 27 i of E 6 containing the three quark and lepton families decompose under the SU(5) × U(1) N subgroup of E 6 as follows: The first and second quantities in the brackets are the SU (5) representation and extra U(1) N charge while i is a family index that runs from 1 to 3. From Eq. (1) we see that, in order to cancel anomalies, the low energy (TeV scale) spectrum must contain three extra copies of 5 * + 5 of SU (5) in addition to the three quark and lepton families in 5 * + 10.
To be precise, the ordinary SM families which contain the doublets of left-handed quarks Q i and leptons L i , right-handed up-and down-quarks (u c i and d c i ) as well as right-handed charged leptons, are assigned to (10,1) i + (5 * , 2) i . Right-handed neutrinos N c i should be associated with the last term in Eq. (1), (1,0) i . The next-to-last term in Eq. (1), (1,5)   leading to unification at the string scale [12]. However we shall not pursue this possibility in this paper.
Since right-handed neutrinos have zero charges they can acquire very heavy Majorana masses. The heavy Majorana right-handed neutrinos may decay into final states with lepton number L = ±1, thereby creating a lepton asymmetry in the early Universe.
Because the Yukawa couplings of exotic particles are not constrained by the neutrino oscillation data, substantial values of CP-violating lepton asymmetries can be induced even for a relatively small mass of the lightest right-handed neutrino (M 1 ∼ 10 6 GeV) so that successful thermal leptogenesis may be achieved without encountering any gravitino problem [13]. ) and one SM-type singlet field (S ≡ S 3 ) are odd. The Z H 2 symmetry reduces the structure of the Yukawa interactions, and an assumed hierarchical structure of the Yukawa interactions allows to simplify the form of the E 6 SSM superpotential substantially. Keeping only Yukawa interactions whose couplings are allowed to be of order unity leaves us with where α, β = 1, 2 and i = 1, 2, 3, and where the superfields 3 and τ c = e c 3 belong to the third generation and λ i , κ i are dimensionless Yukawa couplings with λ ≡ λ 3 . Here we assume that all right-handed neutrinos are relatively heavy so that they can be integrated out 3 . The SU(2) L doublets H u and H d , that are even under the Z H 2 symmetry, play the role of Higgs fields generating the masses of quarks and leptons after EWSB. The singlet field S must also acquire a large VEV to induce sufficiently large masses for the Z ′ boson. The couplings λ i and κ i should also be sufficiently large to provide heavy enough masses for the exotic fermions to avoid conflict with direct particle searches at present and former accelerators. The couplings λ i and κ i should be also large enough so that the evolution of the soft scalar mass m 2 S of the singlet field S results in negative values of m 2 S at low energies, triggering the breakdown of the U(1) N symmetry.
However the Z H 2 can only be approximate (otherwise the exotics would not be able to decay). To prevent rapid proton decay in the E 6 SSM a generalised definition of R-parity should be used. We give two examples of possible symmetries that can achieve that. If 3 We shall ignore the presence of right-handed neutrinos in the subsequent RG analysis.
symmetry while the lepton superfields (L i , e c i , N c i ) are odd (Model I) then the allowed superpotential is invariant with respect to a U(1) B global symmetry with the exotic D i and D i identified as diquark and anti-diquark, i.e. B D = −2/3 and B D = 2/3. An alternative possibility is to assume that the exotic quarks D i and D i as well as lepton superfields are all odd under Z B 2 whereas the others remain even. In this case (Model II) the D i and D i are leptoquarks [8].
After the breakdown of the gauge symmetry H u , H d and S form three CP-even, one CP-odd and two charged states in the Higgs spectrum. The mass of one CP-even Higgs particle is always very close to the Z ′ boson mass M Z ′ . The masses of another CP-even, the CP-odd and the charged Higgs states are almost degenerate. Furthermore, like in the MSSM and NMSSM, one of the CP-even Higgs bosons is always light irrespective of the SUSY breaking scale. However, in contrast with the MSSM, the lightest Higgs boson in the E 6 SSM can be heavier than 110 − 120 GeV even at tree level. In the two-loop approximation the lightest Higgs boson mass does not exceed 150 − 155 GeV [8]. Thus the SM-like Higgs boson in the E 6 SSM can be considerably heavier than in the MSSM and NMSSM, although in the considered "early discovery" benchmark points in this Letter, it will always be close to the current LEP2 limit.

The Constrained E 6 SSM
The simplified superpotential of the E 6 SSM involves seven extra couplings (µ ′ , κ i and λ i ) as compared with the MSSM with µ = 0. The soft breakdown of SUSY gives rise to many new parameters. The number of fundamental parameters can be reduced drastically though within the constrained version of the E 6 SSM (cE 6 SSM). Constrained SUSY models imply that all soft scalar masses are set to be equal to m 2 0 at some high energy scale M X , taken here to be equal to the GUT scale, all gaugino masses M i (M X ) are equal to M 1/2 and trilinear scalar couplings are such that A i (M X ) = A 0 . Thus the cE 6 SSM is characterised by the following set of Yukawa couplings, which are allowed to be of the order of unity, and universal soft SUSY breaking terms, where h t (M X ), h b (M X ) and h τ (M X ) are the usual t-quark, b-quark and τ -lepton Yukawa couplings, and λ i (M X ), κ i (M X ), are the extra Yukawa couplings defined in Eq. (2). The universal soft scalar and trilinear masses correspond to an assumed high energy soft SUSY breaking potential of the universal form, where Y ijk are generic Yukawa couplings from the trilinear terms in Eq. (2) and the 27 i represent generic fields from Eq. (1), and in particular those which appear in Eq. (2).
To simplify our analysis we assume that all parameters in Eq. (3) are real and M 1/2 is positive. In order to guarantee correct EWSB m 2 0 has to be positive. The set of the cE 6 SSM parameters in Eq. (3) should be in principle supplemented by µ ′ and the associated bilinear scalar coupling B ′ . However, since µ ′ is not constrained by the EWSB and the term µ ′ H ′ H ′ in the superpotential is not suppressed by E 6 , the parameter µ ′ will be assumed to be ∼ 10 TeV so that H ′ and H ′ decouple from the rest of the particle spectrum. As a consequence the parameters B ′ and µ ′ are irrelevant for our analysis.
To calculate the particle spectrum within the cE 6 SSM one must find sets of parameters which are consistent with both the high scale universality constraints and the low scale EWSB constraints. To evolve between these two scales we use two-loop renormalisation group equations (RGEs) for the gauge and Yukawa couplings together with two-loop RGEs for M a (µ) and A i (µ) as well as one-loop RGEs for m 2 i (µ). The RGE evolution is performed using a modified version of SOFTSUSY 2.0.5 [14] and the RGEs for the E 6 SSM will be presented in a longer paper [10]. The details of the procedure we followed are summarized below.
1. The gauge and Yukawa couplings are determined independently of the soft SUSY breaking mass parameters as follows: VEVs of the Higgs fields H u and H d ).
(ii) We set the gauge couplings g 1 , g 2 and g 3 equal to the experimentally measured values at M Z .
(iii) We fix the low energy Yukawa couplings h t , h b , and h τ using the relations between the running masses of the fermions of the third generation and VEVs of the Higgs fields, (v) At the GUT scale M X we set g ′ 1 = g 0 and select values for κ i (M X ) and λ i (M X ), which are input parameters in our procedure. An iteration is then performed between M X and the low energy scale to obtain the values of all the gauge and Yukawa couplings which are consistent with our input values for κ i (M X ), λ i (M X ), gauge coupling unification and our low scale boundary conditions, derived from experimental data. Although correct EWSB is not guaranteed in the cE 6 SSM, remarkably, there are always solutions with real A 0 , M 1/2 and m 0 for sufficiently large values of κ i , which drive m 2 S negative. This is easy to understand since the κ i couple the singlet to a large multiplicity of coloured fields, thereby efficiently driving its squared mass negative to trigger the breakdown of the gauge symmetry.

Using the obtained solutions we calculate the masses of all exotic and SUSY particles
for each set of fundamental parameters in Eq. (3).
Finally at the last stage of our analysis we vary Yukawa couplings, tan β and s to establish the qualitative pattern of the particle spectrum within the cE 6 SSM. To avoid any conflict with present and former collider experiments as well as with recent cosmological observations we impose the set of constraints specified in the next section. These bounds restrict the allowed range of the parameter space in the cE 6 SSM.

Experimental and Theoretical Constraints
The experimental constraints applied in our analysis are: m h ≥ 114 GeV, all sleptons and charginos are heavier than 100 GeV, all squarks and gluinos have masses above 300 GeV and the Z ′ boson has a mass which is larger than 861 GeV [15]. We also impose the most conservative bound on the masses of exotic quarks and squarks that comes from the HERA experiments [16], by requiring them to be heavier than 300 GeV. Finally we require that the inert Higgs and inert Higgsinos are heavier than 100 GeV to evade limits on Higgsinos and charged Higgs bosons from LEP.
In addition to a set of bounds coming from the non-observation of new particles in experiments we impose a few theoretical constraints. We require that the lightest SUSY particle (LSP) should be a neutralino. We also restrict our consideration to values of the Yukawa couplings λ i (M X ), κ i (M X ), h t (M X ), h b (M X ) and h τ (M X ) less than 3 to ensure the applicability of perturbation theory up to the GUT scale.
In our exploration of the cE 6 SSM parameter space we first looked at scenarios with a universal coupling between exotic coloured superfields and the third generation singlet field S, κ(M X ) = κ 1,2,3 (M X ), and fixed the inert Higgs couplings λ 1,2 (M X ) = 0.1. In fixing λ 1,2 like this we are deliberately pre-selecting for relatively light inert Higgsinos.
The third generation Yukawa λ = λ 3 was allowed to vary along with κ. Splitting λ 3 from λ 1,2 seems reasonable since λ 3 plays a very special role in E 6 SSM models in forming the effective µ-term when S develops a VEV. Eventually we allowed non-universal κ i (M X ).
For fixed values of tan β = 3, 10, 30, we scanned over s, κ, λ. From these input parameters, the sets of soft mass parameters, A 0 , M 1/2 and m 0 , which are consistent with the correct breakdown of electroweak symmetry, are found. We find that for fixed values of the Yukawas the soft mass parameters scale with s, while if s and tan β are fixed, varying the Yukawas, λ and κ, then produces a bounded region of allowed points. The value of s determines the location and extent of the bounded regions. As s is increased the lowest values of m 0 and M 1/2 , consistent with experimental searches and EWSB requirements, increase. This is shown in Fig. 1 where the allowed regions for three different values of the singlet VEV, s = 3, 4 and 5 TeV, are compared, with the allowed regions in red, green, magenta respectively and the excluded regions in white. These regions overlap since we are finding soft masses consistent with EWSB conditions that have a non-linear dependence on the VEVs and Yukawas. varying, which pass experimental constraints from LEP and Tevatron data. On the left hand side of each allowed region the chargino mass is less than 100 GeV, while underneath the inert Higgses are less than 100 GeV or becoming tachyonic. The region ruled out immediately to the right of the allowed points is due to m h < 114 GeV. The results show that m 0 > M 1/2 for each value of s. They also show that higher M 1/2 are correlated with higher s (and thus higher Z ′ masses).

5.
Predictions of the cE 6 SSM 5.1 Overview of the spectrum and decay signatures

SUSY spectrum and signatures
From Fig. 1 we see that m 0 > M 1/2 for each value of s and also that lower M 1/2 is weakly correlated with lower s and thus lower Z ′ masses. A remarkable feature of the cE 6 SSM is that the low energy gluino mass parameter M 3 is driven to be smaller than M 1/2 by RG running. The reason for this is that the E 6 SSM has a much larger (super)field content than the MSSM (three 27's instead of three 16's) so much so that at one-loop order the QCD beta function (accidentally) vanishes in the E 6 SSM, and at two loops it loses asymptotic freedom (though the gauge couplings remain perturbative at high energy). This implies that the low energy gaugino masses are all less than M 1/2 in the cE 6 SSM, being given Since m 0 > M 1/2 the squarks and sleptons are also much heavier than the light gauginos.
Thus, throughout all cE 6 SSM regions of parameter space there is the striking prediction that the lightest sparticles always include the gluinog, the two lightest neutralinos χ 0 1 , χ 0 2 , and a light chargino χ ± 1 . This is a general prediction of the cE 6 SSM as these particles must be lighter than all the sfermions of ordinary matter due to the above discussion.
Therefore pair production of χ 0 2 χ 0 2 , χ 0 2 χ ± 1 , χ ± 1 χ ∓ 1 andgg should always be possible at the LHC irrespective of the Z ′ mass. Due to the hierarchical spectrum the gluinos can be relatively narrow states because Γg ∝ M 5 g /m 4 q . In particular their width can be comparable to that of W ± and Z bosons. They will decay throughg → qq * → qq + E miss T , so gluino pair production will result in an appreciable enhancement of the cross section for pp → qqqq + E miss T + X, where X refers, hereafter, to any number of light quark/gluon jets. The second lightest neutralino decays through χ 0 2 → χ 0 1 + ll and so would produce an excess in pp → llll + E miss T + X, which could be observed at the LHC.

Exotic spectrum and signatures
Other possible manifestations of the E 6 SSM at the LHC are related to the presence of a Z ′ and of exotic multiplets of matter. The production of a TeV scale Z ′ will provide an unmistakable and spectacular LHC signal even in the first data [8]. When the Yukawa couplings κ i of the exotic fermions D i and D i have a hierarchical structure, some of them can be relatively light so that their production cross section at the LHC can be comparable with the cross section of tt production [8]. In the E 6 SSM the D i and D i fermions are SUSY particles with negative R-parity so they must be pair produced and decay into quark-squark (if diquarks) or quark-slepton, squark-lepton (if leptoquarks), leading to final states containing missing energy from the LSP. The decays of the exotic coloured fermions are governed by Z H 2 violating couplings. Assuming that D i and D i fermions couple most strongly to the third family (s)quarks and (s)leptons the lightest exotic D i and D i fermions decay intotb, tb,tb,tb (if they are diquarks) ortτ , tτ ,bν τ , bν τ (if they are leptoquarks). This can lead to a substantial enhancement of the cross section of either . Notice that SM production of ttτ + τ − is (α W /π) 2 suppressed in comparison to the leptoquark decays. Therefore light leptoquarks should produce a strong signal with low SM background at the LHC.
Similar considerations apply to the case of exoticD i andD i scalars except that they are non-SUSY particles so they may be produced singly and decay into quark-quark (if diquarks) or quark-lepton (if leptoquarks) without missing energy from the LSP. It is possible to have relatively light exotic coloured scalars due to mixing effects. Because the RGEs for the soft breaking masses, m 2D i and m 2 1 , resulting in comparatively small splitting between these soft masses, mixing can be large even for moderate values of the A 0 , leading to a large mass splitting between the two scalar partners of the exotic coloured fermions 4 . Recent, as yet unpublished, results from Tevatron searches for dijet resonances [17] rules out scalar diquarks with a mass less than 630 GeV, however scalar leptoquarks may be as light as 300 GeV since at hadron colliders they are pair produced through gluon fusion. Scalar leptoquarks decay into quark-lepton final states through small Z H 2 violating terms, for exampleD → tτ , and pair production leads to an enhancement of pp → ttττ (without missing energy) at the LHC.
In addition, the inert Higgs bosons and Higgsinos (i.e. the first and second families of Higgs doublets predicted by the E 6 SSM which couple weakly to quarks and leptons and do not get VEVs) can be light or heavy depending on their free parameters. The light inert Higgs bosons decay via Z H 2 violating terms which are analogous to the Yukawa interactions of the Higgs superfields, H u and H d . So the neutral inert Higgs bosons decay predominantly into 3rd generation fermion-anti-fermion pairs like H 0 1, i → bb. The charged inert Higgs bosons decays are also into fermion-anti-fermion pairs, but in this case it is the antiparticle of the fermions' EW partner, e.g. H − 1, i → τν τ . The inert Higgs bosons may also be quite heavy, so that the only light exotic particles are the inert Higgsinos.
Similar couplings also govern the decays of the inert Higgsinos. The electromagnetically neutral Higgsinos predominantly decay into fermion-anti-sfermion pairs (e. g.H 0 i → tt * , H 0 i → ττ * ). The charged Higgsinos decays are similar but in this case the sfermion is the SUSY partner of the EW partner of the fermion (e.g.

The benchmark input parameters
In Tab. 2 we present a set of "early discovery" benchmark points, each associated with a Z ′ gauge boson mass close to 1 TeV which should be discovered using first LHC data.
The first block of Tab. 2 shows the input parameters which define the benchmark points.
We have selected s = 2.7 − 3.3 TeV corresponding to M Z ′ = 1020 − 1250 GeV, where We have also restricted ourselves to (m 0 , M 1/2 ) < (700, 400) GeV leading to very light gauginos, associated with the three low gaugino masses M i , and in addition a light stop and Higgs mass. Note that for all the benchmark points the trilinear soft mass is fixed to lie in the range A 0 = 650 − 1150 GeV in order to achieve EWSB.
The benchmark points cover three different values of tan β = 3, 10, 30. In each case we have taken |λ 3 | to be larger than λ 1,2 = 0.1 (fixed) at the GUT scale. In benchmark points A, B, E (corresponding to tan β = 3, 10, 30) we have taken the κ i to be universal at the GUT scale and large enough to trigger EWSB. Since the κ i 's control the exotic coloured fermion masses, this implies that all the D i and D i fermions are all very heavy in these cases. However it is not necessary for the κ i 's to be universal and these Yukawa couplings may be hierarchical as for the quark and lepton couplings. To illustrate this possibility we have considered two benchmark points, C and D, both for tan β = 10, in which κ 3 ≫ κ 1,2 at the GUT scale. In these points C, D we have taken κ 3 to be large enough to trigger EWSB, while allowing κ 1,2 to be low enough to yield light D 1,2 and D 1,2 fermion masses.

The benchmark spectra
The full spectrum for each of the benchmark points is given in Tab. 2 and illustrated in Fig. 2. The benchmark points all exhibit the characteristic SUSY spectrum described above of a light gluinog, two light neutralinos χ 0 1 , χ 0 2 , and a light chargino χ ± 1 . The lightest neutralino χ 0 1 is essentially pure bino, while χ 0 2 and χ ± 1 are the degenerate components of the wino. Since M 1/2 < 400 GeV for all the points the (two-loop corrected) gluino mass is below 350 GeV, and the wino mass just above the LEP2 limit of 100 GeV, while the bino is around 60 GeV in each case. The question of the resulting cosmological dark matter relic abundance is not considered in this paper but one should not regard such points with a light bino as being excluded by cosmology for reasons that will be discussed later. The lightest stop mass is in the range 430 − 550 GeV for all the benchmark points, with the remaining squark and slepton masses being all significantly heavier than the stop mass but below 1 TeV. Note that the gluino mass, being below 350 GeV, is always lighter than all the squark masses for all the benchmark points.

Conclusions
We have discussed the predictions of a constrained version of the exceptional supersymmetric standard model (cE 6 SSM), based on a universal high energy soft scalar mass m 0 , soft trilinear mass A 0 and soft gaugino mass M 1/2 . We have seen that the cE 6 SSM predicts a characteristic SUSY spectrum containing a light gluino, a light wino-like neutralino and chargino pair, and a light bino-like neutralino, with other sparticle masses except the lighter stop being much heavier. In addition, the cE 6 SSM allows the possibility of light exotic colour triplet charge 1/3 fermions and scalars, leading to early exotic physics signals at the LHC.
We have focussed on the possibility of low values of (m 0 , M 1/2 ) < (700, 400) GeV, and a Z ′ gauge boson with mass close to 1 TeV, which would correspond to an early LHC discovery using "first data", and have proposed a set of benchmark points to illustrate this in Tab. 2 and Fig. 2. For some of the benchmarks (C and D) there are exotic colour triplet charge ±1/3 D fermions and scalars below 500 GeV, with distinctive final states as discussed in Section 5.1.2. All the benchmark points have a SM-like Higgs close to the LEP2 limit of 115 GeV with the rest of the Higgs spectrum significantly heavier.
The inert Higgs bosons may be relatively light, but will be difficult to produce, having zero VEVs and small couplings to quarks and leptons. The lightest stop mass is in the range 430 − 550 GeV for all the benchmark points, with the remaining squark and slepton masses being all significantly heavier than the stop mass but below 1 TeV. The gluino mass is very light, being below 350 GeV in all cases, and in particular is lighter than the stop squark for all the benchmark points. The chargino and second neutralino masses are just above the LEP2 limit of 100 GeV, while the lightest neutralino is around 60 GeV.
We have not considered the question of cosmological cold dark matter (CDM) relic abundance due to the neutralino LSP and so one may be concerned that a bino-like lightest neutralino mass of around 60 GeV might give too large a contribution to Ω CDM . Indeed a recent calculation of Ω CDM in the USSM [19], which includes the effect of the MSSM states plus the extra Z ′ and the active singlet S, together with their superpartners, indicates that for the benchmarks considered here that Ω CDM would be too large. However the USSM does not include the effect of the extra inert Higgs and Higgsinos that are present in the E 6 SSM. While we have considered the inert Higgsino masses given by µH α = λ α s/ √ 2, we have not considered the mass of the inert singlinos which are generated by mixing with the Higgs and inert Higgsinos, and are thus of order f v 2 /s where their masses are controlled by additional Yukawa couplings f which we have not specified in our analysis.
Since s ≫ v it is quite likely that the LSP neutralino in the cE 6 SSM will be an inert singlino with a mass lighter than 60 GeV. This would imply that the state χ 0 1 considered here is not cosmologically stable but would decay into lighter singlinos. The question of the calculation of the relic abundance of such an LSP singlino within the framework of the cE 6 SSM is beyond the scope of this Letter and will be considered elsewhere. In summary, it is clear that one should not regard the benchmark points with |m χ 0 1 | ≈ 60 GeV as being excluded by Ω CDM .
To conclude, in this Letter we have argued that the cE 6 SSM is a very well motivated SUSY model and leads to distinctive predictions at the LHC. We have presented sample benchmark points for which not only the Higgs boson, but also SUSY particles such as gauginos and stop, and even more exotic states such as a light Z ′ and colour triplet charge ±1/3 D fermions and scalars, could be just around the corner in early LHC data.
If such states are discovered, this would not only represent a revolution in particle physics, but would also point towards an underlying high energy E 6 gauge structure, providing a window into string theory.