A constrained supersymmetric left-right model

We present a supersymmetric left-right model which predicts gauge coupling unification close to the string scale and extra vector bosons at the TeV scale. The subtleties in constructing a model which is in agreement with the measured quark masses and mixing for such a low left-right breaking scale are discussed. It is shown that in the constrained version of this model radiative breaking of the gauge symmetries is possible and a SM-like Higgs is obtained. Additional CP-even scalars of a similar mass or even much lighter are possible. The expected mass hierarchies for the supersymmetric states differ clearly from those of the constrained MSSM. In particular, the lightest down-type squark, which is a mixture of the sbottom and extra vector-like states, is always lighter than the stop. We also comment on the model's capability to explain current anomalies observed at the LHC.


Introduction
Supersymmetry (SUSY) has been the leading candidate for physics beyond the Standard Model (SM) for many years. Amongst many other appealing features, the minimal supersymmetric Standard Model (MSSM) predicts the existence of gauge coupling unification in the vicinity of the Planck scale [1][2][3][4][5][6][7]. This has been considered as a clear hint that SUSY is the next step towards a grand unified theory (GUT), see for instance Ref. [8] and references therein.
In the past the Ansatz has often been made that all additional states beyond the MSSM, which are present in the GUT model, are superheavy and subsequently do not play any role below the GUT scale. However, relaxing this condition and including either threshold effects of these states [9][10][11], or allowing some states to be ligher by orders of magnitude [12][13][14][15] could conceivably yield some insights into the GUT model even if TeV scale physics is still described by the MSSM, potentially extended by the Weinberg operator. However, the MSSM is facing increasing pressure over the last years: Minimal SUSY has problems explaining the size of the measured Higgs mass without losing attractiveness in terms of naturalness, see e.g. Ref. [16] and references therein, or being forced into regions with possibly dangerous charge-and colour-breaking minima of the scalar potential [17,18]. Recently, the most minimal model, the constrained minimal supersymmetric standard model (CMSSM), has been ruled out at the 95 % confidence level [19]. Furthermore, minimal SUSY models require additional mechanisms in order to explain the measured neutrino mixings.
In the presence of additional gauge symmetries the Higgs mass can be increased at treelevel leading to enhanced naturalness [20,21]. Additionally the presence of right-handed neutrinos, as predicted by SO(10) GUT theories, allows for natural seesaw-like mechanisms [22]. A well motivated scenario which has not yet been studied is an SO(10) GUT model which predicts left-right symmetry close to the TeV scale.
Lately, left-right-symmetric theories have received increased interest. This is due to the observation of anomalies in the 8 TeV LHC data occurring around 2 TeV [23][24][25] as they can be interpreted as decays of a heavy W boson, see Refs. [26][27][28] and references therein. However, there has not yet been any attempt to embed these ideas in a top-down approach as it would be a natural candidate to originate from a GUT model.
There are many different realisations of left-right models proposed in the literature. The most striking difference among different left-right theories can be found in the sector that eventually breaks the larger gauge group down to the SM gauge group. The most appealing choice would be the introduction of SU (2) R triplets which allow for an automatic seesaw-mechanism of type I after left-right symmetry breaking, see, e.g., Refs. [29][30][31]. However, besides being heavily constrained from vacuum stability arguments [32], the requirement of gauge coupling unification usually requires the addition of extra intermediate supermultiplets [33]. In the presence of doublets, instead of triplets, supersymmetric models consistent with gauge coupling unification and a TeV-scale spectrum can be easily found [34,35], while in the non-supersymmetric case models with triplets are also possible [36]. In the supersymmetric variants special care has to be taken not to destroy the gauge coupling unification which already works well in the MSSM. The resulting conditions on the particle content of the models, called the "sliding scale" mechanism in these papers, have been discussed in Refs. [34,35].
In this work, we present a left-right supersymmetric model consistent with gauge coupling unification and a minimal set of boundary conditions at the unification scale which maintains left-right symmetry down to energies accessible by the LHC without the need of an intermediate scale. This paper is organised as follows: First, we discuss the basic model features and the necessary conditions for successful gauge coupling unification as well as radiative symmetry breaking. We then present the quark and lepton sectors in some detail. In section 3, we address the Higgs mass and mixing as well as the expected squark hierarchies which differ from the CMSSM expectations. We close by commenting on two of the current LHC excesses.

Particle content, superpotential and gauge symmetry breaking
We assume that SO(10) is broken at the GUT scale and below this scale the remaining gauge group is left-right symmetric down to the SUSY scale, i.e. G = SU (3) C × SU (2) L × SU (2) R × U (1) B−L . The particle content of the model under consideration is given in Table 1. Here, Φ is a bi-doublet which comes in two generations Field Multiplicity Note that We also assume the usual matter parity.
The SM-like Higgs will be in general a superposition of the four neutral components of these bi-doublets. The conventions for the fields which will be responsible for the breaking of SU (2) R × U (1) B−L are: Using this field content the renormalizable superpotential allowed under both the gauge symmetries G and matter parity [37,38] is Here, all generation, SU (3) and SU (2) indices are suppressed. Spontaneous symmetry breaking occurs when the neutral components of Φ and χ-fields receive vacuum expectation values (VEVs) We make use of the following definitions of the VEVs where we use three angles to parametrise the VEVs In this parametrisation v L is the electroweak VEV and β is the usual mixing angle projecting out the SU (2) L would-be-Goldstone bosons as in the MSSM. In general, the gauge symmetries are broken in two steps However, if v R does not exceed the TeV range, one can assume to a good approximation a one-step breaking G → G SM which also occurs close to the SUSY breaking scale M SUSY = √ mt 1 mt 2 , wheret 1 andt 2 are the two mostly stop-like up-type squarks.
We show in Fig. 1 the running of the gauge couplings in this model. This shows, the assumption of a left-right breaking close to the TeV scale is consistent with gauge coupling unification. We find that the unification scale is significantly larger than in the MSSM, lying in the range (1-4) × 10 17 GeV. The increased scale of unification arises for two reasons. Firstly, the one-loop threshold corrections are large. This is due to the mass spectrum being spread over several TeV leading to large logarithms in the threshold corrections. Secondly, the beta coefficient of the U (1) B−L gauge coupling is large, taking the value 29/2. Consequently the unification scale becomes extremely sensitive on the initial value of g BL , which also generically receives large corrections due to the thresholds. Subsequently, maintaining gauge coupling unification requires that the mass spectrum of the theory remain as light as possible, leading to the prediction of a small SU (2) R breaking scale. Finally, the running values of the new couplings at M SUSY are g BL 0.44 and g R 0.59.  Figure 1. Running of the gauge couplings at one-loop (dashed lines) and two-loop (solid lines) in the left-right phase of the model. The two-loop results includes the one-loop threshold corrections arising at both the electroweak and SUSY scales. Additionally the running of the couplings is shown from the SUSY scale rather than the SU (2) R breaking scale v R . In this figure the GUT normalised g BL is plotted. The normalisation is given by g BL = 3 2 g GUT BL . The parameters for the two-loop running are t β = 5, t βu = 6.5, t β R = 0.85, m 0 = 1.5 TeV, As a consequence of the symmetry breaking, there are two additional massive gauge boson. Their masses can be approximated by Beside the Weinberg angle, two additional rotation angles for the neutral gauge bosons are required, while only one extra angle is required for the charged gauge bosons. The mixing angles between the mass eigenstates of the new gauge bosons are given by where we have used the abbreviations t β = tan β, t βu = tan β u and t β d = tan β d .
There are a number of choices for which parameters to solve the six minimisation conditions for the vacuum. Here we solve for the following parameters This set of parameters allows for unified soft-masses at the GUT scale while also allowing the minimisation conditions to be solved analytically. The second advantage of this set of parameters is that both µ χc and B µχ c appear in only two of the six tadpole equations and can therefore be solved independently of the remaining parameters. We obtain We assume that SUSY breaking in the visible sector is triggered by gravity and therefore make use of mSugra-like boundary conditions at the GUT scale, i.e. subsequently we impose the unification of the following soft-parameters: The trilinear soft-breaking couplings are related to the superpotential couplings by an univeral parameter A 0 14) The resulting free parameters at the GUT scale that are of interest for phenomenological studies 1 are Using these boundary conditions, the running of the soft masses appearing in Eq. (2.12) can be approximated analytically at the one-loop level. This yields the results In order to obtain spontaneous symmetry breaking one requires µ 2 χc ≥ 0, namely the RHS of Eq. (2.12a) must be greater than or equal to zero. This constraint excludes an area of the parameter space as a function of the couplings Y δ d , Y ψ , Y S , the soft-breaking parameters m 0 , A 0 and the SU (2) R VEV v R . As the large SU (2) R D-terms in Eq. (2.12a) add negatively to |µ 2 χc |, the contribution from the soft masses has to account for the positivity requirement. From Eq. (2.15a) one sees that m 2 χc > m 2 χc as long as 12b) requires t β R close to, but smaller than one. Values of t β R significantly smaller than unity require a large splitting ∆m 2 χc , which can be achieved by increasing m 0 , A 0 or ∆Y 2 . We exemplify this behaviour in Fig. 2 where we show the contours of different µ 2 χc values as functions of t β R , m 0 and Y δ d , 2 highlighting the |µ χc | 2 = 0 contour in red.

Running of first and second generation Sfermions and gauginos
In the CMSSM, which contains similar boundary conditions, one can obtain simple expressions at the one-loop level for the first and second generation sfermion soft-masses relating their size at M SUSY to the high-scale parameters m 0 and M 1/2 [40]: Using the same Ansatz in our model, assuming M SUSY v R , we obtain: Even if one must bear in mind that the correct coefficients get modified at the two-loop level, one can already see two main differences: (i) the mass splitting between left-and right-sleptons and squarks respectively is comparatively smaller than in the CMSSM, (ii) the squark masses don't grow so rapidly with increasing M 1/2 as they do in the CMSSM. For the running gaugino masses one can obtain a rough estimate of the expectations of the CMSSM against this model at one-loop using the relation M a = g 2 a /g 2 GU T M 1/2 . In the CMSSM, one obtains Thus, the lightest gaugino is the one of the U (1) B−L gauge group. Moreover, the gluino is also lighter for the same value of M 1/2 as in the CMSSM despite the increased GUT scale.

Quark masses and mixing
In the simplest left-right model with only one generation of bi-doublets and no vector-like quarks, the quark mixing is trivial and the CKM matrix can't be generated. An Ansatz often used in literature to cure this problem is to add vector-like quarks which generate the CKM matrix via the mixing with the SM quarks. In the case of vector-like states which mix with the d-quarks and only one generation of bi-doublets, the two mass matrices read To be very general, we kept a termm which is actually absent in our model.
whereŨ u is U u enlarged artificially by a row and column of zeros apart from the (4,4) entry which is set to 1. One can always assume a basis, where U u is diagonal and the entire quark mixing is encoded in U d L . In this case and for M δ d m b , one finds the seesaw condition . (2.23b) for an invertible matrix A and vectors u,v, one finds that the determinant of the RHS of Eq. (2.22) always vanishes. This observation together with the extension of the same lemma where u, v are n × m matrices yields the condition for the LHS. Keeping in mind that Y Q is diagonal in the chosen basis, we finally find Thus, there is only a solution to Eq. (2.22) if quark mixing vanishes, otherwise the system is over constrained. We checked numerically that this conclusion holds also independently of the seesaw matrix and that the inclusion of radiative corrections does not alleviate this problem if one demands that all interactions are perturbative. Therefore, the best way to incorporate correct quark mixing in left-right models is to include a second generation of bi-doublets. However, the vector-like quarks in this model play still a crucial role because they are needed for radiative symmetry breaking as discussed below.
In the presence of two generations of bi-doublets, the Yukawa coupling in the left-right phase is related to the usual up-and down-type MSSM Yukawas Y u , Y d via perturbative up to the GUT scale, either t βu or t β d is restricted to very small values. Therefore we choose to always take t β d = 0.
Our Ansatz to calculate Y Q numerically is as follows: we derive values for Y d and Y u to reproduce the known CKM matrix and quark masses. Here, two difficulties have to be taken into account: (i) the mixing with the vector-like quarks which is inevitable because we need a non-vanishing Y δ d , and (ii) the full one-loop radiative corrections to all quarks. From the obtained values of Y d and Y u , Y Q is calculated. Since Y Q affects the one-loop corrections to the quarks entering the calculation of Y d and Y u , this procedure is iterated until a convergence has been reached.
We now briefly comment on the constraints arising from introducing vector-like quarks. Firstly, let us consider the constraints arising from quark flavour observables due to mixing between the vector-like and down-type quarks. The key point to note is that the introduced vector-like quarks only mix with the right-handed SM quarks due to the superpotential term Y δ d Q cχc δ d . The strongest bound stems from the kaon mixing where one also has to include the mixing of heavy vector bosons which scale as v 2 L /v 2 R , see Eq. (2.9) and (2.10). Recent collider data requires that the W mass be at least approximately 2 TeV [41]. Apart from that, it has also been shown that kaon mixing constraints require the W boson in leftright models to be at least approximately 3 TeV in the non-supersymmetric case, [42] and at least 2 TeV in supersymmetric models due to gluino contributions [43]. Both of these bounds must be recast for the specific model in question; however, they do not change the conclusion that both the W − W and Z − Z mixing should be highly suppressed. As discussed in Section 3.3.1, the vector boson mixing is at most 10 −3 in our model. The mixing in the right-handed d-quark sector is at most m b /M δ < ∼ 10 −2 . In the kaon mixing, both the squares of the quark and vector boson mixing enters, implying that we can easily avoid this bound.
Lastly, one must consider the impact of the vector-like quarks on the electroweak precision observables. Due to the tree-level coupling of the vector-like quarks to Z-bosons, there will in general be a non-negligible contribution. The corresponding bounds have been obtained in Ref. [44]: while the masses of the vector-like quarks should be > ∼ 600 GeV, the mixing with the SM quarks is constrained to |V 4×4 CKM,34 | < ∼ 0.04. 3

Lepton sector
In the lepton sector, we find equivalent relations between Y L 1 , Y L 2 and both the lepton Yukawa coupling Y e as well as neutrino Yukawa coupling Y ν as Eqs. (2.26a) and (2.26b) for the quark sector. Because of the additional gauge singlet S as well as the two generations of extra vector-like leptons Ψ, Ψ c , there are more free parameters in the lepton sector as in the quark sector. Thus, the calculation of Y e and Y ν ≡ √ 2m D /v u is in general more complicated. In the limit vχ c Y Ψ M −1 Ψ → 0, the SM charged leptons decouple from the vector-like states and correspondingly, v d Y e = − a v da Φ Y La can be diagonalized as usual, which fixes one linear combination of Y L 1 and Y L 2 . The other necessary combination of Y L 1 and Y L 2 can be obtained from neutrino data.
The neutrino masses can be calculated in the the seesaw approximation, which give the following expressions for light (heavy) neutrinos [45]: While the light neutrinos are Majorana states, the six heavy states form three quasi-Dirac pairs. Since the right-handed neutrinos are part of the L c doublets, it is in general not possible to simultaneously diagonalize Y e and Y S , as opposed to inverse seesaw models with the SM gauge group or with U (1) R × U (1) B−L . However, one can always choose a basis with diagonal Y e , µ S and M Ψ . Therefore, the PMNS matrix can be fitted by the linear combination − a Alternatively, one can work with diagonal m D and use Y S to fit neutrino data, or allow off-diagonals in both terms.

Phenomenology
In this section we discuss various phenomenological features of the model, focusing on aspects of the mass spectrum that differ compared to the MSSM, as well as on current excesses reported by the LHC experiments. A discussion of the rich flavour phenomenology of this model which provides several new sources for lepton and quark flavour violation, as well as of the dark matter scenarios is beyond the scope if this work and will be given elsewhere.
The numerical results of the model have been calculated using SPheno [46,47], while the implementation of the model into SPheno was performed using the mathematica code SARAH [48][49][50][51][52][53]. This allows one to calculate the full one-loop spectrum as well as the dominant two-loop contributions to the CP-even Higgs masses [54,55].

Higgs sector
After the would-be Goldstone bosons are rotated out, the Higgs sector comprises six neutral CP -even states (σ i , see Eqs. (2.4a -2.4d)), four neutral CP -odd and four charged states which each mix among themselves to form the mass eigenstates h i , A i and H ± i . In the following discussion, we will denote the lightest mostly electroweak Higgs state as h and the lightest mostly right-doublet Higgs as h R . In the limit t β R → 1, h R becomes massless at the tree level. In this case, the SU (2) R -and the electroweak Higgs states decouple from each other and the second-lightest Higgs is purely SU (2) L -doublet-like. The tree-level mass of h is enhanced with respect to the MSSM prediction due to the effect of the extra Dterms from the enlarged gauge sector. The absolute upper bound on this mass can be evaluated in the limits t β R → 1, t β → ∞, tan β u → ∞ and is given by which is the generic upper limit for supersymmetric left-right theories where electroweak symmetry is broken by bidoublets [56,57] as well as in model variants where only the subgroup U (1) R × U (1) B−L survives down to the TeV scale [58,59]. As soon as t β R departs from one, a mixing between h and h R sets in which rises with increasing ∆ = 1 − t β R . This mixing also pushes up the heavier mass of both eigenstates. Treating ∆ as a small perturbation, one can evaluate the corresponding 2 × 2 mass matrix of said states which reads in the basis (h, h R ): µχ c is the mass of the pseudoscalar Higgs boson of the SU (2) R sector. After the level crossing of the eigenstates, h R continues getting more massive whereas the mass of the electroweak eigenstate converges towards which is exactly the same as in the MSSM. The last equality follows because of the relation between the hypercharge coupling g Y and the 'new' couplings: 1/g 2 Y = 1/g 2 BL + 1/g 2 R . Taking into account the measured Higgs properties, the mixing between the Higgs states of the different SU (2) sectors has to be small. Hence, there are two possibilities in our model: • values of t β R close to one, resulting in a light SU (2) R -doublet Higgs and a secondlightest Higgs with SM properties and an enhanced tree-level mass • significant departure from t β R = 1, in which case the lightest Higgs has SM properties but no D-term enhancement of the tree-level mass with respect to the MSSM.
In Fig. 3, we show the masses as well as admixtures of the two lightest CP -even Higgs states at the tree level as well as the one-and two-loop level as a function of tan β R . Apart from the usual large corrections of several ten per-cent for the SM-like Higgs, the most apparent feature in the loop corrections is the dependence on tan β R which is altered at the loop level due to the coupling of χ c to the vector-like coloured sector via Y δ d : Since the average of the scalar masses can be smaller than the corresponding fermion mass, the loop corrections are negative in contrast to the well known feature of large positive (s)quark corrections in the MSSM. In Fig. 3 we have chosen M δ = 1 TeV as well as a relatively large coupling Y δ d = 0.09 (corresponding to Y δ d = 0.26 at M SUSY ) to maximise these corrections.
As a consequence of those radiative corrections, a second-lightest SM-like Higgs can be accompanied by a very light h R state of O(10 GeV), in contrast to the constrained U (1) R × U (1) B−L model where the loop corrections in the absence of vector-like states always enhance m h R , i.e. one finds O(50 GeV) even for tan β R → 1 [59,60]. We remark that the branching ratio for the decay h 2 → h 1 h 1 is below a percent for these points even when the h − h R mixing is of O(10 %).

Squark sector
The down-squark mass matrix is enlarged to an 8 × 8 matrix. The additional entries correspond to the vector-like quarks' scalar superpartners. The addition of these vectorlike squarks modifies the expected hierarchy of the light-squark masses in comparison to the MSSM. Namely, we observe that the lightest down-squark is generically lighter than the lightest up-squark which is always the light stopt 1 . This behaviour arises as the vector-like quarks modify the RGE running of the quark soft-masses, and have a potentially large mixing with the standard down-type squarks.
To illustrate this behaviour we consider for the moment only the third-generation of left and right down-type squarks as well as the vector-like squarks. In the basis {b L ,b R ,δ d ,δ d } the mass matrix reads Here, the electroweak VEVs have been neglected and we have assumed t β R → 1 as these quantities give only a shift to the diagonal elements, but play a negligible role in the mixing with the vector-like states. From the form of the mass matrix we arrive at the following conclusions: • There is no mixing between the left-sbottoms and the vector-like squarks based on these assumptions.
• For fixed values of M δ , the relative size of the mixing between the right-sbottoms and the vector-like states is determined by three parameters, namely Y δ d , A 0 and v R . Typically one requires these parameters to take large values in order to arrive at a phenomenologically viable model 4 . Therefore the right-sbottoms are typically strongly mixed with the vector-like states. This mixing reduces their mass compared to pureb L/R eigenstates.  In Fig. 4 on the left-hand panel the mixing of the lightest sbottom with the vector-like states is shown as a function of Y δ d , where a value of 1.0 corresponds to a purely vectorlike squark and zero corresponds to a pure MSSM sbottom state. Here we observe that depending on M δ there exists a minimum value of Y δ d required for significant mixing with the vector-like states. In the right-hand panel we show the effect of T Y δ d on the splitting of the squark masses. As Eq. (3.4) suggests, T Y δ d contributes strongly to this splitting. One should note that the value of this trilinear coupling is strongly correlated with M 1/2 due to RGE running, increasing with larger M 1/2 . RGE running effects result in a splitting of the quark soft masses where (m (3,3) Q ) 2 > (m (3,3) Qc ) 2 . This splitting arises through two main sources. Firstly, the running of the gaugino masses in the left-right sector is asymmetric. This results in the splitting being a function of M 1/2 which can be analytically estimated at the one-loop level: Here, g GUT 0.8, M GUT 1.5 × 10 17 GeV and M SUSY 2.5 TeV. In Fig. 5 the results of the fully numerical scan are shown. The bold red line corresponds to the above function, whereby we see that this function provides an adequate approximation to the minimal splitting of the soft-masses. Secondly, as is also illustrated by Fig. 5, additional splitting occurs due to Y δ d = 0. The precise value of this contribution depends strongly upon numerous parameters in the model.

ATAS diboson excess
The ATLAS collaboration observed an excess with a local significance of 3.4 σ at an invariant mass of around 2 TeV in their search for diboson events in the W Z channel [23]. Many models have been proposed to explain that excess, in particular left-right symmetric models where a W decays into W Z caused by a significant W − W mixing. The best-fit point for the amount of mixing that needs to be present in minimal non-SUSY left-right models lies around Θ W W 1.4 × 10 −3 , while g R /g L 0.6 [27]. The ratio g R /g L cannot be much larger than this value in the minimal model as the bounds from dijet searches are otherwise too constraining [61]. In our model g R is not a free parameters, but predicted to be g R /g L 0.9. This is still consistent with observation because of the extra decay modes of W into supersymmetric particles which increase its width and accordingly reduce its dijet production cross section. Parameterising the process in the narrow width approximation as σ(pp → W ) × BR(W → W Z), with σ(pp → W ) ∝ g 2 R and to a first approximation , where ξ > 1 parameterises the increased width due to the supersymmetric final states, we see that, to first order, g R drops out of those considerations and we actually need somewhat larger values of Θ W W than in the simplest model due to the influence of ξ.
Using Eq. (2.10), we see that Θ W W is maximised for t β = 1 and t βu = t β d reaching the required size of Θ W W 1.4 × 10 −3 . However, this suffers from several problems: the former condition corresponds to a saddle point of the potential and predicts a tiny treelevel Higgs mass, while the latter condition leads to non-perturbative Yukawa couplings, cf. Eq. (2.26b), which makes it impossible to achieve the required size of W − W mixing. Thus far we have neglected the impact of the extended (s)quark sector and the effect of mixing with the vector-like states. In Ref. [62], the Ansatz was made that the light quarks are predominantly comprised by extra vector-like quark states which considerably reduces the W coupling to light quarks. The excess can then be fit with a W −q − q coupling smaller by a factor of 5 compared to the SM value and tan β < 5 for g R /g L 0.9. The latter is still clearly disfavoured in light of Higgs data keeping in mind the limit on the mass spectrum coming from gauge coupling unification, whereas the huge mixing is very hard to realize: casting aside all problems of inducing large flavour changing neutral currents and just focusing on the feasibility of this possibility in our model, we would need a hierarchy of vχ c Y δ d /( √ 2 M δ d ) ∼ 5 , which is in principle achievable for M δ d of O(100 GeV). However, the problem is expected to occur in the down-squark mixing where the absence of a reasonably large M δ d typically leads to tachyonic states. In order to easily see this, we apply a few approximations. The soft SUSY-breaking masses m 2 Qc and m 2 δ d will be of similar size even after RGE running as the contributions from the gluino are the same. Therefore we will set both to the common squared mass m 2 . Furthermore, if we write T δ d as A 0 Y δ d and consider the limit M δ d → 0, the diagonalization of Eq. (3.4) leads to the mass eigenstates which leads to a negative state for typical GUT-scale values of m 0 , A 0 because of the strong running of A 0 Y δ d and accordingly A 0 µ χc at M SUSY unless the value of A 0 at the GUT scale is tuned to approximately cancel µ χc . In light of the numerous essential tunings required to obtain the necessary conditions, we conclude that our model cannot fit the excess and simultaneously remain a consistent high-scale model.

CMS eejj excess
In the seach for dilepton plus dijet events in the 8 TeV data, CMS has announced an excess of signal events with a local significance of 2.8 σ [24]. This excess can be interpreted as the on-shell production of a W R with M W R 2.1 TeV and its subsequent decay into ν h , with ν h → jj. The comparatively low pp → jj cross-section which fits the excess cannot be explained in the framework of simplified left-right-symmetric models which only introduce a W and three copies of right-handed neutrinos, predicting a cross-section which is higher by a factor of 3 − 4 if g R g L . Furthermore, as the excess features dileptons of differing signs, it cannot be explained by heavy neutrinos of Majorana nature which would predict ± ± final states at the same rate as ± ∓ . As discussed in section 2.4, the heavy neutrinos in the present model form quasi-Dirac pairs because of the inverse seesaw mechanism at work. As a consequence, the lepton appearing in the ν h decay will have the opposite sign as the one in the W decay to ν h , in agreement with the measured effect. Additionally, a reduction of the cross section is achieved by the interplay with the lightest charged Higgs state H ± 1 , analogously to Ref. [63]: the mass of the mostly H 1− d -like state is, to a good approximation, m 2 , which is usually in the range of a few hundred GeV for the typical values of tan β R . Heavy neutrinos couple to this state by the admixture of χ − c . Consequently, with m ν h of O(1 TeV), the two-body decays ν h → H ± 1 reduce the branching ratio of ν h → jj by several tens of percent and hence also the jj cross section by the right amount.
A further reduction is possible due to the mixing of the light neutrinos with the heavy states which opens the additional decay modes ν h → W/νh/νZ. As the mixing only depends on the ratio m D vχ c Y −1 S but the light neutrino masses scale with µ S m 2 D , neutrino data also allows the possibility that µ S is very small and m D sizeable. Hence, while the effect of the mixing is still small for values of µ S of O(10 −4 GeV), it already gets important for µ S = 10 −5 GeV, where for the required masses of M W 2 m ν R 2 TeV those decays are already of the same size as the W -mediated three-body decay. Should the excess be confirmed, this could be the main source of cross section reduction in the case of a large deviation of tan β R from one and the associated heavier charged Higgs state.

Conclusion
We have presented a constrained left-right supersymmetric model which predicts a low SU (2) R × U (1) B−L breaking scale. The model is constructed in a manner where gauge coupling unification is maintained, based on the requirement that SU (2) R × U (1) B−L is broken purely through SU (2) R doublets. As the left-right breaking scale is assumed to be close to the SUSY scale, gauge coupling unification dictates that additional matter must be introduced. This extra matter takes the form of vector-like quarks and leptons charged under U (1) B−L but being singlets with respect to the SU (2) factors.
Due to the fast running of the U (1) B−L gauge coupling and large one-loop threshold corrections, the model predicts a unification scale close to the string scale. These large threshold corrections are a product of large values of the gauge coupling beta functions in conjunction with a large spread in the mass spectrum. For unification to remain unspoilt by threshold corrections, one naturally predicts the SU (2) R breaking scale to lie close to M SUSY . Finally, the presence of vector-like quarks are an essential ingredient in driving spontaneous symmetry breaking in the left-right phase: under the assumption of mSUGRAlike boundary conditions, the couplings of these quarks must be non-vanishing to trigger radiative gauge symmetry breaking.
We have demonstrated why the usual paradigm of using vector-like quarks in conjunction with the seesaw mechanism provides insufficient degrees of freedom to fit both the quark masses and mixings simultaneously. Subsequently, we have implemented both the quark masses and mixing through the introduction of an additional Higgs bi-doublet, raising the total number of electroweak VEVs to four.
The phenomenology of this model contains a number of interesting features. Here, we have focused on the mass spectrum. Firstly the CP-even Higgs sector displays two distinctive tendencies. For t β R → 1, the lightest CP-even Higgs mass tends to O(10)GeV values while the second lightest Higgs becomes SM-like. For sufficient deviation from t β R = 1, the MSSM-like limit is produced. Note, that the lightest state is essentially a SM gauge singlet. In the squark sector due to both the RGE running and the enlarged down-squark sector the lightest down squark is always lighter than the lightest stop.
Finally we comment on two of the recently observed excesses seen at the LHC. We show that due to constraints arising from RGE running sufficient mixing of the W -bosons cannot be achieved to naturally explain the diboson excess. Even if one can make use of the vectorlike quarks to weaken this conclusion, we consider a concrete realisation of that idea in this model to be very unlikely. However, the CMS eejj excess can be successfully explained due to the model incorporating an inverse seesaw and the presence of extra two-body decays.