Living Orthogonally: Quasi-universal Extra Dimensions

The minimal Universal Extra Dimension scenario is highly constrained owing to opposing constraints from the observed relic density on the one hand, and the non-observation of new states at the LHC on the other. Simple extensions in five-dimensions can only postpone the inevitable. Here, we propose a six-dimensional alternative with the key feature being that the SM quarks and leptons are localized on orthogonal directions whereas gauge bosons traverse the entire bulk. Several different realizations of electroweak symmetry breaking are possible, while maintaining agreement with low energy observables. This model is not only consistent with all the current constraints opposing the minimal Universal Extra Dimension scenario but also allows for a multi-TeV dark matter particle without the need for any fine-tuning. In addition, it promises a plethora of new signatures at the LHC and other future experiments.


I. INTRODUCTION
Although the spectacular discovery of the long-sought for Higgs boson [1][2][3] is cited as the completion and the latest vindication of the Standard Model (SM), certain questions remain unanswered.
These pertain to the existence of Dark Matter (DM), the origin of the baryon asymmetry in the Universe, the existence of multiple generations of fermions, the hierarchy in fermion masses and mixing, and, last but not the least, the stability of the Higgs sector under quantum corrections.
The pursuit of answers to such questions has led to two different paradigms for the exploration of physics beyond the SM. The top to bottom approach posits a UV complete model, usually motivated to solve one or more of the outstanding problems (including the hierarchy), and delves into its "low-energy" consequences. Unfortunately, the most straightforward of them, whether it be supersymmetry or warped extra dimensions are faced with stringent constraints from observations. Hence, one is forced to consider non-minimal versions. an exercise that could, potentially, be non intuitive on account of the lack of clear principles. The second, or bottom to top approach envisages simplified models, which while not addressing the UV scale physics, can explain certain anomalies in particle physics experiments (including but not limited to those at colliders) and possibly also cosmological observations. Over the years, several attempts have been made to address the aforementioned questions, albeit only with partial success. One such stream of thought envisages a world in more than three space dimensions as a possible panacea to some of the ills of the SM, and, in this paper, we concentrate on this possibility. A particularly simplistic version was given the name Minimal Universal Extra Dimensions (MUED), wherein the SM is extended to propagate in a 5 dimensional space-time orbifolded to M 4 ⊗ S 1 /Z 2 , with M 4 being the four-dimensional space-time with Lorentz symmetry.
If the radius of the fifth dimension be small enough, this leaves us with an effective 4-dimensional theory with every SM particle having a corresponding infinite tower of Kaluza Klein (KK) modes separated at equal energy gaps related to the inverse of the compactification scale.
Being an non-renormalizable model, MUED is considered as an effective theory valid up to a cutoff Λ, typically assumed to be 5-40 times the inverse radius. One of the main attractions of MUED was the fact that, while the conservation of the KK-number (or, in other words, the momentum in the compactified direction) is broken by quantum corrections, a Z 2 symmetry, called KK-parity, is maintained nevertheless. This has the consequence that the lightest of the level-1 KK partners (upon accounting for the radiative effects [4], normally the cousin of the hypercharge gauge boson) is absolutely stable, thereby being a natural candidate for the Dark Matter particle [5][6][7][8][9]. This model has been studied in great detail, since it bore resemblance with the LHC signatures of the minimal supersymmetric standard model, except for the spin of the individual particles.
While the electroweak [10] and flavour [11,12] observables impose only relatively weak bounds on the compactification scale, namely R −1 y 750 GeV and R −1 y 600 GeV respectively, the current LHC bounds are much stronger, and emanate from the study of a variety of final states [13][14][15], such as multijets, or dileptons with jets, each accompanied by missing transverse energy ( E T ), owing to the presence of the lightest KK-particle. With ΛR (R being the compactification scale) determining the mass splittings, the detection efficiency (for a given R −1 ) and, hence, the reach are also determined by this. The excellent agreement of the ATLAS data (at 13 TeV) on dileptons [16] and multijets with a single-lepton [17] with the SM expectations, serves to exclude R −1 1400 GeV (for ΛR 10) or R −1 1500 GeV (for ΛR 10) at 95% C.L.
On the other hand, the agreement of the consequent relic density with the WMAP [18] or the Planck [19] data demands that 1250 GeV R −1 1500 GeV [9]. These two sets of results are in serious conflict with each other, and continuing validity of this model would require substantial alterations. The simplest solution, of course, would be to break KK-parity and give up on the DMcandidate. A more attractive proposition would be to somehow alter the spectrum so as to either suppress the relic abundance or relax the LHC constraints by raising the masses of the strongly interacting particles. A partial solution can be achieved by invoking perfectly-tuned brane localized and/or higher dimensional terms in the Lagrangian. While the existence of such terms is anticipated as the UED is only an effective field theory with a cutoff Λ, the symmetric character of such terms (necessary for stability of the DM) is to be assured by imposing a KK-parity. Attractive as this proposition might be, it only offers a partial solution as the twin constraints (LHC and relic density) would require rather large sizes for these terms, that, ostensibly, arise from quantum corrections.
While for reasons of simplicity (and on account of the constraints from electroweak observables being relatively mild in this case), most models have concentrated on a five-dimensional world, this, though, need not be the case. Indeed, the extension to six dimensions [20][21][22][23][24] brings forth its own advantages, e.g., in the context of explaining the existence of three fermion generations, or the reconciliation with the non-observance of proton decay. On the other hand, the simplest generalization, typically, results in even stronger constraints from relic density [25]. Thus, smarter generalizations are called for. Embedding the UED in a 6-dimensional warped space [26,27], for example, makes it possible to evade the relic density bounds by exploiting the s-channel annihilation channel with graviton mediated by a KK-graviton exchange. In this paper we offer a different solution, one that leads to a very rich collider phenomenology.
The rest of this article is constructed as follows. We begin by setting up the formalism, followed by details of the model including the breaking of the electroweak symmetry and culminating with the Feynman rules. This is followed (in Sec. III) by an examination of the mass-splittings wrought by quantum corrections. A detailed study of the relic abundance and the consequent constraints imposed on the parameter space of the theory is presented in Section IV. Also discussed are the prospects for direct and indirect detection experiments. An independent set of constraints arise from new particle searches at the LHC and these are discussed in Section V. Finally, we conclude in Section VI and list some open questions.

II. THE MODEL
Consider a 6-dimensional flat space-time orbifolded on M 4 ⊗ (S 1 /Z 2 ) ⊗ (S 1 /Z 2 ) parametrized by the coordinates (x µ , x 4 , x 5 ), where M 4 is the 4-dimensional space (x µ ) that obeys Lorentz symmetry, and x 4,5 are compact and dimensionless. The line element for this space-time is given as, where R q and r are the compactification radii in the x 4 and x 5 directions respectively. The latter are orbifolded by individual Z 2 's, and periodic boundary conditions (x 4 → x 4 + πR q and x 5 → x 5 + πr ) are assumed. This particular orbifolding demands the sides of the six-dimensional space to be protected by 4-branes (or 4+1 dimensional hyper surfaces). This feature is distinctively different from the toroidal orbifolding (T 2 /Z 2 ) where the branes are present only at the corners and are co-dimension 2.
The key feature is that the SM quarks and leptons are extended not to the entire bulk, but only to orthogonal directions. Apart from other consequences (to be elaborated on later) this immediately decouples the inter-level mass splittings for quarks and leptons, thereby raising the possibility that the LHC bounds could be evaded while satisfying the constraints from relic abundance. To be specific, we assume that the leptons are localized on the 4-brane at x 4 = 0 while quarks are at the branes at x 5 = 0 and x 5 = π. This immediately means that the Z 2 associated with x 4 -direction is broken explicitly, while the other may be trivially retained. To remind us of this aspect (one which will have immense consequences), we will denote the discrete symmetry of the model by Z 2 ⊗ Z q 2 (where the slash denotes the explicit breaking). The free Lagrangian for the fermions is, then, given by where L/Q are the lepton/quark doublets and E/U/D are the lepton/quark singlets and √ g 1 = R q , √ g 2 = r . The fermions, being 5-dimensional, are vector like. The unwanted zero-mode chiral states can be projected out by orbifolding appropriately, viz., for The corresponding Fourier decompositions of the fermion fields are given by As expected, both the leptons and quarks have a single tower each. The former has only the (0, p) modes with masses being given by m (0,p) = p r −1 where we have neglected the SM mass for the zero mode. The quarks, on the other hand, possess only the (n, 0) modes with masses m (n,0) q = n R −1 q . Naively, one would expect that we would need R −1 q to be sufficiently larger than r −1 . However, as we shall see later, this requirement is not strictly true.
With quarks and leptons being extended in different directions, it is obvious that at least the electroweak gauge bosons must traverse the entire six-dimensional bulk 1 . Before we delve into this, we offer a quick recount of the gauge sector in a generic higher-dimensional model.

A. Gauge Bosons: A lightning review
Naively, a five-dimensional gauge field, on compactification, should decompose into a fourdimensional vector field and an adjoint scalar, whereas for a six-dimensional field, there should be two such scalars instead. However, a simple counting of the degrees of freedom (especially for the KK-levels), shows immediately that, in each case, one of the scalar modes must vanish identically.
To begin with, we look at the simpler abelian case and, then, graduate to the Standard Model gauge content. The action is given by where √ g = R q r . To eliminate the spurious degrees of freedom corresponding to the gauge freedom, viz, we choose to work with the generalized R ξ gauge and This has the further advantage of eliminating terms connecting A µ to A 4,5 . To compactify on the orbifold, we need to impose boundary conditions which are summarized in Table I. We may, now, 1 An alternative would be to consider separate electroweak gauge groups for the two sectors, confining each to the corresponding branes. This could be broken down to the diagonal subgroup (to be identified with the SM symmetry) through appropriate Higgses [28][29][30]. We eschew this path.
The factor π R q r serves to maintain canonical commutation relations for the KK components on compactification down to four dimensions. Clearly, A (j,k) 4,5 transform as four-dimensional Lorentz scalars. Although, for j, k = 0, the kinetic terms mix the fields, these can be diagonalized provided we redefine them as where, as usual, M 2 j,k = j 2 /R 2 q + k 2 /r 2 . Under such a redefinition, after integrating out the extra dimensions, the effective four-dimensional Lagrangian density is Using Eq 5, it is trivial to see that V 1 does not exist if j = 0 or k = 0. This reflects the orbifolding we have in this geometry. Thus, we have a double Kaluza-Klein tower for a vector field along with a pair of charge-neutral scalars, with these being degenerate at every level 2 . In the unitary gauge become non propagating and the only (real) scalar fields left are V This disappearance of one tower of the adjoint scalars can be understood in terms of the appearance of the longitudinal modes for the corresponding gauge boson levels.

B. The complete field assignment
The decomposition for non-abelian gauge boson is identical to that for the abelian case discussed above, with the added complication of the self interactions and the ghost fields needed to consistently define the quantum theory. The gauge field is now expressible as A M = A a M t a , and the field strength tensor as where t a are the generators and g the six dimensional coupling constant. Once again, the gauge Lagrangian is written as apart from the gauge fixing and the ghost terms. For convenience, we separate F M N into three sets F µν , F 4µ , F 5µ and F 45 as in the abelian case, with the understanding that each continues to be a function of all six dimensions. The bilinear terms, on KK reduction give rise, in analogy with the abelian case, to double towers of gauge bosons as well as of a pair of scalars V 1,2 in the adjoint representation. Once again, in the unitary gauge, V 2 decouples entirely. We desist from expanding the Lagrangian further to include the ghosts etc, since that is not germane to the issues under consideration.
Since we want to decouple the compactification scales for the strongly-interacting particles from those having only electroweak interactions, we localize the gluons on the very same branes where the quarks are located. Thus, the Lagrangian for the gauge sector is given by where a = 1, 2, 3 and ℵ = 1 . . . 8. While the mode decomposition for the electroweak gauge bosons would be analogous to that presented in the preceding section (we will discuss symmetry breaking shortly), that for the gluon is simpler and is given by namely a single tower with masses given by n/R q . In the unitary gauge, expectedly, no adjoint scalar remains.
To define the Feynman rules for the gauge interactions, it is convenient to define the following In terms of these, the gauge couplings can be expressed as in Table II.

C. Electroweak Symmetry Breaking
Several realizations of the Higgs sector is possible, each with its own distinctive consequences.
We adopt here a particularly simple one, wherein the Higgs field is localized to 3-branes at the four corners of the rectangle that the compact space is. The corresponding Lagrangian is, then, given by A nontrivial vacuum expectation value for φ breaks the electroweak symmetry down to U (1) em . The very presence of the δ-functions in L φ has an interesting consequence in that non-diagonal mass terms connecting the even gauge boson modes are engendered. As a result, the physical W -and Z-bosons will have an admixture of all the even KK-modes. The mixings would be suppressed, though, by factors of the order of g 2 v 2 /M 2 KK where v is the electro-weak scale and g the coupling constant.
The Yukawa coupling is as usual, namely The particular localization of of the Higgs (as in eq.(11)) implies that, of the various fermion excitations, only the left-handed SU (2) L -doublets and right-handed singlets couple to the Higgs.
The wavefunctions for the other (wrong) chiralities vanish identically at the corners-see eq.
(2)which constitutes the only support of the Higgs. The existence of non-diagonal (in the level space) Yukawa as well as gauge couplings, both resulting from the localization of the Higgs on co-dimension 2 branes, has an immense bearing on the stability of the Higgs potential. Quantum corrections to the quartic Higgs vertex now emanate from a plethora of diagrams, with the negative contributions from the multitude of top (and top-cousin) loops, each proportional to λ 4 t , thereby, quickly destabilizing the potential. The larger multitude of diagrams, potentially, renders the problem even worse than that within the mUED [31]. Consequently, the cutoff Λ needs to be relatively low.
An alternate way out of the problem would be to allow the Higgs to propagate in the branes or even just the branes containing the quarks. This would imply that, as far as the tree-level Yukawa interactions in particular, the ones involving the top-sector) are concerned, KK-number is now, rendered a good symmetry. These vertices being level-diagonal greatly reduces the number of fermion (top) loops contributing to the Higgs quartic coupling, postponing any instability to much higher energies 3 . We, however, will not follow this route as this detail is not germane to the issues at hand. The interactions of the Higgs boson are summarized in Table II.

III. QUANTUM CORRECTIONS TO THE SPECTRUM
As we have seen in the preceding sections, with the quarks being localized symmetrically on the pair of end-of-world 4-branes at x 5 = 0 and x 5 = π, there exists a Z 2 symmetry, namely x 5 → π − x 5 . This is reflected by the corresponding wavefunctions being either symmetric (even p) or antisymmetric (odd p) about x 5 = π/2. This Z 2 is analogous to the KK-parity in mUED, but operative only on modes along the x 5 -direction. On the other hand, with the leptons being localized on the 4-brane at x 4 = 0 alone, the corresponding symmetry in this direction is lost entirely. Thus, while the lightest of the F (0,1) particles (where F is an arbitrary field in the theory) is stable, this is not true for the F (1,0) .
The identification of the lightest of the level-1 excitations in either direction proceeds quite analogously to that in mUED. At the tree-level, the level-(0, 1) leptons and the B While, within mUED, it has been argued that the stability of electroweak vacuum [32] dictates Λ ≤ 4 R −1 , this constraint is not strictly applicable here. Vertices liket (n,0) t (m,0) H introduce additional box diagrams which tend to drive the effective Higgs self-coupling negative, thereby tending to destabilize the vacuum. These are only partially offset by the contributions from the W (n,m) (and Z (n,m) ) loops. Although this problem can be ameliorated to a great extent by allowing the Higgs to traverse the entire quark brane (thereby eliminatingt (n,0) t (m,0) H (0,0) vertices for n = m) instead of localizing it to the corners, we do not adopt this course of action. Rather, we take heart from the fact that Λ ∼ 3 max(R −1 q , r −1 ) is a choice quite safe from the viewpoint of Higgs stability, and we adopt this in this paper To ease comparison with the literature (pertaining to mUED) we also demonstrate results for a case with a different choice as well 4 , namely, Λ = 20 max(R −1 q , r −1 ). The mass corrections can be separated into two primary classes, namely those due to bulk corrections and that due to the orbifolding. Though calculation is quite straightforward [4]. Care must be taken, though, of the fact that, in the present case, additional contributions accrue on account of non-diagonal couplings. It is useful to define where g i are the (4-dimensional) gauge coupling constants and µ is the renormalization scale. In terms of these, the masses are as given in Table III. The terms proportional to the Riemann ζ (3) function denote the correction due to the orbifolding, while the rest are due to the various loops.
Of particular interest are the terms 8 a 1 L (4 a 2 L) pertaining to B (n,0) µ (W µ a (n, 0)). Appearing on account of the non-diagonal coupling of these bosons to lepton-pairs (originating, in turn, due to the broken Z q 2 ), these terms have no counterpart in mUED scenarios. These corrections are quite significant (and, indeed are the dominant ones for B are, thus, the lightest excitations in the respective directions. The latter, being stable, is the DM candidate, while the former decays promptly and, predominantly, to the SM leptons. It is interesting to note that, in the event of r ≈ R q , the DM candidate is actually the heavier of the two.

A. The Relic Density
Given the smallness of the mass splittings, in the early universe, the DM particle and the nextto-lightest KK particles would have decoupled around the same epoch. This can affect the relic abundance of DM in three ways. Before we list these, though, it should be pointed out that, contrary to mUED-like scenarios, not all KK-excitations of similar masses behave similarly. While the excitations along the leptonic (x 5 ) direction behave analogously to the NLKPs of mUED-like scenarios,In other words, it is the next-to-lightest lepton-direction excitations (NLLE) that are germane to the issue with the rest of the NLKPs (relevant only if R q ≈ r ) playing a subservient role. With this understanding, • NLLEs, after decoupling from the thermal bath, would decay to the lightest KK excitation i.e., the DM, thereby increasing the latter's number density.
• The NLLEs would also have been interacting with the other SM particles before they decoupled, to replenish the DM and can keep the DM in equilibrium a little longer, thereby diluting their number density.
• Similarly, the NLLEs could also co-annihilate with the DM-to a pair of SM particles-again maintaining it (and themselves) in equilibrium longer.
The net effect would be determined by a complicated interplay of all such effects. A key issue is whether the NLLE decouples from the SM sector at or before the same epoch as the DM, or significantly later. In the latter case, the number density of the NLLE at the epoch of its own decoupling may be well below that of the DM, leading to only low levels of replenishment. In such a situation, it is often the second effect above that wins the day. Note that this is quite in contrast with the case of the mUED, where the inclusion of the co-annihilation channels increases the relic abundance thereby strengthening the upper bound on R −1 . This aspect would prove to be crucial in the context of our model.
To compute the relic density, we have implemented our model with the interactions discussed in section II in micrOMEGAs [33] using LanHEP [34]. As a check, we have compared against the CalcHEP model file discussed in Ref. [35]. Care must be taken while calculating the relic density in micrOMEGAs. To produce the plot in Fig.1, we have considered upto four KK levels, including the fourth.(This required the modification of the array size used in micrOMEGAs.) The resultant behavior of Ωh 2 as a function of R −1 q is depicted in Fig.1. To understand several issues need to be appreciated: • In mUED-like scenarios, there are a plethora of particles nearly degenerate with the DM.
While their co-annihilation with the DM serves to drive down the latter's relic density, this is more than offset by the twin effects of (a) these interacting with the SM particles prior to decoupling so as to replenish the DM and keep it in equilibrium for a longer a while, and (b) once decoupled, these decay into the DM, thereby enhancing the latter's relic density. Overall, the existence of these particles serve to increase Ω DM h 2 .
In the present context, the excitations in the hadronic direction (x 4 ) play essentially no role in the aforementioned processes. Thus, one would expect the extent of the enhancement to be smaller.
• A further crucial difference emanates from our having confined the Higgs field to the corners of the brane-box. Consequently, there are no Higgs KK-excitations. Within the mUED, the second-level excitations appear as s-channel propagators in processes such as B , with the fermionic vertices being generated at one-loop order. The suppression due to the latter is offset by the fact of these processes occurring close to resonance. (Note that the reverse process is not nearly as efficient.) With the absence of the Higgs-excitations in our model, this means of suppression of the relic density is no longer available.
• Overall, then, one would imagine that the relic density should depend on the mass of the DM particle (∼ r −1 ) in much the same way as in the mUED (i.e when Higgs-excitations are not included). This naive expectation does describe the situation well for R −1 q r −1 (the right part of each panel in Fig.1).
As a closer study of Fig.1 reveals, in this limit, the relic density, as a function of the DMmass, is slightly higher than in the mUED case. This is expected due to the absence of the Higgs-excitations in our model. Consequently, somewhat lower values of the DM-mass are now consistent with the Planck results for R −1 q r −1 .
• A further feature is that the relic density increases with Λ. This dependence is more pronounced away from the resonance. This owes itself to the fact that larger Λ leads to heavier NLLE, and has a positive impact on Ω DM h 2 .
• To understand the shape of the Ω DM h 2 -plots away from the right-edge, we need to remind ourselves of B (n,0) µ (the excitations along the x 4 -direction). Since these couple to all fermion pairs (including excitations), they mediate (unsuppressed) interactions between them. For R −1 q ≈ 2 r −1 , the s-channel diagram mediated by B (1,0) µ would be close to resonance, leading to highly enhanced cross-sections. Consequently, the NLLEs would remain in equilibrium (with the SM sector) until a later era. This reduces their number densities at the epochs of their own decoupling, and, thereby the replenishment of the DM number density through their decays. In addition, this late decoupling allows the co-annihilation processes to occur for longer time, further suppressing Ω DM h 2 .
• The suppression (in the relic density) discussed above is caused not by the B (1,0) µ alone, but by all B (n,0) µ , with each coming into prominence when 2 r −1 ≈ n R −1 q (see Fig.1). Numerically, even more important (on account of the gauge coupling g 2 being larger than g 1 ) are the roles of the W a (n,0) µ . With these being close in mass with the B (n,0) µ , the individual peaks cannot be distinguished in the plots.
The shape of the individual dips is largely governed by two factors. The width of the gauge boson excitations is the primary one The slightly asymmetric nature is caused by the interplay of the cross-sectional behavior and dependence of the multitude of particle fluxes on the mass scale.
It should be appreciated that, so far, the exploration of this parameter space has paid no heed to other observables, such as those at dedicated DM experiments or collider constraints. We turn our attention to these next.

B. Direct and Indirect search experiments
Direct detection experiments have, traditionally, depended upon the DM particle scattering (both elastic and inelastic) off nuclei. In the present context, the only tree-order diagram contributing to DM-quark interactions is that mediated by the Higgs. This, naturally, is suppressed by the size of the Yukawa coupling and is too small to be of any consequence in the current experiments. It should also be noted that loop-diagrams leading to an effective B Some of the currently operating direct detection experiments are also sensitive to DM-electron interactions. The sensitivity to the effective coupling strength is lower, though (as compared to the DM-nucleon interaction). In the present context, such scattering can take place through s-and t-channel exchanges of the electron excited states (namely, e (0,1) and E (0,1) ). Naively, it might seem that a resonance is possible. However, the DM has very little kinetic energy, and the electron too is not only non-relativistic, but bound too. Consequently, the cross sections are too small to be of any interest.
Indirect detection proceeds through the annihilation of a DM-pair into SM particles, which are then detected (typically, by satellite-based detectors) either directly or through their cascades. In the present case, a B (0,1) µ -pair can annihilate into either a lepton-pair (t-and u-channel e (0,1) or E (0,1) exchanges) or to W + W − /ZZ/tt/HH (all through a s-channel Higgs exchange). This would be manifested in terms of both prompt and secondary continuum emissions. The thermal-averaged annihilation cross sections for these final states (as displayed in Fig.2) are, however, several orders of magnitude below the most restrictive limits from Fermi-LAT [36]. → τ + τ − (red) as a function of the DM mass for Λ = 3 max(R −1 q , r −1 ). Also shown are the median upper limits on the DM annihilation cross-section as derived from a combined analysis of the Fermi-LAT data [36].

V. LHC SIGNATURES
In the preceding section, we saw that this model admits much heavier DM candidates (consistent with the relic abundance) than allowed within the minimal-UED paradigm (whether 5-or 6dimensional). It now behoves us to examine the collider phenomenology of the same. Naively, a constriction of the moduli (r , R q ) that this model allows for would render the fields heavier, thereby suppressing the production rates and easing the collider bounds as compared to UED-like scenarios.
On the other hand, the very structure of the theory, namely that only one of the possibly two Z 2 parities is conserved, brings forth new modes, both in the production arena as well as in decays.
To this end, we begin by reminding ourselves of some the particularly interesting couplings.
is not an exact symmetry, with the quark and gluon fields being confined to the 4-branes at x 4 = 0 and x 4 = πR q respectively, this symmetry is effectively an exact one in the context of the strong interactions. Thus, the first KK-state of the quarks (q (1,0) ) and gluons (g (1,0) ) can, essentially, be produced only in pairs. The latter, being heavier, would decay predominantly into q (1,0) +q (0,0) pairs. The q (1,0) , on the other hand, would decay into a SM-quark and the B • An interesting alternative would be the resonant production pp → g (2,0) + X starting with a qq pair (or, the analogous q + g → q (2,0) ). Either of these vertices are loop-suppressed, leading to small cross sections. Once again, g (2,0) → q (1,0) +q (1,0) with the subsequent cascades as in the preceding cases. The signal too is similar, but of a markedly smaller size. It might seem that a invariant mass reconstruction (possible, in principle, for the 4 + soft jets final state) would increase the signal significance. Given the smallness of the signal cross section, and the softness of the jets (leading to potential confusion with other sources such as pileups and multiple collisions), this is quite unlikely. A more definitive statement would require a full simulation beyond the scope of this paper.
• More interestingly, a SMq q ( ) pair has unsuppressed couplings with each 5 of B and W µ a (0, 2n) for all n ∈ Z + . The higher states, though, have nontrivial branching fractions into the quark KK-states, a mode that is not necessarily available for n = 1. [37]. It should be noted that the inclusion of all the four electroweak (0, 2) KK-states would translate to a stronger bound. Furthermore, the aforementioned limits were obtained from the analysis of only 12.9 fb −1 of data and assuming that no such anomaly would show up in the current round would push the bound up considerably. Thus, it might be safely assumed that r −1 < ∼ 1.7 TeV would be strongly disfavored.

TeV
• For r −1 > R −1 q , on the other hand, the situation is altered quite dramatically. The B

VI. SUMMARY
Non-observation of any new state at the LHC has severely constrained the parameter space for a host of well-motivated theories going beyond the SM. In particular, the minimal UED, suffers from the problem that this non-observation militates strongly against the upper limit on the compactification scale dictated by the observed DM relic density. The ensuing tension can be relieved, to an extent, by invoking a non-minimal theory with boundary-localized terms (respecting a Z 2 symmetry so that an explanation for the DM can be retained). However, the continuing absence of any signals requires the size of such terms (ostensibly, the result of quantum corrections) to become ever larger, thereby severely straining the entire paradigm.
To mitigate the problems faced by the minimal UED, in this work, we considered a quasi-universal six-dimensional theory, which naturally inherits a much richer phenomenology compared to its fivedimensional (or, even, unravel six-dimensional) counterpart. Apart from the interesting double- Naively duplicating the canonical mUED structure, however, is not phenomenologically viable as this would have left behind a pair of Z 2 -symmetries, thereby leaving behind three DM fields, one each for the lightest excitations in the (1, 0), (0, 1) and (1, 1) sectors. Two of these masses would be determined by the quark-excitation scale and would run foul of the relic density measurements.
To this end, we propose that the leptonic fields are localized on a pair of parallel end-of-the-world 4-branes, while the quarks (and gluons) are localized on a single such brane orthogonal to the other two. The electroweak gauge bosons must, obviously, extend across the entire bulk. For the Higgs, several alternatives are possibles, such as localizing them to the corners of the brane-box (adopted herein) or allowing them to be localized on the boundary-branes etc.
The hard breaking of one of the two Z 2 's engenders unsuppressed tree-level couplings, amongst others, for certain level-1 KK-excitations with a pair of SM fields. This not only renders two of the putative DM candidates unstable (leaving behind the B (0,1) µ as the only cosmologically stable particle), but also has immense consequences as far as LHC signals are concerned. The prompt decay of all the excitations along the quark-direction into SM particles severely depletes the missing transverse momentum signal, a cornerstone of LHC search strategies. Instead, they are manifested in terms of a dijet final state, or final states with leptons and soft jets. As of the present instant, it is the former modes that present the strongest constraints, with the negative searches for leptophobic W /Z , together, requiring that a DM mass < ∼ 1.7 TeV would be strongly disfavored.
This bound is even slightly stronger than that imposed, by considerations of the relic density, on the mUED candidate for the DM. In other words, this seems to bely our stated objective of easing the twin-constraints (LHC and DM). However, the aforementioned breaking of one of the Z 2 's manifests in a nontrivial way in the determination of the number densities. With the quark-direction excitations of the electroweak gauge bosons now having unsuppressed couplings with all the SM fermions, as well as their own (unidirectional) excitations, these can mediate interactions between the SM particles and the first excited states of the leptons (which are close to the DM in mass). As a consequence, these leptonic states remain in equilibrium until a later epoch, thereby suppressing their density at decoupling. This, in turn, translates to their decays-into the SM leptons and the DM-no longer being effective means to replenish the relic density. Since this replenishment is actually the major contributor to the relic density in UED-like scenarios, this effect can suppress Ω DM to levels well below the observed one, especially for 2 r −1 ∼ n R −1 q (n ∈ Z + ), namely regions of parameter space where the aforementioned s-channel processes are relatively close to being on resonance.
This curious effect has profound implications, with multi-TeV DM being quite in consonance with all bounds (relic density, dedicated direct and indirect searches as well as the LHC constraints), without any fine tuning being necessary. In addition, this scenario promises very interesting signals