Can LHC2 phenomenology meet some unified left-right symmetric Pati-Salam (Spectral-like) models?

Welcome back to a blog which has not waited the most popular string theorist blogger** to get interested in and to talk about the provisory signature at the LHC of a potential left-right symmetry in Nature ;-)
Today I report on an article that might be the very first post-higgs phenomenologists' work on the spectral models investigated by noncommutative geometers:
... we feel that [the noncommutative geometrization (NCG) of the Standard Model] may have the potential to develop into a full-fledged paradigm. In particular, from the phenomenological standpoint, the necessity to enlarge the gauge symmetry (via an enlargement of the underlying NCG) to accommodate the Higgs mass can be considered a strength rather than a weakness. It tells us that the approach is restrictive enough for the models to be confronted by experiment, and point us in new directions to explore. Indeed, in a recent paper, Chamseddine, Connes, and van Suijlekom have proposed a new formulation of an NCG based unified left-right symmetric Pati-Salam model, which comes in three different versions differing in Higgs content. In all three, the gauge theory which emerges from the underlying NCG at the unification scale, which we will call MU, is that with gauge symmetry G224 = SU(2)L×SU(2)R×SU(4)C with unified couplings: gL(MU) = gR(MU ) = g4(MU ). In one version, the symmetry is actually G224P = G224 ×P, where P denotes parity which maintains left-right symmetry. G224 or G224P is assumed to break down to G213 = SU(2)L ×U(1)Y ×SU(3)C of the SM at scale MR...For all three versions, which differ in particle content, [Chamseddine et al.] argue that both boundary conditions can be satisfied if MU∼10^15 GeV and MR∼10^13 GeV.
In this paper, we will not attempt to review or justify the derivation of these models, but look at their consequences purely phenomenologically. From that viewpoint, the high value of MR is problematic in light of recent hints of a WR with a mass of around 2 TeV at the LHC. If the LHC signal is indeed the gauge boson of the SU(2)R group, then MR on the order of a few TeV would be more compatible with that possibility... We address the question whether MR for Chamseddine et al.’s NCG models can be lowered by the addition of intermediate breaking scales between MU and MR at which the symmetry breaks down from G224P /G224 to G213 via several intermediate steps. In other words, is any symmetry breaking pattern compatible with a unified left-right symmetric Pati-Salam model at MU , and the SM below MR ∼ few TeV?
(Submitted on 4 Sep 2015)

Summary of Results
... we have looked at whether the IR conditions MR = 5 TeV and gR(MR) = 0.4 could be realized within left-right symmetric, and unified left-right symmetric Pati-Salam models in which the unification/emergence scale is below the Planck mass. The left-right symmetric Pati-Salam demands the unification of gL and gR, while the unified left-right symmetric Pati-Salam demands further unification of gL and gR with g4. The requirements that these couplings unify at a single scale, and the matching conditions between g1, gBL, and gR at MR, and that between gBL, g3 and g4 at MC , place conflicting demands on the various symmetry breaking scales, and it is found that the target IR conditions cannot be realized so easily. In particular, if the Higgs content at various energy intervals is determined based on the Extended Survival Hypothesis (ESM), MR and gR(MR) tend to be much larger than our target values. Lowering these values requires the breaking of ESH. The most promising cases are Models B and C of [Chamseddine et al] with the colored ∆3R field surviving below MC . We note that this may put the ∆3R particles within reach of the LHC. But even for those cases gR(MR) cannot be made as low as 0.4. In all cases, the optimum conditions for minimum MR and/or minimum gR(MR) requires degeneracies of some of the symmetry breaking scales.

While our analysis could suggest that the NCG motivated unified left-right PatiSalam model is not favored phenomenologically by the current LHC data, we note the possibility that the current approach of grafting the NCG spectral action to RG evolution of standard QFT at the GUT scale may not capture the true nature and predictions of NCG theories*... In our view the approach based on NCG (and its related proposal based on the superconnection approach 22) offers a new and, phenomenologically, almost completely unexplored view on the rationale for the SM and also for its natural completion. This approach also offers a possibly exciting relation with the fundamental physics of quantum gravity, thus relating the infrared physics of the current exciting experimental searches conducted at the LHC to the hidden ultraviolet physics of quantum theory of space and time.
//addendum 12 /09/15
Blogger's comments 
One must not let oneself be fooled by the purported resonances in the 2 TeV range reported  by ATLAS and CMS collaborations in the data from the first run of LHC. Their hypothetical theoretical understanding as a signature of a heavy right handed gauge boson WR is exciting and might be motivated by a quite "natural" extension of the Standard model (or theory) but their statistical significance is low. Thus the real interest in this article is - from my biased view - the efforts done by Aydemir et al. to give a simple discussion (in the vernacular language of model builders) about some basic phenomenological aspects like energy scales, gauge couplings and symmetry breaking sequence with the corresponding Higgs spectrum derived from the spectral models recently proposed by the leading group of noncommutative geometry applied to high energy physics (in a frustratingly too brief recent article).

Needless to say, all subtle aspects of the spectral models theoretical motivation can not be addressed in one work as the one quoted above. This might be the reason for some precautions of speech (*). For instance one could expect a discussion of the relevance of the (extended) survival hypothesis in the spectral models context. Indeed as far as I understand it, the usefulness of the noncommutative framework is it does not require such hypothesis since the full Higgs spectrum is not introduced by hand but computed from the vacuum solution of the spectral action derived itself from first principles. Said it differently there is almost no flexibility in the scalar spectrum of these standard model extensions (if the spectral models come into three distinct ways in the last Chamseddine et al. article this seems to me essentially a matter of assumptions on the most general form of the hermitian matrix parametrizing the inverse of the Euclidean propagator of fermions in the discrete noncommutative fine structure of spacetime).

Last but not least there is no offense in my introduction (**) towards string theorists. I just regret that the blogger Lubos Motl has not informed yet his readers from the resilience of the noncommutative geometric inspired physical models after having proposed a review of them in the past. More importantly I am glad to see a former PhD student of Joseph Polchinsky like the second author Djordje Minic get involved in the phenomenological assessment of spectral models! Our common horizon for all physicists is naturally to find the most appropriate M(eeting or Mathematical?) theory to better understand and further explore Nature I guess.