Z ′

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**A reasonably simple informative 2016 paper**

**(not cited yet*)**

**on high energy physics...**

...for the education of my best gifted high school student *with a node to a recent post of another gifted but former high school student, Lubos Motl, who complained about the disappointing composition of top-cited 2016 HEP papers.

An extra U(1)' gauge symmetry is a common presence in many attempts to go beyond the Standard Model (SM). It represents, from a low-energy perspective, the simplest extension that can be attached to the SM gauge group, at the same time, from the opposite high-energy point of view, an extra abelian factor is almost an unavoidable leftover from the breaking of many GUT scenarios[1].

If we adopt a (grand) unification paradigm, it is therefore feasible that a regime ruled by the gauge structureSU(3)⊗_{C}SU(2)⊗_{L}U(1)⊗_{Y}U(1)'could populate the sequence of effective descriptions scaling from the GUT energy, before breaking into the SM one. The last step may be triggered by the nontrivial vacuum expectation of a scalar field χ, that is, consequently, required to be SM-singlet. If such U(1)' breaking is realised at the TeV scale, then there are realistic prospects of an interesting interplay with the current LHC probe, the precise traits of such phenomenological characterisation being dictated by the extended matter content ([2–6]).Beyond the scalar sector, where a SM-singlet accounts for the extra U(1)' breaking, and the neutral vector Z' , to accomplish gauge invariance, one extra fermion per generation is needed to cancel gauge and gravitational anomalies in a minimal way. This scenario has been the subject of a recent up-to-date investigation [7] where we exploited the bounds and the discovery potential of current and forthcoming collider searches.The more promising regions of the allowed parameter space have supplied the boundary conditions for a Next-to-Leading-Order (NLO) vacuum stability analysis, that we performed extrapolating the model to higher energies with two-loop β functions. As a result, the explored regions have been labeled with the maximal energy scale up to which they would provide a coherent (stable and perturbative) extrapolation of the model.

The role of the Renormalisation Group (RG) extrapolation does not exhaust its insight power with the stability analysis. As we will illustrate,for the particular case of our minimal SM⊗U(1)' regime, the RG may draw clear indications also about the high-energy regime that is expected to take place. In a combined effort, all the phenomenological and formal aspects of this analysis will contribute to unveil a consistent link between the low-energy model characterisation, and a stable, perturbative, ultraviolet (UV) completion...

The class of models encompassed in [7] adds, to the SM field content, a massive neutral gauge boson plus a scalar and three extra fermions, all transforming trivially under the SM gauge group. This extended spectrum is naturally introduced to minimally account for gauge invariance, anomaly freedom and the requirement of a massive Z' .We notice, as a valuable consequence of the previous setting, that the presence of a new abelian factor has forced the introduction of states that complete the 16-dimensional representation of SO(10) which is a further motivation to explore the possible UV fate of such model. Anomaly cancellation also rules the possible U(1)’ charges, leaving to the ratio of just two parameters the definition of the allowed charge assignments. In a low-energy investigation the common choice is to highlight the Hypercharge operator Y, so that the generator of the extra U(1)' is constrained to the form Y' = (B − L) + (g/g'1)Y, where B and L are, respectively, the Baryon and the Lepton number of the fields. The overall gauge strength g'1 and the mixing g rule, therefore, the content of the B − L and the Hypercharge operators in Y'.The renormalisable interactions that arise from the extended field content can promptly realise a Type I seesaw mechanism to account for neutrino masses.

...the past investigations of the Z' have been strongly affected by bounds coming from EW Precision Tests (EWPTs) from LEP2. The first Run of LHC at 8 TeV and L = 20 fb−1 has generated even more stringent bounds at the TeV scale. These can be extracted using a signal-to-background analysis for the Drell-Yan channel... Also the extended scalar sector creates numerous chances to reveal and characterise the class of models under study. We have limited the related new parameter space, that we parameterised with the new scalar mass m_{H2}and the mixing angle α, considering the bounds from the direct detection probes, and comparing the signal produced with the one measured of the discovered Higgs at 125.09 GeV...

The presence of multiple abelian factors is a peculiar trait of this class of models. The induced kinetic mixing, absorbed in the contribution of the coupling g to the covariant derivativeD_{µ}= ∂_{µ}+ ig_{1}YB_{µ}+ i(gY + g'_{1}Y_{B-L})B'_{µ}+ . . . , (3)may shed light, supported by a precise RG inspection, on the UV embedding that precedes the U(1)’ regime[10–12].

The key for this analysis is in the matching of the low and the high-energy generators basis, used to describe the abelian sector. In our phenomenological survey, adherence with the SM regime suggested the use of the Hypercharge for one of the two U(1). In turn, within the constraints of anomaly cancellation, we chose B-L for the other. The mixing would then provide the component of the Y 0 generator in the Hypercharge direction. From a high-energy perspective is more appropriate to work with the basis that is naturally provided by the embedding of the abelian factors in the unifying group. For example, a Left-Right (LR) symmetric regime SU(2)_{R}⊗U(1)_{B-L}, which includes U(1)_{R}⊗U(1)_{B-L}, would select the corresponding YR and Y_{B-L}set of generators. Close to the energy scale of the LeftRight symmetry breaking, the mixing between the Y_{R}and Y_{B-L}is zero, being protected by the overall non-abelian gauge symmetry of SU(2)R. It is possible, with the appropriate normalisation, to match our SM-oriented parameters (g_{1}, g'_{1}, g) with the ones corresponding to the (candidate) high-energy basis (g_{R}, g_{B-L}, g_{R/B-L}). Therefore, following the RG evolution of g_{R/B-L}in terms of g_{1}, g'_{1}and g, we can recognise, by its zeroing at a given energy, the restoration of a Left-Right symmetry.

This analysis can be promptly extended to include thresholds of SO(10) that represent a realistic UV embedding. These involve, in addition to the Left-Right case discussed, a direct breaking of a Pati-Salam (PS) group into our model, and the flipped SU(5) case (fig. 2). Choosing as boundary conditions, for the RG extrapolation, benchmarks points inspired by our phenomenological analysis, the parameter space offers regions that, in case of discovery, would clearly reveal the presence of one of the previous embeddings (fig. 3).

Figure 2. The SO(10) breaking chart illustrating the chains investigated in this work. The cases for the Flipped SU(5) and Pati-Salam required also additional unification conditions involving the non-abelian gauge sector

Figure 3. (a) When we consider the stability and perturbativity analysis, the colours refer to the different regions defined by the maximum energy up to which the model is stable and perturbative. The same energy/colour relation is also used for the unification study, referring to regions that fulfil the given unification requirement. (b) Regions with Flipped SU(5) restoration. (c) Regions with LR and PS restoration.

... The minimal character of this U(1)’ extension of the SM makes particularly efficient the use of vacuum stability and perturbativity as constraining requirements to shape the viable parameter space[13–15]. The vacuum stability is addressed asking for the extended scalar potential to be bounded from below, λ1 > 0 , λ2 > 0 , 4λ1λ2 − λ 2 3 > 0 . (4) Together with the perturbativity requirement it is also challenges the viability of a given unification scenario. If we accept the minimal content of the model, then a coherent extrapolation asks for the maximum scale of stability and perturbativity to be greater than the one realising a successful embedding. By relying on the analysis presented in [7], we may exploit this further constrains.Our final results (fig. 4) give an illustration of how the interplay of the tools presented may enrich the forthcoming collider profiling of specific regions of the parameter space. Moreover, in a possible post-discovery phase, frictions with the measured scenarios would help in outlining the degrees of freedom necessary to recover stability, when a promising unification of the gauge sector is at hand.

Elena Accomando, Claudio Coriano, Luigi Delle Rose, Juri Fiaschi, Carlo Marzo, Stefano Moretti (Submitted on 19 Sep 2016)

**A final remark**
In Lubos Motl's post to which I referred in the beginning one can read:

I think that if there are some ingenious undergraduate seniors at a university anywhere in the world, they have a much harder time to turn into stars than in other periods of the history of physics.

I wish a young student should prove him wrong! In the meantime I propose to the most ingenious graduate ones to challenge their mathematical skills and physical intuition reading the two following fascinating 2016 review articles which seemed to have escaped Lubos radar and most popular science outlets. I encourage them to check the proof or

*first build a “mental picture” oftheir own understanding*of these research works and construct more and more penetrating mental and practical tools to explore previously hidden aspects of our reality.The firewall transformation for black holes and some of its implications

Gerard 't Hooft (Submitted on 27 Dec 2016)

A promising strategy for better understanding space and time at the Planck scale, is outlined and further pursued. It is explained in detail, how black hole unitarity demands the existence of transformations that can remove firewalls. This must then be combined with a continuity condition on the horizon, with antipodal identification as an inevitable consequence. The antipodal identification comes with a CPT inversion. We claim to have arrived at 'new physics', but rather than string theory, our 'new physics' concerns new constraints on the topology and the boundary conditions of general coordinate transformations. The resulting theory is conceptually quite non trivial, and more analysis is needed. A strong entanglement between Hawking particles at opposite sides of the black hole is suspected, but questions remain. A few misconceptions concerning black holes, originating from older investigations, are discussed.

(Submitted on 3 Jun 2016)

This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow.In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

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