A well motivated theory that the LHC2 may test (soon)?

TeV scale Resonant Leptogenesis and Majorana neutrinos 
... the observed baryon asymmetry of the Universe (BAU) provides a strong evidence for the existence of new physics beyond the Standard Model (SM).
Many interesting scenarios for successful baryogenesis have been proposed in beyond SM theories; see e.g. [10]. Here we will focus on the mechanism of leptogenesis [11], which is an elegant framework to explain the BAU, while connecting it to another seemingly disparate piece of evidence for new physics beyond the SM, namely, non-zero neutrino masses; for reviews on leptogenesis, see e.g. [12, 13]. The minimal version of leptogenesis is based on the type I seesaw mechanism [14], which requires heavy SM gauge-singlet Majorana neutrinos Nα (with α = 1,2,3) to explain the observed smallness of the three active neutrino masses at tree-level. The out-of-equilibrium decays of these heavy Majorana neutrinos in an expanding Universe create a lepton asymmetry, which is reprocessed into a baryon asymmetry through the equilibrated (B+L)-violating electroweak sphaleron interactions [4]. In the original scenario of thermal leptogenesis [11], the heavy Majorana neutrino masses are typically close to the Grand Unified Theory (GUT) scale, as suggested by natural GUT embedding of the seesaw mechanism. In fact, for a hierarchical heavy neutrino spectrum, i.e. (mN1 ≪ mN2 < mN3 ), the light neutrino oscillation data impose a lower limit on mN1>109GeV [15]. As a consequence, such ‘vanilla’ leptogenesis scenarios [16] are very difficult to test in any foreseeable experiment...

An attractive scenario that avoids the aforementioned problems is resonant leptogenesis (RL) [18, 19], where the ε-type CP asymmetries due to the self-energy effects [20, 21, 22] in the heavy Majorana neutrino decays get resonantly enhanced. This happens when the masses of at least two of the heavy neutrinos become quasidegenerate, with a mass difference comparable to their decay widths [18]. The resonant enhancement of the CP asymmetry allows one to avoid the lower bound on mN1>109GeV [15] and have successful leptogenesis at an experimentally accessible energy scale [19, 23], while retaining perfect agreement with the light-neutrino oscillation data. The level of testability is further extended in the scenario of Resonant l-Genesis (RLl ), where the final lepton asymmetry is dominantly generated and stored in a single lepton flavor l [2427]. In such models, the heavy neutrinos could be as light as the electroweak scale, while still having sizable couplings to other charged-lepton flavors l' ≠l, thus giving rise to potentially large lepton flavor violation (LFV) effects. In this mini-review, we will mainly focus on low scale leptogenesis scenarios, which may be directly tested at the Energy [28] and Intensity [29] frontiers. For brevity, we will only discuss the type I seesaw-based leptogenesis models; for other leptogenesis scenarios, see e.g. [12, 30]... 
In general, any observation of lepton number violation (LNV) at the LHC will yield a lower bound on the washout factor for the lepton asymmetry and could falsify high-scale leptogenesis as a viable mechanism behind the observed BAU [45]. However, one should keep in mind possible exceptions to this general argument, e.g. scenarios where LNV is confined to a specific flavor sector, models with new symmetries and/or conserved charges which could stabilize the baryon asymmetry against LNV washout, and models where lepton asymmetry can be generated below the observed LNV scale. An important related question is whether low-scale leptogenesis models could be ruled out from experiments. This has been investigated [46, 47, 4849] in the context of Left-Right symmetric models and it was shown that the minimum value of the RH gauge boson mass for successful leptogenesis, while satisfying all experimental constraints in the low-energy sector, is about 10 TeV [48]. Thus, any positive signal for an RH gauge boson at the LHC might provide a litmus test for the mechanism of leptogenesis.
(Submitted on 2 Jun 2015)

TeV scale left-right symmetric models and right-handed charged currents (déjà-vù ;-)?

We show that the excess in the pp → eejj CMS data can be naturally interpreted within the Minimal Left Right Symmetric model (MLRSM), keeping gL = gR, if CP phases and non-degenerate masses of heavy neutrinos are taken into account. As an additional benefit, a natural interpretation of the reported ratio (14:1) of the opposite-sign (OS) pp→l±ljj to the same-sign (SS) pp→l ±l±jj lepton signals is possible. Finally, a suppression of muon pairs with respect to electron pairs in the pp lljj data is obtained, in accordance with experimental data. If the excess in the CMS data survives in the future, it would be a first clear hint towards presence of heavy neutrinos in right-handed charged currents with specific CP phases, mixing angles and masses, which will have far reaching consequences for particle physics directions...   
In a CP-conserving case, CP parities of heavy neutrinos are purely imaginary [36, 37]... Choosing different scenarios have far reaching consequences in phenomenological studies. Let us consider processes where heavy neutrinos propagate as virtual states, then they contributions to the amplitudes must be summed over. In general, constructive or destructive interferences between heavy neutrinos can appear. ...in the neutrinoless double beta decay (ββ)0ν process, or its inverse collider version process e-e-→W-W-...if all heavy neutrinos have the same CP parities, then ... all heavy neutrinos contribute constructively into the amplitudes, otherwise destructive interferences can appear. Such scenarios have been considered in full details in phenomenological analyses in [38]. It has been shown there that cancellations among contributions to the amplitude from heavy neutrinos with opposite CP parities can appear. In this way, low energy (ββ)0ν constraints can be avoided and for instance the collider signal e-e-→W-W-.can be substantial. We will see in the next Section that CP phases of heavy neutrinos play a crucial role also in a case of SS and OS pp → lljj signals...
We also conclude that it is worth to undertaken more careful analyses of the neutrino sector when exclusion plots are considered, otherwise too strong limits can be inferred from a simplified scenario (in this case assuming real neutrino mixing matrix elements with degenerate heavy neutrinos). An example is specific, but conclusions which we can derive are more general as heavy neutrinos are present within many BSM models.

In our analyses we kept MW2 fixed at the CMS value 2.2 TeV, however, in the light of leptogenesis [
46], it would be interesting to check if it is possible to reproduce CMS data with MW2 shifted up to about 3 TeV by relaxing MW2  - MN  mass relation (MN = MW2 /2) and exploring wide space of heavy neutrino mixing angles, phases and masses (not necessarily of the degenerate nature), similarly as we have made in this work. It will be worthwhile to study that issue when better statistics is available.

TeV scale extended gauge models and massive diboson resonances 

Diboson resonances are predicted in several extensions to the SM, such as technicolour [2, 34], warped extra dimensions [5, 67], and Grand Unified Theories [8, 9 ,10 , 11]. To assess the sensitivity of the search, to optimise the event selection, and for comparison with data, two specific benchmark models are used: a Sequential Standard Model (SSM) W0 → WZ where the spin-1 W0 gauge boson has a modified coupling to the SM W and Z bosons, also referred to as the Extended Gauge Model (EGM) [12, 1314], and a spin-2 graviton, GRS → WW or ZZ, a Kaluza–Klein mode [5, 15] of the bulk Randall–Sundrum (RS) graviton [16–18]... 

A search has been performed for massive particles decaying to WW, WZ, or ZZ using 20.3 fb−1 of √s = 8 TeV pp collision data collected at the LHC by ATLAS in 2012. This is the first ATLAS search for resonant diboson production in a fully hadronic final state and strongly relies on the suppression of the dijet background with a substructure-based jet grooming and boson tagging procedure. The boson tagging selection includes different jet mass criteria to identify W and Z boson candidates and thus produces three overlapping sets of selected events for the searches in the WW, WZ, and ZZ decay channels. The most significant discrepancy with the background-only model occurs around 2 TeV in the WZ channel with a local significance of 3.4 σ and a global significance, taking the entire mass range of the search in all three channels into account, of 2.5 σ. Upper limits on the production cross section times branching ratio of massive resonances are set in each diboson channel as a function of the resonance mass, using an EGM W0 → WZ as a benchmark for the WZ channel, and an excited bulk graviton GRS to represent resonances decaying to WW and ZZ. A W0with EGM couplings and mass between 1.3 and 1.5 TeV is excluded at 95% CL.

(Submitted on 2 Jun 2015)
//Last edition 6 June 2015
The blogger cannot guarantee the reader that the three quoted articles converge exactly to a unique coherent theoretical framework as the title seems to indicate it. The common feature is obviously the energy scale that is currently under experimental scrutiny (thanks to the start of the second run for the LHC and its four detectors evocated in the former post) and intriguingly the similar energy range where CMS and then ATLAS have reported a possible excess of events in two different search channels (with different final states). That could be interpreted as our first encounter with a new heavy W gauge boson, indicating a possible extension of the Standard Model to a minimal (natural ;-) left-right symmetric model or a more elaborate partial unification in the Pati-Salam's way not to mention grand unification theories. 

...and a hypothetical change of paradigm? ;-)
Another common feature one could notice is the absence of any explicit reference to supersymmetry or naturalness argument in the former three articles. In so far as these useful ideas and ideologies would not be necessary anymore to convince physicists and people "that new physics will appear at energies accessible to accelerators" (to quote Joseph Polchinski in 1992) this is not surprising!

Of course the experimental results are still very preliminary but they have been made public. Once more I regret not to have the expertise to make a guess when LHC2 will provide more definite information but the question has been asked to a capable blogger!(*) Talking about bloggers here is a comment by another famous one that illustrates im my opinion the possible change of paradigm that might occur.

... In recent hours, I sort of convinced myself that the left-right symmetric models are more natural than the Standard Model.
The electric charge in the Standard Model is Q = Y/2 + T3
where T3 is the third component of SU(2) acting on the left-handed fermions. The hypercharges Y are "random rational numbers" for the left- and right- components of quarks and leptons.
Well,there's a more comprensible way to write this thing if the hypercharge is written as 2*T3R + (B-L). We get Q = (B-L)/2 + T3L + T3R
Now, it's manifest that the electric charges of the left-handed and right-handed parts of the spinors are the same, because those are doubled under one of those SU(2) groups. And one may easily verify that the average charge of the doublets is always (B-L)/2. Well, it is -1/2 for the electron-neutrino and +1/6 for the quarks. And B, L are easier to deal with than the chatic Y - one only has the values like +/- 1/3 and +/- 1.
This SU(2)xSU(2) may be embedded to SO(10) GUTs, not SU(5), so the discovery would immediately falsify both SM and SU(5).
There are also interesting "alternative left-right symmetric models" based on a different embedding of the SM group to an E6, and those may arrive from nice heterotic string models.
Lubos Motl
//added on Thursday 11 June 2015
(*) Flutke alors !
Looking for another theoretical article dealing with our main issue in this post:

... we remark that if the CMS excess is due to either of the W′ or Z ′ production processes discussed, trilepton signals should also show up with a moderate increase in the statistics and/or a dedicated search. In the case of W′ , 1/3 of the N decays in
 pp → W′ → ℓiN →  ℓi ℓkW′* →  ℓi ℓkjj
involve a t¯b pair, which is a trademark for this process. With the statistics available in the LHC run 2, final states eet¯b with reconstructed top quarks could be searched for. In the case of Z′, trilepton and four lepton signals appear when one or the two W bosons in
 pp → Z′ → NN → ℓiW ℓkW , W → jj ,
decay leptonically. In both scenarios, the predicted signals are compatible with small excesses found by the CMS Collaboration [33], but this should be confirmed or discarded with more statistics. Searches in the eµ final state are also interesting, as potential excesses may show up in this channel too. Conversely, the absence of a signal would further constrain the heavy neutrino coupling and mixing parameter space. In this respect, a classification of ℓℓjj events by missing energy is also useful [26] to identify the secondary leptons from τ decays. 
(Submitted on 11 Aug 2014)

... I followed a link to the well known blog of an experimantalist and CMS collaborator claiming the following warning:
... the signal which the theorists refer to is a mere 2.8σ statistical fluke in a wide mass histogram, practically a single high bin in the four-body mass distribution of events with two electrons and two hadronic jets. A local significance of 2.8 standard deviations means very little, as globally the probability to see one such effect is well above the few percent level.
By Tommaso Dorigo | August 12th 2014

(*) Update : Jester has answered "us" in an informative post today
Merci à lui :-) Here is his conclusion :
For sure this is something to observe in the early run-2. However, due to experimental inconsistencies and theoretical challenges there's little reason to get excited yet.
On the LHC diboson excess, Jester, 13 June 2015
//edit 30 June 2015