Looking for accessible (thus falsifiable) beyond standard model phenomenology....

... in non-supersymmetric SO(10) Grand Unified Theory (GUT) with Pati-Salam symmetry
This post is a follow-up of the ideas pursued in the former ones :
Why-saving-Pati-Salam? and What could a hint of non-supersymmetric physics beyond the standard model look like at the LHC?
The current low energy data from solar, atmospheric and reactor neutrinos [1] established the oscillation hypothesis with very small masses (≤ 1 eV) for the three generations of light neutrinos. Depending on whether neutrinos are Dirac [2] (having distinct antiparticles) or Majorana [3] (they are their own antiparticles) fermions, these masses originate from the corresponding Dirac or Majorana mass terms. The goal of the current experimental neutrino programme is to determine the nine degrees of freedom of the neutrino sector: three light neutrino masses (m1,m2,m3), three mixing angles (θ12,θ23,θ13) and potentially up to three CP phases: one Dirac phase (δ) and two Majorana phases (α,β). The oscillation experiments allowed us so far to measure the two mass squared differences and the three mixing angles, but we are yet to determine the absolute mass scale, the presence of CP violation and whether neutrinos are Dirac or Majorana fermions. If neutrinos are Dirac fermions then lepton number is an exact symmetry of the low energy effective theory. On the other hand, if neutrinos are Majorana fermions, there will be a violation of lepton number by two units. The latter would necessarily predict neutrinoless double beta decay (0νββ), i.e. the nuclear decay (A,Z) → (A,Z + 2)+ 2e− of various nuclei. The experimental non-observation currently provides lower bounds on the half life of this process in various isotopes, of the order T1/2 > ∼ 2×1025 yr [4–8]. This can be translated to a bound on the so-called effective 0νββmass parameter as mee ≤ 0.2−0.6 eV, with a large uncertainty due to the theoretical error on the relevant nuclear matrix elements. Future experiments aim to improve the sensitivity on the 0νββ by about an order of magnitude, with a corresponding improvement in mee by a factor of 3. Thus the Majorana nature of light neutrinos will be probed at future 0νββ experiments which will not only shed light on the absolute mass scale of the left-handed (LH) neutrinos but may also indicate the mass hierarchy and mass mechanism for LH active neutrinos (for details, see ref. [9]). If we assume that the SM light Majorana neutrinos are only contributing to this rare 0νββ decay, then the present experimental bound on the 0νββ half life can be saturated with a quasi-degenerate (QD) pattern of light neutrinos, while normal hierarchy (NH) and inverted hierarchy (IH) patterns of light neutrinos remain unreachable within the sensitivities of current experiments. On the other hand, Planck [10] and other astrophysical observations give a stringent bound on sum of masses of the light neutrinos, i.e,Pi mi ≤ 0.23 eV (95% C.L.) which is in tension with the QD nature of the neutrinos and hence does not support the idea of light neutrinos being QD which saturate the present 0νββ experimental bound. Hence, if this rare decay process were to be observed with currently running experiments, it would indicate new physics contributions to 0νββ decay. 
At present various seesaw mechanisms exist which could elegantly explain the small Majorana masses of three active neutrinos without fine tuning. In the type-I seesaw mechanism [11] three right-handed (RH) neutrinos, which are singlets under the SU(2)L gauge group, are added to the Standard Model (SM). Integrating out the RH neutrinos with heavy Majorana masses of the order MR ≈ 1014 GeV, the light neutrinos masses are generated as mν ≈ M2EW/MR. Generally, the Majorana masses of the singlet RH neutrinos are free parameters of the model and hence can vary from the GUT scale down to TeV scale or even lower. On the other hand, in the type-II seesaw mechanism [12] one adds a scalar triplet ∆ with hyper charge 2 to the SM spectrum. After electroweak phase transition, ∆ acquires an induced vacuum expectation value (VEV) and generates a Majorana mass matrix mν = fh∆i for the three active neutrinos through its symmetric coupling f∆LL to the lepton doublet in the SM. Note that the masses of the RH neutrinos and the scalar triplet are not controlled by the SM gauge group. 
A well motivated framework of beyond the Standard Model physics is the left-right symmetric model (LRSM) which is based on the gauge group SU(2)L ×SU(2)R ×U(1)B−L [13]. In this case the masses of RH neutrinos and scalar triplets are governed by the scale of SU(2)R ×U(1)B−L breaking. The neutrino mass matrix receives contributions from both type-I and type-II seesaw mechanisms. If the breaking scale of SU(2)R ×U(1)B−L is at the TeV scale, the RH neutrinos, the scalar triplet and the RH gauge bosons acquire TeV scale masses. This leads to many interesting phenomena in the low energy effective theory. In particular, here we will focus on 0νββ, lepton flavor violation (LFV) and collider signatures of these TeV scale particles. 
There are many studies [14–33] of various TeV scale models and their phenomenological consequences.[...]  All these studies so far assumed an explicitly symmetric structure of the left-right model at TeV scales, i.e gL = gR. Although these models provide a rich phenomenology while keeping a low scale of left-right symmetry breaking, it is difficult to justify them while being consistent with gauge coupling unification in a non-supersymmetric framework. However, there exists another class of LRSMs with spontaneous D parity breaking [35, 36, 38] where a discrete left-right symmetry called D parity is broken at a higher scale compared to the SU(2)R symmetry breaking scale. As a result, an asymmetry is generated between the left- and RH Higgs fields making the coupling constants of SU(2)R and SU(2)L evolve separately under the renormalization group from the scale of D parity breaking down to the TeV scale where the SU(2)R gauge symmetry is allowed to break. Consequently, the corresponding gauge couplings strengths are no longer equal, gL ≠gR at the TeV scale which crucially affects low energy and LHC processes. Hence the effect of gL ≠gR should be examined carefully while deriving important conclusions at TeV scales.
In this paper we make an attempt to study the effect of gLgR in 0νββ decay, LFV and collider processes involving RH currents in a class of TeV scale LRSMs with spontaneous D parity breaking. We ensure that the masses of RH particles are of the order of the TeV scale by extending the left-right gauge group SU(2)L×SU(2)R×U(1)B−L with a D parity and make sure that the discrepancy between the SU(2)L coupling gL and the SU(2)R coupling gR is indeed sufficiently large. By embedding this framework in a non-supersymmetric SO(10) Grand Unified Theory (GUT) with Pati-Salam symmetry at the highest intermediate breaking step, we obtain gR/gL ≈ 0.6 at th TeV scale. Below the GUT scale, the D parity breaks first at a high scale ≈109 GeV below which gL and gR evolve differently. Moreover, the breaking creates a large mass splitting between the LH and RH scalar particles. We assume that the LH scalar particles are heavy leaving the RH scalar particles at TeV scales. Subsequently, SU(2)R breaks to U(1)R at a scale of ≈ 10 TeV, and the RH WR boson acquires a TeV scale mass. In the next step, U(1)R ×U(1)B−L breaks at a scale of O(TeV), leading to RH ZR boson and neutrino masses potentially accessible at the LHC. Consequently, the heavy RH states can all be as light as the TeV scale. Moreover, the suppressed gauge coupling gR allows us to interpret an excess of events observed in the range of 1.9 TeV to 2.4 TeV by the CMS group [39] at LHC as the signature of a right handed gauge boson of LRSMs with spontaneous D parity breaking as pointed out in [40] and in subsequent works [41, 42]. 
(Submitted on 23 Oct 2014)

Earlier this year, a small discrepancy in a search for right-handed (RH) W bosons at the LHC [1] lead to renewed interest in left-right symmetric models [2–12]. Left-right symmetric models were first discussed in the seventies [13–19] during the early years [20–23] of grand unification theory (GUT). At moderate energies, such models are described by the gauge symmetries SU(2)L ×SU(2)R, (1) and a discrete symmetry, such as parity or charge conjugation, playing the role of left-right symmetry, all of which are spontaneously broken at low energy. These symmetries require RH analogues of the Standard Model (SM) W and Z bosons and of the SM neutrinos. In the SM, the flavor structure of left-handed (LH) quark charged interactions is governed by the CKM matrix [24, 25];similarly,in a left-right symmetric model, distinct quark mixing matrices describe the flavor structure of LH and RH quark charged interactions. In our previous work [6], we found that future experiments at the LHC could detect discrepancies between the LH and RH quark mixing matrices.
[...] testing the unitarity of a RH quark mixing matrix is challenging with 20/fb due to the poor efficiencies for the two b-tag category and moderate backgrounds. On the other hand, our method could cast powerful bounds on unitarity with 3000/fb and if future experiments confirmed the anomaly hinting at a WR boson, it could aid the interpretation of the latter.
(Submitted on 17 Dec 2014)

The excess of eejj events has been explained from WR decay by embedding the LRSM in a class of SO(10) model in Ref. [3] and by considering general flavour mixing in the LRSM in Ref. [4]. Additional tests to study right-handed currents at LHC are proposed in Ref. [5]. 
However confirmation of these excess events for the given range of the WR mass has severe implications for the leptogenesis mechanism [6], which offers a very attractive possibility to explain the baryon asymmetry of the universe. The seesaw mechanism [7] which provides a natural solution to the smallness of neutrino masses, offers a mechanism for generating a lepton asymmetry (and hence a B −L asymmetry) before the electroweak phase transition, which then gets converted to the baryon asymmetry of the universe via B+L violating anomalous processes in equilibrium [6, 8]. The lepton asymmetry can be generated in two possible ways. One way is via the decay of right-handed Majorana neutrinos (N) which does not conserve lepton number [6]; another way is via the decay of very heavy Higgs triplet scalars with inter- actions that break lepton number [9]. In the LRSM, the right-handed neutrinos interact with the SU(2)R gauge bosons. By taking into account the effect of such interactions of WR on the primordial lepton asymmetry of the universe, phenomenologically successful high-scale leptogenesis requires MWR to be very heavy for both MN > MWR and MWR > MN cases [10]. Thus, an observed 1.8TeV < MWR < 2.2TeV implies that the decay of right-handed neutrinos can not generate the required lepton asymmetry of the universe. Furthermore, since the WR interactions erase any primordial B−L asymmetry, the observed baryon asymmetry of the universe must be generated at a scale lower than the SU(2)R breaking scale. Attempts have been made to explain the required amount of lepton asymmetry in the context of resonant leptogenesis [11] while pushing the mass of WR to as low as 3TeV for relatively large Yukawa couplings [12, 13]. In this article, we point out certain lepton number violat- ing processes involving the doubly charged right-handed Higgs triplet in the LRSM which stay in equilibrium close to the electroweak phase transition for MWR in the range of a few TeV. We show that these processes are effective enough to wash out any lepton asymmetry created after the B − L breaking, thus ruling out the possibility of resonant leptogenesis in the LRSM for the WR mass in the CMS signal range. Similar arguments hold true even for the extended LRSM models which can be formed by extending the U(1) gauge group of the LRSM. 
(Submitted on 5 Feb 2015)