Low-mass right-handed gauge bosons from minimal grand unified theories

Prediction of low-mass $W_R$ and $Z_R$ gauge bosons in popular grand unified theories has been the subject of considerable attention over the last three decades. In this work we show that when gravity induced corrections due to dim.5 operator are included the minimal symmetry breaking chain of $SO(10)$ and $E_6$ GUTs can yield $W_R^{\pm}$ and $Z_R$ bosons with masses in the range $(3-10)$ TeV which are accessible to experimental tests at the Large Hordan Collider. The RH neutrinos turn out to be heavy pseudo-Dirac fermions. The model can fit all fermion masses and manifest in rich structure of lepton flavor violation while proton life time is predicted to be much longer than the accessible limit of Super-Kamiokande or planned Hyper-Kamiokande collaborations.

Left-right symmetric gauge theory [1,2] originally suggested to explain parity violation as monopoly of weak interaction has also found wide applications in many areas of particle physics beyond the standard model including neutrino masses and mixings, lepton number and lepton flavor violations,CP-violation , K −K and B −B mixings and baryogenesis through leptogenesis. This theory is expected to make substantial new impact on weak interaction phenomenology if the associated W ± R , Z R bosons have masses in the TeV range. Finally the new gauge bosons can be detected at the Large Hardon Collider (LHC) where ongoing experimental searches have set the bounds M W R ≥ 2.5 and M Z R ≥ 1.162 [3]. Over the years considerable attention has been focussed on the S O(10) realisation of the left-right(LR) gauge symmetry, accompanied by the left-right discrete symmetry (g 2L = g 2R ) or without it (g 2L g 2R ) and this latter symmetry is denoted as G 2213A [4].
The purpose of this work is to show that these gauge boson masses can be realised quite effectively in the minimal symmetry breraking chain of S O (10) or E 6 GUT: To accunt for tiny neutrino masses we use inverse seesaw formula [6] for which we include three additional singlet fermions S i (i = 1, 2, 3), one per each generation in case of S O(10) but they are parts of standard fermion representations 27 F i of E 6 .
We now give some details in S O(10) by using Higgs representations Φ 210 in the first step, χ 16 in the second step, and H 10 in the third step to achieve the low-1 energy symmetry. In addition to conventional renormalizable interactin, we also include the effect of nonrenormalisable dim.5 operator [5] induced by gravity effects for which M C ∼ M Planck leading to the GUT-scale boundary conditions on the two-loop estimated GUT-scale gauge couplings where α G is the effective GUT fine structure constant and here M U = solution to the GUT scale that includes corrections due to dim.5 operator and the above boudary condition emerges by beaking the GUT symmetry through the VEVs of < η(1,  Table. 1. The right-handed doublet χ(1, 2, −1, 1) breaks the symmetry G 2213A −→ G 213 and also generates N − S mixing mass term M which results in the inverse seesaw mechanism for neutrino masses. This also contributes significantly towards lepton flavor violation. The predicted proton life time for the decay p → e + π 0 in our model turns out to be in the range ∼ 10 37 − 10 38 yrs. which is beyond the accessible ranges of Super-Kamiokande (τ p (p → e + π 0 ) ≥ 1.4 × 10 34 yrs) and proposed investigations at Hyper-Kamiokande (τ p (p → e + π 0 ) ≥ 1.3 × 10 35 yrs).
As noted above,this model admits inverse seesaw formula for light neutrino masses [6]

) >> M D and µ S is small S O(10)-singlet-fermion mass term that violates a SM global symmetry .
The Dirac neutrino mass matrix M D is determined by fitting the extrapolated values of all charged fermion masses at the GUT scale and running it down to the TeV scale following top-down approach [7,8]. We may have to use D h = 2 for this purpose but to achieve near TeV scale G 2213A symmetry D h = D χ = 1 is sufficient The heavy neutrinos in this model are three pairs of pseudo-Dirac fermions which mediate charged lepton flavor violating decays with predictions on branching ratios shown in Table.2. The present experimental limits on branching ratios are Br(µ → eγ) ≤ 2.4 × 10 −12 [9], Br(τ → eγ) ≤ 1.2 × 10 −7 and Br(τ → µγ) ≤ 4.5 × 10 −8 [10]. For verification of model predictions, improved measurements with accuracy upto 3−4 orders are needed. The inverse seesaw formula fits the neutrino oscillation data quite well for all the three types of light neutrino mass hierarchies. All corresponding Higgs representations being present in E 6 GUT, the same approach leads to identical results but now the three S O(10) fermion singlets are in 27 F i each of which has 10 non-standard fermions compared to 16 F + 1 F .
We have discussed a novel method of realising low mass RH gauge bosons in minimal GUTs accessible to LHC using gravitational corrections through dim.5 operator. The model successfully accounts for the neutrino oscillation data through inverse seesaw mechanism. The heavy fermions in the model are pseudo Dirac particles which are also verifiable by their trilepton signatures at LHC. We have obtained similar solutions with D h = D χ = D T = 1 where 2   [11].