We analyze the compatibility of the recent LHC signals and the TeV-scale left right model(s) in the minimal nonsupersymmetric SO(10) framework. We show that the models in which the Higgs content is selected based on the extended survival hypothesis do not allow the W-R boson to be at the TeV-scale. By relaxing this conjecture, we investigate various scenarios where a number of colored-scalars, originated from various Pati-Salam multiplets, are light and whence they survive down to the low energies. Performing a detailed renormalization group analysis with various low-energy Higgs configurations and symmetry breaking chains, while keeping the high energy Higgs content unmodified; we find that, among a number of possibilities, the models which have a light color-triplet scalar, and its combination with a light color-sextet, particularly stand out. Although these models do allow a TeV-scale W-R boson, generating the required value of the gauge coupling g(R) at this scale is nontrivial.

We investigate the possibility of TeV-scale scalars as low energy remnants arising in the nonsupersymmetric SO(10) grandunification framework where the field content is minimal.We consider a scenario where the SO(10) gauge symmetry is broken intothe gauge symmetry of the Standard Model (SM) through multiple stages of symmetry breaking, and a colored and hyperchargedscalar 𝜒 picks a TeV-scale mass in the process. The last stage of the symmetry breaking occurs at the TeV-scale where the leftrightsymmetry, that is, SU(2)𝐿 ⊗ SU(2)𝑅 ⊗ U(1)𝐵−𝐿 ⊗ SU(3)𝐶, is broken into that of the SM by a singlet scalar field S of mass𝑀S ∼ 1TeV, which is a component of an SU(2)𝑅-triplet scalar field, acquiring a TeV-scale vacuum expectation value. For the LHCphenomenology, we consider a scenario where S is produced via gluon-gluon fusion through loop interactions with 𝜒 and alsodecays to a pair of SM gauge bosons through 𝜒 in the loop.We find that the parameter space is heavily constrained from the latestLHC data.We use a multivariate analysis to estimate the LHC discovery reach of S into the diphoton channel.

We discuss the physical implications of formulating the Standard Model (SM) in terms of the superconnection formalism involving the superalgebra su(2/1). In particular, we discuss the prediction of the Higgs mass according to the formalism and point out that it is similar to 170 GeV, in clear disagreement with experiment. To remedy this problem, we extend the formalism to the superalgebra su(2/2), which extends the SM to the left-right symmetric model (LRSM) and accommodates a similar to 126 GeV Higgs boson. Both the SM in the su(2/1) case and the LRSM in the su(2/2) case are argued to emerge at similar to 4 TeV from an underlying theory in which the spacetime geometry is modified by the addition of a discrete extra dimension. The formulation of the exterior derivative in this model space suggests a deep connection between the modified geometry, which can be described in the language of noncommutative geometry, and the spontaneous breaking of the gauge symmetries. The implication is that spontaneous symmetry breaking could actually be geometric/quantum gravitational in nature. The nondecoupling phenomenon seen in the Higgs sector can then be reinterpreted in a new light as due to the mixing of low energy (SM) physics and high energy physics associated with quantum gravity, such as string theory. The phenomenology of a TeV scale LRSM is also discussed, and we argue that some exciting discoveries may await us at the LHC, and other near-future experiments.

We analyze the compatibility of the unified left-right symmetric Pati-Salam models motivated by noncommutative geometry and the TeV-scale right-handed W boson suggested by recent LHC data. We find that the unification/matching conditions place conflicting demands on the symmetry breaking scales and that generating the required W-R mass and coupling is nontrivial.

We discuss a possible interpretation of the 750 GeV diphoton resonance, recently reported at the large hadron collider (LHC), within a class of SU(2)(L) x SU(2)(R) x SU(4) models with gauge coupling unification. The unification is imposed by the underlying noncommutative geometry (NCG), which in these models is extended to a left-right symmetric completion of the Standard Model (SM). Within such unified SU(2)(L) x SU(2)(R) x SU(4) models the Higgs content is restrictively determined from the underlying NCG, instead of being arbitrarily selected. We show that the observed cross-sections involving the 750 GeV diphoton resonance could be realized through a SM singlet scalar field accompanied by colored scalars, present in these unified models. In view of this result, we discuss the underlying rigidity of these models in the NCG framework and the wider implications of the NCG approach for physics beyond the SM.