In effective field theories it is common to identify the onset of new physics with the violation of tree-level unitarity. However, we show that this is parametrically incorrect in the case of chiral perturbation theory, and is probably theoretically incorrect in general. In the chiral theory, we explore perturbative unitarity violation as a function of the number of colors and the number of flavors, holding the scale of the"new physics" (i.e. QCD) fixed. This demonstrates that the onset of new physics is parametrically uncorrelated with tree-unitarity violation. When the latter scale is lower than that of new physics, the effective theory must heal its unitarity violation itself, which is expected because the field theory satisfies the requirements of unitarity. In the chiral theory, the self-healing results in a resonant structure with scalar quantum numbers. In the electroweak variant of this argument, the structure must have the properties of the Higgs and must couple proportional to the mass in both gauge boson and fermion scattering. A similar example can be seen in the case of general relativity coupled to multiple matter fields, where iteration of the vacuum polarization diagram restores unitarity. We present arguments that suggest the correct identification should be connected to the onset of inelasticity rather than unitarity violation. We describe how the onset of inelasticity can occur in the effective theory, although it does not appear possible to predict the onset reliably.

We analyze the compatibility of the unified left–right symmetric Pati–Salam models motivated by noncommutative geometry and the TeV-scale right-handed [Formula: see text] 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 [Formula: see text] mass and coupling is nontrivial.

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 -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 -1 2 6 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 -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 investigate the physical implications of formulating the electroweak (EW) part of the Standard Model (SM) in terms of a superconnection involving the supergroup SU (2/1). In particular, we relate the observed Higgs mass to new physics at around 4 TeV. The ultraviolet incompleteness of the superconnection approach points to its emergent nature. The new physics beyond the SM is associated with the emergent supergroup SU (2/2), which is natural from the point of view of the Pati-Salam model. Given that the Pati-Salam group is robust in certain constructions of string vacua, these results suggest a deeper connection between low energy (4 TeV) and high energy (Planck scale) physics via the violation of decoupling in the Higgs sector.

Motivated by the R D ( * ) anomalies, we investigate an SO(10) grand unification scenario where a charge −1/3 scalar leptoquark (S1) remains as the only new physics candidate at the TeV scale. This leptoquark along with the Standard Model (SM) Higgs doublet originates from the same ten-dimensional real scalar multiplet in the SO(10) grand unification framework taking its mass close to the electroweak scale. We explicitly show how the gauge coupling unification is achieved with only one intermediate symmetrybreaking scale at which the Pati-Salam gauge group is broken into the SM group. We investigate the phenomenological implications of our scenario and show that an S1 with a specific Yukawa texture can explain the R D ( * ) anomalies. We perform a multiparameter scan considering the relevant flavour constraints on R D ( * ) , FL(D * ), Pτ (D * ) and R νν K ( * ) as well as the constraint coming from the Z → τ τ decay and the latest τ τ resonance search data at the LHC. Our analysis shows that a single leptoquark solution to the observed R D ( * ) anomalies with S1 is still a viable solution.