International Journal of Modern Physics A

I will begin with a brief review of the triumph of Yang–Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.

The series expansion of neutrino evolution matrix “$S$”, up to first-order in small reactor mixing angle ${\theta }_{13}$ is very useful formalism to study experiments quantitatively. The formalism has been used especially to investigate CP-violating phase ${\delta }_{\mathrm{\text{CP}}}$. In order to perform a broad investigation for the possible measurement of ${\delta }_{\mathrm{\text{CP}}}$ phase, we will study small baseline experiments: Chooz $(L=1.03\mathrm{\text{Km}})$, T2K $(L=295\mathrm{\text{Km}})$ and ESS $(L=500\mathrm{\text{Km}})$, medium baseline experiment: NO$\nu$A $(L=810\mathrm{\text{Km}})$ and long baseline experiment: LBNE $(L=1300\mathrm{\text{Km}})$.

We study a neutrino mass model based on $S_4$ flavor symmetry which accommodates lepton mass, mixing with nonzero ${\theta }_{13}$ and CP violation phase. The spontaneous symmetry breaking in the model is imposed to obtain the realistic neutrino mass and mixing pattern at the tree-level with renormalizable interactions. Indeed, the neutrinos get small masses from one $SU{(2)}_L$ doublet and two $SU{(2)}_L$ singlets in which one being in $\underline{2}$ and the two others in $\underline{3}$ under $S_4$ with both the breakings $S_4\to S_3$ and $S_4\to Z_3$ are taken place in charged lepton sector and $S_4\to {𝒦}$ in neutrino sector. The model also gives a remarkable prediction of Dirac CP violation ${\delta }_{\mathrm{\text{CP}}}=\frac{\pi }{2}$ or $-\frac{\pi }{2}$ in both the normal and inverted spectrum which is still missing in the neutrino mixing matrix. The relation between lepton mixing angles is also represented.

The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais–Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.

We construct momentum space expansions for the wave functions that solve the Klein–Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space–time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.

We study Friedmann inflation in general Horava–Lifshitz (HL) gravity with detailed and nondetailed and also without the projectability conditions. Accordingly, we derive the modifications in the Friedmann equations due to single scalar field potentials describing power-law and minimal-supersymmetrically extended inflation. By implementing four types of the equations-of-state characterizing the cosmic background geometry, the dependence of the tensorial and spectral density fluctuations and their ratio on the inflation field is determined. The latter characterizes the time evolution of the inflation field relative to the Hubble parameter. Furthermore, the ratio of tensorial-to-spectral density fluctuations is calculated in dependence on the spectral index. The resulting slow-roll parameters apparently differ from the ones deduced from the standard General Relativity (Friedmann gravity). We also observe that the tensorial-to-spectral density fluctuations continuously decrease when moving from nondetailed HL gravity, to Friedmann gravity, to HL gravity without the projectability, and to detailed HL gravity. This regular pattern is valid for three types of cosmic equations-of-state and different inflation potential models. The results fit well with the recent Planck observations.

Since flavor neutrino masses $M_{\mu \mu ,\tau \tau ,\mu \tau }$ can be expressed in terms of $M_{ee,e\mu ,e\tau }$, mutual dependence among $M_{\mu \mu ,\tau \tau ,\mu \tau }$ is derived by imposing some constraints on $M_{ee,e\mu ,e\tau }$. For appropriately imposed constraints on $M_{ee,e\mu ,e\tau }$ giving rise to both maximal CP violation and the maximal atmospheric neutrino mixing, we show various specific textures of neutrino mass matrices including the texture with $M_{\tau \tau }=M_{\mu \mu }^{\ast }$ derived as the simplest solution to the constraint of $M_{\tau \tau }-M_{\mu \mu }=\mathrm{\text{imaginary}}$, which is required by the constraint of $M_{e\mu }cos{\theta }_{23}-M_{e\tau }sin{\theta }_{23}=\mathrm{\text{real}}$ for $cos2{\theta }_{23}=0$. It is found that Majorana CP violation depends on the phase of $M_{ee}$.

In this paper, we explore the zeta function arising from a small perturbation on a surface of revolution and the effect of this on the functional determinant and on the change of the Casimir energy associated with the surface.