International Journal of Modern Physics A

We explore a simple supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah–Singer theorem.

Over the last century the method of particle acceleration to high energies has become the prime approach to explore the fundamental nature of matter in laboratory. It appears that the latest search of the contemporary accelerator based on the colliders shows a sign of saturation (or at least a slow-down) in increasing its energy and other necessary parameters to extend this frontier. We suggest two pronged approach enabled by the recent progress in high intensity lasers. First we envision the laser-driven plasma accelerator may be able to extend the reach of the collider. For this approach to bear fruit, we need to develop the technology of high averaged power laser in addition to the high intensity. For this we mention that the latest research effort of ICAN is an encouraging sign. In addition to this, we now introduce the concept of the noncollider paradigm in exploring fundamental physics with high intensity (and large energy) lasers. One of the examples we mention is the laser wakefield acceleration (LWFA) far beyond TeV without large luminosity. If we relax or do not require the large luminosity necessary for colliders, but solely in ultrahigh energy frontier, we are still capable of exploring such a fundamental issue. Given such a high energetic particle source and high-intensity laser fields simultaneously, we expect to be able to access new aspects on the matter and the vacuum structure from fundamental physical point of views. LWFA naturally exploits the nonlinear optical effects in the plasma when it becomes of relativistic intensity. Normally nonlinear optical effects are discussed based upon polarization susceptibility of matter to external fields. We suggest application of this concept even to the vacuum structure as a new kind of order parameter to discuss vacuum-originating phenomena at semimacroscopic scales. This viewpoint unifies the following observables with the unprecedented experimental environment we envision; the dispersion relation of photons at extremely short wavelengths in vacuum (a test of the Lorentz invariance), the dispersion relation of the vacuum under high-intensity laser fields (nonperturbative QED and possibly QCD effects), and wave-mixing processes possibly caused by exchanges of low-mass and weakly coupling fields relevant to cosmology with the coherent nature of high-flux photons (search for light dark matter and dark energy). These observables based on polarization susceptibility of vacuum would add novel insights to phenomena discovered in cosmology and particle physics where order parameters such as curvature and particle masses are conventionally discussed. In other words the introduction of high intensity laser and its methodology enriches the approach of fundamental and particle physics in entirely new dimensions.

In the last few years, several approaches have been developed to compute the exact Casimir interaction energy between two nonplanar objects, all lead to the same functional form, which is called the TGTG formula. In this paper, we explore the TGTG formula from the perspective of mode summation approach. Both scalar fields and electromagnetic fields are considered. In this approach, one has to first solve the equation of motion to find a wave basis for each object. The two T's in the TGTG formula are -matrices representing the Lippmann–Schwinger T-operators, one for each of the objects. Each -matrix can be found by matching the boundary conditions imposed on the object, and it is independent of the other object. However, it depends on whether the object is interacting with an object outside it, or an object inside it. The two G's in the TGTG formula are the translation matrices, relating the wave basis of an object to the wave basis of the other object. These translation matrices only depend on the wave basis chosen for each object, and they are independent of the boundary conditions on the objects. After discussing the general theory, we apply the prescription to derive the explicit formulas for the Casimir energies for the sphere–sphere, sphere–plane, cylinder–cylinder and cylinder–plane interactions. First the -matrices for a plane, a sphere and a cylinder are derived for the following cases: the object is imposed with Dirichlet, Neumann or general Robin boundary conditions; the object is semitransparent; and the object is a magnetodielectric object immersed in a magnetodielectric media. Then the operator approach developed by R. C. Wittman [IEEE Trans. Antennas Propag.36, 1078 (1988)] is used to derive the translation matrices. From these, the explicit TGTG formula for each of the scenarios can be written down. On the one hand, we have summarized all the TGTG formulas that have been derived so far for the sphere–sphere, cylinder–cylinder, sphere–plane and cylinder–plane configurations. On the other hand, we provide the TGTG formulas for some scenarios that have not been considered before.

We derive and discuss, at both the classical and quantum levels, generalized supersymmetric quantum mechanical sigma models describing the motion over an arbitrary real or an arbitrary complex manifold with extra torsions. We analyze the relevant vacuum states to make explicit the fact that their number is not affected by adding the torsion terms.

We have analyzed the electron antineutrino scattering off electrons and the electron antineutrino–nuclei coherent scattering in order to obtain constraints on tensorial couplings. We have studied the formalism of nonstandard interactions (NSI) as well as the case of unparticle physics. For our analysis we have focused on the recent TEXONO collaboration results and we have obtained current constraints to possible electron antineutrino–electron tensorial couplings in both new physics formalisms. The possibility of measuring electron antineutrino–nucleus coherent scattering for the first time and its potential to further constrain electron antineutrino–quark tensorial couplings is also discussed.

The decays are analyzed in the standard model (SM) extended to fourth generation of quarks (SM4). The decay rate, forward–backward asymmetry, lepton polarization asymmetries, the helicity fractions of the final state meson and CP asymmetry are discussed using the form factors calculated in the light-cone sum rules (LCSR) approach. We utilized the constraints on different fourth generation parameters obtained from the experimental information on K, B and D decays and from their recent searches at the ATLAS and CMS experiments to explore their impact on the decays. We find that the values of above mentioned physical observables deviate significantly from their minimal SM predications. In the present study, we will also perform the analysis of CP asymmetry in decays within SM4, which is one of the most interesting observable in the study of SM4.

The study of the relative phase between strong and electromagnetic amplitudes is of great importance for understanding the dynamics of charmonium decays. The information of the phase can be obtained model-independently by fitting the scan data of some special decay channels, one of which is ψ′ →K⁺K^-. To find out the optimal data taking strategy for a scan experiment in the measurement of the phase in ψ′ →K⁺ K^-, the minimization process is analyzed from a theoretical point of view. The result indicates that for one-parameter fit, only one data taking point in the vicinity of a resonance peak is sufficient to acquire the optimal precision. Numerical results are obtained by fitting simulated scan data. Besides the results related to the relative phase between strong and electromagnetic amplitudes, the method is extended to analyze the fits of other resonant parameters, such as the mass and the total decay width of ψ′.

We consider a (4+N)-dimensional Einstein gravity coupled to a nonlinear sigma model. This theory admits a solution in which the N extra dimensions contract exponentially while the ordinary space expand exponentially. Physically, the nonlinear sigma fields induce the dynamical compactification of the extra dimensions, which in turn drives inflation. No inflatons are required.