Geometrical hierarchies in classical supergravity

We introduce a $N=1$ supergravity model with a very simple hidden sector coupled to the electroweak gauge and Higgs sectors of the MSSM. At the classical level, supersymmetry and $SU(2)\times U(1)$ are both spontaneously broken, with vanishing vacuum energy. Two real flat directions control the two symmetry-breaking scales $m_{3/2}$ and $m_Z$. The two massless scalars are a gauge singlet and the standard Higgs boson. All other unobserved particles have masses of order $m_{3/2}$. This may be a new starting point for studying the compatibility of naturalness with the observed mass hierarchies.Comment: 5 pages, no figure

A minimal approach to the scattering of physical massless bosons

Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A range of proof-of-concept examples is presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control color quantum numbers of scattering amplitudes with matter.Comment: 65 pages, exposition improved, typos correcte

Revisit to Non-decoupling MSSM

Dipole operator $\bar{s}\sigma_{\mu\nu}F^{\mu\nu}b$ requires the helicity flip in the involving quark states thus the breaking of chiral $U(3)_{Q}\times U(3)_{d}$. On the other hand, the $b$-quark mass generation is also a consequence of chiral $U(3)_{Q}\times U(3)_{d}$ symmetry breaking. Therefore, in many models, there might be strong correlation between the $b\to s\gamma$ and $b$ quark Yukawa coupling. We use non-decoupling MSSM model to illustrate this feature. The light Higgs boson may evade the direct search experiments at LEPII or Tevatron while the 125 GeV Higgs-like boson is identified as the heavy Higgs boson in the spectrum. A light charged Higgs is close to the heavy Higgs boson which is of 125 GeV and its contribution to $b\to s \gamma$ requires large supersymmetric correction with large PQ and $R$ symmetry breaking. The large supersymmetric contribution at the same time significantly modifies the $b$ quark Yukawa co upling. With combined flavor constraints $B\to X_{s}\gamma$ and $B_{s}\to \mu^{+}\mu^{-}$ and direct constraints on Higgs properties, we find best fit scenarios with light stop of $\cal O$(500 GeV), negative $A_{t}$ around -750 GeV and large $\mu$-term of 2-3 TeV. In addition, reduction in $b\bar{b}$ partial width may also result in large enhancement of $\tau\tau$ decay branching fraction. Large parameter region in the survival space under all bounds may be further constrained by $H\to \tau\tau$ if no excess of $\tau\tau$ is confirmed at LHC. We only identify a small parameter region with significant $H\to hh$ decay that is consistent with all bounds and reduced $\tau\tau$ decay branching fraction.Comment: 18pages, 6 figure

Study of polymer crystalline structure with (S)TEM imaging

The crystallinity of polymers has a significant impact on the material's properties, as polymer solids are usually semi-crystalline in nature. Thus, revealing the local structure through direct (Scanning) Transmission Electron Microscope (S)TEM imaging can greatly enhance our understanding of the material properties. However, there are challenges to obtaining high resolution images of polymers using (S)TEM, including irreversible beam damage and low contrast generated by the light elements. Additionally, low and high spatial frequencies are present in polymer semi-crystalline specimens, which require an advanced imaging techniques to resolve. In this study, low dose STEM ptychography was used to acquire high resolution images from poly (ethylene 2,6-naphthalate) (PEN) and poly (ethylene terephthalate) (PET). The beam damage was controlled by a low dose condition that ensured the polymer specimen structure was not altered during the data acquisition process, including ptychography and bright-field (BF) STEM imaging. The phase images obtained with single side band (SSB) reconstruction from 4D-STEM dataset have a sufficient level of phase contrast and resolution across a wide range of spatial frequencies. The critical dose and beam damage of PEN have been studied by tracking the evolution of diffraction intensity versus accumulated dose as part of the development of imaging methodologies. A decay model was constructed with the intention of interpreting the correlation of 'diffraction intensity versus dose' as a latency followed by an exponential decay. The critical dose was determined as (+); where is a “latent dose” from where the exponential decay started, and Dc is the dose at which the intensity had decayed to 1/e of the intensity at the start of the exponential decay. The critical dose calculated based on the decay model was in the range of 700-1000 e/Å2, which was relatively high compared to empirical data of organic materials. The images acquired from semi-crystalline PEN thin film revealed the local molecular conformation of the crystalline structure, and the discrepancy of local structure against the average structure derived from conventional diffraction methods, e.g., XRD, electron diffraction, can be identified. For example, a periodic feature was resolved between planes (2 0 0), and this feature was only observed in experimental images. The periodicity of the feature between strong layers (2 0 0) was identical to the periodicity of a plane within (2 0 0), while the half-spacing of this plane was absent in the experimental image but resolved in the simulated image. Thus, the chemical structure related to the absent half-spacing plane in the experimental image is likely to be the source of the structural discrepancy. A possible explanation for this discrepancy is the rotation of some molecular segments, e.g. the oxygen atoms connected to aliphatic carbons. These discrepancies indicate distinct local structures in comparison to the structure predicted by the model based on XRD data, which implies a modified model. In light of the discrepancy between experimental and simulated ptychography phase images, it was possible to identify the chemical structure from which it may have originated. In a semi-crystalline PEN or PET thin film specimen with a thickness of around 50nm, multiple grains of varying sizes are dispersed in the film at different depths. The optical sectioning technique with election as illumination can not only resolve the crystalline structure at different depths, but also reveal the relative orientation of the grains. With optical sectioning, it was discovered that Moiré fringes can be formed by stacking lattices from different domains or by twisting internal lattices within one grain. The depth profiles of PEN specimens indicate that polymer crystalline lattices will tend to bend or twist, which is likely due to the relatively weak intermolecular interactions. Using established STEM ptychography and optical sectioning techniques, images of PET semi-crystalline specimens revealed new structures. In addition to the fully crystalline ‘ordered’ structure, a new type of ‘partially-ordered’ structure, distinct from either crystalline or amorphous, was discovered for the first time. In the partially-ordered regions, there are clear ‘peaks’ implying a molecular backbone aligned to the viewing direction for 20-30nm, with random short-range periodicity in the lateral dimension, which is in some respects reminiscent of a ‘liquid crystal’ structure. The ‘peaks’ could be molecules aligned to the viewing direction, and the peak-to-peak distance might represent intermolecular distance. Theoretically, the intermolecular distance obtained from the close-packed van de Waals radius of atoms should be the smallest distance, and the intermolecular distance should be the smallest in the crystalline state. Across all partially-ordered features from multiple images, the average peak-to-peak distance is consistently much smaller but not far from half of the intermolecular distance in the crystalline model. Assuming the molecules of the partially-ordered feature are aligned with the viewing direction, there may be rotational symmetry along the molecular axis, and the atoms in the side groups may stack and form the peaks. The ordered features in PET images can be either crystalline or non-crystalline structure depending on their connection with the partially-ordered features. PET models constructed from empirical diffraction data can be used to interpret part of the crystalline structures in the ordered region, particularly the grains in images without partially-ordered features. These ordered features should be crystalline in nature. However, some ordered structures in images containing partially-ordered features show considerable discrepancies with the model, which indicates a significant structural difference with the presence of these partially-ordered features. It appears that these ordered features are a form of more tightly packed molecules of the partially ordered features. This suggests that these ordered features might be in a 'pre-crystalline' state, and together with the junctional partially-ordered feature, a “snapshot” of the transition status has been obtained. Therefore, PET images involving partially-ordered features might reveal pre-order of molecules before crystallization, and there may be rotational symmetry along the molecular axis. The development of a new model could provide evidence and contribute to the understanding of polymer crystallization mechanisms

Population Modeling by Differential Equations

A general model for the population of Tibetan antelope is constructed. The present model shows that the given data is reasonably logistic. From this model the extinction of antelopes in China is predicted if we don’t consider the effects of humans on the population. Moreover, this model shows that the population is limited. A projected limiting number is given by this model. Some typical mathematical models are introduced such as exponential model and logistic model. The solutions of those models are analyzed

The Goldstino Field in Linear and Nonlinear Realizations of Supersymmetry

A Goldstino field in the nonlinear realization of supersymmetry is constructed from an appropriate chiral super-multiplet of the linear theory, in general O'Raifeataigh-like models. The linear theories can thus be reformulated into their nonlinear versions, via the standard procedure. The Goldstino field disappears totally from the original Lagrangian in the process, but reemerges in the Jacobian of the transformation and covariant derivatives. Vertices with Goldstino fields carry at least one space-time derivative, as one would have expected.Comment: 7+1 pages, Late