The Full Two-Loop R-parity Violating Renormalization Group Equations for All Minimal Supersymmetric Standard Model Couplings

We present the full two-loop $\beta$-functions for the minimal supersymmetric standard model couplings, extended to include R-parity violating couplings through explicit R-parity violation

Violation of Leggett inequalities in orbital angular momentum subspaces

We report an experimental test of Leggett's non-local hidden variable theory in an orbital angular momentum (OAM) state space of light. We show that the correlations we observe are in conflict with Leggett's model, thus excluding a particular class of non-local hidden variable theories for the first time in a non-polarization state space. It is known that the violation of the Leggett inequality becomes stronger as more detection settings are used. The required measurements become feasible in an OAM subspace, and we demonstrate this by testing the inequality using three and four settings. We observe excellent agreement with quantum predictions and a violation of five and six standard deviations, respectively, compared to Leggett's non-local hidden variable theory

Infra-red fixed points in supersymmetry

Model independent constraints on supersymmetric models emerge when certain couplings are drawn towards their infra-red (quasi) fixed points in the course of their renormalization group evolution. The general principles are first reviewed and the conclusions for some recent studies of theories with R-parity and baryon and lepton number violations are summarized.Comment: 5 pages Latex with 2 figures embedded as eps files Talk given at WHEPP6, Chennai, India, January 3-15, 2000, to appear in special issue of Praman

Nociceptive neuropeptide increases and periorbital allodynia in a model of traumatic brain injury.

OBJECTIVE: This study tests the hypothesis that injury to the somatosensory cortex is associated with periorbital allodynia and increases in nociceptive neuropeptides in the brainstem in a mouse model of controlled cortical impact (CCI) injury. METHODS: Male C57BL/6 mice received either CCI or craniotomy-only followed by weekly periorbital von Frey (mechanical) sensory testing for up to 28 days post-injury. Mice receiving an incision only and naïve mice were included as control groups. Changes in calcitonin gene-related peptide (CGRP) and substance P (SP) within the brainstem were determined using enzyme-linked immunosorbent assay and immunohistochemistry, respectively. Activation of ionized calcium-binding adaptor molecule-1-labeled macrophages/microglia and glial fibrillary acidic protein (GFAP)-positive astrocytes were evaluated using immunohistochemistry because of their potential involvement in nociceptor sensitization. RESULTS: Incision-only control mice showed no changes from baseline periorbital von Frey mechanical thresholds. CCI significantly reduced mean periorbital von Frey thresholds (periorbital allodynia) compared with baseline and craniotomy-only at each endpoint, analysis of variance P \u3c .0001. Craniotomy significantly reduced periorbital threshold at 14 days but not 7, 21, or 28 days compared with baseline threshold, P \u3c .01. CCI significantly increased SP immunoreactivity in the brainstem at 7 and 14 days but not 28 days compared with craniotomy-only and controls, P \u3c .001. CGRP levels in brainstem tissues were significantly increased in CCI groups compared with controls (incision-only and naïve mice) or craniotomy-only mice at each endpoint examined, P \u3c .0001. There was a significant correlation between CGRP and periorbital allodynia (P \u3c .0001, r = -0.65) but not for SP (r = 0.20). CCI significantly increased the number of macrophage/microglia in the injured cortex at each endpoint up to 28 days, although cell numbers declined over weeks post-injury, P \u3c .001. GFAP(+) immunoreactivity was significantly increased at 7 but not 14 or 28 days after CCI, P \u3c .001. Craniotomy resulted in transient periorbital allodynia accompanied by transient increases in SP, CGRP, and GFAP immunoreactivity compared with control mice. There was no increase in the number of macrophage/microglia cells compared with controls after craniotomy. CONCLUSION: Injury to the somatosensory cortex results in persistent periorbital allodynia and increases in brainstem nociceptive neuropeptides. Findings suggest that persistent allodynia and increased neuropeptides are maintained by mechanisms other than activation of macrophage/microglia or astrocyte in the injured somatosensory cortex

Hyper-Rayleigh scattering in centrosymmetric systems

Hyper-Rayleigh scattering (HRS) is an incoherent mechanism for optical second harmonic generation. The frequency-doubled light that emerges from this mechanism is not emitted in a laser-like manner, in the forward direction; it is scattered in all directions. The underlying theory for this effect involves terms that are quadratic in the incident field and involves an even-order optical susceptibility (for a molecule, its associated hyperpolarizability). In consequence, HRS is often regarded as formally forbidden in centrosymmetric media. However, for the fundamental three-photon interaction, theory based on the standard electric dipole approximation, representable as E13, does not account for all experimental observations. The relevant results emerge upon extending the theory to include E12M1 and E12E2 contributions, incorporating one magnetic dipolar or electric quadrupolar interaction, respectively, to a consistent level of multipolar expansion. Both additional interactions require the deployment of higher orders in the multipole expansion, with the E12E2 interaction analogous in rank and parity to a four-wave susceptibility. To elicit the correct form of response from fluid or disordered media invites a tensor representation which does not oversimplify the molecular components, yet which can produce results to facilitate the interpretation of experimental observations. The detailed derivation in this work leads to results which are summarized for the following: perpendicular detection of polarization components both parallel and perpendicular to the pump radiation, leading to distinct polarization ratio results, as well as a reversal ratio for forward scattered circular polarizations. The results provide a route to handling data with direct physical interpretation, to enable the more sophisticated design of molecules with sought nonlinear optical properties

The Fayet-Iliopoulos D-term and its renormalisation in the MSSM

We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken supersymmetric gauge theory with a non-simple gauge group containing an abelian factor, and present the associated beta-function through three loops. We also include in an appendix the result for several abelian factors. We specialise to the case of the minimal supersymmetric standard model (MSSM), and investigate the behaviour of the Fayet-Iliopoulos coupling for various boundary conditions at the unification scale. We focus particularly on the case of non-standard soft supersymmetry breaking couplings, for which the Fayet-Iliopoulos coupling evolves significantly between the unification scale and the weak scale.Comment: 18 pages, Revtex, 2 figures. Expanded version including general results for gauge groups with several abelian factors. Minor typos correcte