Lattice (Φ 4)4 effective potential giving spontaneous symmetry breaking and the role of the Higgs mass

We present a critical reappraisal of the available results on the broken phase ofλ(Φ ⁴)₄ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squaredm _h ² is proportional to its “renormalized” self-couplingλ _R is not valid outside perturbation theory: the appropriate continuum limit hasm _h finite and vanishingλ _R . A Monte Carlo lattice computation of theλ(Φ ⁴)₄ effective potential, both in the single-component and in theO(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept ofλ _R ) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar “triviality” of theλ(Φ ⁴)₄ theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.     

Atropisomerism in 1,5-bridged calix[8]arenes

[structure: see text] The first example of two discrete calix[8]arene conformational isomers, 2 and 2a, has been obtained by exhaustive benzylation of 1,5-tetramethylene-bridged calix[8]arene 1. It is demonstrated, with the aid of X-ray crystallography, that these atropisomers have two 3/4-cone halves oriented syn or anti with respect to the bridge/bridgeheads moiety. VT NMR studies indicate that the tert-butyl-through-the-annulus inversion is inhibited in 1, while groups larger than n-hexyl or benzyl are required for curtailing the O-through-the-annulus route.     

Polymer supported calixarene derivative useful for solid-phase synthesis application

A calix[4]arene derivative has been anchored to carboxyl CPG and TentaGel supports by an easily cleavable ester bond and DMT groups allow a simple loading evaluation via UV-vis spectroscopy. The loading of the calixarene on TentaGel resin has also been estimated by HR-MAS NMR experiments. The potential of the polymer supported calixarenes (9 and 10) in solid phase synthesis has been tested by condensation of four thymine nucleotide units onto the upper rim of the calix[4]arene skeleton.     

Renormalization-group flow for the field strength in scalar self-interacting theories

We consider the renormalization-group coupled equations for the effective potential V(?)$V(?)$ and the field strength Z(?)$Z(?)$ in the spontaneously broken phase as a function of the infrared cutoff momentum k  . In the k→0$k\to 0$ limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(?)$V(?)$, indicates a sharp peaking of Z(?)$Z(?)$ close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.     

Self-assembly of a nucleotide-calixarene hybrid in a triangular supramolecule

The self-assembly of a thymine nucleotide-calixarene hybrid (1) in CDCl₃ as a solvent was investigated. FT-IR, ESI-MS, ¹H and DOSY-NMR spectra evidenced that compound 1 (ammonium or sodium salt) self-assembles in a triangular trimeric supramolecule by thymine-thymine hydrogen bonding. The saline form is crucial for the arrangement in the cyclic trimer as the protonation of the nucleotide phosphate groups leads the assembly toward a dimeric species.     

A sinapic acid–calix[4]arene hybrid selectively binds Pb over Hg and Cd

The binding affinity for Pb²⁺, Cd²⁺ and Hg²⁺ of the sinapic acid–calix[4]arene hybrid 2, having four sinapyl pendants at the upper rim, has been investigated via an UV–Vis study. Compound 2 has better complexing ability than the monomeric p-phenetidine derivative 1. This highlights that the clustering of sinapyl units in a basket-like structure, dictated by the calixarene scaffold, greatly enhances the complexing properties. Ligand 2 forms complexes even with Hg²⁺, which is not complexed by 1 at all; the complexes formed by 2 with Pb²⁺ and Cd²⁺ are much stronger than the analogous complexes formed by 1. The UV–Vis investigation shows that the hybrid 2 markedly favors Pb²⁺ over Cd²⁺ and Hg²⁺. Information on the structural properties of the complex species was obtained by ¹H NMR spectroscopy. NMR data show that all three metal ions are placed into the cavity consisting of the calixarene scaffold and the sinapyl pendants, though their binding affects the coordinating regions to a different extent.     

Quantification of individual zein isoforms resolved by two-dimensional electrophoresis: genetic variability in 45 maize inbred lines

A two-dimensional (2-D) electrophoresis procedure was optimized to obtain well-resolved and reproducible patterns of zein polypeptides in maize. All zein isoforms obtained through zein-specific extraction were observed from whole meal extracted with a urea/Triton/2-mercaptoethanol solution. Loading the protein samples at the acidic side of the gradient, using an amino acid solution as catholyte and running for a short time period under high Vh reduced shrinking and instability at the basic side of the isoelectric focusing (IEF) gels. Good quality and reproducible 2-D patterns were thus obtained, allowing automatic spot quantification. A linear relationship between spot intensity and zein isoform amount was established for 20 of 22 zeins detected in a 5.5-8.5 pH range using colloidal Coomassie blue staining in one maize line. The analysis of 45 genetically diverse inbred lines allowed the detection of 59 isoforms belonging to the four classes of zeins, and revealed a large qualitative and quantitative variability of individual isoforms. The classical decrease in zein amount in o2 mutant genotype was observed, and could be quantified for every isoform. The improved technique will be useful to dissect the genetic control of zein expression in maize.