The emergence of the Cabibbo angle in non-degenerate coupled systems of fermions

Investigating, in direct continuation of our previous paper hep-ph/0606303 the implications of the non-unitarity of mixing matrices for non-degenerate coupled systems that we demonstrated there, we examine more accurately the vicinity of Cabibbo-like mixing in quantum field theory. We show that it is possible to preserve one of its main features, namely that, in the space of mass eigenstates, the two requirements -- of universality for weak diagonal currents and -- of the absence of their non-diagonal counterparts, although not fulfilled separately any more, can however reduce to a single condition for a unique mixing angle theta\_c. This leads to tan (2 theta\_c)=+/- 1/2, or cos theta\_c \approx 0.9732, only 7/10000 away from experimental results. No mass ratio appears in the argumentation.Comment: This is a different version of hep-ph/0607193, with a simplified argumentation, a clearer connection with hep-ph/0606303. The solution for the Cabibbo angle is also expressed in terms of the golden number. To appear in Phys. Lett.

Non-Hermitian Hamiltonians and supersymmetric quantum mechanics

Théori

Quark Lagrangian diagonalization versus non-diagonal kinetic terms

Loop corrections induce a dependence on the momentum squared of the coefficients of the Standard Model Lagrangian, making highly non-trivial (or even impossible) the diagonalization of its quadratic part. Fortunately, the introduction of appropriate counterterms solves this puzzle.Comment: 2 pages, 1 figur

Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities. The case of a single fermion-antifermion pair

Starting from Wigner's symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman's definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance.Comment: 37 pages, LaTeX. version to appear in "Annals of Physics (N.Y.)

Mutation Bias is the Driving Force of Codon Usage in the Gallus gallus genome

Synonymous codons are used with different frequencies both among species and among genes within the same genome and are controlled by neutral processes (such as mutation and drift) as well as by selection. Up to now, a systematic examination of the codon usage for the chicken genome has not been performed. Here, we carried out a whole genome analysis of the chicken genome by the use of the relative synonymous codon usage (RSCU) method and identified 11 putative optimal codons, all of them ending with uracil (U), which is significantly departing from the pattern observed in other eukaryotes. Optimal codons in the chicken genome are most likely the ones corresponding to highly expressed transfer RNA (tRNAs) or tRNA gene copy numbers in the cell. Codon bias, measured as the frequency of optimal codons (Fop), is negatively correlated with the G + C content, recombination rate, but positively correlated with gene expression, protein length, gene length and intron length. The positive correlation between codon bias and protein, gene and intron length is quite different from other multi-cellular organism, as this trend has been only found in unicellular organisms. Our data displayed that regional G + C content explains a large proportion of the variance of codon bias in chicken. Stepwise selection model analyses indicate that G + C content of coding sequence is the most important factor for codon bias. It appears that variation in the G + C content of CDSs accounts for over 60% of the variation of codon bias. This study suggests that both mutation bias and selection contribute to codon bias. However, mutation bias is the driving force of the codon usage in the Gallus gallus genome. Our data also provide evidence that the negative correlation between codon bias and recombination rates in G. gallus is determined mostly by recombination-dependent mutational patterns

Magnetic fields in noncommutative quantum mechanics

We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between various approaches and results that are scattered in the literature.Comment: Dedicated to the memory of Julius Wess. Work presented by F. Gieres at the conference `Non-commutative Geometry and Physics' (Orsay, April 2007

Genomic survey of the non-cultivatable opportunistic human pathogen, Enterocytozoon bieneusi

© 2009 The Authors. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in PLoS Pathogens 5 (2009): e1000261, doi:10.1371/journal.ppat.1000261.Enterocytozoon bieneusi is the most common microsporidian associated with human disease, particularly in the immunocompromised population. In the setting of HIV infection, it is associated with diarrhea and wasting syndrome. Like all microsporidia, E. bieneusi is an obligate, intracellular parasite, but unlike others, it is in direct contact with the host cell cytoplasm. Studies of E. bieneusi have been greatly limited due to the absence of genomic data and lack of a robust cultivation system. Here, we present the first large-scale genomic dataset for E. bieneusi. Approximately 3.86 Mb of unique sequence was generated by paired end Sanger sequencing, representing about 64% of the estimated 6 Mb genome. A total of 3,804 genes were identified in E. bieneusi, of which 1,702 encode proteins with assigned functions. Of these, 653 are homologs of Encephalitozoon cuniculi proteins. Only one E. bieneusi protein with assigned function had no E. cuniculi homolog. The shared proteins were, in general, evenly distributed among the functional categories, with the exception of a dearth of genes encoding proteins associated with pathways for fatty acid and core carbon metabolism. Short intergenic regions, high gene density, and shortened protein-coding sequences were observed in the E. bieneusi genome, all traits consistent with genomic compaction. Our findings suggest that E. bieneusi is a likely model for extreme genome reduction and host dependence.This research was supported by National Institutes of Health (NIH) grants R21 AI064118 (DEA) and R21 AI52792 (ST). HGM was supported in part by NIH contracts HHSN266200400041C and HHSN2662004037C (Bioinformatics Resource Centers) and by the G. Unger Vetlesen Foundation

The +4G Site in Kozak Consensus Is Not Related to the Efficiency of Translation Initiation

The optimal context for translation initiation in mammalian species is GCCRCCaugG (where R = purine and “aug” is the initiation codon), with the -3R and +4G being particularly important. The presence of +4G has been interpreted as necessary for efficient translation initiation. Accumulated experimental and bioinformatic evidence has suggested an alternative explanation based on amino acid constraint on the second codon, i.e., amino acid Ala or Gly are needed as the second amino acid in the nascent peptide for the cleavage of the initiator Met, and the consequent overuse of Ala and Gly codons (GCN and GGN) leads to the +4G consensus. I performed a critical test of these alternative hypotheses on +4G based on 34169 human protein-coding genes and published gene expression data. The result shows that the prevalence of +4G is not related to translation initiation. Among the five G-starting codons, only alanine codons (GCN), and glycine codons (GGN) to a much smaller extent, are overrepresented at the second codon, whereas the other three codons are not overrepresented. While highly expressed genes have more +4G than lowly expressed genes, the difference is caused by GCN and GGN codons at the second codon. These results are inconsistent with +4G being needed for efficient translation initiation, but consistent with the proposal of amino acid constraint hypothesis