Integrating out the heaviest quark in N--flavour ChPT

We extend a known method to integrate out the strange quark in three flavour chiral perturbation theory to the context of an arbitrary number of flavours. As an application, we present the explicit formulae to one--loop accuracy for the heavy quark mass dependency of the low energy constants after decreasing the number of flavours by one while integrating out the heaviest quark in N--flavour chiral perturbation theory.Comment: 18 pages, 1 figure. Text and references added. To appear in EPJ

Variation of Grain Yield, Grain Protein Content and Nitrogen Use Efficiency Components under Different Nitrogen Rates in Mediterranean Durum Wheat Genotypes

Nitrogen (N) is a crucial nutrient for plant growth and development. To optimize agricultural environments, N fertilizers represent a critical tool to regulate crop productivity. The improvement of nitrogen use efficiency (NUE) represents a promising tool that may enable cereal production to meet future food demand. Wheat reported contrasting behaviors in N utilization showing specific abilities depending on genotype. This study selected two landraces and two improved genotypes from Northern Africa to investigate grain yield (GY), grain protein content (GPC) and NUE. Plants were grown under three levels of N supply: 0, 75, 150 kg N ha−1 and for two consecutive years. Results reported a better NUE (0.40 kg.kg N−1) obtained under 150 kg N ha−1, while N utilization efficiency (NUtE) showed a 13% increase using 75 kg N ha−1 compared with 150 kg N ha−1. Under low nitrogen rate (0 N), crop N supply (CNS) and N uptake efficiency (NUpE) were shown as determinant factors for improved genotypes GY (R2 = 0.72), while NUtE represented the most determinant component for GPC in landraces (R2 = 0.92). Multivariate regression models explained the dependence in GPC on NUE, NUpE, and NUtE. In conclusion, our results recognize GPC and NUtE as suitable selection traits to identify durum wheat with higher NUE

Energy and decay width of the pi-K atom

The energy and decay width of the pi-K atom are evaluated in the framework of the quasipotential-constraint theory approach. The main electromagnetic and isospin symmetry breaking corrections to the lowest-order formulas for the energy shift from the Coulomb binding energy and for the decay width are calculated. They are estimated to be of the order of a few per cent. We display formulas to extract the strong interaction S-wave pi-K scattering lengths from future experimental data concerning the pi-K atom.Comment: 37 pages, 5 figures, uses Axodra

Isospin breaking corrections to low-energy pi-K scattering

We evaluate the matrix elements for the processes pi^0 K^0 -> pi^0 K^0 and pi^- K^+ -> pi^0 K^0 in the presence of isospin breaking terms at leading and next-to-leading order. As a direct application the releveant combination of the S-wave scattering lengths involved in the pion-kaon atom lifetime is determined. We discuss the sensitivity of the results with respect to the input parameters.Comment: 33 pages, plain latex, 2 figure

Non-Relativistic Pion Interactions and the Pionium Lifetime

We construct an effective Lagrangian for interacting pions with non-relativistic energies. The coupling constants can be expressed in terms of the different scattering lengths and slopes. When used in the calculation of the pionium decay rate, the scattering slope contribution gives a correction of about 8% compared with the lowest order contribution coming from the scattering lengths alone.Comment: 8 pages, 5 figure

Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments

A large number of treatments of the meson spectrum have been tried that consider mesons as quark - anti quark bound states. Recently, we used relativistic quantum "constraint" mechanics to introduce a fully covariant treatment defined by two coupled Dirac equations. For field-theoretic interactions, this procedure functions as a "quantum mechanical transform of Bethe-Salpeter equation". Here, we test its spectral fits against those provided by an assortment of models: Wisconsin model, Iowa State model, Brayshaw model, and the popular semi-relativistic treatment of Godfrey and Isgur. We find that the fit provided by the two-body Dirac model for the entire meson spectrum competes with the best fits to partial spectra provided by the others and does so with the smallest number of interaction functions without additional cutoff parameters necessary to make other approaches numerically tractable. We discuss the distinguishing features of our model that may account for the relative overall success of its fits. Note especially that in our approach for QCD, the resulting pion mass and associated Goldstone behavior depend sensitively on the preservation of relativistic couplings that are crucial for its success when solved nonperturbatively for the analogous two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content

The Relativistic N-body Problem in a Separable Two-Body Basis

We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body Hamiltonian is relativistically covariant. It can be easily separated in terms of the center-of-mass and the relative motion of any two-body subsystem. It can also be separated into an unperturbed Hamiltonian with a residual interaction. In a system of two-body composite particles, the solutions of the unperturbed Hamiltonian are relativistic two-body internal states, each of which can be obtained by solving a relativistic Schr\"odinger-like equation. The resultant two-body wave functions can be used as basis states to evaluate reaction matrix elements in the general N-body problem. We prove a relativistic version of the post-prior equivalence which guarantees a unique evaluation of the reaction matrix element, independent of the ways of separating the Hamiltonian into unperturbed and residual interactions. Since an arbitrary reaction matrix element involves composite particles in motion, we show explicitly how such matrix elements can be evaluated in terms of the wave functions of the composite particles and the relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe

Public opinion on energy crops in the landscape: considerations for the expansion of renewable energy from biomass

Public attitudes were assessed towards two dedicated biomass crops – Miscanthus and Short Rotation Coppice (SRC), particularly regarding their visual impacts in the landscape. Results are based on responses to photographic and computer-generated images as the crops are still relatively scarce in the landscape. A questionnaire survey indicated little public concern about potential landscape aesthetics but more concern about attendant built infrastructure. Focus group meetings and interviews indicated support for biomass end uses that bring direct benefits to local communities. Questions arise as to how well the imagery used was able to portray the true nature of these tall, dense, perennial plants but based on the responses obtained and given the caveat that there was limited personal experience of the crops, it appears unlikely that wide-scale planting of biomass crops will give rise to substantial public concern in relation to their visual impact in the landscape

(Pi+Pi-) Atom in Chiral Perturbation Theory

Hadronic (Pi+Pi-) atom is studied in the relativistic perturbative approach based on the Bethe-Salpeter equation. The general expression for the atom lifetime is derived. Lowest-order corrections to the relativistic Deser-type formula for the atom lifetime are evaluated within the Chiral Perturbation Theory.Comment: 36 pages, LaTeX-file (revtex.sty