Electromagnetic properties of ground and excited state pseudoscalar mesons

The axial-vector Ward-Takahashi identity places constraints on particular properties of every pseudoscalar meson. For example, in the chiral limit all pseudoscalar mesons, except the Goldstone mode, decouple from the axial-vector current. Nevertheless, all neutral pseudoscalar mesons couple to two photons. The strength of the \pi_n^0 \gamma \gamma coupling, where n=0 denotes the Goldstone mode, is affected by the Abelian anomaly's continuum contribution. The effect is material for n \neq 0. The \gamma* \pi_n \gamma* transition form factor, T_{\pi_n}(Q^2), is nonzero for all n, and T_{\pi_n}(Q^2) \approx (4\pi^2/3) (f_{\pi_n}/Q^2) at large Q^2. For all pseudoscalars but the Goldstone mode, this leading contribution vanishes in the chiral limit. In this instance the ultraviolet power-law behaviour is 1/Q^4 for n \neq 0, and we find numerically T_{\pi_1}(Q^2) \simeq (4\pi^2/3) (-/Q^4). This subleading power-law behaviour is always present. In general its coefficient is not simply related to f_{\pi_n}. The properties of n \neq 0 pseudoscalar mesons are sensitive to the pointwise behaviour of the long-range piece of the interaction between light-quarks.Comment: 13 pages, 5 figure

The relevance of particulate organic carbon (POC) for carbon composition in the pore water of drained and rewetted fens of the "Donauried" (South-Germany)

International audienceNumerous studies have dealt with carbon (C) concentrations in Histosols, but there are no studies quantifying the relative importance of all individual C components in pore waters. For this study, measurements were made of all the carbon components (i.e., particulate organic carbon, POC; dissolved organic carbon, DOC; dissolved inorganic carbon, DIC; dissolved methane, CH4) in the soil pore water of a calcareous fen under three different water management regimes (re-wetted, deeply and moderately drained). Pore water was collected weekly or biweekly (April 2004 to April 2006) at depths between 10 and 150 cm. The main results obtained were: (1) DIC (94?280 mg C l?1) was the main C-component. (2) POC and DOC concentrations in the pore water (14?125 mg C l?1 vs. 41?95 mg C l?1) were pari passu. (3) Dissolved CH4 was the smallest C component (0.005?0.9 mg C l?1). Interestingly, about 30% of the POM particles were colonized by microbes indicating that they are active in the internal C transfer in the soil profile ("C-Shuttles"). Consequently, it was concluded that POC is at least as important as DOC for internal soil C turnover. There is no reason to assume significant biochemical differences between POC and DOC as they only differ in size. Therefore, both POC and DOC fractions are essential components of C budgets of peatlands. Furthermore dissolved CO2 in all forms of DIC apparently is an important part of peatland C-balances

Survey of nucleon electromagnetic form factors

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincare' covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensurate with the pion's charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are: r_1^{n,u}>r_1^{n,d}, owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.Comment: 43 pages, 17 figures, 12 tables, 5 appendice

Current quark mass dependence of nucleon magnetic moments and radii

A calculation of the current-quark-mass-dependence of nucleon static electromagnetic properties is necessary in order to use observational data as a means to place constraints on the variation of Nature's fundamental parameters. A Poincare' covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is used to calculate this dependence The results indicate that, like observables dependent on the nucleons' magnetic moments, quantities sensitive to their magnetic and charge radii, such as the energy levels and transition frequencies in Hydrogen and Deuterium, might also provide a tool with which to place limits on the allowed variation in Nature's constants.Comment: 23 pages, 2 figures, 4 tables, 4 appendice

Sigma Terms of Light-Quark Hadrons

A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature's fundamental parameters. A hadron's sigma-term is a measure of this dependence. The connection between a hadron's sigma-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit sigma_pi = m_pi/2. This truncation also provides a decent estimate of sigma_rho because the two dominant self-energy corrections to the rho-meson's mass largely cancel in their contribution to sigma_rho. The truncation is less accurate for the omega, however, because there is little to compete with an omega->rho+pi self-energy contribution that magnifies the value of sigma_omega by ~25%. A Poincare' covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Delta, and thereby sigma_N and sigma_Delta. This "quark-core" piece is augmented by the "pion cloud" contribution, which is positive. The analysis yields sigma_N~60MeV and sigma_Delta~50MeV.Comment: 22 pages, reference list expande

Current quark mass effects on chiral phase transition of QCD in the improved ladder approximation

Current quark mass effects on the chiral phase transition of QCD is studied in the improved ladder approximation. An infrared behavior of the gluon propagator is modified in terms of an effective running coupling. The analysis is based on a composite operator formalism and a variational approach. We use the Schwinger-Dyson equation to give a ``normalization condition'' for the Cornwall-Jackiw-Tomboulis effective potential and to isolate the ultraviolet divergence which appears in an expression for the quark-antiquark condensate. We study the current quark mass effects on the order parameter at zero temperature and density. We then calculate the effective potential at finite temperature and density and investigate the current quark mass effects on the chiral phase transition. We find a smooth crossover for $T>0$, $\mu=0$ and a first-order phase transition for $\mu>0$, T=0. Critical exponents are also studied and our model gives the classical mean-field values. We also study the temperature dependence of masses of scalar and pseudoscalar bosons. A critical end point in the $T$-$\mu$ plane is found at $T \sim 100$ MeV, $\mu \sim 300$ MeV.Comment: 19 pages, 13 figure

Nucleon electromagnetic form factors

Elastic electromagnetic nucleon form factors have long provided vital information about the structure and composition of these most basic elements of nuclear physics. The form factors are a measurable and physical manifestation of the nature of the nucleons' constituents and the dynamics that binds them together. Accurate form factor data obtained in recent years using modern experimental facilities has spurred a significant reevaluation of the nucleon and pictures of its structure; e.g., the role of quark orbital angular momentum, the scale at which perturbative QCD effects should become evident, the strangeness content, and meson-cloud effects. We provide a succinct survey of the experimental studies and theoretical interpretation of nucleon electromagnetic form factors.Comment: Topical review invited by Journal of Physics G: Nuclear and Particle Physics; 34 pages (contents listed on page 34), 11 figure

Bethe-Salpeter equation and a nonperturbative quark-gluon vertex

A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic content is enumerable. We illustrate that fact using a vertex obtained via the complete resummation of dressed-gluon ladders. While this vertex is planar, the vertex-consistent kernel is nonplanar and that is true for any dressed vertex. In an exemplifying model the rainbow-ladder truncation of the gap and Bethe-Salpeter equations yields many results; e.g., pi- and rho-meson masses, that are changed little by including higher-order corrections. Repulsion generated by nonplanar diagrams in the vertex-consistent Bethe-Salpeter kernel for quark-quark scattering is sufficient to guarantee that diquark bound states do not exist.Comment: 16 pages, 12 figures, REVTEX

Masses of ground and excited-state hadrons

We present the first Dyson-Schwinger equation calculation of the light hadron spectrum that simultaneously correlates the masses of meson and baryon ground- and excited-states within a single framework. At the core of our analysis is a symmetry-preserving treatment of a vector-vector contact interaction. In comparison with relevant quantities the root-mean-square-relative-error/degree-of freedom is 13%. Notable amongst our results is agreement between the computed baryon masses and the bare masses employed in modern dynamical coupled-channels models of pion-nucleon reactions. Our analysis provides insight into numerous aspects of baryon structure; e.g., relationships between the nucleon and Delta masses and those of the dressed-quark and diquark correlations they contain.Comment: 25 pages, 7 figures, 4 table

State sampling dependence of the Hopfield network inference

The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the form of state sampling. When a single state is sampled to compute magnetizations and correlations, the inference error is almost indistinguishable irrespective of the sampled state. However, the error can be greatly reduced if the data is collected with state transitions. Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.Comment: 4 pages, 1 figure, further discussions added and relevant references adde