Vector meson form factors and their quark-mass dependence

The electromagnetic form factors of vector mesons are calculated in an explicitly Poincar\'e covariant formulation, based on the Dyson--Schwinger equations of QCD, that respects electromagnetic current conservation, and unambiguously incorporates effects from vector meson poles in the quark-photon vertex. This method incorporates a 2-parameter effective interaction, where the parameters are constrained by the experimental values of chiral condensate and $f_{\pi}$. This approach has successfully described a large amount of light-quark meson experimental data, e.g. ground state pseudoscalar masses and their electromagnetic form factors; ground state vector meson masses and strong and electroweak decays. Here we apply it to predict the electromagnetic properties of vector mesons. The results for the static properties of the $\rho$-meson are: charge radius $= 0.54 {\rm fm}^2$, magnetic moment $\mu = 2.01$, and quadrupole moment ${\cal Q} = -0.41$. We investigate the quark mass dependence of these static properties and find that our results at the charm quark mass are in agreement with recent lattice simulations. The charge radius decreases with increasing quark mass, but the magnetic moment is almost independent of the quark mass.Comment: 13 pages, 7 figure

Asteroid detection at millimetric wavelengths with the Planck survey

The Planck mission, originally devised for cosmological studies, offers the opportunity to observe Solar System objects at millimetric and submillimetric wavelengths. We concentrate in this paper on the asteroids of the Main Belt. We intend to estimate the number of asteroids that can can be detected during the mission and to evaluate the strength of their signal. We have rescaled the instrument sensitivities, calculated by the LFI and HFI teams for sources fixed in the sky, introducing some degradation factors to properly account for moving objects. In this way a detection threshold is derived for asteroidal detection that is related to the diameter of the asteroid and its geocentric distance. We have developed a numerical code that models the detection of asteroids in the LFI and HFI channels during the mission. This code perfoprms a detailed integration of the orbits of the asteroids in the timespan of the mission and identifies those bodies that fall in the beams of Planck and their signal stenght. According to our simulations, a total of 397 objects will be observed by Planck and an asteroidal body will be detected in some beam in 30% of the total sky scan--circles. A significant fraction (in the range from ~50 to 100 objects) of the 397 asteroids will be observed with a high S/N ratio. Flux measurements of a large sample of asteroids in the submillimeter and millimeter range are relevant since they allow to analyze the thermal emission and its relation to the surface and regolith properties. Furthermore, it will be possible to check on a wider base the two standard thermal models, based on a nonrotating or rapidly rotating sphere. Our method can also be used to separate Solar System sources from cosmological sources in the survey. This work is based on Planck LFI activities.Comment: Contact person [email protected]. Accepted for pubblication in New Astronomy (2002). 1 figure in .eps format. Needs elsart.cls style + harvard.st

Strong Decays of Light Vector Mesons

The vector meson strong decays rho-->pi pi, phi-->KK, and K^star-->pi K are studied within a covariant approach based on the ladder-rainbow truncation of the QCD Dyson--Schwinger equation for the quark propagator and the Bethe--Salpeter equation for the mesons. The model preserves the one-loop behavior of QCD in the ultraviolet, has two infrared parameters, and implements quark confinement and dynamical chiral symmetry breaking. The 3-point decay amplitudes are described in impulse approximation. The Bethe--Salpeter study motivates a method for estimating the masses for heavier mesons within this model without continuing the propagators into the complex plane. We test the accuracy via the rho, phi and K^{star} masses and then produce estimates of the model results for the a_1 and b_1 masses as well as the mass of the proposed exotic vector pi_1(1400).Comment: Submitted for publication; 10x2-column pages, REVTEX 4, 3 .eps files making 3fig

K_{l3} transition form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson bound state amplitudes and the dressed quark-W vertex in a manifestly covariant calculation of the K_{l3} transition form factors and decay width in impulse approximation. With model gluon parameters previously fixed by the chiral condensate, the pion mass and decay constant, and the kaon mass, our results for the K_{l3} form factors and the kaon semileptonic decay width are in good agreement with the experimental data.Comment: 8 pages, 3 figures, Revte

Confinement Phenomenology in the Bethe-Salpeter Equation

We consider the solution of the Bethe-Salpeter equation in Euclidean metric for a qbar-q vector meson in the circumstance where the dressed quark propagators have time-like complex conjugate mass poles. This approximates features encountered in recent QCD modeling via the Dyson-Schwinger equations; the absence of real mass poles simulates quark confinement. The analytic continuation in the total momentum necessary to reach the mass shell for a meson sufficiently heavier than 1 GeV leads to the quark poles being within the integration domain for two variables in the standard approach. Through Feynman integral techniques, we show how the analytic continuation can be implemented in a way suitable for a practical numerical solution. We show that the would-be qbar-q width to the meson generated from one quark pole is exactly cancelled by the effect of the conjugate partner pole; the meson mass remains real and there is no spurious qbar-q production threshold. The ladder kernel we employ is consistent with one-loop perturbative QCD and has a two-parameter infrared structure found to be successful in recent studies of the light SU(3) meson sector.Comment: Submitted for publication; 10.5x2-column pages, REVTEX 4, 3 postscript files making 3 fig

Chirally symmetric quark description of low energy \pi-\pi scattering

Weinberg's theorem for \pi-\pi scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold \pi-\pi scattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.Comment: 10 pages, 7 figures, Revtex

Evaluation of Directive-Based GPU Programming Models on a Block Eigensolver with Consideration of Large Sparse Matrices

Achieving high performance and performance portability for large-scale scientific applications is a major challenge on heterogeneous computing systems such as many-core CPUs and accelerators like GPUs. In this work, we implement a widely used block eigensolver, Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG), using two popular directive based programming models (OpenMP and OpenACC) for GPU-accelerated systems. Our work differs from existing work in that it adopts a holistic approach that optimizes the full solver performance rather than narrowing the problem into small kernels (e.g., SpMM, SpMV). Our LOPBCG GPU implementation achieves a 2.8$${\times }$$–4.3$${\times }$$ speedup over an optimized CPU implementation when tested with four different input matrices. The evaluated configuration compared one Skylake CPU to one Skylake CPU and one NVIDIA V100 GPU. Our OpenMP and OpenACC LOBPCG GPU implementations gave nearly identical performance. We also consider how to create an efficient LOBPCG solver that can solve problems larger than GPU memory capacity. To this end, we create microbenchmarks representing the two dominant kernels (inner product and SpMM kernel) in LOBPCG and then evaluate performance when using two different programming approaches: tiling the kernels, and using Unified Memory with the original kernels. Our tiled SpMM implementation achieves a 2.9$${\times }$$ and 48.2$${\times }$$ speedup over the Unified Memory implementation on supercomputers with PCIe Gen3 and NVLink 2.0 CPU to GPU interconnects, respectively

Can IRT solve the missing data problem in test equating?

In this paper test equating is considered as a missing data problem. The unobserved responses of the reference population to the new test must be imputed to specify a new cutscore. The proportion of students from the reference population that would have failed the new exam and those having failed the reference exam are made approximately the same. We investigate whether item response theory (IRT) makes it possible to identify the distribution of these missing responses and the distribution of test scores from the observed data without parametric assumptions for the ability distribution. We show that while the score distribution is not fully identifiable, the uncertainty about the score distribution on the new test due to non-identifiability is very small. Moreover, ignoring the non-identifiability issue and assuming a normal distribution for ability may lead to bias in test equating, which we illustrate in simulated and empirical data examples

The π\pi, K+K^+, and K0K^0 electromagnetic form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed quark-photon vertex in a self-consistent Poincar\'e-invariant study of the pion and kaon electromagnetic form factors in impulse approximation. We demonstrate explicitly that the current is conserved in this approach and that the obtained results are independent of the momentum partitioning in the Bethe-Salpeter amplitudes. With model gluon parameters previously fixed by the condensate, the pion mass and decay constant, and the kaon mass, the charge radii and spacelike form factors are found to be in good agreement with the experimental data.Comment: 8 pages, 6 figures, Revte

Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.Comment: 13 pages, 11 Figure