A New Class of Theta Function Identities in Two Variables

Copyright © 2010 Nova Science PublishersWe describe a new class of identities, which hold for certain general theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta function, Jacobi theta functions, and various theta functions of Ramanujan

Prevention of acute malnutrition: distribution of special nutritious foods and cash, and addressing underlying causes--what to recommend when, where, for whom, and how

Acute malnutrition is associated with increased morbidity and mortality risk. When episodes are prolonged or frequent, acute malnutrition is also associated with poor growth and development, which contributes to stunting Nutrition-specific and nutrition-sensitive strategies to prevent undernutrition during the first 1,000 days from conception to 24 months of age can reduce the risks of wasting, stunting, and micronutrient deficiencies. Under circumstances that exacerbate the underlying causes of undernutrition and increase the incidence of wasting, such as food insecurity related to lean seasons or emergencies, or increased incidence of illness, such as diarrhea or measles, additional efforts are required to prevent and treat wasting. Special nutritious foods directly meet the increased nutrient requirements of children at risk for wasting; assistance to vulnerable households, in the form of cash or food, enables households to better meet the food, health, and other needs of household members and may increase resilience; water, sanitation, and hygiene (WASH) and health interventions help prevent and address illness and hence reduce wasting risk. The contributions of specific interventions to reducing the incidence of wasting are difficult to assess under emergency conditions, due to ethical constraints and to the fact that multiple strategies are implemented at the same time. However, pragmatic studies under real-life circumstances, using different designs, e.g., including a group receiving "best possible" treatment, can provide evidence about what works, to what extent, at what cost, and under which circumstances. Programs should address the most important causes in given contexts, be feasible to implement at scale, and assess implementation, coverage, and outcomes

Photoproduction of pi0 omega off protons for E(gamma) < 3 GeV

Differential and total cross-sections for photoproduction of gamma proton to proton pi0 omega and gamma proton to Delta+ omega were determined from measurements of the CB-ELSA experiment, performed at the electron accelerator ELSA in Bonn. The measurements covered the photon energy range from the production threshold up to 3GeV.Comment: 8 pages, 13 figure

High statistics study of the reaction γp→p 2π0\gamma p\to p\;2\pi^0

The photoproduction of 2$\pi^0$ mesons off protons was studied with the Crystal Barrel/TAPS experiment at the electron accelerator ELSA in Bonn. The energy of photons produced in a radiator was tagged in the energy range from 600\,MeV to 2.5\,GeV. Differential and total cross sections and $p\pi^0\pi^0$ Dalitz plots are presented. Part of the data was taken with a diamond radiator producing linearly polarized photons, and beam asymmetries were derived. Properties of nucleon and $\Delta$ resonances contributing to the $p\pi^0\pi^0$ final state were determined within the BnGa partial wave analysis. The data presented here allow us to determine branching ratios of nucleon and $\Delta$ resonances for their decays into $p\pi^0\pi^0$ via several intermediate states. Most prominent are decays proceeding via $\Delta(1232)\pi$, $N(1440)1/2^+\pi$, $N(1520)3/2^-\pi$, $N(1680)5/2^+\pi$, but also $pf_0(500)$, $pf_0(980)$, and $pf_2(1270)$ contribute to the reaction.Comment: 28 pages, 17 figures, 7 table

Modification of the ω\omega-Meson Lifetime in Nuclear Matter

The photo production of $\omega$ mesons on the nuclei C, Ca, Nb and Pb has been measured using the Crystal Barrel/TAPS detector at the ELSA tagged photon facility in Bonn. The dependence of the $\omega$ meson cross section on the nuclear mass number has been compared with three different types of models, a Glauber analysis, a BUU analysis of the Giessen theory group and a calculation by the Valencia theory group. In all three cases, the inelastic $\omega$ width is found to be $130-150 \rm{MeV/c^2}$ at normal nuclear matter density for an average 3-momentum of 1.1 GeV/c. In the restframe of the $\omega$ meson, this inelastic $\omega$ width corresponds to a reduction of the $\omega$ lifetime by a factor $\approx 30$. For the first time, the momentum dependent $\omega$N cross section has been extracted from the experiment and is in the range of 70 mb.Comment: 5 pages, 4 figure

In-medium ω\omega mass from the γ+Nb→π0γ+X\gamma + Nb \to \pi^{0}\gamma + X reaction

Data on the photoproduction of $\omega$ mesons on nuclei have been re-analyzed in a search for in-medium modifications. The data were taken with the Crystal Barrel(CB)/TAPS detector system at the ELSA accelerator facility in Bonn. First results from the analysis of the data set were published by D. Trnka et al. in Phys. Rev. Lett 94 (2005) 192303 \cite{david}, claiming a lowering of the $\omega$ mass in the nuclear medium by 14$$ at normal nuclear matter density. The extracted $\omega$ line shape was found to be sensitive to the background subtraction. For this reason a re-analysis of the same data set has been initiated and a new method has been developed to reduce the background and to determine the shape and absolute magnitude of the background directly from the data. Details of the re-analysis and of the background determination are described. The $\omega$ signal on the $Nb$ target, extracted in the re-analysis, does not show a deviation from the corresponding line shape on a $LH_2$ target, measured as reference. The earlier claim of an in-medium mass shift is thus not confirmed. The sensitivity of the $\omega$ line shape to different in-medium modification scenarios is discussed.Comment: 13 pages and 11 figures, submitted for publicatio

The {\eta}'-carbon potential at low meson momenta

The production of $\eta^\prime$ mesons in coincidence with forward-going protons has been studied in photon-induced reactions on $^{12}$C and on a liquid hydrogen (LH$_2$) target for incoming photon energies of 1.3-2.6 GeV at the electron accelerator ELSA. The $\eta^\prime$ mesons have been identified via the $\eta^\prime\rightarrow \pi^0 \pi^0\eta \rightarrow 6 \gamma$ decay registered with the CBELSA/TAPS detector system. Coincident protons have been identified in the MiniTAPS BaF$_2$ array at polar angles of $2^{\circ} \le \theta _{p} \le 11^{\circ}$. Under these kinematic constraints the $\eta^\prime$ mesons are produced with relatively low kinetic energy ($\approx$ 150 MeV) since the coincident protons take over most of the momentum of the incident-photon beam. For the C-target this allows the determination of the real part of the $\eta^\prime$-carbon potential at low meson momenta by comparing with collision model calculations of the $\eta^\prime$ kinetic energy distribution and excitation function. Fitting the latter data for $\eta^\prime$ mesons going backwards in the center-of-mass system yields a potential depth of V = $-$(44 $\pm$ 16(stat)$\pm$15(syst)) MeV, consistent with earlier determinations of the potential depth in inclusive measurements for average $\eta^\prime$ momenta of $\approx$ 1.1 GeV/$c$. Within the experimental uncertainties, there is no indication of a momentum dependence of the $\eta^\prime$-carbon potential. The LH$_2$ data, taken as a reference to check the data analysis and the model calculations, provide differential and integral cross sections in good agreement with previous results for $\eta^\prime$ photoproduction off the free proton.Comment: 9 pages, 13 figures. arXiv admin note: text overlap with arXiv:1608.0607

Quasi-free photoproduction of eta-mesons of the neutron

Quasi-free photoproduction of eta-mesons off nucleons bound in the deuteron has been measured with the CBELSA/TAPS detector for incident photon energies up to 2.5 GeV at the Bonn ELSA accelerator. The eta-mesons have been detected in coincidence with recoil protons and recoil neutrons, which allows a detailed comparison of the quasi-free n(gamma,eta)n and p(gamma,eta)p reactions. The excitation function for eta-production off the neutron shows a pronounced bump-like structure at W=1.68 GeV (E_g ~ 1 GeV), which is absent for the proton.Comment: accepted for publication in Phys. Rev. Let

Photoproduction of meson pairs: First measurement of the polarization observable I^s

The polarization observable I^s, a feature exclusive to the acoplanar kinematics of multi-meson final states produced via linearly polarized photons, has been measured for the first time. Results for the reaction g p -> p pi0 eta are presented for incoming photon energies between 970 MeV and 1650 MeV along with the beam asymmetry I^c. The comparably large asymmetries demonstrate a high sensitivity of I^s to the dynamics of the reaction. Fits using Bonn-Gatchina partial wave analysis demonstrate that the new polarization observables carry significant information on the contributing partial waves.Comment: 11 pages, 6 figures, v2 to appear in Phys. Lett.

K^0 pi^0 Sigma^+ and K^*0 Sigma^+ photoproduction off the proton

The exclusive reactions $\gamma p \to K^{*0} \Sigma^+(1189)$ and $\gamma p \to K^{0} \pi^{0}\Sigma^+(1189)$, leading to the p 4$\pi^{0}$ final state, have been measured with a tagged photon beam for incident energies from threshold up to 2.5 GeV. The experiment has been performed at the tagged photon facility of the ELSA accelerator (Bonn). The Crystal Barrel and TAPS detectors were combined to a photon detector system of almost 4$\pi$ geometrical acceptance. Differential and total cross sections are reported. At energies close to the threshold, a flat angular distribution has been observed for the reaction $\gamma p\to K^{0} \pi^{0}\Sigma^+$ suggesting dominant s-channel production. $\Sigma^*(1385)$ and higher lying hyperon states have been observed. An enhancement in the forward direction in the angular distributions of the reaction $\gamma p \to K^{*0}\Sigma^+$ indicates a $t$-channel exchange contribution to the reaction mechanism. The experimental data are in reasonable agreement with recent theoretical predictions.Comment: 11 pages, 13 figures, submitted to EPJ