Measuring longitudinal amplitudes for electroproduction of pseudoscalar mesons using recoil polarization in parallel kinematics

We propose a new method for measuring longitudinal amplitudes for electroproduction of pseudoscalar mesons that exploits a symmetry relation for polarization observables in parallel kinematics. This polarization technique does not require variation of electron scattering kinematics and avoids the major sources of systematic errors in Rosenbluth separation.Comment: intended for Phys. Rev. C as a Brief Repor

Measurement of the recoil polarization in the p (\vec e, e' \vec p) pi^0 reaction at the \Delta(1232) resonance

The recoil proton polarization has been measured in the p (\vec e,e'\vec p) pi^0 reaction in parallel kinematics around W = 1232 MeV, Q^2 = 0.121 (GeV/c)^2 and epsilon = 0.718 using the polarized c.w. electron beam of the Mainz Microtron. Due to the spin precession in a magnetic spectrometer, all three proton polarization components P_x/P_e = (-11.4 \pm 1.3 \pm 1.4) %, P_y = (-43.1 \pm 1.3 \pm 2.2) %, and P_z/P_e = (56.2 \pm 1.5 \pm 2.6) % could be measured simultaneously. The Coulomb quadrupole to magnetic dipole ratio CMR = (-6.4\pm 0.7_{stat}\pm 0.8_{syst}) % was determined from P_x in the framework of the Mainz Unitary Isobar Model. The consistency among the reduced polarizations and the extraction of the ratio of longitudinal to transverse response is discussed.Comment: 5 pages LaTeX, 1 table, 2 eps figure

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Final State Interaction Effects in pol 3He(pol e,e'p)

Asymmetries in quasi-elastic pol 3He(pol e,e'p) have been measured at a momentum transfer of 0.67 (GeV/c)^2 and are compared to a calculation which takes into account relativistic kinematics in the final state and a relativistic one-body current operator. With an exact solution of the Faddeev equation for the 3He-ground state and an approximate treatment of final state interactions in the continuum good agreement is found with the experimental data.Comment: 11 pages, 6 figures, submitted to Phys. Lett. B, revised version, sensitivity study to relativity and NN-potential adde

Deuteron photodisintegration cross-sections 50-155 MeV

The study of the photodisintegration of the deuteron should be a rewarding area over the next few years both as a result of the increased sophistication of recent theoretical treatments and also because of the potential, which has only just begun to be realised, of much more accurate and reliable photoreaction data

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

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

Measurement of the LT-asymmetry in \pi^0 electroproduction at the energy of the \Delta (1232) resonance

The reaction p(e,e'p)pi^0 has been studied at Q^2=0.2 (GeV/c)^2 in the region of W=1232 MeV. From measurements left and right of q, cross section asymmetries \rho_LT have been obtained in forward kinematics \rho_LT(\theta_\pi^0=20deg) = (-11.68 +/- 2.36_stat +/- 2.36_sys)$ and backward kinematics \rho_LT(\theta_\pi^0=160deg) =(12.18 +/- 0.27_stat +/- 0.82_sys). Multipole ratios \Re(S_1+^* M_1+)/|M_1+|^2 and \Re(S_0+^* M_1+)/|M_1+|^2 were determined in the framework of the MAID2003 model. The results are in agreement with older data. The unusally strong negative \Re(S_0+^* M_1+)/|M_1+|^2 required to bring also the result of Kalleicher et al. in accordance with the rest of the data is almost excluded.Comment: 7 pages, 7 figures, 4 tables. Changed content. Accepted for publication in EPJ

Measurement of polarisation observables in Ks0Σ+K^0_s\Sigma^+ photoproduction off the proton

The reaction $\gamma \, p \rightarrow K^0_S\,\Sigma^+$ is studied in the photon energy range from threshold. Linearly polarised photon beams from coherent bremsstrahlung enabled the first measurement of photon beam asymmetries in this reaction up to $E_\gamma = 2250$ MeV. In addition, the recoil hyperon polarisation was determined through the asymmetry in the weak decay $\Sigma^+ \rightarrow p \pi^0$ up to $E_\gamma = 1650$ MeV. The data are compared to partial wave analyses, and the possible impact on the interpretation of a recently observed cusp-like structure near the $K^*$ thresholds is discussed.Comment: 6 pages, 5 figures. References [8,9,10,11] which were not on the original submission are now include

Separated cross sections in \pi^0 electroproduction at threshold at Q^2 = 0.05 GeV^2/c^2

The differential cross sections \sigma_0=\sigma_T+\epsilon \sigma_L, \sigma_{LT}, and \sigma_{TT} of \pi^0 electroproduction from the proton were measured from threshold up to an additional center of mass energy of 40 MeV, at a value of the photon four-momentum transfer of Q^2= 0.05 GeV^2/c^2 and a center of mass angle of \theta=90^\circ. By an additional out-of-plane measurement with polarized electrons \sigma_{LT'} was determined. This showed for the first time the cusp effect above the \pi^+ threshold in the imaginary part of the s-wave. The predictions of Heavy Baryon Chiral Perturbation Theory are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.Comment: 6 pages, 4 figure