Lower Bounds for Heights in Relative Galois Extensions

The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic number $\alpha$ when the base field $\mathbb{K}$ is a number field and $\mathbb{K}(\alpha)/\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any non-zero element $\alpha$ which is not a root of unity in a Galois extension $\mathbb{F}/\mathbb{K}$, depending on the degree of $\mathbb{K}/\mathbb{Q}$ and the number of conjugates of $\alpha$ which are multiplicatively independent over $\mathbb{K}$. As a consequence, we obtain a height bound for such $\alpha$ that is independent of the multiplicative independence condition

Phenomenology of the Deuteron Electromagnetic Form Factors

A rigorous extraction of the deuteron charge form factors from tensor polarization data in elastic electron-deuteron scattering, at given values of the 4-momentum transfer, is presented. Then the world data for elastic electron-deuteron scattering is used to parameterize, in three different ways, the three electromagnetic form factors of the deuteron in the 4-momentum transfer range 0-7 fm^-1. This procedure is made possible with the advent of recent polarization measurements. The parameterizations allow a phenomenological characterization of the deuteron electromagnetic structure. They can be used to remove ambiguities in the form factors extraction from future polarization data.Comment: 18 pages (LaTeX), 2 figures Feb. 25: minor changes of content and in Table

Parity-Violating Electron Scattering from 4He and the Strange Electric Form Factor of the Nucleon

We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from ^4He at an average scattering angle = 5.7 degrees and a four-momentum transfer Q^2 = 0.091 GeV^2. From these data, for the first time, the strange electric form factor of the nucleon G^s_E can be isolated. The measured asymmetry of A_PV = (6.72 +/- 0.84 (stat) +/- 0.21 (syst) parts per million yields a value of G^s_E = -0.038 +/- 0.042 (stat) +/- 0.010 (syst), consistent with zero

The Quasielastic 3He(e,e'p)d Reaction at Q^2 = 1.5 GeV^2 for Recoil Momenta up to 1 GeV/c

We have studied the quasielastic 3He(e,e'p)d reaction in perpendicular coplanar kinematics, with the energy and momentum transferred by the electron fixed at 840 MeV and 1502 MeV/c, respectively. The 3He(e,e'p)d cross section was measured for missing momenta up to 1000 MeV/c, while the A_TL asymmetry was extracted for missing momenta up to 660 MeV/c. For missing momenta up to 150 MeV/c, the measured cross section is described well by calculations that use a variational ground-state wave function of the 3He nucleus derived from a potential that includes three-body forces. For missing momenta from 150 to 750 MeV/c, strong final-state interaction effects are observed. Near 1000 MeV/c, the experimental cross section is more than an order of magnitude larger than predicted by available theories. The A_TL asymmetry displays characteristic features of broken factorization, and is described reasonably well by available models.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, v3: changed conten

A precise measurement of the deuteron elastic structure function A(Q^2)

The A(Q^2) structure function in elastic electron-deuteron scattering was measured at six momentum transfers Q^2 between 0.66 and 1.80 (GeV/c)^2 in Hall C at Jefferson Laboratory. The scattered electrons and recoil deuterons were detected in coincidence, at a fixed deuteron angle of 60.5 degrees. These new precise measurements resolve discrepancies between older sets of data. They put significant constraints on existing models of the deuteron electromagnetic structure, and on the strength of isoscalar meson exchange currents.Comment: 3 LaTeX pages plus 2 PS figure

Measurement of the 3He(e,e'p)pn reaction at high missing energies and momenta

Results of the Jefferson Lab Hall A quasielastic 3He(e,e'p)pn measurements are presented. These measurements were performed at fixed transferred momentum and energy, q = 1502 MeV/c and omega = 840 MeV, respectively, for missing momenta p_m up to 1 GeV/c and missing energies in the continuum region, up to pion threshold; this kinematic coverage is much more extensive than that of any previous experiment. The cross section data are presented along with the effective momentum density distribution and compared to theoretical models.Comment: 5 pages, 3 figures, updated to reflect published paper: minor text changes from previous version along with updated and added reference

Probing the high momentum component of the deuteron at high Q^2

The d(e,e'p) cross section at a momentum transfer of 3.5 (GeV/c)^2 was measured over a kinematical range that made it possible to study this reaction for a set of fixed missing momenta as a function of the neutron recoil angle theta_nq and to extract missing momentum distributions for fixed values of theta_nq up to 0.55 GeV/c. In the region of 35 (deg) <= theta_nq <= 45 (deg) recent calculations, which predict that final state interactions are small, agree reasonably well with the experimental data. Therefore these experimental reduced cross sections provide direct access to the high momentum component of the deuteron momentum distribution in exclusive deuteron electro-disintegration.Comment: 5 pages, 2 figure

Measurement of Tensor Polarization in Elastic Electron-Deuteron Scattering at Large Momentum Transfer

Tensor polarization observables (t20, t21 and t22) have been measured in elastic electron-deuteron scattering for six values of momentum transfer between 0.66 and 1.7 (GeV/c)^2. The experiment was performed at the Jefferson Laboratory in Hall C using the electron HMS Spectrometer, a specially designed deuteron magnetic channel and the recoil deuteron polarimeter POLDER. The new data determine to much larger Q^2 the deuteron charge form factors G_C and G_Q. They are in good agreement with relativistic calculations and disagree with pQCD predictions.Comment: 5 pages, 4 figures, for associated informations, see http://isnwww.in2p3.fr/hadrons/t20/t20_ang.html clarification about several topics, one figure has been had, extraction of form factors use AQ interpolation in our Q2 range onl

The E00-110 experiment in Jefferson Lab's Hall A: Deeply Virtual Compton Scattering off the Proton at 6 GeV

We present final results on the photon electroproduction ($\vec{e}p\rightarrow ep\gamma$) cross section in the deeply virtual Compton scattering (DVCS) regime and the valence quark region from Jefferson Lab experiment E00-110. Results from an analysis of a subset of these data were published before, but the analysis has been improved which is described here at length, together with details on the experimental setup. Furthermore, additional data have been analyzed resulting in photon electroproduction cross sections at new kinematic settings, for a total of 588 experimental bins. Results of the $Q^2$- and $x_B$-dependences of both the helicity-dependent and helicity-independent cross sections are discussed. The $Q^2$-dependence illustrates the dominance of the twist-2 handbag amplitude in the kinematics of the experiment, as previously noted. Thanks to the excellent accuracy of this high luminosity experiment, it becomes clear that the unpolarized cross section shows a significant deviation from the Bethe-Heitler process in our kinematics, compatible with a large contribution from the leading twist-2 DVCS$^2$ term to the photon electroproduction cross section. The necessity to include higher-twist corrections in order to fully reproduce the shape of the data is also discussed. The DVCS cross sections in this paper represent the final set of experimental results from E00-110, superseding the previous publication.Comment: 48 pages, 32 figure

Deeply Virtual Compton Scattering off the neutron

The present experiment exploits the interference between the Deeply Virtual Compton Scattering (DVCS) and the Bethe-Heitler processes to extract the imaginary part of DVCS amplitudes on the neutron and on the deuteron from the helicity-dependent D$({\vec e},e'\gamma)X$ cross section measured at $Q^2$=1.9 GeV$^2$ and $x_B$=0.36. We extract a linear combination of generalized parton distributions (GPDs) particularly sensitive to $E_q$, the least constrained GPD. A model dependent constraint on the contribution of the up and down quarks to the nucleon spin is deduced.Comment: Published in Phys. Rev. Let