Root multiplicities and number of nonzero coefficients of a polynomial

It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial over a field of characteristic zero is larger than the multiplicity of any of its nonzero roots. We extend this result to an appropriate statement in positive characteristic. Furthermore, we present a new proof of the original result, which produces also the exact number of monic polynomials of a given degree for which the bound is attained. A similar argument allows us to determine the number of monic polynomials of a given degree, multiplicity of a given nonzero root, and number of nonzero coefficients, over a finite field of characteristic larger than the degree.Comment: 6 pages. Minor change from previous version: added Example 6, illustrating the difficulties arising when one tries to relax the hypothesis n<p of Theorem

Covering theorems for Artinian rings

The covering properties of Artinian rings which depend on their additive structure only, are investigated

Search for a new gauge boson in the A′A' Experiment (APEX)

We present a search at Jefferson Laboratory for new forces mediated by sub-GeV vector bosons with weak coupling $\alpha'$ to electrons. Such a particle $A'$ can be produced in electron-nucleus fixed-target scattering and then decay to an $e^+e^-$ pair, producing a narrow resonance in the QED trident spectrum. Using APEX test run data, we searched in the mass range 175--250 MeV, found no evidence for an $A'\to e^+e^-$ reaction, and set an upper limit of $\alpha'/\alpha \simeq 10^{-6}$. Our findings demonstrate that fixed-target searches can explore a new, wide, and important range of masses and couplings for sub-GeV forces.Comment: 5 pages, 5 figures, references adde

The G0 Experiment: Apparatus for Parity-Violating Electron Scattering Measurements at Forward and Backward Angles

In the G0 experiment, performed at Jefferson Lab, the parity-violating elastic scattering of electrons from protons and quasi-elastic scattering from deuterons is measured in order to determine the neutral weak currents of the nucleon. Asymmetries as small as 1 part per million in the scattering of a polarized electron beam are determined using a dedicated apparatus. It consists of specialized beam-monitoring and control systems, a cryogenic hydrogen (or deuterium) target, and a superconducting, toroidal magnetic spectrometer equipped with plastic scintillation and aerogel Cerenkov detectors, as well as fast readout electronics for the measurement of individual events. The overall design and performance of this experimental system is discussed.Comment: Submitted to Nuclear Instruments and Method

A Measurement of the Electric Form Factor of the Neutron through d⃗(e⃗,e′n)p\vec{d}(\vec{e},e'n)p at Q2=0.5Q^2 = 0.5 (GeV/c)2^2

We report the first measurement of the neutron electric form factor $G_E^n$ via $\vec{d}(\vec{e},e'n)p$ using a solid polarized target. $G_E^n$ was determined from the beam-target asymmetry in the scattering of longitudinally polarized electrons from polarized deuterated ammonia, $^{15}$ND$_3$. The measurement was performed in Hall C at Thomas Jefferson National Accelerator Facility (TJNAF) in quasi free kinematics with the target polarization perpendicular to the momentum transfer. The electrons were detected in a magnetic spectrometer in coincidence with neutrons in a large solid angle segmented detector. We find $G_E^n = 0.04632\pm0.00616 (stat.) \pm0.00341 (syst.)$ at $Q^2 = 0.495$ (GeV/c)$^2$.Comment: Latex2e 5 pages, 3 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