Improved Method to extract Nucleon Helicity Distributions using Event Weighting

An improved analysis method to extract quark helicity distributions in leading order (LO) QCD from semi-inclusive double spin asymmetries in deep inelastic scattering is presented. The method relies on the fact that fragmentation functions, describing the fragmentation of a quark into a hadron, have a strong dependence on the energy fraction $z$ of the observed hadron. Hadrons with large $z$ contain more information about the struck quark. This can be used in a weighting procedure to improve the figure of merit (= inverse of variance). In numerical examples it is shown that one could gain 15-39\% depending on the quark flavor and cut on $z$. Mathematically the problem can be described as finding an optimal solution in terms of the figure of merit for parameters $\boldsymbol \Theta$ determined from a system of linear equations ${\bf B}(x) {\boldsymbol \Theta} ={\bf Y}(x)$, where the measured input vector ${\bf Y}(x)$ is given as event distributions depending on a random variable $x$, the coefficients of the matrix ${\bf B}(x)$ depend as well on $x$, whereas the parameter vector $\boldsymbol\Theta$ to be determined does not.Comment: 13 pages, 3 figure

Spin Physics with COMPASS

COMPASS is a fixed target experiment at CERN studying the spin structure of the nucleon via deep inelastic muon-nucleon scattering. Hadron spectroscopy and structure are investigated using hadronic beams. Themain goal of themuon programis the determination of the gluon helicity contribution, $\Delta G/G$, to the nucleon spin. Experimentally this quantity is accessible via the measurement of double spin asymmetries in two different processes: The first one is the production of hadron pairs with large transverse momentum. The second one is open charm production which provides the cleanest and most direct measurement. The first method has a higher statistical accuracy but is affected by larger systematic uncertainties due to background processes. First results from COMPASS indicate that the helicity contribution of the gluons to the nucleon spin is small. In parallel to the $\Delta G$ measurement longitudinal inclusive and semi-inclusive asymmetries are studied as well. These allow a flavor decomposition of the helicity contribution, $\Delta\Sigma$, of the quarks to the nucleon spin. The spin physics program of COMPASS also includes measurements of single spin asymmetries on a transversely polarized target, giving access to transverse quark distributions in the nucleon. Recent results of the muon program from the data taking periods 2002-2003 will be presented

Amplitude estimation of a sine function based on confidence intervals and Bayes' theorem

This paper discusses the amplitude estimation using data originating from a sine-like function as probability density function. If a simple least squares fit is used, a significant bias is observed for small amplitudes. It is shown that a proper treatment using the Feldman-Cousins algorithm of likelihood ratios allows one to construct improved confidence intervals. Using Bayes' theorem a probability density function is derived for the amplitude. It is used in an application to show that it leads to better estimates compared to a simple least squares fit

Extraction of Azimuthal Asymmetries using Optimal Observables

Azimuthal asymmetries play an important role in scattering processes with polarized particles. This paper introduces a new procedure using event weighting to extract these asymmetries. It is shown that the resulting estimator has several advantages in terms of statistical accuracy, bias, assumptions on acceptance and luminosities compared to other estimators discussed in the literature.Comment: 13 pages, 2 figure

Nucleon Spin Structure and Parton Distribution Functions

This article gives an overview over recent results on quark and gluon helicity distributions obtained in deep inelastic lepton nucleon scattering and proton proton interactions. Future experimental programs to study the nucleon structure will be discussed as well

Simultaneous Determination of Signal and Background Asymmetries

This article discusses the determination of asymmetries. We consider a sample of events consisting of a peak of signal events on top of some background events. Both signal and background have an unknown asymmetry, e.g. a spin or forward-backward asymmetry. A method is proposed which determines signal and background asymmetries simultaneously using event weighting. For vanishing asymmetries the statistical error of the asymmetries reaches the minimal variance bound (MVB) given by the Cram\'er-Rao inequality and it is very close to it for large asymmetries. The method thus provides a significant gain in statistics compared to the classical method of side band subtraction of background asymmetries. It has the advantage with respect to the unbinned maximum likelihood approach, reaching the MVB as well, that it does not require loops over the event sample in the minimization procedure

Moving towards inclusion: A case study of one urban school in the Maldives

This case study explores and documents the development of inclusive education in one urban school in the Maldives. It focuses on the steps taken to move the school towards inclusion, the practices and experiences of different stakeholders involved in the process, and the factors that influenced inclusive education in the school. Qualitative data was collected through interviews with some of the key members of the school community and through classroom observations and documents. Findings have revealed that the development of inclusive education in the school came about through a school leader rather than policies. In spite of recognized efforts towards inclusion, a range of exclusionary practices was still observed. Various impediments constrained the development of inclusive education, including, lack of collaboration between the SEN (Special Educational Needs) and the general staff, limited knowledge, awareness and positive understanding about inclusion, scarcity of resources and support services. Factors such as large classes, undifferentiated curriculum, and rigid time tables also negatively affected the developmental process. Findings indicate the complexity of developing inclusive education. The findings also suggest that changes on the societal level, in the education ministry and, in the school and classroom level could help sustain the development of inclusive education. The factors that could contribute to the development of inclusive education at these levels are discussed, as are the implications for the successful development of inclusive education in schools

Phase locking the spin precession in a storage ring

This letter reports the successful use of feedback from a spin polarization measurement to the revolution frequency of a 0.97 GeV/$c$ bunched and polarized deuteron beam in the Cooler Synchrotron (COSY) storage ring in order to control both the precession rate ($\approx 121$ kHz) and the phase of the horizontal polarization component. Real time synchronization with a radio frequency (rf) solenoid made possible the rotation of the polarization out of the horizontal plane, yielding a demonstration of the feedback method to manipulate the polarization. In particular, the rotation rate shows a sinusoidal function of the horizontal polarization phase (relative to the rf solenoid), which was controlled to within a one standard deviation range of $\sigma = 0.21$ rad. The minimum possible adjustment was 3.7 mHz out of a revolution frequency of 753 kHz, which changes the precession rate by 26 mrad/s. Such a capability meets a requirement for the use of storage rings to look for an intrinsic electric dipole moment of charged particles

Leading-order determination of the gluon polarisation from semi-inclusive deep inelastic scattering data

Using a novel analysis technique, the gluon polarisation in the nucleon is re-evaluated using the longitudinal double-spin asymmetry measured in the cross section of semi-inclusive single-hadron muoproduction with photon virtuality $Q^2>1~({\rm GeV}/c)^2$. The data were obtained by the COMPASS experiment at CERN using a 160 GeV/$c$ polarised muon beam impinging on a polarised $^6$LiD target. By analysing the full range in hadron transverse momentum $p_{\rm T}$, the different $p_{\rm T}$-dependences of the underlying processes are separated using a neural-network approach. In the absence of pQCD calculations at next-to-leading order in the selected kinematic domain, the gluon polarisation $\Delta g/g$ is evaluated at leading order in pQCD at a hard scale of $\mu^2= \langle Q^2 \rangle = 3 ({\rm GeV}/c)^2$. It is determined in three intervals of the nucleon momentum fraction carried by gluons, $x_{\rm g}$, covering the range $0.04 \!<\! x_{ \rm g}\! <\! 0.28$~ and does not exhibit a significant dependence on $x_{\rm g}$. The average over the three intervals, $\langle \Delta g/g \rangle = 0.113 \pm 0.038_{\rm (stat.)}\pm 0.036_{\rm (syst.)}$ at $\langle x_{\rm g} \rangle \approx 0.10$, suggests that the gluon polarisation is positive in the measured $x_{\rm g}$ range.Comment: 14 pages, 6 figure