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Register a new userThe Spin Structure Function $g_1^{rm p}$ of the Proton and a Test of the Bjorken Sum Rule
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New results for the double spin asymmetry $A_1^{rm p}$ and the proton longitudinal spin structure function $g_1^{rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{rm p}(x)$ by about a factor of two in the region $xlesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $Delta Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{rm p}$. The uncertainty of $Delta Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{rm A}/g_{rm V}| = 1.22 pm 0.05~({rm stat.}) pm 0.10~({rm syst.})$, which validates the sum rule to an accuracy of about 9%.
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Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a $^6$LiD target. The data were taken at $160~{rm GeV}$ beam energy and the results are shown for the kinematic range $1~({rm GeV}/c)^2 < Q^2 < 100~({rm GeV}/c)^2$ in photon virtuality, $0.004<x<0.7$ in the Bjorken scaling variable and $W > 4~{rm GeV}/c^2$ in the mass of the hadronic final state. The deuteron double-spin asymmetry $A_1^{rm d}$ and the deuteron longitudinal-spin structure function $g_1^{rm d}$ are presented in bins of $x$ and $Q^2$. Towards lowest accessible values of $x$, $g_1^{rm d}$ decreases and becomes consistent with zero within uncertainties. The presented final $g_1^{rm d}$ values together with the recently published final $g_1^{rm p}$ values of COMPASS are used to again evaluate the Bjorken sum rule and perform the QCD fit to the $g_1$ world data at next-to-leading order of the strong coupling constant. In both cases, changes in central values of the resulting numbers are well within statistical uncertainties. The flavour-singlet axial charge $a_0$, {which is identified in the $overline{rm MS}$ renormalisation scheme with the total contribution of quark helicities to the nucleon spin}, is extracted from only the COMPASS deuteron data with negligible extrapolation uncertainty: $a_0 (Q^2 = 3~({rm GeV}/c)^2) = 0.32 pm 0.02_{rm stat} pm0.04_{rm syst} pm 0.05_{rm evol}$. Together with the recent results on the proton spin structure function $g_1^{rm p}$, the results on $g_1^{rm d}$ constitute the COMPASS legacy on the measurements of $g_1$ through inclusive spin-dependent deep inelastic scattering.
We present a precise measurement of the proton longitudinal double-spin asymmetry $A_1^{rm p}$ and the proton spin-dependent structure function $g_1^{rm p}$ at photon virtualities $0.006~({rm GeV}/c)^2<Q^2 < 1~({rm GeV}/c)^2$ in the Bjorken $x$ range of $4 times 10^{-5} < x < 4 times 10^{-2}$. The results are based on data collected by the COMPASS Collaboration at CERN using muon beam energies of $160~{rm GeV}$ and $200~{rm GeV}$. The statistical precision is more than tenfold better than that of the previous measurement in this region. In the whole range of $x$, the measured values of $A_1^{rm p}$ and $g_1^{rm p}$ are found to be positive. It is for the first time that spin effects are found at such low values of $x$.
Precise measurements of the spin structure functions of the proton $g_1^p(x,Q^2)$ and deuteron $g_1^d(x,Q^2)$ are presented over the kinematic range $0.0041 leq x leq 0.9$ and $0.18 $ GeV$^2$ $leq Q^2 leq 20$ GeV$^2$. The data were collected at the HERMES experiment at DESY, in deep-inelastic scattering of 27.6 GeV longitudinally polarized positrons off longitudinally polarized hydrogen and deuterium gas targets internal to the HERA storage ring. The neutron spin structure function $g_1^n$ is extracted by combining proton and deuteron data. The integrals of $g_1^{p,d}$ at $Q^2=5$ GeV$^2$ are evaluated over the measured $x$ range. Neglecting any possible contribution to the $g_1^d$ integral from the region $x leq 0.021$, a value of $0.330 pm 0.011mathrm{(theo.)}pm0.025mathrm{(exp.)}pm 0.028$(evol.) is obtained for the flavor-singlet axial charge $a_0$ in a leading-twist NNLO analysis.
We perform a global analysis of all available spin-dependent proton structure function data, covering a large range of Q^2, 1 < Q^2 < 30 GeV^2, and calculate the lowest moment of the g_1 structure function as a function of Q^2. From the Q^2 dependence of the lowest moment we extract matrix elements of twist-4 operators, and determine the color electric and magnetic polarizabilities of the proton to be chi_E = 0.026 +- 0.015 (stat) + 0.021/-0.024 (sys) and chi_B = -0.013 -+ 0.007 (stat) - 0.010/+0.012 (sys), respectively.
We study the semileptonic branching fraction of $B$-meson into higher resonance of charmed meson $D^{**}$ by using the Bjorken sum rule and the heavy quark effective theory(HQET). This sum rule and the current experiment of $B$-meson semileptonic decay into $D$ and $D^*$ predict that the branching ratio into $D^{**}l u_l$ is about 1.7%. This predicted value is larger than the value obtained by the various theoretical hadron models based on the HQET.
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