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 $x\lesssim 0.02$. 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\%.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in ($x$, $Q^2$) bins.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^{\rm p}$ for the 2007 COMPASS data at 160 GeV in ($x$, $Q^2$) bins.
The inclusive double-spin asymmetry, $A^p_1$, has been measured at COMPASS in deepinelastic polarised muon scattering off a large polarised NH3 target. The data, collected in the year 2007, cover the range $Q^2 > 1 (GeV/c)^2, 0.004 < x < 0.7$ and improve the statistical precision of $g^p_1(x)$ by a factor of two in the region $x < 0.02$. The new proton asymmetries are combined with those previously published for the deuteron to extract the non-singlet spin-dependent structure function $g^{NS}_1(x,Q^2)$. The isovector quark density, $\Delta_{q3}(x,Q^2)$, is evaluated from a NLO QCD fit of $g^{NS}_1$. The first moment of $\Delta_{q3}$ is in good agreement with the value predicted by the Bjorken sum rule and corresponds to a ratio of the axial and vector coupling constants $|g_A/g_V$ = $1.28\pm 0.07(stat)\pm 0.10$(syst).
Values of A1P and G1P as a function of X with corresponding average values of Q**2.
Values of $A_1^p$ and $g_1^p$ as a function of $x$ with corresponding average values of $Q^2$.
Values of $g_1^p$ for the 2007 COMPASS proton data at 160 GeV in ($x$, $Q^2$) bins.
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.
Values of $A_1^d$ and $g_1^d$ for the COMPASS deuteron data at 160 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^d$ and $g_1^d$ for the COMPASS deuteron data at 160 GeV in (x, $Q^2$) bins.
Values of $g_1^{NS}$ for the COMPASS data in $x$ bins averaged over $Q^2$.
Results are presented for F2d/F2p and Rd-Rp from simultaneous measurements of deep inelastic muon scattering on hydrogen and deuterium targets, at 90, 120, 200 and 280 GeV. The difference Rd-Rp, determined in the range 0.002<x<0.4 at an average Q^2 of 5 GeV^2, is compatible with zero. The x and Q^2 dependence of F2d/F2p was measured in the kinematic range 0.001<x<0.8 and 0.1<Q^2<145 GeV^2 with small statistical and systematic errors. For x>0.1 the ratio decreases with Q^2.
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Results are presented on the ratio of neutron and proton structure functions, F 2 n / F 2 p , deduced from deep inelastic scattering of muon from hydrogen and deuterium. The data, which were obtained at the CERN muon beam at 90 and 280 GeV incident energy, cover the kinematic range x = 0.002−0.80 and Q 2 = 0.1−190 GeV 2 . The measured structure function ratios have small statistical and systematic errors, particularly at small and intermediate x . The observed Q 2 dependence in the range x = 0.1−0.4 is stronger than predicted by perturbative QCD. From the present data together with results from other experiments it is suggested that the twist-four coefficient for the proton is smaller than that for the neutron for x larger than 0.2.
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Merged 90 and 280 GeV data.
The structure functions F p 2 and F d 2 measured by deep inelastic muon scattering at incident energies of 90 and 280 GeV are presented. These measurements cover a large kinematic range, 0.006⩽ x ⩽0.6 and 0.5⩽ Q 2 ⩽55GeV 2 , and include the first precise data at small x , where large scaling violations are observed. The data agree with earlier results from SLAC and BCDMS but exhibit differences with respect to those of EMC-NA2. Extrapolations to small x of recent phenomenological parton distributions are shown to disagree with the present results.
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Results are presented on the difference in R , the ratio of longitudinally to transversely polarised virtual photon absorption cross sections, for the deuteron and the proton. They are obtained by comparing the ratio of cross sections for the deep inelastic scattering of muons from deuterium and hydrogen targets at 90 and 280 GeV incident energy. The results cover the range x =0.01–0.30, at an average Q 2 of 9 GeV 2 . The measured difference R d - R p shows no significant x dependence and is compatible with zero, as well as with expectations from perturbative QCD. We use the same method to obtain the difference R Ca - R C from cross section ratios measured on carbon and calcium targets at 90 and 200 GeV incident energy.
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Average overall x values.
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Experimental results obtained at the CERN Super Proton Synchrotron on the structure-function ratio F2n/F2p in the kinematic range 0.004<x<0.8 and 0.4<Q2<190 GeV2, together with the structure function F2d determined from a fit to published data, are used to derive the difference F2p(x)-F2n(x). The value of the Gottfried sum F(F2p-F2n)dx/x=0.240±0.016 is below the quark-parton-model expectation of 1/3.
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The proton and deuteron structure functions F2p and F2d were measured in the kinematic range 0.006<x<0.6 and 0.5<Q~2<75 GeV~2, by inclusive deep inelastic muon scattering at 90, 120, 200 and 280 GeV. The measurements are in good agreement with earlier high precision results. The present and earlier results together have been parametrised to give descriptions of the proton and deuteron structure functions F2 and their uncertainties over the range 0.006<x<0.9.
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We present a new determination of the nonsinglet structure function ${\mathit{F}}_{2}^{\mathit{p}}$ - ${\mathit{F}}_{2}^{\mathit{n}}$ at ${\mathit{Q}}^{2}$=4 ${\mathrm{GeV}}^{2}$ using recently measured values of ${\mathit{F}}_{2}^{\mathit{d}}$ and ${\mathit{F}}_{2}^{\mathit{n}}$/${\mathit{F}}_{2}^{\mathit{p}}$. A new evaluation of the Gottfried sum is given, which remains below the simple quark-parton model value of 1/3.
Errors of F2(D) are the estimated total uncertainties and those on the ratio and difference are statistical only.
Values of the Gottfried Sum Rule integral (GS) defined as the integral between X(C=MIN) and X = 0.8 of (F2(P)-F2(N))DX/X.
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