New high precision measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised 6LiD target are presented. The data were taken in 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. Both the Collins and Sivers asymmetries turn out to be compatible with zero, within the present statistical errors, which are more than a factor of 2 smaller than those of the published COMPASS results from the 2002 data. The final results from the 2002, 2003 and 2004 runs are compared with naive expectations and with existing model calculations.
Collins asymmetry against PT for all negative hadrons.
Collins asymmetry against Bjorken X for all negative hadrons.
Collins asymmetry against Z for all negative hadrons.
The measurements of the Collins and Sivers asymmetries of identified hadrons produced in deep-inelastic scattering of 160 GeV/c muons on a transversely polarised 6LiD target at COMPASS are presented. The results for charged pions and charged and neutral kaons correspond to all data available, which were collected from 2002 to 2004. For all final state particles both the Collins and Sivers asymmetries turn out to be small, compatible with zero within the statistical errors, in line with the previously published results for not identified charged hadrons, and with the expected cancellation between the u- and d-quark contributions.
The Collins and Sivers asymmetry as a function of X for 'ALL' positive pions from the 2003-2004 data.. Errors are statistical only.
The Collins and Sivers asymmetry as a function of PT for 'ALL' positive pions from the 2003-2004 data.. Errors are statistical only.
The Collins and Sivers asymmetry as a function of Z for 'ALL' positive pions from the 2003-2004 data.. Errors are statistical only.
The COMPASS Collaboration at CERN has measured the transverse spin azimuthal asymmetry of charged hadrons produced in semi-inclusive deep inelastic scattering using a 160 GeV positive muon beam and a transversely polarised NH_3 target. The Collins asymmetry of the proton was extracted in the Bjorken x range 0.003<x<0.7. These new measurements confirm with higher accuracy previous measurements from the COMPASS and HERMES collaborations, which exhibit a definite effect in the valence quark region. The asymmetries for negative and positive hadrons are similar in magnitude and opposite in sign. They are compatible with model calculations in which the u-quark transversity is opposite in sign and somewhat larger than the d-quark transversity distribution function. The asymmetry is extracted as a function of Bjorken $x$, the relative hadron energy $z$ and the hadron transverse momentum p_T^h. The high statistics and quality of the data also allow for more detailed investigations of the dependence on the kinematic variables. These studies confirm the leading-twist nature of the Collins asymmetry.
The Collins asymmetry, from the 2010 data set, for positive hadrons as a function of X for full range. Also shown are the mean values of other variables plus the correlation with the Sivers data measurments.
The Collins asymmetry, from the 2010 data set, for negative hadrons as a function of X for full range. Also shown are the mean values of other variables plus the correlation with the Sivers data measurments.
The Collins asymmetry, from the 2010 data set, for positive hadrons as a function of PT for full range. Also shown are the mean values of other variables plus the correlation with the Sivers data measurments.
The COMPASS Collaboration at CERN has measured the transverse spin azimuthal asymmetry of charged hadrons produced in semi-inclusive deep inelastic scattering using a 160 GeV positive muon beam and a transversely polarised NH_3 target. The Sivers asymmetry of the proton has been extracted in the Bjorken x range 0.003<x<0.7. The new measurements have small statistical and systematic uncertainties of a few percent and confirm with considerably better accuracy the previous COMPASS measurement. The Sivers asymmetry is found to be compatible with zero for negative hadrons and positive for positive hadrons, a clear indication of a spin-orbit coupling of quarks in a transversely polarised proton. As compared to measurements at lower energy, a smaller Sivers asymmetry for positive hadrons is found in the region x > 0.03. The asymmetry is different from zero and positive also in the low x region, where sea-quarks dominate. The kinematic dependence of the asymmetry has also been investigated and results are given for various intervals of hadron and virtual photon fractional energy. In contrast to the case of the Collins asymmetry, the results on the Sivers asymmetry suggest a strong dependence on the four-momentum transfer to the nucleon, in agreement with the most recent calculations.
The Sivers asymmetry, from the 2010 data set, for positive hadrons as a function of X for full range. Also shown are the mean values of other variables plus the correlation with the Collins data measurments.
The Sivers asymmetry, from the 2010 data set, for negative hadrons as a function of X for full range. Also shown are the mean values of other variables plus the correlation with the Collins data measurments.
The Sivers asymmetry, from the 2010 data set, for positive hadrons as a function of PT for full range. Also shown are the mean values of other variables plus the correlation with the Collins data measurments.
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 $Q^2$.
First measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarized 6-LiD target are presented. The data were taken in 2002 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. The Collins asymmetry turns out to be compatible with zero, as does the measured Sivers asymmetry within the present statistical errors.
Asymmetries as a function of X for LEADING hadrons.
Asymmetries as a function of Z for LEADING hadrons.
Asymmetries as a function of PT for LEADING hadrons.
We present a LO evaluation of helicity densities of valence, \Delta u_v+\Delta d_v, non-strange sea, \Delta\bar{u}+\Delta\bar{d}, and strange quarks, \Delta s (assumed to be equal to \Delta\bar{s}). They have been obtained from the inclusive asymmetry A_{3,d} and the semi-inclusive asymmetries A^{\pi+}_{1,d}, A^{\pi-}_{1,d}, A^{K+}_{1,d}, A^{K-}_{1,d} measured in polarised deep inelastic muon-deuteron scattering. The full deuteron statistics of COMPASS (years 2002-2004 and 2006) has been used. The data cover the range Q^2 > 1 (GeV/c)^2 and 0.004<x<0.3. Both non-strange densities are found to be in a good agreement with previous measurements. The distribution of \Delta s(x) is compatible with zero in the whole measured range, in contrast to the shape of the strange quark helicity distribution obtained in most LO and NLO QCD fits. The sensitivity of the values of \Delta s(x) upon the choice of fragmentation functions used in the derivation is discussed.
Inclusive asymmetry as a function of X.
Charged pion and kaon semi-inclusive asymmetries as functions of X.
Correlations coefficients of the unfolded asymmetries.
Multiplicities of charged hadrons produced in deep inelastic muon scattering off a $^6$LiD target have been measured as a function of the DIS variables $x_{Bj}$, $Q^2$, $W^2$ and the final state hadron variables $p_T$ and $z$. The $p_T^2$ distributions are fitted with a single exponential function at low values of $p_T^2$ to determine the dependence of $\langle p_T^2 \rangle$ on $x_{Bj}$, $Q^2$, $W^2$ and $z$. The $z$-dependence of $\langle p_T^2 \rangle$ is shown to be a potential tool to extract the average intrinsic transverse momentum squared of partons, $\langle k_{\perp}^2 \rangle$, as a function of $x_{Bj}$ and $Q^2$ in a leading order QCD parton model.
PT dependences of the differential multiplicities for 0.0045 < x_Bjorken < 0.0060 and 1.00 < Q^2 < 1.25 GeV^2 for Positive hadrons.
PT dependences of the differential multiplicities for 0.0060 < x_Bjorken < 0.0080 and 1.00 < Q^2 < 1.30 GeV^2 for Positive hadrons.
PT dependences of the differential multiplicities for 0.0060 < x_Bjorken < 0.0080 and 1.30 < Q^2 < 1.70 GeV^2 for Positive hadrons.
We have performed the most comprehensive resonance-model fit of $\pi^-\pi^-\pi^+$ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction $\pi^- + p \to \pi^-\pi^-\pi^+ + p_\text{recoil}$ with a 190 GeV/$c$ pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, $0.5 < m_{3\pi} < 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 < t' < 1.0$ $($GeV$/c)^2$, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{++}$, $2^{-+}$, $4^{++}$, and spin-exotic $1^{-+}$ quantum numbers. The model contains the well-known resonances $\pi(1800)$, $a_1(1260)$, $a_2(1320)$, $\pi_2(1670)$, $\pi_2(1880)$, and $a_4(2040)$. In addition, it includes the disputed $\pi_1(1600)$, the excited states $a_1(1640)$, $a_2(1700)$, and $\pi_2(2005)$, as well as the resonancelike $a_1(1420)$. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 $t'$ bins. We extract the relative branching fractions of the $\rho(770) \pi$ and $f_2(1270) \pi$ decays of $a_2(1320)$ and $a_4(2040)$, where the former one is measured for the first time. In a novel approach, we extract the $t'$ dependence of the intensity of the resonances and of their phases. The $t'$ dependence of the intensities of most resonances differs distinctly from the $t'$ dependence of the nonresonant components. For the first time, we determine the $t'$ dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances.
Real and imaginary parts of the normalized transition amplitudes $\mathcal{T}_a$ of the 14 selected partial waves in the 1100 $(m_{3\pi}, t')$ cells (see Eq. (12) in the paper). The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the transition amplitudes in the column headers. The $m_{3\pi}$ values that are given in the first column correspond to the bin centers. Each of the 100 $m_{3\pi}$ bins is 20 MeV/$c^2$ wide. Since the 11 $t'$ bins are non-equidistant, the lower and upper bounds of each $t'$ bin are given in the column headers. The transition amplitudes define the spin-density matrix elements $\varrho_{ab}$ for waves $a$ and $b$ according to Eq. (18). The spin-density matrix enters the resonance-model fit via Eqs. (33) and (34). The transition amplitudes are normalized via Eqs. (9), (16), and (17) such that the partial-wave intensities $\varrho_{aa} = |\mathcal{T}_a|^2$ are given in units of acceptance-corrected number of events. The relative phase $\Delta\phi_{ab}$ between two waves $a$ and $b$ is given by $\arg(\varrho_{ab}) = \arg(\mathcal{T}_a) - \arg(\mathcal{T}_b)$. Note that only relative phases are well-defined. The phase of the $1^{++}0^+ \rho(770) \pi S$ wave was set to $0^\circ$ so that the corresponding transition amplitudes are real-valued. In the PWA model, some waves are excluded in the region of low $m_{3\pi}$ (see paper and [Phys. Rev. D 95, 032004 (2017)] for a detailed description of the PWA model). For these waves, the transition amplitudes are set to zero. The tables with the covariance matrices of the transition amplitudes for all 1100 $(m_{3\pi}, t')$ cells can be downloaded via the 'Additional Resources' for this table.
Decay phase-space volume $I_{aa}$ for the 14 selected partial waves as a function of $m_{3\pi}$, normalized such that $I_{aa}(m_{3\pi} = 2.5~\text{GeV}/c^2) = 1$. The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the decay phase-space volume in the column headers. The labels are identical to the ones used in the column headers of the table of the transition amplitudes. $I_{aa}$ is calculated using Monte Carlo integration techniques for fixed $m_{3\pi}$ values, which are given in the first column, in the range from 0.5 to 2.5 GeV/$c^2$ in steps of 10 MeV/$c^2$. The statistical uncertainties given for $I_{aa}$ are due to the finite number of Monte Carlo events. $I_{aa}(m_{3\pi})$ is defined in Eq. (6) in the paper and appears in the resonance model in Eqs. (19) and (20).
Spin-averaged asymmetries in the azimuthal distributions of positive and negative hadrons produced in deep inelastic scattering were measured using the CERN SPS muon beam at $160$ GeV/c and a $^6$LiD target. The amplitudes of the three azimuthal modulations $\cos\phi_h$, $\cos2\phi_h$ and $\sin\phi_h$ were obtained binning the data separately in each of the relevant kinematic variables $x$, $z$ or $p_T^{\,h}$ and binning in a three-dimensional grid of these three variables. The amplitudes of the $\cos \phi_h$ and $\cos 2\phi_h$ modulations show strong kinematic dependencies both for positive and negative hadrons.
ASYMUU(SIN(PHI(HADRON))) asymmetries for positive and negative hadrons as a function of XB. The errors are statistical and systematic.
ASYMUU(SIN(PHI(HADRON))) asymmetries for positive and negative hadrons as a function of Z. The errors are statistical and systematic.
ASYMUU(SIN(PHI(HADRON))) asymmetries for positive and negative hadrons as a function of PT(HADRON). The errors are statistical and systematic.
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