No Arabic abstract
New data on the Sivers azimuthal asymmetry measured in semi-inclusive deep-inelastic scattering processes have recently been released by the COMPASS Collaboration at CERN. Their increased precision and their particular binning, in terms of $Q^2$ as well as $x$, motivates a new extraction of the Sivers function, within the framework of a simple and transparent parametrization. Signals of TMD effects visible in the Sivers asymmetries are critically assessed. A thorough study of the uncertainties affecting the extracted Sivers function is presented, including the low-$x$ and large-$x$ regions.
We perform a global fit of the available polarized Semi-Inclusive Deep Inelastic Scattering (SIDIS), polarized pion-induced Drell-Yan (DY) and $W^pm/Z$ boson production data at N$^3$LO and NNLO accuracy of the Transverse Momentum Dependent (TMD) evolution, and extract the Sivers function for $u$, $d$, $s$ and for sea quarks. The Qiu-Sterman function is determined in a model independent way via the operator product expansion from the extracted Sivers function. The analysis is supplemented by additional studies, such as the estimation of applicability region, the impact of the unpolarized distributions uncertainties, the universality of the Sivers functions, positivity constraints, the significance of the sign-change relation, and the comparison with the existing extractions
We consider the azimuthal distribution of the final observed hadron in semi-inclusive deep-inelastic scattering and the lepton pair in the Drell-Yan process. In particular, we focus on the $cos phi$ modulation of the unpolarized cross section and on its dependence upon transverse momentum. At low transverse momentum, for these observables we propose a factorized expression based on tree-level approach and conjecture that the same formula is valid in transverse-momentum dependent (TMD) factorization when written in terms of subtracted TMD parton distributions. Our formula correctly matches with the collinear factorization results at high transverse momentum, solves a long-standing problem and is a necessary step towards the extension of the TMD factorization theorems up to the subleading twist.
We perform the global analysis of polarized Semi-Inclusive Deep Inelastic Scattering (SIDIS), pion-induced polarized Drell-Yan (DY), and $W^pm/Z$ boson production data and extract the Sivers function for $u$, $d$, $s$ and for sea-quarks. We use the framework of transverse momentum dependent factorization at N$^3$LO accuracy. The Qiu-Sterman function is determined in a model-independent way from the extracted Sivers function. We also evaluate the significance of the predicted sign change of Sivers function in DY with respect to SIDIS.
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.
Hadron leptoproduction in Semi-Inclusive measurements of Deep-Inelastic Scattering (SIDIS) on unpolarised nucleons allows one to get information on the intrinsic transverse momentum of quarks in a nucleon and on the Boer-Mulders function through the measurement of azimuthal modulations in the cross section. These modulations were recently measured by the HERMES experiment at DESY on proton and deuteron targets, and by the COMPASS experiment using the CERN SPS muon beam and a $^6$LiD target. In both cases, the amplitudes of the $cosphi_h$ and $cos 2phi_h$ modulations show strong kinematic dependences for both positive and negative hadrons. It has been known since some time that the measured final-state hadrons in those SIDIS experiments receive a contribution from exclusive diffractive production of vector mesons, particularly important at large values of $z$, the fraction of the virtual photon energy carried by the hadron. In previous measurements of azimuthal asymmetries this contribution was not taken into account, because it was not known that it could distort the azimuthal modulations. Presently, a method to evaluate the contribution of the exclusive reactions to the azimuthal asymmetries measured by COMPASS has been developed. The subtraction of this contribution results in a better understanding of the kinematic effects, and the remaining non-zero $cos 2phi_h$ modulation gives indication for a non-zero Boer-Mulders effect.