In the list of the main items studied by the CERN COMPASS experiment there are the transverse spin and momentum effects visible in the azimuthal distributions of hadrons produced in the deep inelastic scattering. In the years 2002-2004 COMPASS has collected data with a 6LiD target with the polarization oriented transversely with respect to the muon beam direction for about 20% of the running time; in 2007, COMPASS has used for the first time a proton NH_3 target with the data taking time equally shared between longitudinal and transverse polarization of the target. After reviewing the results obtained with the deuteron, the new results for the Collins and Sivers asymmetries of the proton will be presented.
We investigate the Sivers asymmetry in the pion-induced single polarized Drell-Yan process in the theoretical framework of the transverse momentum dependent factorization up to next-to-leading logarithmic order of QCD. Within the TMD evolution formalism of parton distribution functions, the recently extracted nonperturbative Sudakov form factor for the pion distribution functions as well as the one for the Sivers function of the proton are applied to numerically estimate the Sivers asymmetry in the $π^- p$ Drell-Yan at the kinematics of the COMPASS at CERN. In the low $b$ region, the Sivers fu…
The SIDIS transverse spin asymmetries weighted with powers of $P_T$, the hadron transverse momentum in the $γN$ reference system,have been introduced already twenty years ago and are considered quite interesting. While the amplitudes of the modulations in the azimuthal distribution of the hadrons are the ratios of convolutions over transverse momenta of the transverse--momentum dependent parton distributions and of the corresponding fragmentation functions, and can be evaluated analytically only making assumptions on the transverse--momentum dependence of these functions, the weighted asymmetr…
After reviewing the most important COMPASS results on transverse spin effects in SIDIS, I will present the recent work we have done on weighted Sivers asymmetries and "transversity induced" $Λ$ polarisation. Using the high statistics data collected in 2010 on a transversely polarised proton target COMPASS has evaluated the transverse momentum weighted Sivers asymmetries both in $x$- and in $z$-bins. The results are also compared with the standard unweighted asymmetries. Using the whole data sample collected over the years on transversely polarised deuteron and proton targets COMPASS has measur…
The production of vector mesons in SIDIS is a particularly interesting channel to study the polarized fragmentation and related phenomena. Preliminary COMPASS results for the first measurement of inclusive $ρ^0$ Collins and Sivers transverse-spin asymmetries are presented here for the first time. The analysis is based on the data-set collected by COMPASS in $2010$ using a $160\, \rm{GeV}/c$ $μ^+$ beam and a transversely polarized $NH_3$ target. The asymmetries are extracted as function of Bjorken-$x$, of the total transverse momentum of the oppositely charged hadron pair and of the fraction of…
We present predictions and projections for hadron-in-jet measurements and electron-jet azimuthal correlations at the future Electron-Ion Collider (EIC). These observables directly probe the three-dimensional (3D) structure of hadrons, in particular, the quark transversity and Sivers parton distributions and the Collins fragmentation functions. We explore the feasibility of these experimental measurements by detector simulations and discuss detector requirements. We conclude that jet observables have the potential to enhance the 3D imaging EIC program.
Since 2005, measurements of Collins and Sivers asymmetries from the HERMES and COMPASS experiments have allowed to assess that the transversity and the Sivers PDFs are different from zero and measurable in semi-inclusive DIS on transversely polarised targets. Most of the data were collected on proton targets, only small event samples were collected in the early phase of the COMPASS experiment on a deuteron ($^6$LiD) target and more recently at JLab, on $^3$He, so that the $d$-quark and the sea-quarks PDFs are much more poorly known than the $u$-quark PDFs. This constitutes an important limitat…
We perform global fit to the quark Sivers function within the transverse momentum dependent (TMD) factorization formalism in QCD. We simultaneously fit Sivers asymmetry data from Semi-Inclusive Deep Inelastic Scattering (SIDIS) at COMPASS, HERMES, and JLab, from Drell-Yan lepton pair production at COMPASS, and from $W/Z$ boson at RHIC. This extraction is performed at next-to-leading order (NLO) and next-to-next-to leading logarithmic (NNLL) accuracy. We find excellent agreement between our extracted asymmetry and the experimental data for SIDIS and Drell-Yan lepton pair production, while tensi…
We extend the improved Collins-Soper-Sterman (iCSS) $W+Y$ construction recently presented in~\cite{Collins:2016hqq} to the case of polarized observables, where we focus in particular on the Sivers effect in semi-inclusive deep-inelastic scattering. We further show how one recovers the expected leading-order collinear twist-3 result from a (weighted) $q_T$-integral of the differential cross section. We are also able to demonstrate the validity of the well-known relation between the (TMD) Sivers function and the (collinear twist-3) Qiu-Sterman function within the iCSS framework. This relation al…
COMPASS is a fixed-target experiment in operation at the CERN North Area (SPS, M2 beam-line) since 2002. An important part of the broad physics programme of the experiment is dedicated to the exploration of the transverse spin-structure of the nucleon studying target transverse spin dependent azimuthal asymmetries (TSAs) arising in the Semi-Inclusive DIS (SIDIS) and Drell-Yan (DY) cross-sections. In addition to those measurements, COMPASS has recently studied also the TSAs weighted by powers of the hadron transverse momentum (in SIDIS) and virtual photon transverse momentum, $q_T$ (in DY). In …
Proton transverse-spin azimuthal asymmetries are extracted from the COMPASS 2010 semi-inclusive hadron measurements in deep inelastic muon-nucleon scattering in those four regions of the photon virtuality $Q^2$, which correspond to the four regions of the di-muon mass $\sqrt{Q^2}$ used in the ongoing analysis of the COMPASS Drell-Yan measurements. This allows for a future direct comparison of the nucleon transverse-momentum-dependent parton distribution functions extracted from these two alternative measurements. Various two-dimensional kinematic dependences are presented for the azimuthal asy…
In the polarised Drell-Yan experiment at the COMPASS facility at CERN the beam of negatively-charged pions with 190 GeV/c momentum and intensity about $10^8$ pions/s interacted with transversely polarised NH$_3$ target. Muon pairs produced in Drell-Yan process (DY) were detected. Recently, the first ever Transverse Spin Asymmetries (TSAs) measurement in DY has been presented by COMPASS. A complementary analysis of the TSAs weighted by powers of the dimuon transverse momentum $q_T$ are presented. In the Transverse Momentum Dependent (TMD) PDF formalism, the $q_T$-weighted TSAs can be written in…
The exploration of the transverse spin structure of the nucleon by measuring spin (in)dependent azimuthal asymmetries in semi-inclusive DIS (SIDIS) and in Drell-Yan processes is one of the main objectives of the COMPASS experiment at CERN (SPS, M2 beamline). During the first phase of the experiment (2002-2011) a series of SIDIS measurements were performed, using a longitudinally polarized muon beam impinging on transversely polarized $^6$LiD or NH$_3$ targets. As a part of the COMPASS-II programme, in 2015 and 2018 the experiment performed Drell-Yan measurements with a $π^-$ beam interacting w…
The role of Cahn and Sivers effects in Deep Inelastic Scattering
内在$\bfk_\perp$在包含和半包含深非弹性散射过程中的作用在QCD部分子模型中，在首阶下研究了（$\ell p \to \ell h X$）的精确运动学;非极化截面对轻子和强子产生面之间方位角的依赖性（Cahn效应）与实验数据进行了比较，并用于估算夸克分布函数和碎裂函数中的$k_\perp$平均值。由此产生的图片被施加到描述的加权单自旋不对称性$A_{UT}^{\sin(ϕ_π- ϕ_S)}$最近测量的HERMES合作在DESY，这允许提取一些简单的模型的夸克Sivers功能。这些是比较成功地描述数据的横向单自旋不对称性在$\pup p \to πX$过程中的Sivers功能，这两套功能是不一致的。提取的Sivers功能给出的COMPASS测量的$A_{UT}^{\sin(ϕ_π- ϕ_S)}$与最近的初步数据一致的预测，而他们的贡献HERMES $A_{UL}^{\sinϕ_π}$计算和发现是小的。对在HERMES产生K介子的$A_{UT}^{\sin(ϕ_K - ϕ_S)}$也作了预测。
We apply recent developments in large momentum effective theory (LaMET) to formulate a non-perturbative calculation of the single-transverse spin asymmetry in terms of the quasi transverse-momentum-dependent quark distribution functions from the so-called Sivers mechanism. When the spin asymmetry is defined as the ratio of the quark Sivers function over the spin averaged distribution, it can be directly calculated in terms of the relevant quasi distributions with the soft functions and perturbative matching kernels cancelling out. Apart from the general formula presented, we have verified the …
Muon pairs created in the Drell-Yan process of a negative pion beam of 190 GeV/c momentum impinging on a transversely polarised NH$_3$ target were detected with the COMPASS spectrometer at CERN in 2015. In addition to the extraction of the transverse spin asymmetries (TSAs) from these data, a complementary analysis of the TSAs weighted by powers of the dimuon momentum $q_T$ has been performed and is presented in this paper. In the transverse momentum dependent parton distribution functions (TMD PDFs) formalism, the $q_T$-weighted TSAs can be interpreted in terms of products of the TMD PDFs of …
