Narrow Results

The study of transverse spin and transverse momentum effects is part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS. For these studies, a 160 GeV/c momentum muon beam is scattered on a transversely polarized nucleon target, and the scattered muon and the forward going hadrons produced in DIS processes are reconstructed and identified in a magnetic spectrometer. The measurements have been performed on a deuteron target in 2002, 2003 and 2004, and on a proton target in 2007. The main results obtained measuring single spin asymmetries are reviewed, with particular emphasis on the most recent proton measurements. After two years of spectroscopy measurements with hadron beams, in 2008 and 2009, the Collaboration will resume measurements with the muon beam and a transversely polarized target in 2010.

Parton distribution functions, which represent the flavor and spin structure of the nucleon, provide invaluable information in illuminating quantum chromodynamics in the confinement region. Among various processes that measure such parton distribution functions, semi-inclusive deep inelastic scattering is regarded as one of the golden channels to access transverse momentum dependent parton distribution functions, which provide a 3D view of the nucleon structure in momentum space. The Jefferson Lab experiment E06-010 focuses on measuring the target single and double spin asymmetries in the reaction with a transversely polarized ³He target in Hall A with a 5.89 GeV electron beam. A leading pion and the scattered electron are detected in coincidence by the left High-Resolution Spectrometer at 16° and the BigBite spectrometer at 30° beam right, respectively. The kinematic coverage concentrates in the valence quark region, x ~ 0.1–0.4, at Q² ~ 1–3 GeV². The Collins and Sivers asymmetries of ³He and neutron are extracted. In this review, an overview of the experiment and the final results are presented. Furthermore, an upcoming 12-GeV program with a large acceptance solenoidal device and the future possibilities at an electron–ion collider are discussed.

We show that the transverse momentum dependent transversity function is proportional to the longitudinal polarization of a quark in a transversely polarized proton. This result suggests an alternative, convenient method for determining transversity, without knowing unusual fragmentation functions. The method consists of measuring the double spin azimuthal asymmetry in semi-inclusive pion leptoproduction by a transversely polarized proton target. The asymmetry, which is twist 3, is estimated to be more than 10% under the most favorable conditions. The experiment we suggest is feasible in facilities like DESY and CERN.

We study several azimuthal asymmetries in semiinclusive deep inelastic scattering and in Drell–Yan, interpreting them within the formalism of the quark correlator, with a particular reference to T-odd functions. The correlator contains an undetermined energy scale, which we fix on the basis of a simple and rather general argument. We find a different value than the one assumed in previous treatments of T-odd functions. This implies different predictions on the Q² dependence of the above mentioned asymmetries. Our theoretical result on unpolarized Drell–Yan is compared with available data. Predictions on other azimuthal asymmetries could be tested against yields of planned experiments of Drell–Yan and semiinclusive deep inelastic scattering.

Meson electro-production is used in Hall C at Jefferson Lab to probe nucleon, baryon and nuclear structure. The experimental program in Hall C includes studies of semi-inclusive pion production, p, d(e, e′π^±)X, where low energy factorization has been observed, suggesting that these reactions can be used to probe nucleon structure, including transverse momentum distributions of quarks, at energies available at JLab after the upcoming 12 GeV upgrade.

We update the well-known BLNY fit to the low transverse momentum Drell–Yan lepton pair productions in hadronic collisions, by considering the constraints from the semi-inclusive hadron production in deep inelastic scattering (SIDIS) from HERMES and COMPASS experiments. We follow the Collins–Soper–Sterman (CSS) formalism with the $b_{\ast }$-prescription. A nonperturbative form factor associated with the transverse momentum dependent quark distributions is found in the analysis with a new functional form different from that of BLNY. This releases the tension between the BLNY fit to the Drell–Yan data with the SIDIS data from HERMES/COMPASS in the CSS resummation formalism.

Quantum chromodynamics is a fundamental non-Abelian gauge theory of strong interactions. The physical quantum chromodynamics vacuum state is a linear superposition of the $n$-vacua states with different topological numbers. Because of the configuration of the gauge fields, the tunneling events can induce the local parity-odd domains. Those interactions that occur in these domains can be affected by these effects. Considering the hadron (nucleon) system, we introduce the parity-odd parton distribution functions in order to describe the parity-odd structures inside the hadron in this paper. We obtain 8 parity-odd parton distribution functions at leading twist for spin-1/2 hadrons and present their properties. By introducing the parity-odd quark–quark correlator, we find the parity-odd effects vanish from the macroscopic point of view. In this paper, we consider the high energy semi-inclusive deeply inelastic scattering process to investigate parity-odd effects by calculating the spin asymmetries.

In 2016 and 2017, the COMPASS Collaboration at CERN collected a large sample of DIS events with a longitudinally polarized 160 GeV/$c$ muon beam scattering off a liquid hydrogen target. Part of the collected data has been analyzed to extract preliminary results for the amplitudes of the modulations in the azimuthal angle of the charged hadrons and for their transverse momentum distributions. These observables give relevant information for the study of the transverse momentum and spin structure of the nucleon. The results, presented here for the first time, have been obtained from part of the data collected in 2016. In the analysis, a new method for the evaluation of the contribution of exclusive diffractive processes has been implemented. The azimuthal asymmetries exhibit strong kinematic dependencies, similar to those observed in COMPASS deuteron measurements. The transverse momentum distributions show smooth exponential trends and are compatible with the previous measurement on deuteron.

Semi-inclusive deep inelastic scattering experiments allow us to probe the motion of quarks inside the proton in terms of so-called transverse momentum dependent parton distribution functions (TMD PDFs), but the information is convoluted with fragmentation functions (TMD FFs) and soft factors. It has long been known that weighting the measured event counts with powers of the hadron momentum before forming angular asymmetries de-convolutes TMD PDFs and TMD FFs in an elegant way, but this also entails an undesirable sensitivity to high momentum contributions. Using Bessel functions as weights, we find a natural generalization of weighted asymmetries that preserves the de-convolution property and features soft-factor cancellation, yet allows us to be less sensitive to high transverse momenta. The formalism also relates to TMD quantities studied in lattice QCD. We briefly show preliminary lattice results from an exploratory calculation of the Boer-Mulders shift using lattices generated by the MILC and LHP collaborations at a pion mass of 500 MeV.

The study of the transverse spin and transverse momentum structure of the nucleon is an important part of the scientific program of COMPASS, a fixed target experiment taking data at the CERN SPS since 2002. In these ten years COMPASS has produced a number of interesting results by measuring the forward going hadrons produced in deep inelastic scattering of a 160 GeV muon beam off polarized deuteron and proton targets. The COMPASS contribution to the understanding of the transverse structure of the nucleon, and the possible future contributions, are briefly reviewed here.

The investigation of the partonic degrees of freedom beyond collinear approximation (3D description) has been gained increasing interest in the last decade. The Thomas Jefferson National Laboratory, after the CEBAF upgrade to 12 GeV, will become the most complete facility for the investigation of the hadron structure in the valence region by scattering of polarized electron off various polarized nucleon targets. A compendium of the planned experiments is here presented.

COMPASS is a high-energy physics experiment operating at the SPS at CERN. Wide physics program of the experiment comprises study of hadron structure and spectroscopy with high energy muon and hadrons beams. As for the muon-program, one of the important objectives of the COMPASS experiment is the exploration of the transverse spin structure of the nucleon via spin (in)dependent azimuthal asymmetries in single-hadron production in deep inelastic scattering of polarized leptons off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and transversely polarized ${}^{6}LiD$ (in 2002, 2003 and 2004) and $N{H}_3$ (in 2007 and 2010) targets. The experimental results obtained by COMPASS for unpolarized target azimuthal asymmetries, Sivers and Collins effects and other azimuthal observables play an important role in the general understanding of the three-dimensional nature of the nucleon. Giving access to the entire twsit-2 set of transverse momentum dependent parton distribution functions and fragmentation functions COMPASS data triggers constant theoretical interest and is being widely used in phenomenological analyses and global data fits. In this review main focus is given to the very recent results obtained by the COMPASS collaboration from first ever multi-dimensional extraction of transverse spin asymmetries.

Unpolarised semi-inclusive deep inelastic scattering is receiving a growing interest as a powerful tool to access poorly known transverse momentum dependent parton distributions and fragmentation functions that play a key role in many processes, in particular in the study of the spin structure of the nucleon. These functions can be investigated through experimental observables. New results on these observables by the COMPASS experiment at CERN will be shown and discussed.

Transverse-momentum dependent parton distribution functions (TMDs) provide a description of nucleon structure in terms of the parton transverse momentum and its transverse spin. At leading twist there are eight TMDs, each offering a unique feature of quarks in a polarized or an unpolarized nucleon. The Sivers distribution is one of the most interesting TMD due to its non-universality. It has been extracted using the data from semi-inclusive deep-inelastic scattering (SIDIS), but there is no data yet from spin-dependent Drell-Yan (DY) process. Such measurement will provide a crucial test of TMD formalism which predicts an equal magnitude and opposite sign for the Sivers function extracted from SIDIS and DY process. We will discuss key future measurements of TMDs using both SIDIS and DY process with a focus on Hall A SoLID SIDIS program at Jefferson Lab.

We applied collinear expansion to the semi-inclusive deeply inelastic lepton-nucleon (nucleus) scattering process $e+N(A)\to e+q+X$ with both polarized beam and polarized target up to twist-3, and unpolarized process up to twist-4. The differential cross section and azimuthal asymmetries are expressed in terms of gauge invariant twist-3 and twist-4 TMD parton distribution/correlation functions. Measurements of such azimuthal asymmetries provide methods to study different spin and transverse momentum aspects of the partonic structure of nucleon. We further study the nuclear dependence of azimuthal asymmetries and adopt Gaussian ansatz for TMD distribution/correlation functions to estimat the semi-quantitive behaviour of the nuclear dependence. We predict the A-dependence of azimuthal asymmetries which can be tested in the planned EIC’s.

Successful realization of polarized Drell-Yan physics program is one of the main goals of the second stage of the COMPASS experiment. Drell-Yan measurements with high energy (190 GeV/c) pion beam and transversely polarized NH3 target have been initiated by a pilot-run in the October 2014 and will be followed by 140 days of data taking in 2015. In the past twelve years COMPASS experiment performed series of SIDIS measurements with high energy muon beam and transversely polarized deuteron and proton targets. Results obtained for Sivers effect and other target transverse spin dependent and unpolarized azimuthal asymmetries in SIDIS serve as an important input for general understanding of spin-structure of the nucleon and are being used in numerous theoretical and phenomenological studies being carried out in the field of transvers-spin physics. Measurement of the Sivers and all other azimuthal effects in polarized Drell-Yan at COMPASS will reveal another side of the spin-puzzle providing a link between SIDIS and Drell-Yan branches. This will be a unique possibility to test universality and key-features of transverse momentum dependent distribution functions (TMD PDFs) using essentially same experimental setup and exploring same kinematic domain. In this review main physics aspects of future COMPASS polarized Drell-Yan measurement of azimuthal transverse spin asymmetries will be presented, giving a particular emphasis on the link with very recent COMPASS results obtained for SIDIS transverse spin asymmetries from four ”Drell-Yan” $Q^2$-ranges.

We present recent results on studies of spin orbit correlations using the Jefferson Lab CLAS detector and discuss both near term and long-term future plans with CLAS, including measurements with longitudinally and transversely polarized targets. Single Spin Asymmetries (SSAs) were measured with CLAS for unpolarized and longitudinally polarized targets using a longitudinally polarized beam. Measurements of SSA for charged and neutral pions indicate that there are significant spin and azimuthal asymmetries, which can be interpreted in terms of transverse momentum dependent (TMD) distributions.

Transverse spin and transverse momentum distribution functions of the constituents of the nucleon are a crucial input for a complete description of the nucleon. COMPASS measured such for longitudinally and transversely polarized deuterons and protons. In the following we will focus on recent results from the 2007 transverse proton data and on the results for unpolarized deuterons.