Narrow Results

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.