Transversity 2022 is the 6th international workshop on transverse phenomena in hard processes and the transverse structure of the proton, following those held in 2005 on Lake Como (Italy), 2008 in Ferrara (Italy), 2011 in Lošinj (Croatia), 2014 in Cagliari (Italy), and 2017 in Frascati (Italy). Originally foreseen in 2020, due to Covid19 the workshop has been postponed to 2022.
The aim of the workshop is to present and discuss in depth theoretical and experimental knowledge in the field of transversity, transversemomentum dependent distribution and fragmentation functions, as well as generalised parton distribution functions. The workshop represents a valuable opportunity to gather the spin physics community, with a broad participation of theorists, as well as of experimentalists working in international collaborations at BEPCII, BNL, CERN, DESY, KEK and Jefferson Lab, all deeply involved in this area of research. Developments related to the Electron Ion Collider will also be discussed. The workshop will also be a unique occasion for young researchers to form a detailed and uptodate perspective on this fastdeveloping research field, and to present and discuss their own work and projects in a highly stimulating and reactive context.
An overview of the progress regarding the transversity distribution, the tensor charge and other transverse spin distributions will be given. Gluonic analogues will be discussed, as well as
transversity GPDs and GTMDs.
TMD Measurements at high momentum transfer have been carried out in polarized protonproton collisions at RHIC, in pion induced DrellYan scattering off transversely polarized proton targets in COMPASS and in electronpositron annihilation in Belle and BaBar. Available results will be reviewed and the impact of future measurements at RHIC and the SPS will be discussed.
A review of recent SIDIS results about transverse spin and momentum dependent observables will be given. Results that are expected to come in the near future from running experiments will also be discussed.
In this talk, I will present our recent results on nucleon tomography study by utilizing jet observables in various hadronic collisions.
The SIDIS data collected from 2002 to 2010 in COMPASS using a high energy muon beam and transversely polarised proton and deuteron targets, have allowed to performed many unique measurements. In this talk the main results and their interpretation, as well as the new expected measurements, will be reviewed. The need of the more deuteron data and the perspectives from the future COMPASS data taking will also be summarised.
Correlators such as parton distribution functions (PDFs) exhibit flavor dependence, which is accessible from complementary SemiInclusive Deep Inelastic Scattering (SIDIS) measurements with proton and neutron targets. SIDIS off the neutron can be explored using nuclear targets, in particular the deuteron, wherein the quark flavor combination differs from that of the proton. Recent $\pi^+\pi^$ dihadron beam spin asymmetry measurements allow for a pointbypoint extraction of the collinear twist3 PDF $e(x)$, which gives further insight into quark and gluon interactions. These measurements were performed with a proton target, but complementary measurements with a neutron target are necessary for disentangling the flavor dependence of $e(x)$. The presented study offers a first look at a comparison of $\pi^+\pi^$ beam spin asymmetries from proton and deuteron targets at CLAS12.
In this short talk, we discuss chiralodd PDFs that can be accessed through dihadron observables: the transversity PDF and the twist3 scalar PDF e(x).
The former is subject to positivity constraints, the Soffer bound. Recent analyses have explored the role of theoretical constraints on the tensor charge. We comment on that point, in view of future improvements in all global analyses.
As for the scalar PDF, its extended relation to nonperturbative manifestations of QCD makes it a unique object. We discuss its first extraction in a collinear framework as well as possible and necessary extensions towards a full QCD analysis.
We report the first measurements of deep inelastic scattering spindependent azimuthal asymmetries in backtoback hadron electroproduction, where one hadron is produced in the current fragmentation region and the other in the target fragmentation region. The data were taken with a 10.2 and 10.6 GeV longitudinally polarized electron beam incident on an unpolarized liquid hydrogen target using the CLAS12 Spectrometer at Jefferson Lab. Observed nonzero $\sin\Delta\phi$ modulations in $ep \rightarrow e'p\pi^+X$ events, where $\Delta\phi$ is the difference of the azimuthal angles of the proton and pion in the virtual photontarget nucleon centerofmass frame, indicate that correlations between the spin and transverse momenta of hadrons produced in the target and current fragmentation regions may be significant. The measured beamspin asymmetries provide a first access in dihadron production to a previously unobserved leadingtwist spin and transverse momentumdependent fracture function. The fracture functions describe the hadronization of the target remnant after the hard scattering of a virtual photon off a quark in the target particle and provide a new avenue for studying nucleonic structure and hadronization.
Studies of the properties and the azimuthal distribution of hadrons produced in the Target Fragmentation Region serve as a test of our complete understanding of the different mechanisms in the SIDIS production of hadrons and provide additional information on the QCD dynamics that are not accessible with single hadron production in the Current Fragmentation Region. We present first Multidimensional studies of beam SSA for semiinclusive protons (ep → e′p'+X), produced in the TFR, that can be related to higher twist Fracture Functions describing the F_LU structure function. Such measurements were performed with the CLAS12 detector in Hall B at Jefferson lab using a longitudinally polarized 10.6~GeV electron beam on an unpolarized hydrogen target. Preliminary results of this study captured the transition between the TFR and CFR regions showing a clear sign change of the SSA for protons produced in the backward region in CM, dominated by TFR protons providing a criteria for experimental separation of CFR and TFR regions. These findings are opening a new avenue for studies of nucleon structure.
Optional tour of some parte of the palace of Collegio Borromeo
In this talk I will briefly address the state of the art for our understanding of transversemomentumdependent distributions, with a focus on their phenomenology. I will introduce some of the topics which are currently under investigation and highlight the fundamental role of the present and future experimental facilities for the advancement of the field.
Single and dihadron fragmentation functions (FFs) are an essential tool in accessing the transverse spin and momentum structure of the nucleon. The chiralodd FFs provide nearly unique access to the transvsersity distributions and the related tensor charges. Transverse momentum dependent FFs enable the study of various transverse momentum dependent distribution functions in the nucleon. Furthermore, both polarized and unpolarized FFs add flavor sensitivity that would not be available with either inclusive or jet related measurements.
FFs can be accessed particularly well in electronpositron annihilation, due to the clean initial state. The present status of FF related measurements will be presented.
In semiinclusive deep inelastic scattering (SIDIS) the nonzero transverse momentum of partons is reflected in the transverse momentum $P_T$ of the produced hadrons. Assuming Gaussian dependence of transverse momentum dependent (TMD) PDFs and fragmentation functions (FFs) upon quark transverse momentum, exponential distribution of $P_T^2$ is expected. In 2016 and 2017, COMPASS experiment at CERN collected a large sample of SIDIS events using a longitudinally polarised 160~GeV/$c$ muon beam scattering on a liquid hydrogen target. The $P_T^2$ distributions of charged hadrons have been extracted from part of the data. They can be described by two exponentials and they qualitatively agree with earlier COMPASS measurements with an isoscalar target.
The azimuthal asymmetries, given by the amplitudes of the modulations in the azimuthal angle $\phi_{h}$ of the hadrons produced in SIDIS, give access to the TransverseMomentumDependent structure of the nucleon. In unpolarized SIDIS, of particular interest are the $\cos\phi_{h}$ and $\cos2\phi_{h}$ modulations, generated by the Cahn effect and by the BoerMulders TMD PDF $h_1^{\perp}$, convoluted with the Collins fragmentation function. Additional information on $h_1^{\perp}$ can be gained by measuring the azimuthal asymmetries of hadron pairs.
In 2016 and 2017, the COMPASS Collaboration at CERN collected a large sample of DIS events with a longitudinally polarised 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 azimuthal asymmetry of the charged hadrons and of the hadron pairs, the latter shown here for the first time.
Transverse momentum dependent (TMD) distributions match collinear parton density functions (PDF) in the limit of small transverse distances, which is accounted for by global extractions of TMD distributions. We study the influence of the PDF choice on the determination of unpolarized TMDPDFs and the description of TMD DrellYanpair and Zboson production data. We find that PDF essentially biases the extraction of TMDPDF. The bias is alleviated once the PDF uncertainty is taken into account and the nonperturbative TMD profile is flavordependent. Both points improve the agreement between theory and experiment, substantially increase the uncertainty in extracted TMD distributions, and should be taken into account in future global analyses.
In this talk, I will discuss our update to the global analysis of transverse singlespin asymmetries that now extracts the novel quarkgluonquark fragmentation function \tilde{H} and explores the role played by the Soffer bound on transversity and lattice QCD computations of the isovector tensor charge.
In this presentation, I will discuss the physics opportunities with the ElectronIon Collider (EIC) and the current status of the EIC.
Data from Belle Collaboration for associated (with a light unpolarized hadron) and singleinclusive production of transversely polarized $\Lambda$hyperons in $e^+e^$ annihilation processes allowed to extract, for the first time, the $\Lambda$ polarizing fragmentation function, by adopting a simplified TMD approach. Recent theoretical developments on the computation of cross sections for singleinclusive hadron production in $e^+e^$ annihilation, within a Soft Collinear Effective Theory approach, combined with the CSS formalism for the doublehadron production case, have been used to perform a renewed analysis, adopting a proper TMD factorization scheme. A detailed a comparison with the former analysis will be discussed. Preliminary estimates for the transverse $\Lambda$ polarization at OPAL and at $\sqrt s = M_Z$ will also be presented.
Extending TMD factorization to thrustdependent observables entails difficulties ultimately associated with the behavior of soft radiation. As a consequence, the definition of the TMDs has to be revised, while keeping (and extending) its universality properties. Moreover, the regularization of the rapidity divergences intertwines with the thrust dependence, leading to a new kind of factorization theorem, with unexpected features. In this talk, I will show how to properly factorize the thrust distribution of $e^+e^$ annihilation into a single hadron, whose transverse momentum is measured with respect to the thrust axis. The cross section is presented up to NNLLaccuracy in thrust and compared with BELLE data.
Soft gluon resummation is essential to obtain precise predictions for QCD processes with more scales involved. The formalism to follow in such scenarios is the Transverse Momentum Dependent factorization theorem. However, for practical applications a Monte Carlo approach is needed. We present the Parton Branching (PB) method a Monte Carlo approach to obtain QCD collider predictions based on TMDs. We discuss its connection to standard resummation approaches. We present examples of recent PB applications to inclusive and exclusive observables, in the low and hight pt region.
Being motivated mainly by the LHC physics, the currently used Monte Carlo Event Generators (MCEGs) lack of the quark spin degree of freedom in their hadronization models, and can not reproduce observed transverse spin effects such as the Collins and the dihadron asymmetries, and longitudinal spin effects such as the jet handedness. To guide the interpretation of SIDIS and $𝑒^+𝑒^−$ data as well as to make predictions for experiments at future facilities such as the EIC, a MCEG capable of reproducing quark spin effects in hadronization is necessary. To achieve this goal, we have started a systematic implementation of spin effects in the hadronization part of the Pythia 8 event generator for the polarized SIDIS process via the external package StringSpinner, which is publicly available. Spin effects are enabled for pseudoscalar meson production by using the string+${}^3P_0$ model of polarized quark fragmentation and parametrizations of the transversity PDFs.
This talk is dedicated to a recent major development of StringSpinner which allows for the introduction of vector meson production and decay in the polarized Pythia 8 string fragmentation. After being validated, the package is used to simulate the Collins and dihadron asymmetries in SIDIS and a comparison with currently available data is shown.
TBA


Deeply Virtual Compton Scattering (DVCS) and Hard Exclusive Meson Production (HEMP) are valuable processes to study Generalized Parton Distributions (GPDs). By correlating the longitudinal momentum of the partons to their transverse spatial distribution inside the nucleon, GPDs reveal the 3dimensional structure of the nucleon in QCD. Following a test run in 2012, exclusive measurements were performed at COMPASS in 2016 and 2017 at the M2 beamline of the CERN SPS. The 160 GeV muon beam impinged on a 2.5m long liquid hydrogen target that was surrounded by a barrelshaped timeoffight system to detect the recoiling target proton. The scattered muons and the particles produced were detected by the COMPASS spectrometer, which was supplemented by an additional electromagnetic calorimeter for the largeanglephoton detection.
The DVCS cross section is extracted from the sum of cross sections measured with opposite beam charge and polarization, with special attention made to separate DVCS from exclusive ?0 production. In the COMPASS kinematic domain, the DVCS cross section is closely related to the GPD H and gives a measure of the transverse extension of the partons in the proton, in the seaquark regime of Bjorkenx. On the other hand, the measurement of the cross section of exclusive pi0 production and the Spin Density Matrix Elements (SDMEs) of rho0 and omega production can provide important inputs for the understanding of chiraleven and chiralodd GPDs, as well as insights into the reaction mechanisms involved. The current progress on the study of these exclusive channels will be presented.
A key step towards a better understanding of the nucleon structure is the study of Generalized Parton Distributions (GPDs). GPDs are nowadays the object of an intense effort of research since they convey an image of the nucleon structure where the longitudinal momentum and the transverse spatial position of the partons inside the nucleon are correlated. Moreover, GPDs give access to the contribution of the orbital momentum of the quarks to the nucleon spin, improtant to the understanding of the origins of the nucleon spin.
Deeply Virtual Compton scattering (DVCS), the electroproduction of a real photon off the nucleon at the quark level, is the golden process directly interpretable in terms of GPDs of the nucleon. Depending on different arrangements of the target and beam polarizations, different DVCS observable can be measured: cross sections, target or beamspin asymmetries, etc... . Each measured observable provides different sensitivity to the various GPDs, and considering both the target nucleons, proton or neutron, the quarkflavour separation of GPDs can be exploited. GPDs can also be accessed in other exclusive leptoproduction reactions, such as Timelike Compton Scattering, Double DVCS (final state photon is also virtual), or the exclusive electroproduction of mesons.
This talk is intended to provide an overview on recent GPDrelated experimental results obtained at Jefferson Lab. These data open the way to a “tomographic” representation of the structure of the nucleon, allowing the extraction of transverse space densities of the quarks at fixed longitudinal momentum, as well as providing an insight on the distribution of forces inside the nucleon.
We will report on recent attempts to access universal
GPDs from Deeply virtual Compton scattering and Deeply
virtual meson production.
We discuss the problem of model dependency in the phenomenology of generalised parton distributions (GPDs). We present results of our resent analyses, where we have addressed this problem. This includes the extraction of Dterm, which is related to the socalled mechanical properties of the nucleon, and the analysis on the deconvolution of deeply virtual Compton scattering (DVCS) amplitudes. A new way of effectively nonparametric modelling of GPDs based on machine learning techniques will be presented as well. Getting a better grip on the control of systematic effects, our line of research will help GPD phenomenology to achieve its maturity in the precision era commenced by the new generation of experiments.
Generalized TMDs (GTMDs) of hadrons are the most general twoparton correlation functions. The Fourier transforms of GTMDs are partonic Wigner functions. During the past few years, several interesting developments have taken place in this field. In this talk, we give a brief overview of these objects and the various developments that has taken place, including, in particular, the stateoftheart of observables for these quantities.
Public conference, in Italian, open to the city of Pavia.
I will discuss how quarkonium production can be used to probe transversemomentumdependent functions (TMDs), and the role played by a new type of nonperturbative functions: the TMD shape functions.
We study the polar and azimuthal decay angular distributions of $J/\psi$ mesons produced in semiinclusive, deepinelastic electronproton scattering. For the description of the quarkonium formation mechanism, we adopt the framework of nonrelativistic QCD, with the inclusion of the intermediate coloroctet channels that are suppressed at most by a factor $v^4$ in the velocity parameter $v$ relative to the leading colorsinglet channel. We put forward factorized expressions for the helicity structure functions in terms of transverse momentum dependent gluon distributions and shape functions, which are valid when the $J/\psi$ transverse momentum is small with respect to the hard scale of the process. By requiring that such expressions correctly match with the collinear factorization results at high transverse momentum, we determine the perturbative tails of the shape functions and find them to be independent of the $J/\psi$ polarization. In particular, we focus on the $cos 2\phi$ azimuthal decay asymmetry, which originates from the distribution of linearly polarized gluons inside an unpolarized proton. We therefore suggest a novel experiment for the extraction of this sofar unknown parton density that could be performed, in principle, at the future ElectronIon Collider.
I will discuss recent calculations of jet correlation and substructure observables relevant for spin asymmetries and nucleon structure
I critically appraise current limitations in precision and accuracy of collinear parton distribution and fragmentation function determination. I focus on open issues related to quantifying data inconsistencies, theoretical uncertainties, and methodological bias. I discuss their relevance in relationship with ongoing and future experimental programs at particle colliders.
We compute the singlespin asymmetry A_UL in semiinclusive
deepinelastic scattering of unpolarized leptons and longitudinally polarized
protons at large transverse momentum of the produced hadron. Our calculation is
performed in collinear factorization at the lowest order of QCD perturbation
theory. For photon exchange the asymmetry is Todd and receives contributions
from the interference of the tree level and oneloop absorptive amplitudes. We
consider the behavior of the spin asymmetry at low transverse momentum where
contact to the formalism based on transversemomentum dependent distribution
functions can be made. We also present some phenomenological results relevant
for the COMPASS and HERMES experiments and the future ElectronIon Collider.
I will introduce the problem of the determination of the W boson mass at hadron colliders and the role of nonperturbative effects.
In this talk we present the methodology used in the NNPDF4.0 global analysis. We introduce state of the art techniques in Machine Learning applied to PDF determination, automatised hyperparameter selection and tests to asses the quality and reliability of the methodology.
The entire methodology is open sourced and available for users willing to perform their own PDF analysis.
Some spin observables in the collinear twist3 formalism will be reviewed.
The STAR Collaboration at RHIC investigates the internal spin structure of the proton with a broad range of measurements in polarized $pp$ collisions. Transverse spin studies aim to elucidate 3D transverse momentum structure and parton transversity. Dijet opening angle measurements are sensitive to the Sivers $\langle k_T \rangle$ and a nonzero spin dependent result in $pp$ collisions is observed for the first time. Individual parton contributions ($u$, $d$, gluon+sea) to the measured $\langle k_T \rangle$ are extracted through a matrix inversion of the chargesorted $\langle k_T \rangle$ data. Additionally, transverse singlespin asymmetries of fully reconstructed $W^{\pm}$ bosons from $pp$ collisions address the process dependence of the Sivers function; the increased luminosity of 2017 data at $\sqrt{s} = 510$ GeV significantly improves on previous $W^{\pm}$, as well as related $Z$boson, results. Separately, the transverse spin dependent correlation of charged pion pairs, interference fragmentation functions, are used to probe transversity. Results from $pp$ collisions at $\sqrt{s}$ = 200 and 500 GeV with additional integrated luminosity further enhance the first observations of transversity in $pp$ collisions and the constraints that they provide. Finally, the transverse singlespin dependence of the azimuthal modulation of pions in jets probes the Collins function, while additional modulations ("Collinslike" effect) place limits on gluon linear polarization. The current status of these and related analyses (forward $\pi^0$ and forward EMjet $A_N$), and prospects for their extension in the near future will be presented and discussed.
Phenomenological analyses of hadron structure from semiinclusive observables require the use of models to characterize nonperturbative effects, embedded into a formalism of TMD evolution. Constraints provided by pQCD calculations must be imposed in order to maximize predictive power. This is particularly important when attempting to use phenomenological extractions over wide scale ranges. In this talk, we will discuss how such constraints are not necessarily guaranteed when using arbitrary parametric forms. By considering the special role of observables at low to moderate scales, we will provide a practical recipe for incorporating nonperturvative models into the CSS formalism. Special attention will also be payed to the role of TMD integral relations in building models optimally embedded into the CSS formula.
The TMD factorization at the nexttoleading power has an involved structure of singularities. I discuss the definition and properties of transverse momentum dependent (TMD) distributions of the twistthree including evolution, symmetry relations, parametrization, interpretation, and singularities. I demonstrate that the physical TMD distributions (in terms of which observables are written) require an extra subtraction procedure. As an example of application, I discuss the DrellYan hadronic tensor at the nexttoleading power in terms of physical distributions and explicitly demonstrate the cancellation of rapidity and endpoint divergences. These results complete the construction of TMD factorization at the nexttoleading power.
We present an estimate of the cos$2\phi$ azimuthal asymmetry in backtoback production of $J/\psi$ and a jet in the process: $e~p\to e~J/\psi~Jet~X$. We calculate the asymmetry using TMD factorization in a generalized parton model (GPM) framework and use nonrelativistic QCD (NRQCD) to obtain the $J/\psi$ production rate. We incorporate both color singlet and color octet contributions to the asymmetry. This asymmetry will be useful to probe the linearly polarized gluon distribution at the future electronion collider (EIC). We present numerical estimates of the asymmetry using two recent parametrization of the gluon TMDs, namely spectator model and Gaussian parameterization. We investigate the effect of TMD evolution of gluon TMDs on the asymmetry.
An overview of recent results from PHENIX on transverse spin and transversemomentumdependent observables will be presented.
Nonperturbative parton distributions that arise in the TMD factorization of crosssections have dynamics dominated by the lightcone. This renders them inaccessible to direct lattice QCD calculations due to the sign problem in realtime calculations. To circumvent this issue, one may construct a latticecalculable TMD that shares the same IR physics as the physical TMD appearing in crosssections, and then must prove a factorization theorem connecting these two functions. In this talk, I prove such a relation for quasiTMDs and Collins TMDs for leading power distributions of any spin, for both quarks and gluons.
There was recent theoretical progress on transversemomentumdependent parton distribution functions (TMDs) and parton distribution functions (PDFs) for spin1 hadrons at twists 3 and 4. We expect that the field of structure functions for spin1 hadrons will become an interesting topic in 2020's and 2030' due to experimental projects at the Jefferson Laboratory, the Fermilab, the NICA, the LHCspin, and the electronion colliders in US and China.
We explain TMDs and PDFs for spin1 hadrons up to twist 4 [1,2,3]. Decomposing a quark correlation function with the conditions of the Hermiticity and parity invariance, we found 30 new structure functions at twists 3 and 4 [1]. There are also new fragmentation functions in the spin1 hadrons. Integrating the TMDs over the transverse momentum, we found new collinear PDFs. A twist2 relation and a sum rule exist for the tensorpolarized PDFs $f_{1LL}$ and $f_{LT}$ [2]. In these studies, we also showed that twist3 multiparton distribution functions $F_{LT}$, $G_{LT}$, $H_{LL}^\perp$, and $H_{TT}$ exist for tensorpolarized spin1 hadrons. Relations among these collinear parton and multipartondistribution functions were derived by using the equation of motion for quarks [3]. Useful relations were obtained (1) for the twist3 PDF $f_{LT}$, the trasversemomentum moment PDF $f_{1LT}^{\,(1)}$, and the multiparton distribution functions $F_{G,LT}$ and $G_{G,LT}$; (2) for the twist3 PDF $e_{LL}$, the twist2 PDF $f_{1LL}$, and the multiparton distribution function $H_{G,LL}^\perp$. There is also a Lorentzinvariance relation for $f_{1LT}^{\,(1)}$, $f_{1LL}$, $f_{LT}$, and $F_{G,LT}$. These studies will be useful in future investigations on the spin1 structure functions.
[1] S. Kumano and QinTao Song, Phys. Rev. D 103 (2021) 014025.
[2] S. Kumano and QinTao Song, JHEP 09 (2021) 141.
[3] S. Kumano and QinTao Song, Phys. Lett. B 826 (2022) 136908.
I will present an overview of recent progress and results in Lattice QCD focusing on the direct measure of moments of the transversity PDF, as well as using the quasiPDF/GPD approach.
The CollinsSoper kernel describing the rapidity evolution of TMDPDFs is nonperturbative for large transverse separations or small transverse momenta. I will discuss recent lattice QCD calculations that aim to determine the nonperturbative behavior of the quark CollinsSoper kernel.
The investigation of the nucleon spin structure via measurements of dimuons produced in the DrellYan process is one of the main goals of the phaseII research program of the COMPASS experiment (M2 beamline, SPS, CERN).
In 2015 and 2018, COMPASS performed DrellYan measurements using a 190 GeV/c $\pi^$ beam impinging on a transversely polarized NH$_3$ target and on an unpolarized tungsten target. The measurement of the Sivers and other transversespin dependent azimuthal asymmetries in DrellYan provides a unique opportunity to test the QCD predicted (pseudo)universality features of related transverse momentum dependent parton distribution functions. The angular coefficients $\lambda$, $\mu$ and $\nu$ that characterize the unpolarized DrellYan crosssection were also extracted from the data collected using the tungsten target. The results of this analysis provide input to study various perturbative and nonperturbative QCD effects.
In this talk, recent DrellYan results from COMPASS will be presented along with prospects for ongoing studies.
After fifty years of investigations, the nucleon structure is still far from being understood and continues to represent a unique test bench for QCD. Despite the enormous progresses achieved in five decades of deepinelastic scattering (DIS) experiments, a number of crucial open questions are still on the carpet and subject of intense theoretical and experimental studies. In the last two decades, semiinclusive DIS was established as a unique tool for the study of the noncollinear structure of nucleons, involving the parton transverse momentum pT as an additional degree of freedom. Requiring the detection of at least one final statehadron in coincidence with the scattered lepton, it opened the way not only to measure of the chiralodd transversity distribution, the last missing leadingtwist collinear parton distribution function, but also to a variety of new pTdependent PDFs, known as TMDs. Describing correlations between the quark transverse momentum and the quark or the nucleon spin (spinorbit correlations), TMDs account for a number of intriguing effects observed in polarized and unpolarized reactions, and allow for a 3dimensional description of the nucleon in momentum space. Furthermore, they could provide insights into the yet unmeasured quark orbital angular momentum. At leadingtwist, eight TMDs enter the SIDIS cross section in conjunction with a fragmentation function. In addition, going to the twist3 level allows us to probe novel quarkgluon correlations.
The HERMES experiment collected a wealth of data using the 27.6 GeV polarized HERA lepton beam and various polarized and unpolarized gaseous targets. This allows for a series of unique measurements of observables sensitive to this multidimensional (spin) structure of the nucleon, probed through specific azimuthal modulations in the distribution of hadrons produced in semiinclusive DIS. An overview of the HERMES TMD program will be given and Fourier amplitudes of some of the azimuthal modulations sensitive to the beam and/or target polarization, recently extracted for the first time also in a threedimensional kinematic space, will be presented in more detail.
Fracture functions describes the hadron production in the target fragmentation region (TFR) in the hard processes, namely  the spin and transverse momentum dependent correlations between struck parton in the target and produced hadron in TFR.
In this talk I'll shortly describe the formalism and present the theoretical results for SIDIS and DrellYan processes.
New experimental results on double backtoback hadron production in SIDIS will be also presented.
We will discuss recent updates from JAM on gluon polarization in the nucleon and polarized sea asymmetries and the role of the various theoretical constraints, in particular positivity constraints.