The 3D entangled structure of the proton; transverse degrees of freedom in QCD, momenta, spins and more

Light-front quantized quark and gluon states (partons) play a dominant role in high energy scattering processes. Initial state hadrons are mixed ensembles of partons, while produced pure partonic states appear as mixed ensembles of hadrons. The transition from collinear hard physics to the 3D structure including partonic transverse momenta is related to confinement which links color and spatial degrees of freedom. We outline ideas on emergent symmetries in the Standard Model and their connection to the 3D structure of hadrons. Wilson loops, including those with light-like Wilson lines such as used in the studies of transverse momentum dependent distribution functions (TMDs) may play a crucial role here, establishing a direct link between transverse spatial degrees of freedom and gluonic degrees of freedom.Comment: 8 pages, invited talk presented at the Lightcone 2017 Workshop, 18-22 Sep 2017, Mumbai, India; prepared for proceedings to be published in Few Body Physic

Spin Physics and Transverse Structure

Spin is a welcome complication in the study of partonic structure that has led to new insights, even if theoretically and experimentally not all dust has settled, in particular on quark flavor dependence and gluon spin. At the same time it opened new questions on angular momentum and effects of transverse structure. In this talk the focus is on the role of the transverse momenta of partons. Like for collinear parton distribution functions (PDFs), we are also in the case of transverse momentum dependent (TMD) PDFs, talking about forward matrix elements. TMD PDFs (or in short TMDs) extend collinear PDFs with only spin-spin correlations to PDFs that include spin-momentum correlations, including also time-reversal-odd (T-odd) correlations, relevant for the description of single spin asymmetries. In this way TMDs open up new ways of studying the spin structure. Their operator structure within QCD, however, is more complex leading to various ways of breaking of universality.Comment: 8 pages, to appear in proceedings of DIS2015 (XXIII International Workshop on Deep-Inelastic Scattering and Related Subjects, 27 April - 1 May, 2015, Dallas, USA

Current fragmentation in semiinclusive leptoproduction

Current fragmentation in semiinclusive deep inelastic leptoproduction offers, besides refinement of inclusive measurements such as flavor separation and access to the chiral-odd quark distribution functions $h_1^q(x) = \delta q(x)$, the possibility to investigate intrinsic transverse momentum of hadrons via azimuthal asymmetries.Comment: 14 pages, Latex using aipproc.sty and epsfig.sty; plenary talk given at the Second Workshop on Physics with an Electron Polarized light-Ion Collider (EPIC), Sept. 14-16, 2000, MIT, Cambridge, US

Sivers Effect Asymmetries in Hadronic Collisions

We argue that weighted azimuthal single spin asymmetries in back-to-back jet or pion production in polarized proton-proton scattering can be written as convolutions of universal distribution and fragmentation functions with gluonic pole cross sections as hard functions. Gluonic pole cross sections are gauge-invariant weighted sums of Feynman diagrams. The weight factors are a direct consequence of the (diagram-dependence of) gauge links. The best known consequence of the gauge links is the generation of the Sivers effect that is a source for single-spin asymmetries. Moreover, due to the dependence of the gauge links on the color-flow of the hard diagram the Sivers effect in SIDIS enters with opposite sign as it does in Drell-Yan scattering. The weight factors in the gluonic pole cross sections are the appropriate generalizations to more complicated processes of this relative sign difference. Furthermore, it is argued that the gluon-Sivers effect appears in twofold.Comment: Contribution to the 17th International Spin Physics Symposium (SPIN2006), Kyoto, Japan, Oct. 2-7, 200

Gluonic Pole Cross Sections and Single Spin Asymmetries in Hadron-Hadron Scattering

The gauge-links connecting the parton field operators in the hadronic matrix elements appearing in the transverse momentum dependent distribution functions give rise to T-odd effects. Due to the process-dependence of the gauge-links the T-odd distribution functions appear with different pre-factors. A consequence is that in the description of single spin asymmetries the parton distribution and fragmentation functions are convoluted with gluonic pole cross sections rather than the basic partonic cross sections. In this paper we calculate the gluonic pole cross sections encountered in single spin asymmetries in hadron-hadron scattering. The case of back-to-back pion production in polarized proton-proton scattering is worked out explicitly. It is shown how T-odd gluon distribution functions originating from gluonic pole matrix elements appear in twofold.Comment: v2: includes explicit definitions of polarized cross sections + minor corrections; to appear in JHE

Non-universality of transverse momentum dependent parton distribution functions

In the field theoretical description of hadronic scattering processes, single transverse-spin asymmetries arise due to gluon initial and final state interactions. These interactions lead to process dependent Wilson lines in the operator definitions of transverse momentum dependent parton distribution functions. In particular for hadron-hadron scattering processes with hadronic final states this has important ramifications for possible factorization formulas in terms of (non)universal TMD parton distribution functions. In this paper we will systematically separate the universality-breaking parts of the TMD parton correlators from the universal T-even and T-odd parts. This might play an important role in future factorization studies for these processes. We also show that such factorization theorems will (amongst others) involve the gluonic pole cross sections, which have previously been shown to describe the hard partonic scattering in weighted spin asymmetries.Comment: v2: some textual changes in the paper and corrections in references, to appear in Nucl. Phys.