Recent Key Measurements for Accessing the Transverse Spin and Momentum Structure of the Nucleon

2016 ◽  
Vol 40 ◽  
pp. 1660028 ◽  
Author(s):  
Anna Martin
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Transverse Spin ◽  
Nucleon Structure ◽  
Nucleon Spin ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Azimuthal Asymmetries ◽  
Selection Of

A selection of recent key results obtained in semi-inclusive deeply inelastic scattering (SIDIS) experiments is presented. The observations strongly support the description of the nucleon structure in terms of transverse momentum dependent parton distribution functions, which represent the various correlations between the quarks spins, the quarks transverse momenta and the nucleon spin which give rise to specific spin-dependent azimuthal asymmetries.

scholarly journals GENERALIZED UNIVERSALITY FOR TMD DISTRIBUTION FUNCTIONS

2012 ◽  
Vol 20 ◽  
pp. 66-74 ◽  
Author(s):  
M. G. A. BUFFING ◽  
P. J. MULDERS
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Azimuthal Angle ◽  
High Energy ◽  
Distribution Functions ◽  
Transverse Spin ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Spin Asymmetries ◽  
Azimuthal Asymmetries

Azimuthal asymmetries in high-energy processes, most pronounced showing up in combination with single or double (transverse) spin asymmetries, can be understood with the help of transverse momentum dependent (TMD) parton distribution and fragmentation functions. These appear in correlators containing expectation values of quark and gluon operators. TMDs allow access to new operators as compared to collinear (transverse momentum integrated) correlators. These operators include nontrivial process dependent Wilson lines breaking universality for TMDs. Making an angular decomposition in the azimuthal angle, we define a set of universal TMDs of definite rank, which appear with process dependent gluonic pole factors in a way similar to the sign of T-odd parton distribution functions in deep inelastic scattering or the Drell-Yan process. In particular, we show that for a spin 1/2 quark target there are three pretzelocity functions.

Color Entanglement in Hadronic Processes for Transverse Momentum Dependent Parton Distribution Functions

2015 ◽  
Vol 37 ◽  
pp. 1560022
Author(s):  
M. G. A. Buffing ◽  
P. J. Mulders
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Initial State ◽  
Color Flow ◽  
Transverse Momentum Dependent ◽  
Gauge Link ◽  
Azimuthal Asymmetries ◽  
Different Parts

In the description of protons, we go beyond the ordinary collinear parton distribution functions (PDFs), by including transverse momentum dependent PDFs (TMDs). As such, we become sensitive to polarization modes of the partons and protons that one cannot probe without accounting for transverse momenta of partons, in particular when looking at azimuthal asymmetries. Hadronic processes require the inclusion of gluon contributions forming the gauge links, which are path-ordered exponentials tracing the color flow. In processes with two hadrons in the initial state, such as Drell-Yan (DY), the gauge links from different parts of the process get entangled. We show that in color disentangling this gauge link structure, one becomes sensitive to this color flow. After disentanglement, particular combinations of TMDs will require a different numerical color factor than one naively might have expected. Such color factors will even play a role for azimuthal asymmetries in the simplest hadronic processes such as DY.

scholarly journals INSIGHTS ON NON-PERTURBATIVE ASPECTS OF TMDs FROM MODELS

2009 ◽  
Vol 24 (35n37) ◽  
pp. 2995-3004 ◽  
Author(s):  
H. AVAKIAN ◽  
A. V. EFREMOV ◽  
P. SCHWEITZER ◽  
O. V. TERYAEV ◽  
F. YUAN ◽  
...  
Keyword(s):  
Transverse Momentum ◽  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Perturbative Calculations ◽  
Transverse Momentum Dependent ◽  
Azimuthal Asymmetries

Transverse momentum dependent parton distribution functions are a key ingredient in the description of spin and azimuthal asymmetries in deep-inelastic scattering processes. Recent results from non-perturbative calculations in effective approaches are reviewed, with focus on relations among different parton distribution functions in QCD and models.

BESSEL-WEIGHTED ASYMMETRIES AND TRANSVERSE SPIN EFFECTS

2012 ◽  
Vol 20 ◽  
pp. 168-176
Author(s):  
LEONARD GAMBERG
Keyword(s):  
Transverse Momentum ◽  
Cross Section ◽  
Parton Distribution ◽  
Evolution Equations ◽  
Distribution Functions ◽  
Transverse Spin ◽  
High Transverse Momentum ◽  
Transverse Momentum Dependent ◽  
Fragmentation Functions ◽  
The Cross

We consider the cross section for semi-inclusive deep inelastic scattering in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

scholarly journals DEFINITION AND EVOLUTION OF TRANSVERSE MOMENTUM DISTRIBUTIONS

2012 ◽  
Vol 20 ◽  
pp. 92-108 ◽  
Author(s):  
MIGUEL G. ECHEVARRÍA ◽  
AHMAD IDILBI ◽  
IGNAZIO SCIMEMI
Keyword(s):  
Transverse Momentum ◽  
Evolution Equation ◽  
Gauge Invariance ◽  
Parton Distribution ◽  
Ultra Violet ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Momentum Distributions ◽  
Definition Of

We consider the definition of unpolarized transverse-momentum-dependent parton distribution functions while staying on-the-light-cone. By imposing a requirement of identical treatment of two collinear sectors, our approach, compatible with a generic factorization theorem with the soft function included, is valid for all non-ultra-violet regulators (as it should), an issue which causes much confusion in the whole field. We explain how large logarithms can be resummed in a way which can be considered as an alternative to the use of Collins-Soper evolution equation. The evolution properties are also discussed and the gauge-invariance, in both classes of gauges, regular and singular, is emphasized.

scholarly journals RENORMALIZATION-GROUP ANATOMY OF TRANSVERSE-MOMENTUM DEPENDENT PARTON DISTRIBUTION FUNCTIONS IN QCD

2009 ◽  
Vol 24 (35n37) ◽  
pp. 2913-2923 ◽  
Author(s):  
N. G. STEFANIS ◽  
I. O. CHEREDNIKOV
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Anomalous Dimension ◽  
Distribution Functions ◽  
Divergent Part ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Light Cone Gauge ◽  
Soft Factor ◽  
First Case

The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with q--independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous-dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous dimension defect, while in the second case its ultraviolet-divergent part reduces to unity.

Transverse momentum dependent (TMD) parton distribution functions generated in the modified DGLAP formalism based on the valence-like distributions

2017 ◽  
Vol 32 (19n20) ◽  
pp. 1750121 ◽  
Author(s):  
H. Hosseinkhani ◽  
M. Modarres ◽  
N. Olanj
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Dynamical Variable ◽  
Distribution Functions ◽  
Present Calculation ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Longitudinal Structure Function ◽  
Wide Range

Transverse momentum dependent (TMD) parton distributions, also referred to as unintegrated parton distribution functions (UPDFs), are produced via the Kimber–Martin–Ryskin (KMR) prescription. The GJR08 set of parton distribution functions (PDFs) which are based on the valence-like distributions is used, at the leading order (LO) and the next-to-leading order (NLO) approximations, as inputs of the KMR formalism. The general and the relative behaviors of the generated TMD PDFs at LO and NLO and their ratios in a wide range of the transverse momentum values, i.e. [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are investigated. It is shown that the properties of the parent valence-like PDFs are imprinted on the daughter TMD PDFs. Imposing the angular ordering constraint (AOC) leads to the dynamical variable limits on the integrals which in turn increase the contributions from the lower scales at lower [Formula: see text]. The results are compared with our previous studies based on the MSTW2008 input PDFs and it is shown that the present calculation gives flatter TMD PDFs. Finally, a comparison of longitudinal structure function [Formula: see text] is made by using the produced TMD PDFs and those that were generated through the MSTW2008-LO PDF from our previous work and the corresponding data from H1 and ZEUS collaborations and a reasonable agreement is found.

scholarly journals Key Future Measurements of TMDs at Jefferson Lab and Other Facilities

2016 ◽  
Vol 40 ◽  
pp. 1660035
Author(s):  
Kalyan Allada
Keyword(s):  
Transverse Momentum ◽  
Unique Feature ◽  
Opposite Sign ◽  
Distribution Functions ◽  
Transverse Spin ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Jefferson Lab ◽  
Sivers Function ◽  
Crucial Test

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.

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