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.

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.

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 Polarized Drell-Yan at COMPASS-II: Transverse Spin Physics Program

2016 ◽  
Vol 40 ◽  
pp. 1660109
Author(s):  
Bakur Parsamyan
Keyword(s):  
High Energy ◽  
Muon Beam ◽  
Distribution Functions ◽  
Transverse Spin ◽  
Spin Physics ◽  
Transverse Momentum Dependent ◽  
Spin Asymmetries ◽  
Compass Experiment ◽  
Physics Program ◽  
Azimuthal Asymmetries

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” [Formula: see text]-ranges.

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.

HADRON STRUCTURE STUDY IN FORTHCOMING DRELL–YAN EXPERIMENTS: COMPASS PROJECT AT CERN

2009 ◽  
Vol 24 (35n37) ◽  
pp. 3033-3044 ◽  
Author(s):  
◽  
OLEG DENISOV
Keyword(s):  
Transverse Momentum ◽  
Structure Study ◽  
Distribution Functions ◽  
Proton Target ◽  
Production Mechanism ◽  
Hadron Structure ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Spin Asymmetries ◽  
Hadron Beam

The study of Drell–Yan (DY) processes involving the collision of an (un)polarised hadron beam on an (un)polarised proton target can result in a fundamental improvement of our knowledge on the transverse momentum dependent (TMDs) parton distribution functions (PDFs) of hadrons. The production mechanism of J/ψ and J/ψ - DY duality can also be addressed. One of the forthcoming polarised DY experiments (COMPASS (SPS, CERN)) is discussed in this context. The most important features of this project are briefly reviewed, as well as its sensitivity to the various transverse momentum dependent spin asymmetries.

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.

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