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 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.

scholarly journals Calculation of transverse momentum dependent distributions beyond the leading power

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Valentin Moos ◽  
Alexey Vladimirov
Keyword(s):  
Transverse Momentum ◽  
Cross Section ◽  
Parton Distribution ◽  
Decomposition Method ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Target Mass ◽  
Spinor Formalism ◽  
First Time

Abstract We compute the contribution of twist-2 and twist-3 parton distribution functions to the small-b expansion for transverse momentum dependent (TMD) distributions at all powers of b. The computation is done by the twist-decomposition method based on the spinor formalism for all eight quark TMD distributions. The newly computed terms are accompanied by the prefactor (M2b2)n and represent the target-mass corrections to the resummed cross-section. For the first time, a non-trivial expression for the pretzelosity distribution is derived.

TMD FACTORIZATION AND EVOLUTION FOR TMD CORRELATION FUNCTIONS

2011 ◽  
Vol 04 ◽  
pp. 97-105 ◽  
Author(s):  
S. MERT AYBAT ◽  
TED C. ROGERS
Keyword(s):  
Transverse Momentum ◽  
Correlation Functions ◽  
Parton Distribution ◽  
Higher Order ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Hard Part ◽  
Transverse Momentum Dependent ◽  
Unpolarized Case ◽  
Fragmentation Functions

We discuss the application of transverse momentum dependent (TMD) factorization theorems to phenomenology. Our treatment relies on recent extensions of the Collins-Soper-Sterman (CSS) formalism. Emphasis is placed on the importance of using well-defined TMD parton distribution functions (PDFs) and fragmentation functions (FFs) in calculating the evolution of these objects. We explain how parametrizations of unpolarized TMDs can be obtained from currently existing fixed-scale Gaussian fits and previous implementations of the CSS formalism in the Drell-Yan process, and provide some examples. We also emphasize the importance of agreed-upon definitions for having an unambiguous prescription for calculating higher orders in the hard part, and provide examples of higher order calculations. We end with a discussion of strategies for extending the phenomenological applications of TMD factorization to situations beyond the unpolarized case.

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 PHENOMENOLOGY OF THE SIVERS EFFECT WITH TMD EVOLUTION

2012 ◽  
Vol 20 ◽  
pp. 145-152
Author(s):  
M. ANSELMINO ◽  
M. BOGLIONE ◽  
S. MELIS
Keyword(s):  
Transverse Momentum ◽  
Evolution Equations ◽  
Distribution Functions ◽  
Dependent Data ◽  
Clear Indication ◽  
Transverse Momentum Dependent ◽  
Sidis Data ◽  
Sivers Function ◽  
Theoretical Developments

Recently, theoretical developments have led to the QCD evolution equations for the unpolarized Transverse Momentum Dependent (TMD) distribution functions and for the Sivers function (TMD-evolution). We tested whether the proposed TMD-evolution can already be observed in the SIDIS data on the Sivers asymmetry. Although very preliminary, our analysis shows that data are compatible with such an evolution with a clear indication of evolution in the x-dependent data subsets.

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 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 Extracting the QCD ΛMS¯ parameter in Drell–Yan process using Collins–Soper–Sterman approach

2017 ◽  
Vol 32 (10) ◽  
pp. 1750040 ◽  
Author(s):  
R. Taghavi ◽  
A. Mirjalili
Keyword(s):  
Experimental Data ◽  
Transverse Momentum ◽  
Cross Section ◽  
Center Of Mass ◽  
Distribution Functions ◽  
Mass Energy ◽  
Transverse Momentum Dependent ◽  
Center Of Mass Energy ◽  
Dimensional Transmutation ◽  
High Center

In this work, we directly fit the QCD dimensional transmutation parameter, [Formula: see text], to experimental data of Drell–Yan (DY) observables. For this purpose, we first obtain the evolution of transverse momentum dependent parton distribution functions (TMDPDFs) up to the next-to-next-to-leading logarithm (NNLL) approximation based on Collins–Soper–Sterman (CSS) formalism. As is expecting the TMDPDFs are appearing at larger values of transverse momentum by increasing the energy scales and also the order of approximation. Then we calculate the cross-section related to the TMDPDFs in the DY process. As a consequence of global fitting to the five sets of experimental data at different low center-of-mass energies and one set at high center-of-mass energy, using CETQ06 parametrizations as our boundary condition, we obtain [Formula: see text] MeV corresponding to the renormalized coupling constant [Formula: see text] which is within the acceptable range for this quantity. The goodness of [Formula: see text] shows the results for DY cross-section are in good agreement with different experimental sets, containing E288, E605 and R209 at low center-of-mass energies and [Formula: see text], CDF data at high center-of-mass energy. The repeated calculations, using HERAPDFs parametrizations is yielding us numerical values for fitted parameters very close to what we obtain using CETQ06 PDFs set. This indicates that the obtained results have enough stability by variations in the boundary conditions.

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