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Published: 11 March 2023

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1

BOGLIONE, MARIAELENA. "PHENOMENOLOGY OF TRANSVERSE MOMENTUM DEPENDENT PARTON DENSITIES." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460017. http://dx.doi.org/10.1142/s2010194514600179.

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This talk provides a short overview of the phenomenology of transverse momentum dependent distribution and fragmentation functions, focussing on the most recent phenomenological developments in the study of their Q2 evolution and energy dependence.
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2

Bomhof, C. J., and P. J. Mulders. "Non-universality of transverse momentum dependent parton distribution functions." Nuclear Physics B 795, no. 1-2 (May 2008): 409–27. http://dx.doi.org/10.1016/j.nuclphysb.2007.11.024.

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3

Ji, Xiangdong, Yizhuang Liu, and Yu-Sheng Liu. "Transverse-momentum-dependent parton distribution functions from large-momentum effective theory." Physics Letters B 811 (December 2020): 135946. http://dx.doi.org/10.1016/j.physletb.2020.135946.

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4

BUFFING, M. G. A., and P. J. MULDERS. "GENERALIZED UNIVERSALITY FOR TMD DISTRIBUTION FUNCTIONS." International Journal of Modern Physics: Conference Series 20 (January 2012): 66–74. http://dx.doi.org/10.1142/s2010194512009105.

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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.
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5

SIGNORI, ANDREA, ALESSANDRO BACCHETTA, and MARCO RADICI. "FLAVOR DEPENDENCE OF UNPOLARIZED TMDS FROM SEMI-INCLUSIVE PION PRODUCTION." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460020. http://dx.doi.org/10.1142/s2010194514600209.

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Recent data from semi-inclusive deep inelastic scattering collected by the HERMES collaboration allow for the first time to discuss how the transverse-momentum dependence of unpolarized distribution and fragmentation functions is affected by the flavor of the involved partons. A model built with flavor-dependent Gaussian transverse-momentum distributions fits data better than the same flavor-independent model. The current analysis is performed for totally unpolarized scattering of leptons off protons and deuterons, with detected pions in the final state. There are convincing indications of flavor dependence in the fragmentation functions, while for parton distribution functions the evidence is weaker.
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6

Angeles-Martinez, R., A. Bacchetta, I. I. Balitsky, D. Boer, M. Boglione, R. Boussarie, F. A. Ceccopieri, et al. "Transverse Momentum Dependent (TMD) Parton Distribution Functions: Status and Prospects." Acta Physica Polonica B 46, no. 12 (2015): 2501. http://dx.doi.org/10.5506/aphyspolb.46.2501.

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7

Engelhardt, M., B. Musch, P. Hägler, J. Negele, and A. Schäfer. "Lattice QCD Studies of Transverse Momentum-Dependent Parton Distribution Functions." Few-Body Systems 56, no. 6-9 (April 24, 2015): 447–53. http://dx.doi.org/10.1007/s00601-015-0976-x.

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8

GAMBERG, LEONARD. "BESSEL-WEIGHTED ASYMMETRIES AND TRANSVERSE SPIN EFFECTS." International Journal of Modern Physics: Conference Series 20 (January 2012): 168–76. http://dx.doi.org/10.1142/s201019451200921x.

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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.
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9

Buffing, M. G. A., and P. J. Mulders. "Color Entanglement in Hadronic Processes for Transverse Momentum Dependent Parton Distribution Functions." International Journal of Modern Physics: Conference Series 37 (January 2015): 1560022. http://dx.doi.org/10.1142/s2010194515600228.

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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.
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10

Radici, Marco, Alessandro Bacchetta, Andrea Signori, and Gunar Schnell. "Exploring the Flavor Dependence of Partonic Transverse Momentum." International Journal of Modern Physics: Conference Series 37 (January 2015): 1560024. http://dx.doi.org/10.1142/s2010194515600241.

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Using recently published HERMES data on multiplicities in semi-inclusive deep-inelastic scattering, we discuss the flavor dependence of unpolarized transverse-momentum dependent distribution and fragmentation functions. We find convincing indications that favored fragmentation into pions have smaller average transverse momentum than unfavored ones and fragmentation into kaons. We find weaker indications of flavor dependence in the transverse-momentum dependence of parton distributions.
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11

Mukherjee, Asmita, Sreeraj Nair, and Vikash Kumar Ojha. "Wigner Distributions of Quark." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660055. http://dx.doi.org/10.1142/s2010194516600557.

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Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.
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12

Echevarría, Miguel G., Ahmad Idilbi, and Ignazio Scimemi. "Soft and collinear factorization and transverse momentum dependent parton distribution functions." Physics Letters B 726, no. 4-5 (November 2013): 795–801. http://dx.doi.org/10.1016/j.physletb.2013.09.003.

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13

Kaur, Navdeep, and Harleen Dahiya. "Transverse momentum-dependent parton distributions of pion in the light-front holographic model." International Journal of Modern Physics A 36, no. 08n09 (March 30, 2021): 2150052. http://dx.doi.org/10.1142/s0217751x21500524.

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Using the light-front holographic model, we study the transverse momentum-dependent parton distributions (TMDs) for the case of pion. At leading twist, the unpolarized parton distribution function [Formula: see text] and the Boer–Mulders function [Formula: see text] are obtained for pion. We calculate both the functions using the light-front holographic model with spin improved wave function and compare the predicted results with available results of other models. In order to provide inputs in predicting future experimental data, an LO evolution is performed from model scale to experimental scale for the case of unpolarized parton distribution function [Formula: see text].
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14

AVAKIAN, H., A. V. EFREMOV, P. SCHWEITZER, O. V. TERYAEV, F. YUAN, and P. ZAVADA. "INSIGHTS ON NON-PERTURBATIVE ASPECTS OF TMDs FROM MODELS." Modern Physics Letters A 24, no. 35n37 (December 7, 2009): 2995–3004. http://dx.doi.org/10.1142/s0217732309001200.

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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.
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15

STEFANIS, N. G., and I. O. CHEREDNIKOV. "RENORMALIZATION-GROUP ANATOMY OF TRANSVERSE-MOMENTUM DEPENDENT PARTON DISTRIBUTION FUNCTIONS IN QCD." Modern Physics Letters A 24, no. 35n37 (December 7, 2009): 2913–23. http://dx.doi.org/10.1142/s0217732309001121.

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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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16

Makke, Nour. "Transverse Momentum Dependent Hadron Multiplicities at COMPASS." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660031. http://dx.doi.org/10.1142/s2010194516600314.

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Unpolarised semi-inclusive deep inelastic scattering is receiving a growing interest as a powerful tool to access poorly known transverse momentum dependent parton distributions and fragmentation functions that play a key role in many processes, in particular in the study of the spin structure of the nucleon. These functions can be investigated through experimental observables. New results on these observables by the COMPASS experiment at CERN will be shown and discussed.
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17

Buffing, M. G. A., and P. J. Mulders. "Color Effects for Transverse Momentum Dependent Parton Distribution Functions in Hadronic Processes." Few-Body Systems 56, no. 6-9 (November 5, 2014): 337–42. http://dx.doi.org/10.1007/s00601-014-0921-4.

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18

SCHNELL, GUNAR. "EXPERIMENTAL DATA ON TRANSVERSE-MOMENTUM DISTRIBUTIONS FROM SEMI-INCLUSIVE DEEP-INELASTIC SCATTERING." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460013. http://dx.doi.org/10.1142/s2010194514600131.

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The exploration of the structure of the nucleon reaches a new level of sophistication when explicit dependences on transverse momenta of partons in both parton distributions and fragmentation functions are included. These dependences lead to a manifold of new correlations between the nucleon and quark spin as well as their momenta and thus a wealth of experimental observables. A particular example is the novel Sivers function that—according to firm QCD predictions—has to change sign when going from the Drell-Yan process to semi-inclusive deep-inelastic scattering. Here a review is given on which knowledge has been gathered about transverse-momentum-dependent (TMD) distribution and fragmentation functions from semi-inclusive deep-inelastic scattering experiments.
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19

Cherednikov, I. O., and N. G. Stefanis. "Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis." Nuclear Physics B 802, no. 1-2 (October 2008): 146–79. http://dx.doi.org/10.1016/j.nuclphysb.2008.05.011.

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20

Abdulov, Nizami A., Anatoly V. Kotikov, and Artem Lipatov. "Parametrizations of Collinear and kT-Dependent Parton Densities in Proton." Particles 5, no. 4 (November 28, 2022): 535–60. http://dx.doi.org/10.3390/particles5040039.

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A new type of parametrization for parton distribution functions in the proton, based on their Q2-evolution at large and small x values, is constructed. In our analysis, the valence and nonsinglet parts obey the Gross–Llewellyn–Smith and Gottfried sum rules, respectively. For the singlet quark and gluon densities, momentum conservation is taken into account. Then, using the Kimber–Martin–Ryskin prescription, we extend the consideration to Transverse Momentum Dependent (TMD, or unintegrated) gluon and quark distributions in the proton, which currently plays an important role in a the number of phenomenological applications. The analytical expressions for the latter, valid for both low and large x, are derived for the first time.
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21

BUFFING, M. G. A., P. J. MULDERS, and A. MUKHERJEE. "UNIVERSALITY OF QUARK AND GLUON TMD CORRELATORS." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460003. http://dx.doi.org/10.1142/s2010194514600039.

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Transverse Momentum Dependent (TMD) parton distribution functions (PDFs), in short referred to as TMDs, also take into account the transverse momentum (pT) of the partons. Just as the pT-integrated analogues we want to link them to quark and gluon matrix elements using Operator Product Expansion methods in QCD, involving operators of definite twist. The TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Using the expression for TMDs involving nonlocal matrix elements of quark and gluon fields there is a gauge link dependence, which also introduces an inherent process dependence. Using transverse moments, which are specific pT-weightings, we can establish the link with quark and gluon fields including the higher twist ones. We introduce (a finite number of) universal TMDs of definite rank and show how the process dependent TMDs can be written as combinations of these universal functions.
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22

Martin, Anna. "Recent Key Measurements for Accessing the Transverse Spin and Momentum Structure of the Nucleon." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660028. http://dx.doi.org/10.1142/s2010194516600284.

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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.
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23

ECHEVARRÍA, MIGUEL G., AHMAD IDILBI, and IGNAZIO SCIMEMI. "DEFINITION AND EVOLUTION OF TRANSVERSE MOMENTUM DISTRIBUTIONS." International Journal of Modern Physics: Conference Series 20 (January 2012): 92–108. http://dx.doi.org/10.1142/s2010194512009130.

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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.
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24

Allada, Kalyan. "Key Future Measurements of TMDs at Jefferson Lab and Other Facilities." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660035. http://dx.doi.org/10.1142/s2010194516600351.

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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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25

Hosseinkhani, H., M. Modarres, and N. Olanj. "Transverse momentum dependent (TMD) parton distribution functions generated in the modified DGLAP formalism based on the valence-like distributions." International Journal of Modern Physics A 32, no. 19n20 (July 12, 2017): 1750121. http://dx.doi.org/10.1142/s0217751x17501214.

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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.
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26

GAMBERG, LEONARD, ASMITA MUKHERJEE, and P. J. MULDERS. "ANALYTIC PROPERTIES OF MULTI-PARTON POLE MATRIX ELEMENTS AND UNIVERSALITY OF FRAGMENTATION FUNCTIONS." International Journal of Modern Physics: Conference Series 04 (January 2011): 115–25. http://dx.doi.org/10.1142/s2010194511001620.

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Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. We extend this analysis to the case of multi-partonic pole matrix elements. This result is important in the study of the universality of transverse momentum dependent (TMD) fragmentation functions.
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27

Cherednikov, I. O., A. I. Karanikas, and N. G. Stefanis. "Wilson lines in transverse-momentum dependent parton distribution functions with spin degrees of freedom." Nuclear Physics B 840, no. 1-2 (November 2010): 379–404. http://dx.doi.org/10.1016/j.nuclphysb.2010.07.013.

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28

QIAN, XIN. "SINGLE/DOUBLE-SPIN ASYMMETRY MEASUREMENTS OF SEMI-INCLUSIVE PION ELECTRO-PRODUCTION ON A TRANSVERSELY POLARIZED 3He TARGET THROUGH DEEP INELASTIC SCATTERING." Modern Physics Letters A 27, no. 21 (July 6, 2012): 1230021. http://dx.doi.org/10.1142/s0217732312300212.

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Parton distribution functions, which represent the flavor and spin structure of the nucleon, provide invaluable information in illuminating quantum chromodynamics in the confinement region. Among various processes that measure such parton distribution functions, semi-inclusive deep inelastic scattering is regarded as one of the golden channels to access transverse momentum dependent parton distribution functions, which provide a 3D view of the nucleon structure in momentum space. The Jefferson Lab experiment E06-010 focuses on measuring the target single and double spin asymmetries in the [Formula: see text] reaction with a transversely polarized 3 He target in Hall A with a 5.89 GeV electron beam. A leading pion and the scattered electron are detected in coincidence by the left High-Resolution Spectrometer at 16° and the BigBite spectrometer at 30° beam right, respectively. The kinematic coverage concentrates in the valence quark region, x ~ 0.1–0.4, at Q2 ~ 1–3 GeV 2. The Collins and Sivers asymmetries of 3 He and neutron are extracted. In this review, an overview of the experiment and the final results are presented. Furthermore, an upcoming 12-GeV program with a large acceptance solenoidal device and the future possibilities at an electron–ion collider are discussed.
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29

DENISOV, OLEG. "HADRON STRUCTURE STUDY IN FORTHCOMING DRELL–YAN EXPERIMENTS: COMPASS PROJECT AT CERN." Modern Physics Letters A 24, no. 35n37 (December 7, 2009): 3033–44. http://dx.doi.org/10.1142/s0217732309001248.

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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.
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30

Liu, Y. "Lecture Notes on Transverse-momentum-dependent Parton Distribution Function and Soft Functions in the Large-momentum Effective Theory." Acta Physica Polonica B 53, no. 4 (2022): 1. http://dx.doi.org/10.5506/aphyspolb.53.4-a2.

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31

Choudhury, D. K., and Baishali Saikia. "Parton Distribution Functions and models of proton structure functions with self-similarity." International Journal of Modern Physics A 31, no. 34 (December 6, 2016): 1650176. http://dx.doi.org/10.1142/s0217751x16501761.

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Sometime back, a self-similarity based model of the proton structure function at small [Formula: see text] was proposed by Lastovicka. We make reanalysis of this model with most recent HERA data. No significance difference with the earlier analysis is found. Both the analyses have singularity within the kinematical range of [Formula: see text]: [Formula: see text]. We therefore study the model with the additional assumption that it should be singularity free, imposing positivity conditions on the model parameters. This results in a new model which is, however, phenomenologically valid only in a limited low [Formula: see text] range. We therefore make further generalization of the defining self-similar unintegrated Parton Density Function (uPDF) and show that the with proper generalizations and initial conditions on them not only remove the undesired singularity but also results in a structure function with logarithmic growth in [Formula: see text] closer to QCD. The phenomenological range of validity is then found to be much larger than the earlier versions. We also extrapolate the models to large [Formula: see text] in a parameter-free way. The possibility of incorporation of Transverse Momentum Dependent (TMD) PDF in this approach is explored as well.
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32

DI SALVO, ELVIO. "THE QCD PARTON MODEL: A USEFUL APPROXIMATION." Modern Physics Letters A 22, no. 24 (August 10, 2007): 1787–95. http://dx.doi.org/10.1142/s0217732307024152.

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Approximate relations among transverse momentum dependent quark distribution functions are established in the framework of the QCD parton model. The validity of such results survives QCD evolution effects, owing to the Politzer theorem on equations of motion. Furthermore the model fixes an energy scale, involved in the parametrization of the correlator, which determines the Q2 dependence of the azimuthal asymmetries in inclusive reactions. Some of the present data — in particular the sin 2ϕ single spin asymmetry in semi-inclusive deep inelastic scattering (SIDIS) and the cos ϕ asymmetry in unpolarized SIDIS — support model predictions. Further measurements of SIDIS and Drell–Yan asymmetries are suggested, in particular the SIDIS double spin asymmetry, which allows to determine approximately the proton transversity.
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33

MUSCH, B. U., and A. PROKUDIN. "(BESSEL-)WEIGHTED ASYMMETRIES." International Journal of Modern Physics: Conference Series 04 (January 2011): 126–34. http://dx.doi.org/10.1142/s2010194511001632.

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Semi-inclusive deep inelastic scattering experiments allow us to probe the motion of quarks inside the proton in terms of so-called transverse momentum dependent parton distribution functions (TMD PDFs), but the information is convoluted with fragmentation functions (TMD FFs) and soft factors. It has long been known that weighting the measured event counts with powers of the hadron momentum before forming angular asymmetries de-convolutes TMD PDFs and TMD FFs in an elegant way, but this also entails an undesirable sensitivity to high momentum contributions. Using Bessel functions as weights, we find a natural generalization of weighted asymmetries that preserves the de-convolution property and features soft-factor cancellation, yet allows us to be less sensitive to high transverse momenta. The formalism also relates to TMD quantities studied in lattice QCD. We briefly show preliminary lattice results from an exploratory calculation of the Boer-Mulders shift using lattices generated by the MILC and LHP collaborations at a pion mass of 500 MeV.
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34

CONTALBRIGO, MARCO. "OVERVIEW OF EXPERIMENTAL RESULTS FROM HERMES." International Journal of Modern Physics: Conference Series 20 (January 2012): 19–28. http://dx.doi.org/10.1142/s2010194512009051.

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The investigation of the partonic degrees of freedom beyond collinear approximation (3D description) has been gained increasing interest in the last decade. At the HERMES experiment, azimuthal asymmetries in hard exclusive reactions and in semi-inclusive deep-inelastic scattering of electrons and positrons off a (polarized) hydrogen and deuterium target have been measured. Such asymmetries provide new insights on crucial aspects of the parton dynamics. By measuring various hadron types in the initial and final states, flavor sensitivity is achieved. Non zero signals are reported for azimuthal asymmetries with respect the transverse target polarization in real-photon exclusive-electroproduction, which are related (still in a model dependent way) to the elusive quark orbital motion. Evidence is reported of the poorly known transversity function and of naive-T-odd transverse-momentum-dependent parton distribution functions related to spin-orbit effects. Evidence of spin-orbit effects in quark fragmentation is also observed, which are opposite in sign for favored and disfavored processes.
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35

Li, Hui, Xiaoyu Wang, and Zhun Lu. "Single-spin asymmetry ATsin(2ϕ−ϕS) in π−p Drell-Yan process within TMD factorization." EPJ Web of Conferences 258 (2022): 03002. http://dx.doi.org/10.1051/epjconf/202225803002.

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We study the single-spin asymmetry ATsin(2ϕ−ϕS) in the pion-induced Drell-Yan process within the transverse momentum dependent factorization (TMD factorization). The asymmetry can be expressed as the convolution of the Boer-Mulders function and the transversity function. We numerically estimate the asymmetry ATsin(2ϕ−ϕS) at the COMPASS kinematics with the model results for the pion meson distributions from the light-cone wave function approach and the available parametrization for the proton distributions. We also include the TMD evolution formalism both proton and pion parton distribution functions by using two different parametrizations on nonperturbative Sudakov form factor. We find that the asymmetry ATsin(2ϕ−ϕS) as functions of xp, xπ, xF and q⊥ is qualitatively consistent with the recent COMPASS measurement.
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36

Kumano, S., Qin-Tao Song, and O. V. Teryaev. "Tomography and gravitational radii for hadrons by three-dimensional structure functions." EPJ Web of Conferences 181 (2018): 01025. http://dx.doi.org/10.1051/epjconf/201818101025.

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Three-dimensional tomography of hadrons can be investigated by generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions (TMDs), and generalized distribution amplitudes (GDAs). The GDA studies had been only theoretical for a long time because there was no experimental measurement until recently, whereas the GPDs and TMDs have been investigated extensively by deeply vir- tual Compton scattering and semi-inclusive deep inelastic scattering. Here, we report our studies to determine pion GDAs from recent KEKB measurements on the differen- tial cross section of γ*γ → π0π0. Since an exotic-hadron pair can be produced in the final state, the GDAs can be used also for probing internal structure of exotic hadron candidates in future. The other important feature of the GDAs is that the GDAs contain information on form factors of the energy-momentum tensor for quarks and gluons, so that gravitational form factors and radii can be calculated from the determined GDAs. We show the mass (energy) and the mechanical (pressure, shear force) form factors and radii for the pion. Our analysis should be the first attempt for obtaining gravitational form factors and radii of hadrons by analysis of actual experimental measurements. We believe that a new field of gravitational physics is created from the microscopic level in terms of elementary quarks and gluons.
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37

CHEREDNIKOV, I. O., T. MERTENS, and F. F. VAN DER VEKEN. "LOOP SPACE AND EVOLUTION OF THE LIGHT-LIKE WILSON POLYGONS." International Journal of Modern Physics: Conference Series 20 (January 2012): 109–17. http://dx.doi.org/10.1142/s2010194512009142.

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We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom. The renormalization properties and the differential area evolution of these Wilson polygons are studied by making use of the universal Schwinger quantum dynamical approach. We discuss the appropriateness of the dynamical differential equations in the loop space to the study of the energy evolution of the collinear and transverse-momentum dependent parton distribution functions.
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38

MERT AYBAT, S., and TED C. ROGERS. "TMD FACTORIZATION AND EVOLUTION FOR TMD CORRELATION FUNCTIONS." International Journal of Modern Physics: Conference Series 04 (January 2011): 97–105. http://dx.doi.org/10.1142/s2010194511001607.

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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.
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39

Liang, Zuo-Tang. "Three Dimensional Imaging of the Nucleon — TMD (Theory and Phenomenology)." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660008. http://dx.doi.org/10.1142/s2010194516600089.

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This is intend to provide an overview of the theory and phenomenology parts of the TMD (Transverse Momentum Dependent parton distribution and fragmentation functions) studies. By comparing with the theoretical framework that we have for the inclusive deep inelastic lepton-nucleon scattering and the one-dimensional imaging of the nucleon, I try to outline what we need to do in order to construct a comprehensive theoretical framework for semi-inclusive reactions and the three dimensional imaging of the nucleon. After that, I try to give an overview of what we have already achieved and make an outlook for the future.
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40

Parsamyan, Bakur. "Transverse Spin Azimuthal Asymmetries in SIDIS at COMPASS: Multidimensional Analysis." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660029. http://dx.doi.org/10.1142/s2010194516600296.

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COMPASS is a high-energy physics experiment operating at the SPS at CERN. Wide physics program of the experiment comprises study of hadron structure and spectroscopy with high energy muon and hadrons beams. As for the muon-program, one of the important objectives of the COMPASS experiment is the exploration of the transverse spin structure of the nucleon via spin (in)dependent azimuthal asymmetries in single-hadron production in deep inelastic scattering of polarized leptons off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and transversely polarized [Formula: see text] (in 2002, 2003 and 2004) and [Formula: see text] (in 2007 and 2010) targets. The experimental results obtained by COMPASS for unpolarized target azimuthal asymmetries, Sivers and Collins effects and other azimuthal observables play an important role in the general understanding of the three-dimensional nature of the nucleon. Giving access to the entire twsit-2 set of transverse momentum dependent parton distribution functions and fragmentation functions COMPASS data triggers constant theoretical interest and is being widely used in phenomenological analyses and global data fits. In this review main focus is given to the very recent results obtained by the COMPASS collaboration from first ever multi-dimensional extraction of transverse spin asymmetries.
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41

Cichy, Krzysztof, and Martha Constantinou. "A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results." Advances in High Energy Physics 2019 (June 2, 2019): 1–68. http://dx.doi.org/10.1155/2019/3036904.

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Within the theory of Quantum Chromodynamics (QCD), the rich structure of hadrons can be quantitatively characterized, among others, using a basis of universal nonperturbative functions: parton distribution functions (PDFs), generalized parton distributions (GPDs), transverse momentum dependent parton distributions (TMDs), and distribution amplitudes (DAs). For more than half a century, there has been a joint experimental and theoretical effort to obtain these partonic functions. However, the complexity of the strong interactions has placed severe limitations, and first-principle information on these distributions was extracted mostly from their moments computed in Lattice QCD. Recently, breakthrough ideas changed the landscape and several approaches were proposed to access the distributions themselves on the lattice. In this paper, we review in considerable detail approaches directly related to partonic distributions. We highlight a recent idea proposed by X. Ji on extracting quasidistributions that spawned renewed interest in the whole field and sparked the largest amount of numerical studies within Lattice QCD. We discuss theoretical and practical developments, including challenges that had to be overcome, with some yet to be handled. We also review numerical results, including a discussion based on evolving understanding of the underlying concepts and the theoretical and practical progress. Particular attention is given to important aspects that validated the quasidistribution approach, such as renormalization, matching to light-cone distributions, and lattice techniques. In addition to a thorough discussion of quasidistributions, we consider other approaches: hadronic tensor, auxiliary quark methods, pseudodistributions, OPE without OPE, and good lattice cross-sections. In the last part of the paper, we provide a summary and prospects of the field, with emphasis on the necessary conditions to obtain results with controlled uncertainties.
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42

Xu, Qinghua. "Recent results on cold-QCD from RHIC." EPJ Web of Conferences 235 (2020): 03002. http://dx.doi.org/10.1051/epjconf/202023503002.

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Polarized proton-proton collisions at the Relativistic Heavy Ion Collider (RHIC) provide unique opportunities to study the spin structure of the nucleon. We will highlight recent results on the nucleon spin structure from the STAR and PHENIX experiments at RHIC: (1) A sizable gluon polarization in the proton is measured with longitudinal double spin asymmetries of jet and hadron production; (2) Longitudinal single spin asymmetries in W boson production improve constraints on the sea quark polarization. The new spin asymmetry results for W boson confirmed the SU(2) flavor asymmetry of the light sea quark polarization in the proton; (3) Transverse spin effects in hadronic systems offer new implications on parton distribution functions in the collinear and transverse momentum dependent frameworks. We will also discuss near term plans for the STAR forward detector upgrade and prospects for proton-proton and protonion collisions in the years beyond 2021 at STAR.
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43

Echevarria, Miguel G., Ahmad Idilbi, Zhong-Bo Kang, and Ivan Vitev. "Sivers Asymmetry with QCD Evolution." International Journal of Modern Physics: Conference Series 37 (January 2015): 1560025. http://dx.doi.org/10.1142/s2010194515600253.

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We analyze the Sivers asymmetry in both Drell-Yan (DY) production and semi-inclusive deep inelastic scattering (SIDIS), while considering properly defined transverse momentum dependent parton distribution and fragmentation functions and their QCD evolution. After finding a universal non-perturbative spin-independent Sudakov factor that can describe reasonably well the world's data of SIDIS, DY lepton pair and W/Z production in unpolarized scatterings, we perform a global fitting of all the experimental data on the Sivers asymmetry in SIDIS from HERMES, COMPASS and Jefferson Lab. Then we make predictions for the asymmetry in DY lepton pair and W boson production, which could be compared to the future experimental data in order to test the sign change of the Sivers function.
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44

Taghavi, R., and A. Mirjalili. "Extracting the QCD ΛMS¯ parameter in Drell–Yan process using Collins–Soper–Sterman approach." Modern Physics Letters A 32, no. 10 (March 27, 2017): 1750040. http://dx.doi.org/10.1142/s0217732317500407.

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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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45

Abdulov, Nizami, Artem Lipatov, Gennady Lykasov, and Maxim Malyshev. "Determination of the TMD gluon density in a proton using recent LHC data." EPJ Web of Conferences 204 (2019): 05010. http://dx.doi.org/10.1051/epjconf/201920405010.

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Unintegrated (or transverse momentum dependent, TMD) parton distributions in a proton are important in high-energy physics. Using the latest LHC data on the hadron production in pp collisions, we determine the parameters of the initial TMD gluon density, derived in the framework of quark-gluon string model at the low scale μ0 ~ 1 − 2 GeV and refine its large-x behavior using data on the tt̅ production at $\sqrt s = 13\,{\rm{TeV}}$. Then, by using the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation, we extend the obtained TMD gluon density to the whole kinematic region. We tested the proposed TMD gluon density to the inclusive Higgs production in different decay modes, t-channel single top production at the LHC and to the proton structure functions $F_2^c(x,\,{Q^2})$ and $F_2^b(x,\,{Q^2})$ in a wide region of x and Q2. Good agreement with the latest LHC and HERA data is achieved.
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46

ROGERS, TED C. "OVERVIEW OF TRANSVERSE MOMENTUM DEPENDENT FACTORIZATION BREAKING." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460007. http://dx.doi.org/10.1142/s2010194514600076.

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47

Rogers, Ted. "Transverse moments of TMD parton densities and ultraviolet divergences." Modern Physics Letters A 35, no. 37 (September 14, 2020): 2030021. http://dx.doi.org/10.1142/s0217732320300219.

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I review some open questions relating to the large transverse momentum divergences in transverse moments of transverse momentum dependent (TMD) parton correlation functions. I also explain, in an abbreviated and summarized form, recent work that shows that the resulting violations of a commonly used integral relation are not perturbatively suppressed. I argue that this implies a need for more precise definitions for the correlation functions used to describe transverse moments.
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48

COLLINS, JOHN. "TMD THEORY, FACTORIZATION AND EVOLUTION." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460001. http://dx.doi.org/10.1142/s2010194514600015.

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49

Henneman, A. "Bounds on transverse momentum dependent distribution functions." Czechoslovak Journal of Physics 51, S1 (January 2001): A129—A134. http://dx.doi.org/10.1007/s10582-001-0015-7.

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50

PROKUDIN, ALEXEI. "QCD EVOLUTION OF HELICITY AND TRANSVERSITY TMDs." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460016. http://dx.doi.org/10.1142/s2010194514600167.

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We examine the QCD evolution of the helicity and transversity parton distribution functions when including also their dependence on transverse momentum. Using an appropriate definition of these polarized transverse momentum distributions (TMDs), we describe their dependence on the factorization scale and rapidity cutoff, which is essential for phenomenological applications.
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