Journal articles: 'Gluon TMDs'

1

Signori, Andrea. "Gluon TMDs in Quarkonium Production." Few-Body Systems 57, no. 8 (April 22, 2016): 651–55. http://dx.doi.org/10.1007/s00601-016-1102-4.

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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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Boer, Daniël, Cédric Lorcé, Cristian Pisano, and Jian Zhou. "The Gluon Sivers Distribution: Status and Future Prospects." Advances in High Energy Physics 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/371396.

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We review what is currently known about the gluon Sivers distribution and what are the opportunities to learn more about it. Because single transverse spin asymmetries inp↑p→πXprovide only indirect information about the gluon Sivers function through the relation with the quark-gluon and tri-gluon Qiu-Sterman functions, current data from hadronic collisions at RHIC have not yet been translated into a solid constraint on the gluon Sivers function. SIDIS data, including the COMPASS deuteron data, allow for a gluon Sivers contribution of natural size expected from largeNcarguments, which isO(1/Nc)times the nonsinglet quark Sivers contribution. Several very promising processes to measure the gluon Sivers effect directly have been suggested, which besides RHIC investigations, would strongly favor experiments at AFTER@LHC and a possible future Electron-Ion Collider. Due to the inherent process dependence of TMDs, the gluon Sivers TMD probed in the various processes are different linear combinations of two universal gluon Sivers functions that have different behavior under charge conjugation and that therefore satisfy different theoretical constraints. For this reason both hadronic and DIS type of collisions are essential in the study of the role of gluons in transversely polarized protons.

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Massacrier, L., M. Anselmino, R. Arnaldi, S. J. Brodsky, V. Chambert, W. den Dunnen, J. P. Didelez, et al. "Studies of Transverse-Momentum-Dependent Distributions with a Fixed-Target ExpeRiment Using the LHC Beams (AFTER@LHC)." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660107. http://dx.doi.org/10.1142/s2010194516601071.

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We report on the studies of Transverse-Momentum-Dependent distributions (TMDs) at a future fixed-target experiment –AFTER@LHC– using the [Formula: see text] or Pb ion LHC beams, which would be the most energetic fixed-target experiment ever performed. AFTER@LHC opens new domains of particle and nuclear physics by complementing collider-mode experiments, in particular those of RHIC and the EIC projects. Both with an extracted beam by a bent crystal or with an internal gas target, the luminosity achieved by AFTER@LHC surpasses that of RHIC by up to 3 orders of magnitude. With an unpolarised target, it allows for measurements of TMDs such as the Boer-Mulders quark distributions and the distribution of unpolarised and linearly polarised gluons in unpolarised protons. Using polarised targets, one can access the quark and gluon Sivers TMDs through single transverse-spin asymmetries in Drell-Yan and quarkonium production. In terms of kinematics, the fixed-target mode combined with a detector covering [Formula: see text] allows one to measure these asymmetries at large [Formula: see text] in the polarised nucleon.

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5

Lansberg, J. P. "Back-to-Back Isolated Photon-Quarkonium Production at the LHC and the Transverse-Momentum-Dependent Distributions of the Gluons in the Proton." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660015. http://dx.doi.org/10.1142/s2010194516600156.

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The study of isolated heavy quarkonia, such as [Formula: see text] and [Formula: see text], produced in association with a photon in proton-proton collisions at the LHC, is probably the optimal way to get right away a first experimental determination of two gluon transverse-momentum-dependent distribution (TMDs) in an unpolarized proton, [Formula: see text] and [Formula: see text], the latter giving the distribution of linearly polarized gluons. To substantiante this, we calculate the transverse-momentum-dependent effects that arise in the process under study and discuss the feasibility of their measurements.

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Altinoluk, T., R. Boussarie, C. Marquet, and P. Taels. "Gluon TMDs from Forward $pA$ Collisions in the CGC." Acta Physica Polonica B 50, no. 6 (2019): 969. http://dx.doi.org/10.5506/aphyspolb.50.969.

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7

Echevarria, Miguel G. "T-Odd Gluon TMDs Inside a Transversely Polarized Hadron." Few-Body Systems 57, no. 8 (March 31, 2016): 645–49. http://dx.doi.org/10.1007/s00601-016-1088-y.

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8

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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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

Bhattacharya, Shohini, Andreas Metz, Vikash Kumar Ojha, Jeng-Yuan Tsai, and Jian Zhou. "Exclusive double quarkonium production and generalized TMDs of gluons." Physics Letters B 833 (October 2022): 137383. http://dx.doi.org/10.1016/j.physletb.2022.137383.

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11

Yazdanpanah, M. M., A. Mirjalili, and A. Behjat Ramezani. "Mass and energy dependence of the transverse momentum densities in covariant parton model." Modern Physics Letters A 30, no. 27 (August 13, 2015): 1550133. http://dx.doi.org/10.1142/s0217732315501333.

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The parton densities which are dependent on transverse momentum, open a way to understand better the structure of quarks and gluons in a more complete way. We are investigating a method based on the covariant quark model which enables us to extract the transverse momentum dependent (TMD) densities from the usual parton densities which are just dependent on the longitudinal momentum. In continuation, we obtain the dependence of the TMDs on binding energy and the mass of quarks. We do some calculations to obtain the TMDs in the unpolarized case while the mass and binding energy of partons are varying. Considering these effects, the results for TMDs are in good agreement with the results of the recent related models.

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12

CHEN, JIAN-PING. "EXPERIMENTAL STUDY OF SINGLE SPIN ASYMMETRIES AND TMDs." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460021. http://dx.doi.org/10.1142/s2010194514600210.

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Single Spin Asymmetries and Transverse Momentum Dependent (TMD) distribution study has been one of the main focuses of hadron physics in recent years. The initial exploratory Semi-Inclusive Deep-Inelastic-Scattering (SIDIS) experiments with transversely polarized proton and deuteron targets from HERMES and COMPASS attracted great attention and lead to very active efforts in both experiments and theory. A SIDIS experiment on the neutron with a polarized 3 He target was performed at JLab. Recently published results as well as new preliminary results are shown. Precision TMD experiments are planned at JLab after the 12 GeV energy upgrade. Three approved experiments with a new SoLID spectrometer on both the proton and neutron will provide high precision TMD data in the valence quark region. In the long-term future, an Electron-Ion Collider (EIC) as proposed in US (MEIC@JLab and E-RHIC@BNL) will provide precision TMD data of the gluons and the sea. A new opportunity just emerged in China that a low-energy EIC (1st stage EIC@HIAF) may provide precision TMD data in the sea quark region, complementary to the proposed EIC in US.

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13

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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14

Radici, Marco. "Electron Ion Collider: 3D-Imaging the Nucleon." EPJ Web of Conferences 182 (2018): 02062. http://dx.doi.org/10.1051/epjconf/201818202062.

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The Electron Ion Collider (EIC) is the project for a new US-based, high-energy, high-luminosity facility, capable of a versatile range of beam energies, polarizations, and ion species. Its primary goal is to precisely image quarks and gluons and their interactions inside hadrons, in order to investigate their confined dynamics and elucidate how visible matter is made at its most fundamental level. I will introduce the main physics questions addressed by such a facility, and give some more details on the topic of Transverse Momentum Dependent parton distributions (TMDs).

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Radici, Marco. "Electron Ion Collider: 3D-Imaging the Nucleon." EPJ Web of Conferences 182 (2018): 02103. http://dx.doi.org/10.1051/epjconf/201818202103.

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The Electron Ion Collider (EIC) is the project for a new US-based, high-energy, high-luminosity facility, capable of a versatile range of beam energies, polarizations, and ion species. Its primary goal is to precisely image quarks and gluons and their interactions inside hadrons, in order to investigate their confined dynamics and elucidate how visible matter is made at its most fundamental level. I will introduce the main physics questions addressed by such a facility, and give some more details on the topic of Transverse Momentum Dependent parton distributions (TMDs).

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16

Soudi, Ismail, and Abhijit Majumder. "Azimuthal anisotropies at high-p_T from transverse momentum dependent (TMD) parton distribution and fragmentation functions." EPJ Web of Conferences 296 (2024): 13015. http://dx.doi.org/10.1051/epjconf/202429613015.

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Unpolarized protons can generate transversely polarized quarks or linearly polarized gluons through a distribution known as the Boer-Mulders’ function. The fragmentation of similarly polarized partons to unpolarized hadrons is called the Collins’ function. Both of these functions include correlations between the spin or polarization and the relative transverse momentum of the incoming parton or outgoing hadron, with respect to the parent particle. We explore the effect of including these and other TMDs on the production of high-pT (unpolarized) hadron production from (unpolarized) proton-proton scattering. The resulting initial state anisotropies, modulated with similar final state effects, may account for the observed azimuthal anisotropy of the produced high transverse momentum hadrons, without modification to the angle integrated spectra (RAA). This may be an explanation for the existence of a v2 in high-pT hadron spectra in p-A collisions without any observable nuclear modification of the spectra.

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17

Schindler, Stella T., Iain W. Stewart, and Yong Zhao. "One-loop matching for gluon lattice TMDs." Journal of High Energy Physics 2022, no. 8 (August 5, 2022). http://dx.doi.org/10.1007/jhep08(2022)084.

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Abstract Transverse-momentum-dependent parton distributions (TMDs) can be calculated from first principles by computing a related set of Euclidean lattice observables and connecting them via a factorization formula. This work focuses on the leading-power factorization formula connecting the lattice quasi-TMD and continuum Collins TMD for gluons. We calculate the one-loop gluon matching coefficient, which is known to be independent of spin and exhibits no mixing with quarks. We demonstrate that this coefficient satisfies Casimir scaling with respect to the quark matching coefficient at one-loop order. Our result facilitates reliable lattice QCD calculations of gluon TMDs.

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18

Jung, Hannes, Sara Taheri Monfared, and Thomas Wening. "Photon TMDs from uPDFevolv." SciPost Physics Proceedings, no. 8 (July 13, 2022). http://dx.doi.org/10.21468/scipostphysproc.8.132.

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We present photon TMDs generated using the Parton Branching Method with QED evolution. We discuss the TMD's properties and compare it to the gluon TMD. Two sets of TMDs differing in their initial evolution scale and the choice of the renormalisation scale are defined and compared to each other.

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19

Altinoluk, Tolga, Guillaume Beuf, Alina Czajka, and Cyrille Marquet. "Back-to-back dijet production in DIS at next-to-eikonal accuracy and twist-3 gluon TMDs." Physical Review D 111, no. 1 (January 10, 2025). https://doi.org/10.1103/physrevd.111.014010.

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We consider dijet production in deep inelastic scattering at small x, on a purely gluonic unpolarized target. Starting from earlier results obtained at next-to-eikonal accuracy in the high-energy limit, we perform the expansion in the back-to-back dijet limit, at next-to-leading power accuracy. We rewrite our results in the language of transverse-momentum-dependent (TMD) factorization, in terms of twist-2 and twist-3 TMD gluon distributions (gluon TMDs). Among the next-to-eikonal corrections, we find in particular twist-2 contributions corresponding to the x dependent phase of the twist-2 gluon TMDs. We also find two types of twist-3 unpolarized gluon TMDs, as well as correlators of three gluon field strength tensors. Published by the American Physical Society 2025

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20

Boer, Daniël. "Gluon TMDs in Quarkonium Production." Few-Body Systems 58, no. 2 (January 11, 2017). http://dx.doi.org/10.1007/s00601-016-1198-6.

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Bacchetta, Alessandro, Francesco Giovanni Celiberto, Marco Radici, and Pieter Taels. "Transverse-momentum-dependent gluon distribution functions in a spectator model." European Physical Journal C 80, no. 8 (August 2020). http://dx.doi.org/10.1140/epjc/s10052-020-8327-6.

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Abstract We present a model calculation of transverse-momentum-dependent distributions (TMDs) of gluons in the nucleon. The model is based on the assumption that a nucleon can emit a gluon, and what remains after the emission is treated as a single spectator particle. This spectator particle is considered to be on-shell, but its mass is allowed to take a continuous range of values, described by a spectral function. The nucleon-gluon-spectator coupling is described by an effective vertex containing two form factors. We fix the model parameters to obtain the best agreement with collinear gluon distributions extracted from global fits. We study the tomography in momentum space of gluons inside nucleons for various combinations of their polarizations. These can be used to make predictions of observables relevant for gluon TMD studies at current and future collider facilities.

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22

Ebert, Markus A., Stella T. Schindler, Iain W. Stewart, and Yong Zhao. "Factorization connecting continuum & lattice TMDs." Journal of High Energy Physics 2022, no. 4 (April 2022). http://dx.doi.org/10.1007/jhep04(2022)178.

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Abstract Transverse-momentum-dependent parton distribution functions (TMDs) can be studied from first principles by a perturbative matching onto lattice-calculable quantities: so-called lattice TMDs, which are a class of equal-time correlators that includes quasi-TMDs and TMDs in the Lorentz-invariant approach. We introduce a general correlator that includes as special cases these two Lattice TMDs and continuum TMDs, like the Collins scheme. Then, to facilitate the derivation of a factorization relation between lattice and continuum TMDs, we construct a new scheme, the Large Rapidity (LR) scheme, intermediate between the Collins and quasi-TMDs. The LR and Collins schemes differ only by an order of limits, and can be matched onto one another by a multiplicative kernel. We show that this same matching also holds between quasi and Collins TMDs, which enables us to prove a factorization relation between these quantities to all orders in αs. Our results imply that there is no mixing between various quark flavors or gluons when matching Collins and quasi TMDs, making the lattice calculation of individual flavors and gluon TMDs easier than anticipated. We cross-check these results explicitly at one loop and discuss implications for other physical-to-lattice scheme factorizations.

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23

Balitsky, Ian. "Drell-Yan angular lepton distributions at small x from TMD factorization." Journal of High Energy Physics 2021, no. 9 (September 2021). http://dx.doi.org/10.1007/jhep09(2021)022.

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Abstract The Drell-Yan process is studied in the framework of TMD factorization in the Sudakov region s » Q2 » $$ {q}_{\perp}^2 $$ q ⊥ 2 corresponding to recent LHC experiments with Q2 of order of mass of Z-boson and transverse momentum of DY pair ∼ few tens GeV. The DY hadronic tensors are expressed in terms of quark and quark-gluon TMDs with $$ \frac{1}{Q^2} $$ 1 Q 2 and $$ \frac{1}{N_c^2} $$ 1 N c 2 accuracy. It is demonstrated that in the leading order in Nc the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting hadronic tensors depend on two leading-twist TMDs: f1 responsible for total DY cross section, and Boer-Mulders function $$ {h}_1^{\perp } $$ h 1 ⊥ . The corresponding qualitative and semi-quantitative predictions seem to agree with LHC data on five angular coefficients A0− A4 of DY pair production. The remaining three coefficients A5− A7 are determined by quark-quark-gluon TMDs multiplied by extra $$ \frac{1}{N_c} $$ 1 N c so they appear to be relatively small in accordance with LHC results.

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24

Scarpa, Florent, Daniël Boer, Miguel G. Echevarria, Jean-Philippe Lansberg, Cristian Pisano, and Marc Schlegel. "Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC." European Physical Journal C 80, no. 2 (February 2020). http://dx.doi.org/10.1140/epjc/s10052-020-7619-1.

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Abstract $$J/\psi $$J/ψ- or $$\Upsilon $$Υ-pair production at the LHC are promising processes to study the gluon transverse momentum distributions (TMDs) which remain very poorly known. In this article, we improve on previous results by including the TMD evolution in the computation of the observables such as the pair-transverse-momentum spectrum and asymmetries arising from the linear polarization of gluons inside unpolarized protons. We show that the azimuthal asymmetries generated by the gluon polarization are reduced compared to the tree level case but are still of measurable size (in the 5–10% range). Such asymmetries should be measurable in the available data sets of $$J/\psi $$J/ψ pairs and in the future data sets of the high-luminosity LHC for $$\Upsilon $$Υ pairs.

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Kumano, Shunzo, and Qin-Tao Song. "Gluon transversity and TMDs for spin-1 hadrons." Suplemento de la Revista Mexicana de Física 3, no. 3 (May 24, 2022). http://dx.doi.org/10.31349/suplrevmexfis.3.0308097.

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We explain a gluon transversity, transverse-momentum-dependent parton distribution functions (TMDs), and parton distribution functions (PDFs) for spin-1 hadrons. The gluon transversity exists in hadrons with spin more than or equal to one, and it does not exist in the spin-1/2 nucleons. Since there is no direct contribution from the nucleons, it is an appropriate quantity to probe an exotic component in the spin-1 deuteron beyond a simple bound system of the nucleons. We show how the gluon transversity can be measured at hadron accelerator facilities by the Drell-Yan process in addition to lepton-accelerator experiments. Next, possible TMDs are explained for the spin-1 hadrons at the twists 3 and 4 in addition to twist-2 ones by considering tensor polarizations. We found that 30 TMDs exist in the tensor-polarized spin-1 hadron at the twists 3 and 4 in addition to 10 TMDs at the twist 2. There are 3 collinear PDFs at the twists 3 and 4. We also indicate that the corresponding TMD fragmentation functions exist at the twists 3 and 4. Due to the time-reversal invariance in the collinear PDFs, there are new sum rules on the time-reversal odd TMDs. In addition, we obtained a useful twist-2 relation, a sum rule, and relations with multiparton distribution functions by using the operator product expansion and the equation of motion for quarks. These findings are valuable for experimental investigations on polarized deuteron structure functions in 2020's and 2030's at world accelerator facilities.

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Bacchetta, Alessandro, Francesco Giovanni Celiberto, Marco Radici, and Pieter Taels. "A spectator-model way to transverse-momentum-dependent gluon distribution functions." SciPost Physics Proceedings, no. 8 (July 12, 2022). http://dx.doi.org/10.21468/scipostphysproc.8.040.

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We present exploratory analyses of the 3D gluon content of the proton via a study of unpolarized and polarized gluon TMDs at twist-2, calculated in a spectator model for the parent nucleon. Our approach embodies a flexible parametrization for the spectator-mass function, suited to describe both moderate and small-x effects. All these studies can serve as a useful guidance in the investigation of the gluon dynamics inside nucleons and nuclei, which constitutes one of the major goals of new-generation colliding machines, as the EIC, the HL-LHC, NICA, and the FPF.

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Banu, Khatiza, Asmita Mukherjee, Amol Pawar, and Sangem Rajesh. "Unraveling gluon TMDs in J/ψ and pion production at the EIC." Physical Review D 110, no. 5 (September 11, 2024). http://dx.doi.org/10.1103/physrevd.110.054009.

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We investigate the azimuthal asymmetries such as cos2ϕT and Sivers symmetry for J/ψ and π± production in electron-proton scattering, focusing on scenarios where the J/ψ and the pion are produced in an almost back-to-back configuration. The electron is unpolarized, while the proton can be unpolarized or transversely polarized. For the J/ψ formation, we use nonrelativistic QCD (NRQCD), while π± is formed due to parton fragmentation. In this kinematics, we utilize the transverse momentum-dependent factorization framework to calculate the cross sections and asymmetries. We consider both quark and gluon-initiated processes and show that the gluon contribution dominates. In this work, we used the generalized parton model (GPM) for the transverse momentum distribution (TMD) parametrizations and did not consider the effect of TMD evolution. We provide numerical estimates of the upper bounds on the azimuthal asymmetries, as well as employ a Gaussian parametrization for the gluon TMDs, within the kinematical region accessible by the upcoming Electron-Ion Collider (EIC). Published by the American Physical Society 2024

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Lelek, Aleksandra. "Drell-Yan $p_{\bot}$ with NLO-matched Parton Branching TMDs at energies from fixed-target to LHC." SciPost Physics Proceedings, no. 8 (July 11, 2022). http://dx.doi.org/10.21468/scipostphysproc.8.029.

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The description of the Drell-Yan (DY) transverse momentum spectrum requires matching of fixed order QCD calculations with soft gluon resummation up to all orders in the QCD coupling. It has been noticed in the literature that a consistent description of DY data in a wide kinematic regime from fixed-target to LHC energies is problematic. In this work the predictions for transverse momentum spectrum of DY data coming from experiments in very different kinematic ranges (NuSea, R209, Phenix, LHC 8 TeV and 13 TeV center-of-mass energies \sqrt{s}s) are calculated by applying transverse momentum dependent (TMD) parton distributions obtained from the Parton Branching (PB) method, combined with the next-to-leading-order (NLO) calculation of the hard process in the MCatNLO method. We discuss the problems involved in matching of the fixed order calculation and resummation, especially in the moderate to low mass and p_{\bot}p⊥ region accessible at fixed target experiments. We find that at low DY mass and low \sqrt{s}s even in the region of p_{\bot}/Q\sim 1p⊥/Q∼1 the contribution of multiple soft gluon emissions (included in the PB-TMDs) is essential to describe the measurements, while at larger masses and LHC energies the contribution from soft gluons in the region of p_{\bot}/Q\sim 1p⊥/Q∼1 is small.

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Boer, Daniël, Yoshikazu Hagiwara, Jian Zhou, and Ya-jin Zhou. "Scale evolution of T-odd gluon TMDs at small x." Physical Review D 105, no. 9 (May 17, 2022). http://dx.doi.org/10.1103/physrevd.105.096017.

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30

Cotogno, Sabrina, Tom van Daal, and Piet J. Mulders. "Positivity bounds on gluon TMDs for hadrons of spin ≤ 1." Journal of High Energy Physics 2017, no. 11 (November 2017). http://dx.doi.org/10.1007/jhep11(2017)185.

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31

Boer, Daniël, Sabrina Cotogno, Tom van Daal, Piet J. Mulders, Andrea Signori, and Ya-Jin Zhou. "Gluon and Wilson loop TMDs for hadrons of spin ≤ 1." Journal of High Energy Physics 2016, no. 10 (October 2016). http://dx.doi.org/10.1007/jhep10(2016)013.

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32

Balitsky, I. "Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)046.

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Abstract The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $$ s\gg {Q}^2\gg {q}_{\perp}^2 $$ s ≫ Q 2 ≫ q ⊥ 2 with $$ \frac{1}{Q^2} $$ 1 Q 2 accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading order in Nc the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: f1 responsible for total DY cross section, and Boer-Mulders function $$ {h}_1^{\perp } $$ h 1 ⊥ . The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.

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Martinez, A. Bermudez, P. L. S. Connor, D. Dominguez Damiani, L. I. Estevez Banos, F. Hautmann, H. Jung, J. Lidrych, et al. "The transverse momentum spectrum of low mass Drell–Yan production at next-to-leading order in the parton branching method." European Physical Journal C 80, no. 7 (July 2020). http://dx.doi.org/10.1140/epjc/s10052-020-8136-y.

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Abstract It has been observed in the literature that measurements of low-mass Drell–Yan (DY) transverse momentum spectra at low center-of-mass energies $$\sqrt{s}$$s are not well described by perturbative QCD calculations in collinear factorization in the region where transverse momenta are comparable with the DY mass. We examine this issue from the standpoint of the Parton Branching (PB) method, combining next-to-leading-order (NLO) calculations of the hard process with the evolution of transverse momentum dependent (TMD) parton distributions. We compare our predictions with experimental measurements at low DY mass, and find very good agreement. In addition we use the low mass DY measurements at low $$\sqrt{s}$$s to determine the width $$q_s$$qs of the intrinsic Gauss distribution of the PB-TMDs at low evolution scales. We find values close to what has earlier been used in applications of PB-TMDs to high-energy processes at the Large Hadron Collider (LHC) and HERA. We find that at low DY mass and low $$\sqrt{s}$$s even in the region of $$p_\mathrm{T}/m_\mathrm{DY}\sim 1$$pT/mDY∼1 the contribution of multiple soft gluon emissions (included in the PB-TMDs) is essential to describe the measurements, while at larger masses ($$m_\mathrm{DY}\sim m_{{\mathrm{Z}}}$$mDY∼mZ) and LHC energies the contribution from soft gluons in the region of $$p_\mathrm{T}/m_\mathrm{DY}\sim 1$$pT/mDY∼1 is small.

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Jana, Sujit, Vikash Kumar Ojha, and Tanmay Maji. "Gluon Generalized TMDs and Wigner Distributions in boost invariant longitudinal space." Nuclear Physics A, September 2024, 122958. http://dx.doi.org/10.1016/j.nuclphysa.2024.122958.

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Altinoluk, Tolga, Renaud Boussarie, Cyrille Marquet, and Pieter Taels. "Photoproduction of three jets in the CGC: gluon TMDs and dilute limit." Journal of High Energy Physics 2020, no. 7 (July 2020). http://dx.doi.org/10.1007/jhep07(2020)143.

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Liu, Huachao, Xiupeng Xie, and Zhun Lu. "Gluon TMDs from J/ψ production in longitudinally polarized deeply inelastic scattering." Physics Letters B, January 2024, 138439. http://dx.doi.org/10.1016/j.physletb.2023.138439.

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Kumano, Shunzo, and Qin-Tao Song. "Transverse-momentum-dependent parton distribution functions for spin-1 hadrons." SciPost Physics Proceedings, no. 8 (July 14, 2022). http://dx.doi.org/10.21468/scipostphysproc.8.174.

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We show transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions by taking the decomposition of a quark correlation function in the Lorentz-invariant way with the conditions of Hermiticity and parity invariance. We found 30 new TMDs in the tensor-polarized spin-1 hadron at twists 3 and 4 in addition to 10 TMDs at twist 2. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtained new sum rules for the time-reversal-odd structure functions, {\int d^2 k_T g_{LT} = \int d^2 k_T h_{LL} = \int d^2 k_T h_{3LL} =0}∫d2kTgLT=∫d2kThLL=∫d2kTh3LL=0, at twists 3 and 4. We also indicated that transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs can probe color degrees of freedom, so that they are valuable in providing unique opportunities for creating interdisciplinary physics fields such as gluon condensate, color Aharonov-Bohm effect, and color entanglement. We also found three new collinear PDFs at twists 3 and 4, and a twist-2 relation and a sum rule were derived in analogy to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule on the structure function {g_2}g2.

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38

Zhao, Yong. "Transverse Momentum Distributions from Lattice QCD without Wilson Lines." Physical Review Letters 133, no. 24 (December 13, 2024). https://doi.org/10.1103/physrevlett.133.241904.

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The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge invariantly as the correlators of Coulomb-gauge-dressed fields, which reduce to the standard TMD correlators under principal-value prescription in the infinite boost limit. In the framework of large-momentum effective theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using soft collinear effective theory and verified at one-loop order. Compared to the currently used gauge-invariant correlators, this new method can substantially improve statistical precision and simplify renormalization for the time-reversal-even TMDs, which will greatly enhance the predicative power of lattice QCD in the nonperturbative region. Published by the American Physical Society 2024

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Dong, Xin, Yuanjing Ji, Matthew Kelsey, Sooraj Radhakrishnan, Ernst Sichtermann, and Yuxiang Zhao. "Probing gluon TMDs with reconstructed and tagged heavy flavor hadron pairs at the EIC." Physical Review D 107, no. 7 (April 19, 2023). http://dx.doi.org/10.1103/physrevd.107.074022.

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Bacchetta, Alessandro, Daniël Boer, Cristian Pisano, and Pieter Taels. "Gluon TMDs and NRQCD matrix elements in $${J}{/}{\psi }$$J/ψ production at an EIC." European Physical Journal C 80, no. 1 (January 2020). http://dx.doi.org/10.1140/epjc/s10052-020-7620-8.

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Kishore, Raj, Asmita Mukherjee, Amol Pawar, Sangem Rajesh, and Mariyah Siddiqah. "TMD evolution effect on cos2ϕ azimuthal asymmetry in a back-to-back production of J/ψ and a jet at the EIC." Physical Review D 111, no. 1 (January 8, 2025). https://doi.org/10.1103/physrevd.111.014003.

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A back-to-back semi-inclusive J/ψ+jet production is a promising process to study gluon transverse momentum distribution (TMD) at the future electron-ion collider. A back-to-back configuration allows a higher transverse momentum for J/ψ. We present an extension of a previous work where we studied cos2ϕ azimuthal asymmetry within the TMD factorization framework for this process. We present and compare the effect of TMD evolution on the asymmetry, in two approaches that differ in the parametrization of the perturbative tails of the TMDs and the nonperturbative factors. We show that the asymmetry depends on the parametrizations of the nonperturbative Sudakov factors in the larger bT region and on the perturbative part of the evolution kernel. We use nonrelativistic QCD to estimate the J/ψ production and show the effect of using different long-distance matrix element sets. Overall, the asymmetry after incorporating TMD evolution is small, but increases with the transverse momentum imbalance of the J/ψ-jet pair. Published by the American Physical Society 2025

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Kovchegov, Yuri V., and M. Gabriel Santiago. "Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution." Journal of High Energy Physics 2021, no. 11 (November 2021). http://dx.doi.org/10.1007/jhep11(2021)200.

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Abstract We apply the formalism developed earlier [1, 2] for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken x to construct the small-x asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order: this object can be used to study a variety of quark TMDs at small x. We then express the quark Sivers function in terms of dipole scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant (eikonal) term which contributes to the quark Sivers function at small x is the spin-dependent odderon, confirming the re- cent results of Dong, Zheng and Zhou [3]. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou [4] (see also [5]). We also analyze the sub-eikonal corrections to the quark Sivers function using the constructed “polarized Wilson line” operator. We derive new small-x evolution equations re-summing double-logarithmic powers of αs ln2(1/x) with αs the strong coupling constant. We solve the corresponding novel evolution equations in the large-Nc limit, obtaining a sub-eikonal correction to the spin-dependent odderon contribution. We conclude that the quark Sivers function at small x receives contributions from two terms and is given by$$ {f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots $$ f 1 T ⊥ q x k T 2 = C O x k T 2 1 x + C 1 k T 2 1 x 0 + ⋯ with the function CO(x,$$ {k}_T^2 $$ k T 2 ) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order-x) corrections.

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Abdulhamid, M. I., M. A. Al-Mashad, A. Bermudez Martinez, G. Bonomelli, I. Bubanja, N. Crnković, F. Colombina, et al. "Azimuthal correlations of high transverse momentum jets at next-to-leading order in the parton branching method." European Physical Journal C 82, no. 1 (January 2022). http://dx.doi.org/10.1140/epjc/s10052-022-09997-1.

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AbstractThe azimuthal correlation, $$\Delta \phi _{12}$$ Δ ϕ 12 , of high transverse momentum jets in pp collisions at $$\sqrt{s}=13$$ s = 13 TeV is studied by applying PB-TMD distributions to NLO calculations via MCatNLO together with the PB-TMD parton shower. A very good description of the cross section as a function of $$\Delta \phi _{12}$$ Δ ϕ 12 is observed. In the back-to-back region of $${\Delta \phi _{12}}\rightarrow \pi $$ Δ ϕ 12 → π , a very good agreement is observed with the PB-TMD Set 2 distributions while significant deviations are obtained with the PB-TMD Set 1 distributions. Set 1 uses the evolution scale while Set 2 uses transverse momentum as an argument in $$\alpha _\mathrm {s}$$ α s , and the above observation therefore confirms the importance of an appropriate soft-gluon coupling in angular ordered parton evolution. The total uncertainties of the predictions are dominated by the scale uncertainties of the matrix element, while the uncertainties coming from the PB-TMDs and the corresponding PB-TMD shower are very small. The $$\Delta \phi _{12}$$ Δ ϕ 12 measurements are also compared with predictions using MCatNLO together Pythia8, illustrating the importance of details of the parton shower evolution.

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Journal articles on the topic 'Gluon TMDs'

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