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1

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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2

Zheng, Liang, E. C. Aschenauer, J. H. Lee, Bo-Wen Xiao, and Zhong-Bao Yin. "Measuring Gluon Sivers Function at a Future Electron-Ion Collider." International Journal of Modern Physics: Conference Series 46 (January 2018): 1860021. http://dx.doi.org/10.1142/s2010194518600212.

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In this work, we present a systematic study on the feasibility of probing the largely unexplored gluon Sivers function (GSF) based on the open charm production, charged dihadron and dijet method at a future high energy, high luminosity Electron-Ion Collider (EIC). Sivers function describes the anisotropy of parton distributions inside a transversely polarized nucleon in the momentum space and provides us a complete picture of the 2+1D structure of the nucleons. It is proposed that the GSF can be studied through the single spin asymmetry (SSA) measurement in the photon-gluon fusion channel with electron proton collisions at the EIC. Using a well tuned Monte Carlo model for deep inelastic scatterings, we estimate the possible constraints of the gluon Sivers effect one can draw from the future EIC data. Comparisons of all the possible measurements further illustrate that the dijet method is the most promising way to demonstrate the presence of GSF and pin down its evolution effect.
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3

Yao, Xiaojun, Yoshikazu Hagiwara, and Yoshitaka Hatta. "Computing the gluon Sivers function at small-x." Physics Letters B 790 (March 2019): 361–66. http://dx.doi.org/10.1016/j.physletb.2019.01.029.

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4

Klein, Andi. "Measuring the Sea Quark Sivers Asymmetry: The E1039 Experiment at Fermilab." International Journal of Modern Physics: Conference Series 37 (January 2015): 1560064. http://dx.doi.org/10.1142/s2010194515600642.

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One of the continuing puzzles in QCD is the origin of the nucleon spin. All of the existing experimental data suggest that the contributions from the quark and gluon spins account only for about 50% of the nucleon spin. In order to account for the remaining 50%, one has to include the orbital angular momentum of the quarks and gluons. One way to establish if quarks carry significant angular momentum, is to perform a measurement of the Sivers function, which describes the correlation of the spin direction of the nucleon with the transverse momentum of the quark. We will describe the E1039 experiment at Fermilab, which will measure the Sivers asymmetry of the sea quarks via the Drell-Yan process, using a 120 GeV unpolarized proton beam on a transversely polarized NH 3 target.
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5

MUKHERJEE, ASMITA. "SIVERS ASYMMETRY IN e + p↑ → e + J/ψ + X." International Journal of Modern Physics: Conference Series 20 (January 2012): 162–67. http://dx.doi.org/10.1142/s2010194512009208.

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A recent investigation of the single spin asymmetry (SSA) in low virtuality electroproduction/photoproduction of J/ψ in color evaporation model is presented. It is shown that the asymmetry is sizable and can be used as a probe for the still unknown gluon Sivers function.
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6

Guskov, Alexey, Amaresh Datta, Anton Karpishkov, Igor Denisenko, and Vladimir Saleev. "Probing Gluons with the Future Spin Physics Detector." Physics 5, no. 3 (June 27, 2023): 672–87. http://dx.doi.org/10.3390/physics5030044.

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In this paper, we review the physics studies to be performed with the Spin Physics Detector (SPD) at the Nuclotron-based Ion Collider fAcility (NICA) which is a multi-purpose experiment designed to study nucleon spin structure in the three dimensions. With capabilities to collide polarized protons and deuterons with center-of-mass energy up to 27 GeV and luminosity up to 1032cm−2s−1 for protons (an order of magnitude less for deuterons), the experiment is considered to allow measurements of cross-sections and spin asymmetries of hadronic processes sensitive to the unpolarized and various polarized (helicity, Sivers, Boer-Mulders) gluon distributions inside the nucleons. Results from the SPD will be complimentary to the present high-energy spin experiments at the RHIC (Relativistic Heavy Ion Collider) facility or future experiments such as the Electron-Ion Collider (EIC) at BNL (Brookhaven National Laboratory) and the AFTER experiment at the LHC (Large Hadron Collider) in understanding the spin structure of the basic building blocks of visible matter. Monte Carlo simulation-based results presented here demonstrate the impact of the SPD asymmetry measurements on gluon helicity parton distribution function (PDF) and gluon Sivers functions. With polarized deuteron collisions, the SPD is expected to be the unique laboratory for probing tensor-polarized gluon distributions. Additionally, there are possibilities of colliding other light nuclei, such as carbon, at reduced collision energy and luminosity during the first stage of the experiment.
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7

KANG, ZHONG-BO, and JIAN-WEI QIU. "QCD EVOLUTION OF NAIVE-TIME-REVERSAL-ODD QUARK-GLUON CORRELATION FUNCTIONS." International Journal of Modern Physics: Conference Series 20 (January 2012): 118–28. http://dx.doi.org/10.1142/s2010194512009154.

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In this talk, we examine the existing calculations of QCD evolution kernels for the scale dependence of two sets of twist-3 quark-gluon correlation functions, Tq,F(x, x) and [Formula: see text], which are the first transverse-momentum-moment of the naive-time-reversal-odd Sivers and Boer-Mulders function, respectively. The evolution kernels at the leading order in strong coupling constant αs were derived by several groups with apparent differences. We identify the sources of discrepancies and are able to reconcile the results from various groups.
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8

Wang, Xiaorong, and Feng Wei. "AN of Single Heavy Flavor Decay Muon in the PHENIX Experiment at RHIC." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660043. http://dx.doi.org/10.1142/s2010194516600430.

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Transverse single-spin asymmetries provide valuable information about the spin structure of the nucleon. At RHIC energies, heavy-flavor production is dominated by gluon-gluon fusion, and the subsequent decay into high [Formula: see text] electrons or muons can be observed statistically in a collider detector like PHENIX. The transverse single-spin asymmetry in heavy-flavor production originates from the initial state correlation between the internal transverse momentum of the parton and the transverse spin of the nucleon (similar with the known Sivers effect). The measurement of transverse single-spin asymmetry of single muons from heavy flavor decay at RHIC serves as a clean probe and would provide important information on the gluon Sivers function. In 2012, the PHENIX experiment collected 9.2 [Formula: see text] integrated luminosity in transversely polarized [Formula: see text] collisions at [Formula: see text] = 200 GeV with a polarization of [Formula: see text]. The signal-to-background ratio was improved by a factor of two compared to the previous RHIC 2006 and 2008 results in high transverse momentum region ([Formula: see text]GeV). The recent PHENIX preliminary results of transverse single-spin asymmetries of single heavy flavor decay muon at forward-rapidity will be shown and the possible improvement on this measurement in 2015 with the help of the FVTX detector will be discussed.
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9

VITEV, IVAN, ZHONG-BO KANG, and HONGXI XING. "TRANSVERSE MOMENTUM-WEIGHTED SIVERS ASYMMETRY IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING AT NEXT-TO-LEADING ORDER." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460019. http://dx.doi.org/10.1142/s2010194514600192.

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We summarize the results of a recent study of next-to-leading order perturbative QCD corrections to the transverse momentum-weighted Sivers asymmetry in semi-inclusive hadron production in lepton-proton deep inelastic scattering. The corresponding differential cross section is evaluated as a convolution of a twist-three quark-gluon correlation function, often referred to as Qiu-Sterman function, the usual unpolarized fragmentation function, and a hard coefficient function. By studying the collinear divergence structure, we identify the evolution kernel for the Qiu-Sterman function. The hard coefficient function, which is finite and free of any divergence, is evaluated at one-loop order.
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10

Saleev, V. A., and A. V. Shipilova. "Gluon Sivers Function in Transverse Single-Spin Asymmetries of Direct Photons at NICA." Physics of Atomic Nuclei 85, no. 6 (December 2022): 737–47. http://dx.doi.org/10.1134/s1063778822060114.

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11

Wang, Xiaorong. "Transverse Single Spin Asymmetry of π0 and η Mesons at RHIC/PHENIX." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660044. http://dx.doi.org/10.1142/s2010194516600442.

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We presented measurements of the transverse single spin asymmetries ([Formula: see text]) for neutral [Formula: see text] and [Formula: see text] meson at forward rapidities and central rapidity with the PHENIX detector at RHIC at 62.4 GeV and 200 GeV. At mid-rapidity, [Formula: see text] and [Formula: see text] are reconstructed from di-photon decay. At forward rapidities, [Formula: see text] and [Formula: see text] meson are measured using di-photons decays and electromagnetic clusters due to the photon merging effects are significant for energy [Formula: see text]. The neutral-pion measurement of [Formula: see text] at mid-rapidity is consistent with zero with uncertainties a factor of 20 smaller than previous publications, which will lead to improved constraints on the gluon Sivers function. At higher rapidities, both neutral [Formula: see text] and [Formula: see text] [Formula: see text] exhibit sizable asymmetries. The origin of the forward [Formula: see text] is presently not understood quantitatively. We also measured [Formula: see text] meson cross section for [Formula: see text] GeV/c and [Formula: see text]. It is well described by a NLO pQCD calculation.
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12

Kisslinger, Leonard S., and Debasish Das. "Review of QCD, quark–gluon plasma, heavy quark hybrids, and heavy quark state production in p–p and A–A collisions." International Journal of Modern Physics A 31, no. 07 (March 2, 2016): 1630010. http://dx.doi.org/10.1142/s0217751x16300106.

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This is a review of the Quantum Chromodynamics Cosmological Phase Transitions, the quark–gluon plasma, the production of heavy quark states via [Formula: see text]–[Formula: see text] collisions and Relativistic Heavy Ion Collisions (RHIC) using the mixed hybrid theory for the [Formula: see text] and [Formula: see text] states; and the possible detection of the quark–gluon plasma via heavy quark production using RHIC. Recent research on fragmentation for the production of [Formula: see text] mesons is reviewed, as is future theoretical and experimental research on the Collins and Sivers fragmentation functions for pions produced in polarized [Formula: see text]–[Formula: see text] collisions.
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13

Lewis, Nicole. "Transverse Single-Spin Asymmetries of Midrapidity Direct Photons and Neutral Mesons at PHENIX." SciPost Physics Proceedings, no. 8 (July 11, 2022). http://dx.doi.org/10.21468/scipostphysproc.8.009.

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Results are presented for the transverse single-spin asymmetries of direct photons, neutral pions, and eta mesons for |\eta|<0.35|η|<0.35 from p^\uparrow + pp↑+p collisions with \sqrt{s} = 200s=200 GeV at PHENIX. As hadrons, \pi^0π0 and \etaη mesons are sensitive to both initial- and final-state effects and at midrapidity probe the dynamics of gluons along with a mix of quark flavors. Because direct photon production does not include hadronization, the direct photon TSSA is only sensitive to initial-state effects and at midrapidity provides a clean probe of the gluon dynamics in transversely polarized protons. All three of these results will help constrain the collinear twist-3 trigluon correlation function as well as the gluon Sivers function, improving our knowledge of spin-dependent gluon dynamics in QCD.
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14

Lu, Zhun, and Bo-Qiang Ma. "Gluon Sivers function in a light-cone spectator model." Physical Review D 94, no. 9 (November 18, 2016). http://dx.doi.org/10.1103/physrevd.94.094022.

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15

Godbole, Rohini M., Abhiram Kaushik, Anuradha Misra, Vaibhav Rawoot, and Bipin Sonawane. "Heavy Flavour Production as Probe of Gluon Sivers Function." Few-Body Systems 58, no. 2 (February 27, 2017). http://dx.doi.org/10.1007/s00601-017-1256-8.

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16

D’Alesio, Umberto, Carlo Flore, Francesco Murgia, Cristian Pisano, and Pieter Taels. "Unraveling the gluon Sivers function in hadronic collisions at RHIC." Physical Review D 99, no. 3 (February 19, 2019). http://dx.doi.org/10.1103/physrevd.99.036013.

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17

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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18

Zheng, L., E. C. Aschenauer, J. H. Lee, Bo-Wen Xiao, and Zhong-Bao Yin. "Accessing the gluon Sivers function at a future electron-ion collider." Physical Review D 98, no. 3 (August 13, 2018). http://dx.doi.org/10.1103/physrevd.98.034011.

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19

Godbole, Rohini M., Abhiram Kaushik, Anuradha Misra, and Siddhesh Padval. "Probing the gluon Sivers function through direct photon production at RHIC." Physical Review D 99, no. 1 (January 3, 2019). http://dx.doi.org/10.1103/physrevd.99.014003.

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20

Kang, Zhong-Bo, Jared Reiten, Ding Yu Shao, and John Terry. "QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)286.

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Abstract Using Soft-Collinear Effective Theory, we develop the transverse-momentum-dependent factorization formalism for heavy flavor dijet production in polarized-proton-electron collisions. We consider heavy flavor mass corrections in the collinear-soft and jet functions, as well as the associated evolution equations. Using this formalism, we generate a prediction for the gluon Sivers asymmetry for charm and bottom dijet production at the future Electron-Ion Collider. Furthermore, we compare theoretical predictions with and without the inclusion of finite quark masses. We find that the heavy flavor mass effects can give sizable corrections to the predicted asymmetry.
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21

Padval, Siddhesh, Rohini M. Godbole, Abhiram Kaushik, Anuradha Misra, and Vaibhav S. Rawoot. "Gluon Sivers function and transverse single spin asymmetries in e+p↑→γ+X." Physical Review D 103, no. 3 (February 10, 2021). http://dx.doi.org/10.1103/physrevd.103.036008.

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22

D’Alesio, U., F. Murgia, and C. Pisano. "Investigating the Transverse Momentum Dependent Gluon Sivers Function in Quarkonium Production at pp Colliders." Few-Body Systems 62, no. 2 (April 9, 2021). http://dx.doi.org/10.1007/s00601-021-01605-4.

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23

Godbole, Rohini M., Abhiram Kaushik, and Anuradha Misra. "Low-Virtuality Leptoproduction of Open-Charm as a Probe of the Gluon Sivers Function." Few-Body Systems 59, no. 3 (March 10, 2018). http://dx.doi.org/10.1007/s00601-018-1349-z.

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24

Boussarie, Renaud, Yoshitaka Hatta, Lech Szymanowski, and Samuel Wallon. "Probing the Gluon Sivers Function with an Unpolarized Target: GTMD Distributions and the Odderons." Physical Review Letters 124, no. 17 (April 29, 2020). http://dx.doi.org/10.1103/physrevlett.124.172501.

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25

D’Alesio, Umberto, Francesco Murgia, Cristian Pisano, and Pieter Taels. "Probing the gluon Sivers function in p↑p→J/ψ X and p↑p→DX." Physical Review D 96, no. 3 (August 24, 2017). http://dx.doi.org/10.1103/physrevd.96.036011.

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26

D’Alesio, Umberto, Francesco Murgia, Cristian Pisano, and Sangem Rajesh. "Single-spin asymmetries in $$p^\uparrow p \rightarrow J/\psi +X$$ within a TMD approach: role of the color octet mechanism." European Physical Journal C 79, no. 12 (December 2019). http://dx.doi.org/10.1140/epjc/s10052-019-7551-4.

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AbstractWe calculate the transverse single-spin asymmetry (SSA) for $$J/\psi $$J/ψ production in proton-proton collisions, within non-relativistic QCD, employing the transverse momentum dependent, generalized parton model, which includes both spin and intrinsic motion effects. In particular, we study the role of the color octet mechanism in accessing the gluon Sivers function. In doing that, we also show, within this approach, how the singularities coming from color octet terms in the low-$$P_T$$PT region can be handled, leading to finite cross sections. Predictions for both unpolarized cross sections and SSAs are given and compared against PHENIX data. Estimates for LHCb in the fixed target mode are also presented.
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27

D’Alesio, U., F. Murgia, and C. Pisano. "Towards a first estimate of the gluon Sivers function from A N data in pp collisions at RHIC." Journal of High Energy Physics 2015, no. 9 (September 2015). http://dx.doi.org/10.1007/jhep09(2015)119.

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28

D’Alesio, Umberto, Luca Maxia, Francesco Murgia, Cristian Pisano, and Sangem Rajesh. "Process dependence of the gluon Sivers function in p↑p→J/ψ+X within a TMD scheme in NRQCD." Physical Review D 102, no. 9 (November 13, 2020). http://dx.doi.org/10.1103/physrevd.102.094011.

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29

Godbole, Rohini M., Abhiram Kaushik, and Anuradha Misra. "Transverse single-spin asymmetry in the low-virtuality leptoproduction of open charm as a probe of the gluon Sivers function." Physical Review D 97, no. 7 (April 4, 2018). http://dx.doi.org/10.1103/physrevd.97.076001.

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30

Boer, Daniël, Tom van Daal, Jonathan Gaunt, Tomas Kasemets, and Piet Mulders. "Colour unwound - disentangling colours for azimuthal asymmetries in Drell-Yan scattering." SciPost Physics 3, no. 6 (December 19, 2017). http://dx.doi.org/10.21468/scipostphys.3.6.040.

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It has been suggested that a colour-entanglement effect exists in the Drell-Yan cross section for the ‘double T-odd’ contributions at low transverse momentum \bm{Q_\st}, rendering the colour structure different from that predicted by the usual factorisation formula . These T-odd contributions can come from the Boer-Mulders or Sivers transverse momentum dependent distribution functions. The different colour structure should be visible already at the lowest possible order that gives a contribution to the double Boer-Mulders (dBM) or double Sivers (dS) effect, that is at the level of two gluon exchanges. To discriminate between the different predictions, we compute the leading-power contribution to the low-\bm{Q_\st} dBM cross section at the two-gluon exchange order in the context of a spectator model. The computation is performed using a method of regions analysis with Collins subtraction terms implemented. The results conform with the predictions of the factorisation formula. In the cancellation of the colour entanglement, diagrams containing the three-gluon vertex are essential. Furthermore, the Glauber region turns out to play an important role – in fact, it is possible to assign the full contribution to the dBM cross section at the given order to the region in which the two gluons have Glauber scaling. A similar disentanglement of colour is found for the dS effect.
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