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Published: 11 March 2023

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1

Christova, E., D. Kotlorz, and E. Leader. "A new extraction of the Boer-Mulders function." Journal of Physics: Conference Series 1435 (January 2020): 012003. http://dx.doi.org/10.1088/1742-6596/1435/1/012003.

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2

GAMBERG, LEONARD, and MARC SCHLEGEL. "FINAL STATE INTERACTIONS AND THE TRANSVERSE STRUCTURE OF PION." Modern Physics Letters A 24, no. 35n37 (December 7, 2009): 2960–72. http://dx.doi.org/10.1142/s0217732309001170.

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In the factorized picture of semi-inclusive deep inelastic scattering the naive time reversal-odd parton distributions exist by virtue of the gauge link which is intrinsic to their definition. The link structure describes initial/final-state interactions of the active parton due to soft gluon exchanges with the target remnant. Though these interactions are non-perturbative, calculations of final-state interaction have been performed in a perturbative one-gluon approximation. We include higher-order contributions by applying non-perturbative eikonal methods to calculate the Boer-Mulders function of the pion. Using this framework we explore under what conditions the Boer Mulders function can be described in terms of factorization of final state interactions and a spatial distortion.
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3

Musch, Bernhard U. "Studying the Sivers and Boer-Mulders Function with Lattice QCD." Few-Body Systems 52, no. 3-4 (November 16, 2011): 259–64. http://dx.doi.org/10.1007/s00601-011-0280-3.

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4

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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5

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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6

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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7

Engelhardt, M., B. Musch, P. Hägler, A. Schäfer, and J. Negele. "The Boer-Mulders Transverse Momentum Distribution in the Pion and its Evolution in Lattice QCD." International Journal of Modern Physics: Conference Series 37 (January 2015): 1560034. http://dx.doi.org/10.1142/s2010194515600344.

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Starting from a definition of transverse momentum-dependent parton distributions (TMDs) in terms of hadronic matrix elements of a quark bilocal operator containing a staple-shaped gauge link, selected TMD observables can be evaluated within Lattice QCD. A TMD ratio describing the Boer-Mulders effect in the pion is investigated, with a particular emphasis on its evolution as a function of a Collins-Soper-type parameter which quantifies the proximity of the staple-shaped gauge links to the light cone.
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8

Nakano, Kenichi. "Measurement of Boer-Mulders Function via Drell-Yan Process by SeaQuest Experiment at Fermilab." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660041. http://dx.doi.org/10.1142/s2010194516600417.

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The SeaQuest experiment is being carried out at Fermi National Accelerator Lab (FNAL) to investigate the nucleon structure with the Drell-Yan process. It utilizes the 120-GeV proton beam extracted from the FNAL Main Injector and targets of liquid hydrogen, liquid deuterium, carbon, iron and tungsten. The solid targets are used to measure the nuclear effects. This paper describes the flavor asymmetry of light anti-quark distributions in the proton ([Formula: see text]) and the angular distribution of Drell-Yan process. The Boer-Mulders function ([Formula: see text]) can be derived from the size ([Formula: see text]) of [Formula: see text] modulation. SeaQuest finished the second data-taking period in August 2014. Preliminary results of [Formula: see text] and [Formula: see text] are reported.
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9

Lu, Zhun, Bo-Qiang Ma, and Ivan Schmidt. "Flavor separation of the Boer–Mulders function from unpolarized π−p and π−D Drell–Yan processes." Physics Letters B 639, no. 5 (August 2006): 494–98. http://dx.doi.org/10.1016/j.physletb.2006.06.053.

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10

Ivanov, N. Ya, A. V. Efremov, and O. V. Teryaev. "How to measure the linear polarization of gluons in unpolarized proton using the heavy-quark pair production." EPJ Web of Conferences 204 (2019): 02006. http://dx.doi.org/10.1051/epjconf/201920402006.

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In recent papers [1, 2], two new ways have been proposed to probe the linear polarization of gluons in unpolarized proton: using the azimuthal asymmetries and Callan-Gross ratio in heavy-quark pair leptoproduction, lN → l′QQ̅X. In this talk, we discuss in details the sensitivity of the QCD predictions for the azimuthal cos φ and cos 2φ asymmetries to the contribution of linearly polarized gluons inside unpolarized proton, where the azimuth φ is the angle between the lepton scattering plane (l, l′) and the heavy quark production plane (N, Q). Our analysis shows that the azimuthal distributions under consideration vary from 0 to 1 depending on the value of the gluonic counterpart of the Boer- Mulders function, $h_{1}^{ \bot g}$. We conclude that the cos φ and cos 2φ asymmetries in heavy-quark pair production in DIS processes are predicted to be large in wide kinematic ranges and sensitive to the contribution of linearly polarized gluons.
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11

Burkardt, Matthias, and Brian Hannafious. "Are all Boer–Mulders functions alike?" Physics Letters B 658, no. 4 (January 2008): 130–37. http://dx.doi.org/10.1016/j.physletb.2007.09.064.

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12

Christova, Ekaterina, Elliot Leader, and Michail Stoilov. "Tests for the extraction of Boer-Mulders functions." Journal of Physics: Conference Series 938 (December 2017): 012040. http://dx.doi.org/10.1088/1742-6596/938/1/012040.

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13

Hwang, Dae Sung. "Light-cone wavefunction representations of the Sivers and the Boer-Mulders distribution functions." Journal of the Korean Physical Society 62, no. 4 (February 2013): 581–90. http://dx.doi.org/10.3938/jkps.62.581.

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14

Chang, Wen-Chen. "Nucleon Partonic Spin Structure to be Explored by the Unpolarized Drell-Yan Program of COMPASS Experiment at CERN." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660111. http://dx.doi.org/10.1142/s2010194516601113.

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The observation of the violation of Lam-Tung relation in the [Formula: see text] Drell-Yan process triggered many theoretical speculations. The TMD Boer-Mulders functions characterizing the correlation of transverse momentum and transverse spin for partons in unpolarized hadrons could nicely account for the violation. The COMPASS experiment at CERN will measure the angular distributions of dimuons from the unpolarized Drell-Yan process over a wide kinematic region and study the beam particle dependence. Significant statistics is expected from a successful run in 2015 which will bring further understanding of the origin of the violation of Lam-Tung relation and of the partonic transverse spin structure of the nucleon.
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15

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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16

Liu, Xiaonan, and Bo-Qiang Ma. "Boer–Mulders function of the pion and pretzelosity distribution of the proton in the polarized pion-proton Drell–Yan process at COMPASS." European Physical Journal C 81, no. 7 (July 2021). http://dx.doi.org/10.1140/epjc/s10052-021-09457-2.

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AbstractWe present a phenomenological analysis of the $$q_{\text {T}}$$ q T -weighted transverse spin dependent azimuthal asymmetry recently measured by the COMPASS Collaboration in polarized pion-proton Drell–Yan process. In the kinematical regimes explored by experiments, we consider the leading-twist contributions from the Boer–Mulders distribution functions $$h_{1}^{\perp }(x,k_{\text {T}}^{2})$$ h 1 ⊥ ( x , k T 2 ) of both the pion and the proton, the transversity distribution $$h_{1}(x,k_{\text {T}}^{2})$$ h 1 ( x , k T 2 ) and the pretzelosity distribution $$h_{1\text {T}}^{\perp }(x,k_{\text {T}}^{2})$$ h 1 T ⊥ ( x , k T 2 ) of the proton, with the unpolarized transverse-momentum-dependent distribution function $$f_{1}(x,k_{\text {T}}^{2})$$ f 1 ( x , k T 2 ) of the proton being also involved in the calculation. By comparing the data reported by the COMPASS Collaboration with theoretical calculated results, we find that the COMPASS measurements represent the first experimental evidence of the Boer–Mulders effect in polarized Drell–Yan process. We also test the universality between proton and pion Boer–Mulders functions.
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17

Courtoy, A., S. Scopetta, and V. Vento. "Analyzing the Boer-Mulders function within different quark models." Physical Review D 80, no. 7 (October 27, 2009). http://dx.doi.org/10.1103/physrevd.80.074032.

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18

Lu, Zhun, Bo-Qiang Ma, and Jiacai Zhu. "Boer-Mulders function of the pion in the MIT bag model." Physical Review D 86, no. 9 (November 16, 2012). http://dx.doi.org/10.1103/physrevd.86.094023.

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19

Tan, Chentao, and Zhun Lu. "Quark quasi-Sivers function and quasi-Boer-Mulders function in a spectator diquark model." Physical Review D 106, no. 9 (November 3, 2022). http://dx.doi.org/10.1103/physrevd.106.094003.

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20

Gamberg, Leonard P., Gary R. Goldstein, and Marc Schlegel. "Transverse quark spin effects and the flavor dependence of the Boer-Mulders function." Physical Review D 77, no. 9 (May 21, 2008). http://dx.doi.org/10.1103/physrevd.77.094016.

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21

Christova, E., D. Kotlorz, and E. Leader. "New study of the Boer-Mulders function: Implications for the quark and hadron transverse momenta." Physical Review D 102, no. 1 (July 21, 2020). http://dx.doi.org/10.1103/physrevd.102.014035.

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22

Kovchegov, Yuri V., and M. Gabriel Santiago. "T-odd leading-twist quark TMDs at small x." Journal of High Energy Physics 2022, no. 11 (November 16, 2022). http://dx.doi.org/10.1007/jhep11(2022)098.

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Abstract We study the small-x asymptotics of the flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs), the Sivers and Boer-Mulders functions. While the leading eikonal small-x asymptotics of the quark Sivers function is given by the spin-dependent odderon [1, 2], we are interested in revisiting the sub-eikonal correction considered by us earlier in [3]. We first simplify the expressions for both TMDs at small Bjorken x and then construct small-x evolution equations for the resulting operators in the large-Nc limit, with Nc the number of quark colors. For both TMDs, the evolution equations resum all powers of the double-logarithmic parameter αs ln2(1/x), where αs is the strong coupling constant, which is assumed to be small. Solving these evolution equations numerically (for the Sivers function) and analytically (for the Boer-Mulders function) we arrive at the following leading small-x asymptotics of these TMDs at large Nc:$$ {\displaystyle \begin{array}{l}{f}_{1T}^{\perp NS}\left(x\ll 1,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{3.4\sqrt{\frac{\alpha_s{N}_c}{4\pi }}}\\ {}{h}_1^{\perp \textrm{NS}}\left(x\ll 1,{k}_T^2\right)=C\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{-1}.\end{array}} $$ f 1 T ⊥ NS x ≪ 1 k T 2 = C O x k T 2 1 x + C 1 x k T 2 1 x 3.4 α s N c 4 π h 1 ⊥ NS x ≪ 1 k T 2 = C x k T 2 1 x − 1 . The functions CO(x,$$ {k}_T^2 $$ k T 2 ), C1(x,$$ {k}_T^2 $$ k T 2 ), and C(x,$$ {k}_T^2 $$ k T 2 ) can be readily obtained in our formalism: they are mildly x-dependent and do not strongly affect the power-of-x asymptotics shown above. The function CO, along with the 1/x factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with C1), our result shown above supersedes the one obtained in [3] due to the new contributions identified recently in [4].
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23

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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24

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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25

Wang, Zhengxian, Xiaoyu Wang, and Zhun Lu. "Boer-Mulders function of the pion and the qT -weighted cos2φ asymmetry in the unpolarized π−p Drell-Yan process at COMPASS." Physical Review D 95, no. 9 (May 8, 2017). http://dx.doi.org/10.1103/physrevd.95.094004.

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26

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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27

Lu, Zhun, and Ivan Schmidt. "Updating Boer-Mulders functions from unpolarizedpdandppDrell-Yan data." Physical Review D 81, no. 3 (February 17, 2010). http://dx.doi.org/10.1103/physrevd.81.034023.

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28

Zhang, Bing, Zhun Lu, Bo-Qiang Ma, and Ivan Schmidt. "Extracting Boer-Mulders functions fromp+DDrell-Yan processes." Physical Review D 77, no. 5 (March 13, 2008). http://dx.doi.org/10.1103/physrevd.77.054011.

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29

Pasquini, Barbara, and Feng Yuan. "Sivers and Boer-Mulders functions in light-cone quark models." Physical Review D 81, no. 11 (June 8, 2010). http://dx.doi.org/10.1103/physrevd.81.114013.

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30

Christova, E., E. Leader, and M. Stoilov. "Consistency tests for the extraction of the Boer-Mulders and Sivers functions." Physical Review D 97, no. 5 (March 27, 2018). http://dx.doi.org/10.1103/physrevd.97.056018.

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31

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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