Three-dimensional imaging of the nucleon and semi-inclusive high-energy reactions

Abstract

We present a short overview of studies of the transverse-momentum-dependent parton distribution functions of the nucleon. The aim of such studies is to provide three-dimensional imaging of the nucleon and a comprehensive description of semi-inclusive high-energy reactions. By summarizing what we have done in constructing the theoretical framework for inclusive deep inelastic lepton–nucleon scattering and one-dimensional imaging of the nucleon, we try to sketch out an outline of what we need to do to construct such a comprehensive theoretical framework for semi-inclusive processes in terms of three-dimensional gauge-invariant parton distributions. Next, we present an overview of what we have alr ady achieved, with an emphasis on the theoretical framework for semi-inclusive reactions in leading-order perturbative quantum chromodynamics but with leading and higher twist contributions. We summarize in particular the results for the differential cross section and azimuthal spin asymmetries in terms of the gauge-invariant transverse-momentum-dependent parton distribution functions. We also briefly summarize the available experimental results on semi-inclusive reactions and the parameterizations of transverse-momentum-dependent parton distributions extracted from them and present an outlook for future studies.

Keywords

transverse momentum dependence / parton distribution function / fragmentationfunction / collinear expansion / higher twists

References

[1] For a recent review of experiments, see e.g., A. D.Krisch, Hard collisions of spinning protons: Past, present and future, Eur. Phys. J. A31(4), 417 (2007), there are also a number of reviews on this topic, see e.g., Z. T.Liang and C.Boros, Int. J. Mod. Phys. A15, 927 (2000), V.Barone, F.Bradamante, and A.Martin, Transverse-spin and transverse-momentum effects in high-energy processes, Prog. Part. Nucl. Phys.65(2), 267 (2010)

[2] Z. T.Liang, Three dimensional imaging of the nucleon-- TMD (theory and phenomenology), arXiv: 1502.03896 [hep-ph], Plenary talk at the 21st International Symposium on Spin Physics, <Date>October 20-24</Date>, 2014

[3] D.Boer, Overview of TMD evolution,arXiv: 1502.00899 [hep-ph],Invited talk at the 21st International Symposium on Spin Physics, <Date>October 20-24</Date>, 2014

[4] J.Collins, TMD theory, factorization and evolution, Int. J. Mod. Phys. Conf. <Date>Ser. 25</Date>, 1460001 (2014), arXiv: 1307.2920

[5] There are definitely cases where factorization might break down, see e.g., J. P.Ma, J. X.Wang, and S.Zhao, Breakdown of QCD factorization for P-wave quarkonium production at low transverse momentum, Phys. Lett. B737, 103 (2014), arXiv: 1405.3373 [hep-ph], and the references given there

[6] J. C.Collins, D. E.Soper, and G. F.Sterman, Factorization of Hard Processes in QCD, Adv. Ser. Direct. High Energy Phys.5, 1 (1989), arXiv: hep-ph/0409313

[7] J.Collins, Foundations of perturbative QCD, (Cambridge monographs on particle physics, nuclear physics and cosmology), Cambridge: Cambridge University Press, 2011

[8] R. P.Feynman, Photon Hadron InteractionsW. A.Benjamin, 1972

[9] R. K.Ellis, W.Furmanski, and R.Petronzio, Power corrections to the parton model in QCD, Nucl. Phys. B207(1), 1 (1982)

[10] R. K.Ellis, W.Furmanski, and R.Petronzio, Unravelling higher twists, Nucl. Phys. B212(1), 29 (1983)

[11] J. W.Qiu and G. F.Sterman, Power corrections in hadronic scattering (I): Leading 1/Q2 corrections to the Drell-Yan cross section, Nucl. Phys. B353(1), 105 (1991) J. W.Qiu and G. F.Sterman, Power corrections in hadronic scattering (II): Factorization, Nucl. Phys. B353(1), 137 (1991)

[12] G. L.Kane, J.Pumplin, and W.Repko, Transverse quark polarization in large-p_T reactions, e⁺e- jets, and leptoproduction: A test of quantum chromodynamics, Phys. Rev. Lett.41(25), 1689 (1978)

[13] D. L.Adams, (<BibTranslator>FNAL-E704 Collaboration</BibTranslator>), Analyzing power in inclusive p⁺ and p- production at high xF with a 200 GeV polarized proton beam, Phys. Lett. B264(3-4), 462 (1991)

[14] D. W.Sivers, Single-spin production asymmetries from the hard scattering of pointlike constituents, Phys. Rev. D 41(1), 83 (1990) D. W.Sivers, Hard-scattering scaling laws for single-spin production asymmetries, Phys. Rev. D 43(1), 261 (1991)

[15] C.Boros, Z. T.Liang, and T. C.Meng, Quark spin distribution and quark-antiquark annihilation in single-spin hadron-hadron collisions, Phys. Rev. Lett.70(12), 1751 (1993)

[16] J. C.Collins, Fragmentation of transversely polarized quarks probed in transverse momentum distributions, Nucl. Phys. B396(1), 161 (1993)

[17] S. J.Brodsky, D. S.Hwang, and I.Schmidt, Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering, Phys. Lett. B530(1-4), 99 (2002)

[18] J. C.Collins, Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering, Phys. Lett. B536(1-2), 43 (2002)

[19] X.Ji and F.Yuan, Parton distributions in light-cone gauge: Where are the final-state interactions?Phys. Lett. B543(1-2), 66 (2002)

[20] A. V.Belitsky, X.Ji, and F.Yuan, Final state interactions and gauge invariant parton distributions, Nucl. Phys. B656(1-2), 165 (2003)

[21] H.Georgi and H.Politzer, Clean Tests of Quantum Chromodynamics in mp Scattering, Phys. Rev. Lett.40(1), 3 (1978)

[22] R. N.Cahn, Azimuthal dependence in leptoproduction: A simple parton model calculation, Phys. Lett. B78, 269 (1978)

[23] K.Goeke, A.Metz, and M.Schlegel, Parameterization of the quark–quark correlator of a spin-1/2 hadron, Phys. Lett. B618(1-4), 90 (2005)

[24] P.Mulders, invited talk at the 21st International Symposium on Spin Physics, October 20-24</Date>, 2014, Beijing, China, and lectures in 17th Taiwan nuclear physics summer school, <Date>Aug. 25-28, 2014

[25] A.Bacchetta and P. J.Mulders, Deep inelastic leptoproduction of spin-one hadrons, Phys. Rev. D 62(11), 114004 (2000), arXiv: hep-ph/0007120

[26] K. b.Chen, S. y.Wei, W. h.Yang, and Z. t.Liang, Three dimensional fragmentation functions from the quark-quark correlator, arXiv: 1505.02856 [hep-ph]

[27] M.Gourdin, Semi-inclusive reactions induced by leptons, Nucl. Phys. B49, 501 (1972)

[28] A.Kotzinian, New quark distributions and semi-inclusive electroproduction on polarized nucleons, Nucl. Phys. B441(1-2), 234 (1995)

[29] M.Diehl and S.Sapeta, On the analysis of lepton scattering on longitudinally or transversely polarized protons, Eur. Phys. J. C41(4), 515 (2005)

[30] A.Bacchetta, M.Diehl, K.Goeke, A.Metz, P. J.Mulders and M.Schlegel, Semi-inclusive deep inelastic scattering at small transverse momentum, J. High Energy Phys. 0702, 093 (2007)

[31] S.Arnold, A.Metz, and M.Schlegel, Dilepton production from polarized hadron hadron collisions, Phys. Rev. D 79(3), 034005 (2009)

[32] D.Pitonyak, M.Schlegel, and A.Metz, Polarized hadron pair production from electron-positron annihilation, Phys. Rev. D 89(5), 054032 (2014)

[33] Z.Liang and X. N.Wang, Azimuthal and single-spin asymmetry in deep-inelastic lepton-nucleon scattering, Phys. Rev. D 75(9), 094002 (2007)

[34] Y.Song, J.Gao, Z. T.Liang, and X. N.Wang, Twist-4 contributions to the azimuthal asymmetry in semi-inclusive deeply inelastic scattering, Phys. Rev. D 83(5), 054010 (2011)

[35] Y.Song, J.Gao, Z. T.Liang, and X. N.Wang, Azimuthal asymmetries in semi-inclusive deep inelastic scattering with polarized beam and/or target and their nuclear dependences, Phys. Rev. D89(1), 014005 (2014)

[36] S. y.Wei, Y.Song, and Z.Liang, Higher-twist contribution to fragmentation function in inclusive hadron production in e⁺e-^{annihilation, Phys. Rev. D 89(1), 014024 (2014)}

[37] S. Y.Wei, K.Chen, Y.Song, and Z.Liang, Leading and higher twist contributions in semi-inclusive e⁺e-^{annihilation at high energies, Phys. Rev. D 91(3), 034015 (2015), arXiv: 1410.4314 [hep-ph]}

[38] P. J.Mulders and R. D.Tangerman, The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction, Nucl. Phys. B461(1-2), 197 (1996) [Erratum, Nucl. Phys. B484, 538 (1997)]

[39] D.Boer, R.Jakob, and P. J.Mulders, Asymmetries in polarized hadron production in e⁺e-^{annihilation up to order, Nucl. Phys. B504(1-2), 345 (1997)}

[40] Z.Lu and I.Schmidt, Transverse momentum dependent twist-three result for polarized Drell-Yan processes, Phys. Rev. D 84(11), 114004 (2011)

[41] A. P.Chen, J. P.Ma, and G. P.Zhang, Twist-3 contributions in semi-inclusive DIS with transversely polarized target, arXiv: 1505.03217 [hep-ph]

[42] J. C.Collins and D. E.Soper, Back-to-back jets in QCD, Nucl. Phys. B193(2), 381 (1981) [Erratum, Nucl. Phys. B213, 545 (1983)]

[43] J. C.Collins and D. E.Soper, Parton distribution and decay functions, Nucl. Phys. B194(3), 445 (1982)

[44] J. C.Collins, D. E.Soper, and G. F.Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B250(1-4), 199 (1985)

[45] J. C.Collins, D. E.Soper, and G. F.Sterman, Factorization for short distance hadron-hadron scattering, Nucl. Phys. B261, 104 (1985)

[46] X.Ji, J. P.Ma, and F.Yuan, Factorization of large-x quark distributions in a hadron, Phys. Lett. B610(3-4), 247 (2005)

[47] A.Idilbi, X.Ji, J. P.Ma, and F.Yuan, Collins-Soper equation for the energy evolution of transverse-momentum and spin dependent parton distributions, Phys. Rev. D 70(7), 074021 (2004)

[48] X.Ji, J. P.Ma, and F.Yuan, QCD factorization for spin-dependent cross sections in DIS and Drell–Yan processes at low transverse momentum, Phys. Lett. B597(3-4), 299 (2004)

[49] X.Ji, J.Ma, and F.Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71(3), 034005 (2005)

[50] A. A.Henneman, D.Boer, and P. J.Mulders, Evolution of transverse momentum dependent distribution and fragmentation functions, Nucl. Phys. B620(1-2), 331 (2002)

[51] J.Zhou, F.Yuan, and Z. T.Liang, QCD evolution of the transverse momentum dependent correlations, Phys. Rev. D 79(11), 114022 (2009)

[51] Z. B.Kang, B. W.Xiao, and F.Yuan, QCD resummation for single spin asymmetries, Phys. Rev. Lett.107(15), 152002 (2011)

[53] S. M.Aybat and T. C.Rogers, Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution, Phys. Rev. D 83(11), 114042 (2011)

[54] S. M.Aybat, J. C.Collins, J. W.Qiu, and T. C.Rogers, QCD evolution of the Sivers function, Phys. Rev. D 85(3), 034043 (2012)

[55] M.Anselmino, M.Boglione, and S.Melis, Strategy towards the extraction of the Sivers function with transverse momentum dependent evolution, Phys. Rev. D 86(1), 014028 (2012)

[56] P.Sun and F.Yuan, Transverse momentum dependent evolution: Matching semi-inclusive deep inelastic scattering processes to Drell-Yan and W / Z boson production, Phys. Rev. D 88(11), 114012 (2013)

[57] J. P.Ma and G. P.Zhang, QCD corrections of all structure functions in transverse momentum dependent factorization for Drell-Yan processes, J. High Energy Phys.2014(2), 100 (2014), arXiv: 1308.2044 [hep-ph]

[58] M. G.Echevarria, A.Idilbi, Z. B.Kang, and I.Vitev, QCD evolution of the Sivers asymmetry, Phys. Rev. D 89(7), 074013 (2014)

[59] C. A.Aidala, B.Field, L. P.Gamberg, and T. C.Rogers, Limits on transverse momentum dependent evolution from semi-inclusive deep inelastic scattering at moderate Q, Phys. Rev. D 89(9), 094002 (2014)

[60] Z. B.Kang, A.Prokudin, P.Sun, and F.Yuan, Nucleon tensor charge from Collins azimuthal asymmetry measurements, Phys. Rev. D 91(7), 071501 (2015), arXiv: 1410.4877 [hep-ph]

[61] M. G.Echevarria, A.Idilbi, and I.Scimemi, Unified treatment of the QCD evolution of all (un-)polarized transverse momentum dependent functions: Collins function as a study case, Phys. Rev. D 90(1), 014003 (2014)

[xit62] J.Collins and T.Rogers, Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel, Phys. Rev. D 91(7), 074020 (2015), arXiv: 1412.3820 [hep-ph]

[63] Z. B.Kang, A.Prokudin, P.Sun, and F.Yuan, Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution, arXiv: 1505.05589 [hep-ph]

[64] Armine Rostomyan (for the HERMES collaboration), “Highlights of HERMES”, Plenary talk at the 21st International Symposium on Spin Physics, <Date>October 20-24</Date>, 2014, Beijing, China

[65] M.Stolarski (On behalf of the COMPASS Collaboration), “Latest Results from the COMPASS Experiment”, Plenary talk at the 21st International Symposium on Spin Physics, <Date>October 20-24</Date>, 2014, Beijing, China

[66] A.Airapetian, (HERMES Collaboration), Evidence for a single-spin azimuthal asymmetry in semi-inclusive Pion electroproduction, Phys. Rev. Lett.84(18), 4047 (2000), arXiv: hep-ex/9910062

[67] A.Airapetian, . (HERMES Collaboration), Single-spin asymmetries in semi-inclusive deep-inelastic scattering on a transversely polarized hydrogen target, Phys. Rev. Lett.94(1), 012002 (2005), arXiv: hep-ex/0408013

[68] A.Airapetian, . (HERMES Collaboration), Observation of the naive-T-odd Sivers effect in deep-inelastic scattering, Phys. Rev. Lett.103(15), 152002 (2009), arXiv: 0906.3918 [hep-ex]

[69] A.Airapetian, . (HERMES Collaboration), Effects of transversity in deep-inelastic scattering by polarized protons, Phys. Lett. B693(1), 11 (2010), arXiv: 1006.4221 [hep-ex]

[70] A.Airapetian, . (HERMES Collaboration), Azimuthal distributions of charged hadrons, pions, and kaons produced in deep-inelastic scattering off unpolarized protons and deuterons, Phys. Rev. D 87(1), 012010 (2013), arXiv: 1204.4161 [hep-ex]

[71] V. Y.Alexakhin, (COMPASS Collaboration), First measurement of the transverse spin asymmetries of the deuteron in semi-inclusive deep inelastic scattering, Phys. Rev. Lett.94(20), 202002 (2005), arXiv: hep-ex/0503002

[72] E. S.Ageev, . (COMPASS Collaboration), A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target, Nucl. Phys. B765(1-2), 31 (2007), arXiv: hep-ex/0610068

[73] M.Alekseev, (COMPASS Collaboration), Collins and Sivers asymmetries for pions and kaons in muon–deuteron DIS, Phys. Lett. B673(2), 127 (2009), arXiv: 0802.2160 [hep-ex]

[74] M. G.Alekseev, (COMPASS Collaboration), Measurement of the Collins and Sivers asymmetries on transversely polarised protons, Phys. Lett. B692(4), 240 (2010), arXiv: 1005.5609 [hep-ex]

[75] C.Adolph, . (COMPASS Collaboration), I – Experimental investigation of transverse spin asymmetries in μ-p SIDIS processes: Collins asymmetries,Phys. Lett. B717, 376 (2012), arXiv: 1205.5121 [hep-ex]

[76] C.Adolph, (COMPASS Collaboration), II – Experimental investigation of transverse spin asymmetries in μ-p SIDIS processes: Sivers asymmetries,Phys. Lett. B717, 383 (2012), arXiv: 1205.5122 [hep-ex]

[77] C.Adolph, (COMPASS Collaboration), Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons, Phys. Lett. B744, 250 (2015), arXiv: 1408.4405 [hep-ex]

[78] C.Adolph, (COMPASS Collaboration), Measurement of azimuthal hadron asymmetries in semi-inclusive deep inelastic scattering off unpolarised nucleons, Nucl. Phys. B886, 1046 (2014), arXiv: 1401.6284 [hep-ex]

[79] H.Avakian, (The CLAS Collaboration), Measurement of single- and double-spin asymmetries in deep inelastic pion electroproduction with a longitudinally polarized target, Phys. Rev. Lett.105(26), 262002 (2010), arXiv: 1003.4549 [hep-ex]

[80] M.Aghasyan, H.Avakian, P.Rossi, E.De Sanctis, D.Hasch, M.Mirazita, D.Adikaram, M. J.Amaryan, , Precise measurements of beam spin asymmetries in semi-inclusive π0 production, Phys. Lett. B704, 397 (2011), arXiv: 1106.2293 [hep-ex]

[81] X.Qian, . (Jefferson Lab Hall A Collaboration), Single spin asymmetries in charged Pion production from semi-inclusive deep inelastic scattering on a transversely polarized He³ target at Q² = 1.4 – 2.7 GeV², Phys. Rev. Lett.107(7), 072003 (2011), arXiv: 1106.0363 [nucl-ex]

[82] J.Huang, . (Jefferson Lab Hall A Collaboration), Beam-Target Double-Spin Asymmetry A LT in Charged Pion Production from Deep Inelastic Scattering on a Transversely Polarized He 3 Target at 1.4<Q²<2.7 GeV², Phys. Rev. Lett.108(5), 052001 (2012), arXiv: 1108.0489 [nucl-ex]

[83] Y.Zhang, . (Jefferson Lab Hall A Collaboration), Measurement of “pretzelosity” asymmetry of charged pion production in semi-inclusive deep inelastic scattering on a polarized He³ target, Phys. Rev. C 90(5), 055209 (2014), arXiv: 1312.3047 [nucl-ex]

[84] Y. X.Zhao, . (Jefferson Lab Hall A Collaboration), Single spin asymmetries in charged kaon production from semi-inclusive deep inelastic scattering on a transversely polarized He³ target, Phys. Rev. C 90(5), 055201 (2014), arXiv: 1404.7204 [nucl-ex]

[85] K.Abe, (Belle Collaboration), Measurement of Azimuthal Asymmetries in Inclusive Production of Hadron Pairs in e+e− Annihilation at Belle, Phys. Rev. Lett.96, 232002 (2006), arXiv: hep-ex/0507063

[86] R.Seidl, (Belle Collaboration), Measurement of azimuthal asymmetries in inclusive production of hadron pairs in e+e− annihilation at s= 10.58 GeV, Phys. Rev. D 78(3), 032011 (2008) [Erratum, Phys. Rev. D86, 039905 (2012)], arXiv: 0805.2975 [hep-ex]

[87] A.Vossen, (Belle Collaboration), Observation of transverse polarization asymmetries of charged pion pairs in e+e− annihilation near sqrt s= 10.58 GeV, Phys. Rev. Lett.107(7), 072004 (2011), arXiv: 1104.2425 [hep-ex]

[88] J. P.Lees, (BaBar Collaboration), Measurement of Collins asymmetries in inclusive production of charged pion pairs in e+e− annihilation at BABAR, Phys. Rev. D 90(5), 052003 (2014), arXiv: 1309.5278 [hep-ex]

[89] Y.Guan, I.Garzia, H.Li, X. R.Lyu, and W.Yan, Future results on fragmentation functions from BESIII, EPJ Web Conf.85, 02037 (2015); also talk given at the 21st International Symposium on Spin Physics, <Date>October 20-24</Date>, 2014, Beijing, China

[90] J.Badier, (NA3 Collaboration), Angular distributions in the dimuon hadronic production at 150 GeV/c,Z. Phys. C11, 195 (1981)

[91] S.Falciano, (NA10 Collaboration), Angular distributions of muon pairs produced by 194 GeV/c negative pions,Z. Phys. C31, 513 (1986)

[92] M.Guanziroli, (NA10 Collaboration), Angular distributions of muon pairs produced by negative pions on deuterium and tungsten, Z. Phys. C37, 545 (1988)

[93] J. S.Conway, C. E.Adolphsen, J. P.Alexander, K. J.Anderson, J. G.Heinrich, J. E.Pilcher, A.Possoz, E. I.Rosenberg, C.Biino, J. F.Greenhalgh, W. C.Louis, K. T.McDonald, S.Palestini, F. C.Shoemaker, and A. J. S.Smith, Experimental study of muon pairs produced by 252-GeV pions on tungsten, Phys. Rev. D Part. Fields39(1), 92 (1989)

[94] L. Y.Zhu, . (NuSea Collaboration), Measurement of angular distributions of Drell-Yan dimuons in p+d interactions at 800 GeV/c, Phys. Rev. Lett.99(8), 082301 (2007), arXiv: hep-ex/0609005

[95] L. Y.Zhu, . (NuSea Collaboration), Measurement of angular distributions of Drell-Yan dimuons in p+p interactions at 800 GeV/c, Phys. Rev. Lett.102(18), 182001 (2009), arXiv: 0811.4589 [nucl-ex]

[96] M.Anselmino, M.Boglione, U.D’Alesio, A.Kotzinian, F.Murgia, and A.Prokudin, Role of Cahn and Sivers effects in deep inelastic scattering, Phys. Rev. D 71(7), 074006 (2005)

[97] M.Anselmino, M.Boglione, U.D’Alesio, A.Kotzinian, F.Murgia, A.Prokudin, and C.Turk, Transversity and Collins functions from SIDIS and e⁺e- data, Phys. Rev. D75(5), 054032 (2007)

[98] P.Schweitzer, T.Teckentrup, and A.Metz, Intrinsic transverse parton momenta in deeply inelastic reactions, Phys. Rev. D81(9), 094019 (2010)

[99] A.Signori, A.Bacchetta, M.Radici, and G.Schnell, Investigations into the flavor dependence of partonic transverse momentum, J. High Energy Phys.2013(11), 194 (2013)

[100] M.Anselmino, M.Boglione, J. OGonzalez. , S.Melis, and A.Prokudin, Unpolarised transverse momentum dependent distribution and fragmentation functions from SIDIS multiplicities, J. High Energy Phys. 1404, 005 (2014), arXiv: 1312.6261

[101] A. V.Efremov, K.Goeke, S.Menzel, A.Metz, and P.Schweitzer, Sivers effect in semi-inclusive DIS and in the Drell–Yan process, Phys. Lett. B612(3-4), 233 (2005)

[102] J. C.Collins, A. V.Efremov, K.Goeke, S.Menzel, A.Metz, and P.Schweitzer, Sivers effect in semiinclusive deeply inelastic scattering, Phys. Rev. D 73(1), 014021 (2006)

[103] S.Arnold, A. V.Efremov, K.Goeke, M.Schlegel, and P.Schweitzer, Sivers effect at Hermes, Compass and Clas12, arXiv: 0805.2137 [hep-ph]

[104] M.Anselmino, M.Boglione, U.D’Alesio, A.Kotzinian, S.Melis, F.Murgia, A.Prokudin, and C.Turk, Sivers effect for pion and kaon production in semi-inclusive deep inelastic scattering, Eur. Phys. J. A39(1), 89 (2009)

[105] W.Vogelsang and F.Yuan, Single-transverse-spin asymmetries: From deep inelastic scattering to hadronic collisions, Phys. Rev. D 72(5), 054028 (2005)

[106] A.Bacchetta and M.Radici, Constraining Quark Angular Momentum through Semi-Inclusive Measurements, Phys. Rev. Lett.107(21), 212001 (2011)

[107] M.Anselmino, M.Boglione, U.D’Alesio, S.Melis, F.Murgia, and A.Prokudin, Simultaneous extraction of transversity and Collins functions from new semi-inclusive deep inelastic scattering and e⁺e- data, Phys. Rev. D 87(9), 094019 (2013)

[108] B.Zhang, Z.Lu, B. Q.Ma, and I.Schmidt, Extracting Boer-Mulders functions from p+ D Drell-Yan processes, Phys. Rev. D 77(5), 054011 (2008)

[109] B.Zhang, Z.Lu, B. Q.Ma, and I.Schmidt, cos 2f asymmetries in unpolarized semi-inclusive DIS, Phys. Rev. D 78(3), 034035 (2008)

[110] V.Barone, A.Prokudin, and B. Q.Ma, Systematic phenomenological study of the cos 2f asymmetry in unpolarized semi-inclusive DIS, Phys. Rev. D 78(4), 045022 (2008)

[111] V.Barone, S.Melis, and A.Prokudin, Boer-Mulders effect in unpolarized SIDIS: An analysis of the COMPASS and HERMES data on the cos 2 f asymmetry, Phys. Rev. D81(11), 114026 (2010)

[112] Z.Lu and I.Schmidt, Updating Boer-Mulders functions from unpolarized p d and p p Drell-Yan data, Phys. Rev. D 81(3), 034023 (2010)

[113] J.Zhu and B. Q.Ma, Probing the leading-twist transverse-momentum-dependent parton distribution function h_1T^ via the polarized proton-antiproton Drell-Yan process, Phys. Rev. D 82(11), 114022 (2010)

[114] F.Hautmann, H.Jung, M.Krer, P. J.Mulders, E. R.Nocera, T. C.Rogers, and A.Signori, TMDlib and TMDplotter: Library and plotting tools for transverse-momentum-dependent parton distributions, Eur. Phys. J. C74(12), 3220 (2014)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg