Abstract
The collinear factorization at twist-3 for Drell-Yan processes is studied with the motivation to solve the discrepancy in literature about the single spin asymmetry in the lepton angular distribution, and to show how QCD gauge invariance is realized in the hadronic tensor. The obtained result here agrees with our early result derived with a totally different approach. In addition to the asymmetry we can construct another two observables to identify the spin effect. We show that the gauge invariance of different contributions in the hadronic tensor is made in different ways by summing the effects of gluon exchanges. More interestingly is that we can show that the virtual correction to one structure function of the hadronic tensor, hence to some weighted SSA observables, is completely determined by the quark form factor. This will simplify the calculation of higher order corrections. The corresponding result in semi-inclusive DIS is also given for the comparison with Drell-Yan processes.
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References
A.V. Efremov and O.V. Teryaev, On Spin Effects in Quantum Chromodynamics (in Russian), Sov. J. Nucl. Phys. 36 (1982) 140 [INSPIRE].
A.V. Efremov and O.V. Teryaev, QCD Asymmetry and Polarized Hadron Structure Functions, Phys. Lett. B 150 (1985) 383 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries, Phys. Rev. Lett. 67 (1991) 2264 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries in direct photon production, Nucl. Phys. B 378 (1992) 52 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries in hadronic pion production, Phys. Rev. D 59 (1999) 014004 [hep-ph/9806356] [INSPIRE].
H. Eguchi, Y. Koike and K. Tanaka, Single Transverse Spin Asymmetry for Large-p T Pion Production in Semi-Inclusive Deep Inelastic Scattering, Nucl. Phys. B 752 (2006) 1 [hep-ph/0604003] [INSPIRE].
J. Zhou, F. Yuan and Z.-T. Liang, Transverse momentum dependent quark distributions and polarized Drell-Yan processes, Phys. Rev. D 81 (2010) 054008 [arXiv:0909.2238] [INSPIRE].
J.C. Collins and D.E. Soper, Angular Distribution of Dileptons in High-Energy Hadron Collisions, Phys. Rev. D 16 (1977) 2219 [INSPIRE].
N. Hammon, O. Teryaev and A. Schafer, Single spin asymmetry for the Drell-Yan process, Phys. Lett. B 390 (1997) 409 [hep-ph/9611359] [INSPIRE].
D. Boer, P.J. Mulders and O.V. Teryaev, Single spin asymmetries from a gluonic background in the Drell-Yan process, Phys. Rev. D 57 (1998) 3057 [hep-ph/9710223] [INSPIRE].
D. Boer and P.J. Mulders, Color gauge invariance in the Drell-Yan process, Nucl. Phys. B 569 (2000) 505 [hep-ph/9906223] [INSPIRE].
D. Boer and J.-w. Qiu, Single transverse spin asymmetry in Drell-Yan lepton angular distribution, Phys. Rev. D 65 (2002) 034008 [hep-ph/0108179] [INSPIRE].
J.P. Ma and Q. Wang, On unique predictions for single spin azimuthal asymmetry, Eur. Phys. J. C 37 (2004) 293 [hep-ph/0310245] [INSPIRE].
I.V. Anikin and O.V. Teryaev, Gauge invariance, causality and gluonic poles, Phys. Lett. B 690 (2010) 519 [arXiv:1003.1482] [INSPIRE].
I.V. Anikin and O.V. Teryaev, Asymmetries associated with higher twists: gauge invariance, gluonic poles and twist three, arXiv:1201.2569 [INSPIRE].
J. Zhou and A. Metz, Transverse single spin asymmetry in the Drell-Yan process, Phys. Rev. D 86 (2012) 014001 [arXiv:1011.5871] [INSPIRE].
J.P. Ma and G.P. Zhang, Single Spin Asymmetry in Lepton Angular Distribution of Drell-Yan Processes, JHEP 11 (2012) 156 [arXiv:1203.6415] [INSPIRE].
G. Re Calegari and P.G. Ratcliffe, Single Transverse-Spin Asymmetries in Drell-Yan Processes, Eur. Phys. J. C 74 (2014) 2769 [arXiv:1307.5178] [INSPIRE].
H.G. Cao, J.P. Ma and H.Z. Sang, Single Transverse Spin Asymmetries at Parton Level, Commun. Theor. Phys. 53 (2010) 313 [arXiv:0901.2966] [INSPIRE].
J.P. Ma and H.Z. Sang, Soft-Gluon-Pole Contribution in Single Transverse-Spin Asymmetries of Drell-Yan Processes, JHEP 04 (2011) 062 [arXiv:1102.2679] [INSPIRE].
J.P. Ma and Q. Wang, Scale Dependence of Twist-3 quark-gluon Operators for Single Spin Asymmetries, Phys. Lett. B 715 (2012) 157 [arXiv:1205.0611] [INSPIRE].
J.C. Collins and D.E. Soper, Parton Distribution and Decay Functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].
X.-D. Ji and J. Osborne, An analysis of the next-to-leading order corrections to the g T (= g 1 + g 2) scaling function, Nucl. Phys. B 608 (2001) 235 [hep-ph/0102026] [INSPIRE].
S. Meissner and A. Metz, Partonic pole matrix elements for fragmentation, Phys. Rev. Lett. 102 (2009) 172003 [arXiv:0812.3783] [INSPIRE].
D. Boer and P.J. Mulders, Time reversal odd distribution functions in leptoproduction, Phys. Rev. D 57 (1998) 5780 [hep-ph/9711485] [INSPIRE].
J.P. Ma and G.P. Zhang, QCD Corrections of All Structure Functions in Transverse Momentum Dependent Factorization for Drell-Yan Processes, JHEP 02 (2014) 100 [arXiv:1308.2044] [INSPIRE].
J.-w. Qiu and G.F. Sterman, High twist effects in hadronic collisions, AIP Conf. Proc. 223 (1991) 249 [INSPIRE].
W. Vogelsang and F. Yuan, Next-to-leading Order Calculation of the Single Transverse Spin Asymmetry in the Drell-Yan Process, Phys. Rev. D 79 (2009) 094010 [arXiv:0904.0410] [INSPIRE].
Z.-B. Kang, I. Vitev and H. Xing, Transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering at next-to-leading order, Phys. Rev. D 87 (2013) 034024 [arXiv:1212.1221] [INSPIRE].
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ArXiv ePrint: 1409.2938
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Ma, J.P., Zhang, G.P. Gauge invariance and QCD twist-3 factorization for single spin asymmetries. J. High Energ. Phys. 2015, 163 (2015). https://doi.org/10.1007/JHEP02(2015)163
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DOI: https://doi.org/10.1007/JHEP02(2015)163