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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References
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
L.A. Harland-Lang, A.D. Martin, P. Motylinski and R.S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J. C 75 (2015) 204 [arXiv:1412.3989] [INSPIRE].
S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
S. Alekhin, J. Blümlein, S. Moch and R. Placakyte, Parton distribution functions, αs, and heavy-quark masses for LHC Run II, Phys. Rev. D 96 (2017) 014011 [arXiv:1701.05838] [INSPIRE].
NNPDF collaboration, Parton distributions from high-precision collider data, Eur. Phys. J. C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
T.-J. Hou et al., Progress in the CTEQ-TEA NNLO global QCD analysis, arXiv:1908.11394 [INSPIRE].
S. Bailey, T. Cridge, L.A. Harland-Lang, A.D. Martin and R.S. Thorne, Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs, Eur. Phys. J. C 81 (2021) 341 [arXiv:2012.04684] [INSPIRE].
R.D. Ball et al., The Path to Proton Structure at One-Percent Accuracy, arXiv:2109.02653 [INSPIRE].
A.S. Kronfeld and D.M. Photiadis, Phenomenology on the Lattice: Composite Operators in Lattice Gauge Theory, Phys. Rev. D 31 (1985) 2939 [INSPIRE].
G. Martinelli and C.T. Sachrajda, A Lattice Calculation of the Second Moment of the Pion’s Distribution Amplitude, Phys. Lett. B 190 (1987) 151 [INSPIRE].
C. Best et al., Pion and rho structure functions from lattice QCD, Phys. Rev. D 56 (1997) 2743 [hep-lat/9703014] [INSPIRE].
X. Ji, Parton Physics on a Euclidean Lattice, Phys. Rev. Lett. 110 (2013) 262002 [arXiv:1305.1539] [INSPIRE].
X. Ji, Parton Physics from Large-Momentum Effective Field Theory, Sci. China Phys. Mech. Astron. 57 (2014) 1407 [arXiv:1404.6680] [INSPIRE].
X. Ji, Y.-S. Liu, Y. Liu, J.-H. Zhang and Y. Zhao, Large-momentum effective theory, Rev. Mod. Phys. 93 (2021) 035005 [arXiv:2004.03543] [INSPIRE].
K.-F. Liu and S.-J. Dong, Origin of difference between \( \overline{d} \) and \( \overline{u} \) partons in the nucleon, Phys. Rev. Lett. 72 (1994) 1790 [hep-ph/9306299] [INSPIRE].
Z. Davoudi and M.J. Savage, Restoration of Rotational Symmetry in the Continuum Limit of Lattice Field Theories, Phys. Rev. D 86 (2012) 054505 [arXiv:1204.4146] [INSPIRE].
W. Detmold and C.J.D. Lin, Deep-inelastic scattering and the operator product expansion in lattice QCD, Phys. Rev. D 73 (2006) 014501 [hep-lat/0507007] [INSPIRE].
A.J. Chambers et al., Nucleon Structure Functions from Operator Product Expansion on the Lattice, Phys. Rev. Lett. 118 (2017) 242001 [arXiv:1703.01153] [INSPIRE].
V. Braun and D. Müller, Exclusive processes in position space and the pion distribution amplitude, Eur. Phys. J. C 55 (2008) 349 [arXiv:0709.1348] [INSPIRE].
A.V. Radyushkin, Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions, Phys. Rev. D 96 (2017) 034025 [arXiv:1705.01488] [INSPIRE].
K. Orginos, A. Radyushkin, J. Karpie and S. Zafeiropoulos, Lattice QCD exploration of parton pseudo-distribution functions, Phys. Rev. D 96 (2017) 094503 [arXiv:1706.05373] [INSPIRE].
Y.-Q. Ma and J.-W. Qiu, Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations, Phys. Rev. Lett. 120 (2018) 022003 [arXiv:1709.03018] [INSPIRE].
I. Scimemi and A. Vladimirov, Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum, JHEP 06 (2020) 137 [arXiv:1912.06532] [INSPIRE].
A. Bacchetta et al., Transverse-momentum-dependent parton distributions up to N3LL from Drell-Yan data, JHEP 07 (2020) 117 [arXiv:1912.07550] [INSPIRE].
A. Accardi et al., Electron Ion Collider: The Next QCD Frontier : Understanding the glue that binds us all, Eur. Phys. J. A 52 (2016) 268 [arXiv:1212.1701] [INSPIRE].
R. Abdul Khalek et al., Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report, arXiv:2103.05419 [INSPIRE].
P. Hagler, B.U. Musch, J.W. Negele and A. Schafer, Intrinsic quark transverse momentum in the nucleon from lattice QCD, EPL 88 (2009) 61001 [arXiv:0908.1283] [INSPIRE].
B.U. Musch, P. Hagler, J.W. Negele and A. Schafer, Exploring quark transverse momentum distributions with lattice QCD, Phys. Rev. D 83 (2011) 094507 [arXiv:1011.1213] [INSPIRE].
B.U. Musch, P. Hagler, M. Engelhardt, J.W. Negele and A. Schafer, Sivers and Boer-Mulders observables from lattice QCD, Phys. Rev. D 85 (2012) 094510 [arXiv:1111.4249] [INSPIRE].
M. Engelhardt, P. Hägler, B. Musch, J. Negele and A. Schäfer, Lattice QCD study of the Boer-Mulders effect in a pion, Phys. Rev. D 93 (2016) 054501 [arXiv:1506.07826] [INSPIRE].
B. Yoon et al., Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions using clover and domain wall fermions, in 33rd International Symposium on Lattice Field Theory, Kobe, Japan, 14–18 July 2015 [arXiv:1601.05717] [INSPIRE].
B. Yoon et al., Nucleon Transverse Momentum-dependent Parton Distributions in Lattice QCD: Renormalization Patterns and Discretization Effects, Phys. Rev. D 96 (2017) 094508 [arXiv:1706.03406] [INSPIRE].
X. Ji, P. Sun, X. Xiong and F. Yuan, Soft factor subtraction and transverse momentum dependent parton distributions on the lattice, Phys. Rev. D 91 (2015) 074009 [arXiv:1405.7640] [INSPIRE].
X. Ji, L.-C. Jin, F. Yuan, J.-H. Zhang and Y. Zhao, Transverse momentum dependent parton quasidistributions, Phys. Rev. D 99 (2019) 114006 [arXiv:1801.05930] [INSPIRE].
M.A. Ebert, I.W. Stewart and Y. Zhao, Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD, Phys. Rev. D 99 (2019) 034505 [arXiv:1811.00026] [INSPIRE].
M.A. Ebert, I.W. Stewart and Y. Zhao, Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice, JHEP 09 (2019) 037 [arXiv:1901.03685] [INSPIRE].
M.A. Ebert, I.W. Stewart and Y. Zhao, Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD, JHEP 03 (2020) 099 [arXiv:1910.08569] [INSPIRE].
X. Ji, Y. Liu and Y.-S. Liu, TMD soft function from large-momentum effective theory, Nucl. Phys. B 955 (2020) 115054 [arXiv:1910.11415] [INSPIRE].
X. Ji, Y. Liu and Y.-S. Liu, Transverse-momentum-dependent parton distribution functions from large-momentum effective theory, Phys. Lett. B 811 (2020) 135946 [arXiv:1911.03840] [INSPIRE].
M.A. Ebert, S.T. Schindler, I.W. Stewart and Y. Zhao, One-loop Matching for Spin-Dependent Quasi-TMDs, JHEP 09 (2020) 099 [arXiv:2004.14831] [INSPIRE].
X. Ji, Y. Liu, A. Schäfer and F. Yuan, Single Transverse-Spin Asymmetry and Sivers Function in Large Momentum Effective Theory, Phys. Rev. D 103 (2021) 074005 [arXiv:2011.13397] [INSPIRE].
X. Ji and Y. Liu, Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach, Phys. Rev. D 105 (2022) 076014 [arXiv:2106.05310] [INSPIRE].
P. Shanahan, M.L. Wagman and Y. Zhao, Nonperturbative renormalization of staple-shaped Wilson line operators in lattice QCD, Phys. Rev. D 101 (2020) 074505 [arXiv:1911.00800] [INSPIRE].
P. Shanahan, M. Wagman and Y. Zhao, Collins-Soper kernel for TMD evolution from lattice QCD, Phys. Rev. D 102 (2020) 014511 [arXiv:2003.06063] [INSPIRE].
M. Schlemmer, A. Vladimirov, C. Zimmermann, M. Engelhardt and A. Schäfer, Determination of the Collins-Soper Kernel from Lattice QCD, JHEP 08 (2021) 004 [arXiv:2103.16991] [INSPIRE].
Lattice Parton collaboration, Lattice QCD Calculations of Transverse-Momentum-Dependent Soft Function through Large-Momentum Effective Theory, Phys. Rev. Lett. 125 (2020) 192001 [arXiv:2005.14572] [INSPIRE].
Y. Li et al., Lattice QCD Study of Transverse-Momentum Dependent Soft Function, Phys. Rev. Lett. 128 (2022) 062002 [arXiv:2106.13027] [INSPIRE].
P. Shanahan, M. Wagman and Y. Zhao, Lattice QCD calculation of the Collins-Soper kernel from quasi-TMDPDFs, Phys. Rev. D 104 (2021) 114502 [arXiv:2107.11930] [INSPIRE].
A.A. Vladimirov and A. Schäfer, Transverse momentum dependent factorization for lattice observables, Phys. Rev. D 101 (2020) 074517 [arXiv:2002.07527] [INSPIRE].
J.C. Collins and D.E. Soper, Back-To-Back Jets in QCD, Nucl. Phys. B 193 (1981) 381 [Erratum ibid. 213 (1983) 545] [INSPIRE].
J.C. Collins and D.E. Soper, Back-To-Back Jets: Fourier Transform from B to K-Transverse, Nucl. Phys. B 197 (1982) 446 [INSPIRE].
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. B 250 (1985) 199 [INSPIRE].
J. Collins, Foundations of perturbative QCD, Cambridge University Press, Cambridge, U.K. [Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 32 (2011) 1] [INSPIRE].
J.-H. Zhang, X. Ji, A. Schäfer, W. Wang and S. Zhao, Accessing Gluon Parton Distributions in Large Momentum Effective Theory, Phys. Rev. Lett. 122 (2019) 142001 [arXiv:1808.10824] [INSPIRE].
M. Beneke and T. Feldmann, Factorization of heavy to light form-factors in soft collinear effective theory, Nucl. Phys. B 685 (2004) 249 [hep-ph/0311335] [INSPIRE].
X.-d. Ji, J.-p. Ma and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71 (2005) 034005 [hep-ph/0404183] [INSPIRE].
J.-y. Chiu, F. Golf, R. Kelley and A.V. Manohar, Electroweak Sudakov corrections using effective field theory, Phys. Rev. Lett. 100 (2008) 021802 [arXiv:0709.2377] [INSPIRE].
T. Becher and G. Bell, Analytic Regularization in Soft-Collinear Effective Theory, Phys. Lett. B 713 (2012) 41 [arXiv:1112.3907] [INSPIRE].
J.-y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, The Rapidity Renormalization Group, Phys. Rev. Lett. 108 (2012) 151601 [arXiv:1104.0881] [INSPIRE].
J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory, JHEP 05 (2012) 084 [arXiv:1202.0814] [INSPIRE].
J.-y. Chiu, A. Fuhrer, A.H. Hoang, R. Kelley and A.V. Manohar, Soft-Collinear Factorization and Zero-Bin Subtractions, Phys. Rev. D 79 (2009) 053007 [arXiv:0901.1332] [INSPIRE].
M.G. Echevarria, A. Idilbi and I. Scimemi, Factorization Theorem For Drell-Yan At Low qT And Transverse Momentum Distributions On-The-Light-Cone, JHEP 07 (2012) 002 [arXiv:1111.4996] [INSPIRE].
Y. Li, D. Neill and H.X. Zhu, An exponential regulator for rapidity divergences, Nucl. Phys. B 960 (2020) 115193 [arXiv:1604.00392] [INSPIRE].
M.A. Ebert, I. Moult, I.W. Stewart, F.J. Tackmann, G. Vita and H.X. Zhu, Subleading power rapidity divergences and power corrections for qT, JHEP 04 (2019) 123 [arXiv:1812.08189] [INSPIRE].
T. Becher and M. Neubert, Drell-Yan Production at Small qT, Transverse Parton Distributions and the Collinear Anomaly, Eur. Phys. J. C 71 (2011) 1665 [arXiv:1007.4005] [INSPIRE].
J. Collins and T.C. Rogers, Connecting Different TMD Factorization Formalisms in QCD, Phys. Rev. D 96 (2017) 054011 [arXiv:1705.07167] [INSPIRE].
D. Gutiérrez-Reyes, I. Scimemi and A.A. Vladimirov, Twist-2 matching of transverse momentum dependent distributions, Phys. Lett. B 769 (2017) 84 [arXiv:1702.06558] [INSPIRE].
P.J. Mulders and J. Rodrigues, Transverse momentum dependence in gluon distribution and fragmentation functions, Phys. Rev. D 63 (2001) 094021 [hep-ph/0009343] [INSPIRE].
M.G. Echevarria, T. Kasemets, P.J. Mulders and C. Pisano, QCD evolution of (un)polarized gluon TMDPDFs and the Higgs qT-distribution, JHEP 07 (2015) 158 [Erratum ibid. 05 (2017) 073] [arXiv:1502.05354] [INSPIRE].
X.-d. Ji and F. Yuan, Parton distributions in light cone gauge: Where are the final state interactions?, Phys. Lett. B 543 (2002) 66 [hep-ph/0206057] [INSPIRE].
X. Ji, J.-H. Zhang and Y. Zhao, Renormalization in Large Momentum Effective Theory of Parton Physics, Phys. Rev. Lett. 120 (2018) 112001 [arXiv:1706.08962] [INSPIRE].
J. Green, K. Jansen and F. Steffens, Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field, Phys. Rev. Lett. 121 (2018) 022004 [arXiv:1707.07152] [INSPIRE].
J.R. Green, K. Jansen and F. Steffens, Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach, Phys. Rev. D 101 (2020) 074509 [arXiv:2002.09408] [INSPIRE].
J.G.M. Gatheral, Exponentiation of Eikonal Cross-sections in Nonabelian Gauge Theories, Phys. Lett. B 133 (1983) 90 [INSPIRE].
J. Frenkel and J.C. Taylor, Nonabelian eikonal exponentiation, Nucl. Phys. B 246 (1984) 231 [INSPIRE].
X. Ji and Y. Liu, in preparation.
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The Quark Beam Function at NNLL, JHEP 09 (2010) 005 [arXiv:1002.2213] [INSPIRE].
M.A. Ebert, Analytic results for Sudakov form factors in QCD, JHEP 02 (2022) 136 [arXiv:2110.11360] [INSPIRE].
M. Constantinou, H. Panagopoulos and G. Spanoudes, One-loop renormalization of staple-shaped operators in continuum and lattice regularizations, Phys. Rev. D 99 (2019) 074508 [arXiv:1901.03862] [INSPIRE].
Y. Ji, J.-H. Zhang, S. Zhao and R. Zhu, Renormalization and mixing of staple-shaped Wilson line operators on the lattice revisited, Phys. Rev. D 104 (2021) 094510 [arXiv:2104.13345] [INSPIRE].
J.M. Henn, G.P. Korchemsky and B. Mistlberger, The full four-loop cusp anomalous dimension in \( \mathcal{N} \) = 4 super Yang-Mills and QCD, JHEP 04 (2020) 018 [arXiv:1911.10174] [INSPIRE].
A. Vladimirov, V. Moos and I. Scimemi, Transverse momentum dependent operator expansion at next-to-leading power, JHEP 01 (2022) 110 [arXiv:2109.09771] [INSPIRE].
M.A. Ebert, A. Gao and I.W. Stewart, Factorization for Azimuthal Asymmetries in SIDIS at Next-to-Leading Power, arXiv:2112.07680 [INSPIRE].
C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in B → Xsγ in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [INSPIRE].
C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An Effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
G. Kramer and B. Lampe, Two Jet Cross-Section in e+e− Annihilation, Z. Phys. C 34 (1987) 497 [Erratum ibid. 42 (1989) 504] [INSPIRE].
T. Matsuura and W.L. van Neerven, Second Order Logarithmic Corrections to the Drell-Yan Cross-section, Z. Phys. C 38 (1988) 623 [INSPIRE].
T. Matsuura, S.C. van der Marck and W.L. van Neerven, The Calculation of the Second Order Soft and Virtual Contributions to the Drell-Yan Cross-Section, Nucl. Phys. B 319 (1989) 570 [INSPIRE].
T. Gehrmann, T. Huber and D. Maître, Two-loop quark and gluon form-factors in dimensional regularisation, Phys. Lett. B 622 (2005) 295 [hep-ph/0507061] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, Three-loop results for quark and gluon form-factors, Phys. Lett. B 625 (2005) 245 [hep-ph/0508055] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, The Quark form-factor at higher orders, JHEP 08 (2005) 049 [hep-ph/0507039] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark and gluon form factors to three loops, Phys. Rev. Lett. 102 (2009) 212002 [arXiv:0902.3519] [INSPIRE].
R.N. Lee, A.V. Smirnov and V.A. Smirnov, Analytic Results for Massless Three-Loop Form Factors, JHEP 04 (2010) 020 [arXiv:1001.2887] [INSPIRE].
T. Gehrmann, E.W.N. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP 06 (2010) 094 [arXiv:1004.3653] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO, Eur. Phys. J. C 72 (2012) 2195 [arXiv:1209.0158] [INSPIRE].
T. Gehrmann, T. Lubbert and L.L. Yang, Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case, Phys. Rev. Lett. 109 (2012) 242003 [arXiv:1209.0682] [INSPIRE].
T. Gehrmann, T. Luebbert and L.L. Yang, Calculation of the transverse parton distribution functions at next-to-next-to-leading order, JHEP 06 (2014) 155 [arXiv:1403.6451] [INSPIRE].
Y. Li and H.X. Zhu, Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation, Phys. Rev. Lett. 118 (2017) 022004 [arXiv:1604.01404] [INSPIRE].
M.G. Echevarria, I. Scimemi and A. Vladimirov, Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order, JHEP 09 (2016) 004 [arXiv:1604.07869] [INSPIRE].
T. Lübbert, J. Oredsson and M. Stahlhofen, Rapidity renormalized TMD soft and beam functions at two loops, JHEP 03 (2016) 168 [arXiv:1602.01829] [INSPIRE].
M.-X. Luo, X. Wang, X. Xu, L.L. Yang, T.-Z. Yang and H.X. Zhu, Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case, JHEP 10 (2019) 083 [arXiv:1908.03831] [INSPIRE].
M.-x. Luo, T.-Z. Yang, H.X. Zhu and Y.J. Zhu, Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order, Phys. Rev. Lett. 124 (2020) 092001 [arXiv:1912.05778] [INSPIRE].
M.A. Ebert, B. Mistlberger and G. Vita, Transverse momentum dependent PDFs at N3LO, JHEP 09 (2020) 146 [arXiv:2006.05329] [INSPIRE].
M.-x. Luo, T.-Z. Yang, H.X. Zhu and Y.J. Zhu, Unpolarized quark and gluon TMD PDFs and FFs at N3LO, JHEP 06 (2021) 115 [arXiv:2012.03256] [INSPIRE].
H. Dorn, Renormalization of Path Ordered Phase Factors and Related Hadron Operators in Gauge Field Theories, Fortsch. Phys. 34 (1986) 11 [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson Loops Beyond the Leading Order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].
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Ebert, M.A., Schindler, S.T., Stewart, I.W. et al. Factorization connecting continuum & lattice TMDs. J. High Energ. Phys. 2022, 178 (2022). https://doi.org/10.1007/JHEP04(2022)178
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DOI: https://doi.org/10.1007/JHEP04(2022)178