Transverse Momentum Dependent Parton Distributions at an EIC
Transverse Momentum Dependent Parton Distributions at an EIC Feng Yuan Lawrence Berkeley National Laboratory Thank Hasch, Burton, Prokudin, and many others, INT-Write-up for the EIC 9/9/2020 1
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Kinematics compared to previous machines 9/9/2020 Courtesy from Sichtermann-Vogelsang for 3 EIC-White paper
Physics programs n Spin and parton imaging of nucleon ¨ Quark/gluon n helicity distributions Spin puzzle ¨ 3 -D imaging of partons (OAM) Transverse coordinate space (GPDs) n Transverse momentum space (TMDs) n n Gluon saturation in large nucleus at small-x Electroweak physics, new physics beyond SM Cross-links among the above, and … INT-Write-up, Boer, et al. , ar. Xive: 1108. 1713 9/9/2020 4
Wigner Distribution W(x, r, kt) dz kt d 3 r 2 d T. F. Generalized Parton Distr. H(x, ξ, t) dx d 2 kt Transverse Momentum Dependent PDF f(x, kt) GPD PDF f(x) Form Factors F 1(Q), F 2(Q) 9/9/2020 5
Transverse momentum dependent parton distribution n Straightforward extension ¨ Spin average, helicity, and transversity distributions n Transverse momentum-spin correlations ¨ Nontrivial distributions, STXPT ¨ In quark model, depends on S- and P-wave interference Mulders and Qiu’s talks 9/9/2020 6
Deformation when nucleon is transversely polarized -0. 5 0. 0 0. 5 ky 0. 5 0. 0 -0. 5 kx Quark Sivers function fit to the SIDIS Data, Anselmino, et al. 20009 9/9/2020 Lattice Calculation of the IP density of Up quark, QCDSF/UKQCD Coll. , 2006 7
Where can we learn TMDs Semi-inclusive hadron production in deep inelastic scattering (SIDIS) n Drell-Yan lepton pair, photon pair productions in pp scattering n Dijet correlation in DIS n Relevant e+e- annihilation processes n… n 9/9/2020 8
Semi-inclusive DIS n Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 9 9/9/2020
Spin-orbital correlation n Leading order TMDs All these TMDs can be probed through different azimuthal angle distributions 9/9/2020 10
Two major contributions n Sivers effect in the distribution ST k. T P n Collins effect in the fragmentation (zk+p. T) (k, s. T) n ST (PXk. T) ~p. TXs. T Other contributions… 9/9/2020 11
Universality of the Collins Fragmentation ep--> e Pi X e+e---> Pi Pi X Metz 02, Collins-Metz 02, Yuan 07, Gamberg-Mukherjee-Mulders 08, 10 Meissner-Metz 0812. 3783 Yuan-Zhou, 0903. 4680 9/9/2020 pp--> jet(->Pi) X Exps: BELLE, HERMES, STAR, COMPASS 12
Collins asymmetries in SIDIS Summarized in the EIC Write-up 9/9/2020 13
Collins effects in e+e- BELLE Coll. , 2008 Collins functions extracted from the Data, Anselmino, et al. , 2009 9/9/2020 14
Sivers effect It is the final state interaction providing the phase to a nonzero SSA n Non-universality in general n Only in special case, we have “Special Universality” n Brodsky, Hwang, Schmidt 02 Collins, 02; Ji, Yuan, 02; Belitsky, Ji, Yuan, 02
Sivers asymmetries in SIDIS Non-zero Sivers effects Observed in SIDIS Jlab Hall A 3 He 9/9/2020 16
Great Potential at the EIC High precision, detailed study n Wide range of Q 2 coverage, QCD dynamics n Sea quark TMDs n Gluon TMDs n Large transverse momentum, connecting to collinear factorization n 9/9/2020 17
Electron-Ion Collider Projections: Impressive coverage on Q 2, x, z, and PT 9/9/2020 √S=140, 50, 15 Ge. V 18
Quark Sivers function extracted from the data Leading order fit, simple Gaussian assumption for the Sivers function There are still theoretical uncertaintie In the fit: scale dependence, high order corrections, … Inner band is the impact from the planed EIC kinematics Alexei Prokudin, et al. 9/9/2020 19
Sea quark: 9/9/2020 20
Large transverse momentum Only possible with the EIC n QCD dynamics, evolution effects n Q 2 dependence n Pt dependence n Twist-three mechanism n Qiu’s talk 9/9/2020 21
EIC coverage 120 fb-1 9/9/2020 22
A unified picture (leading pt/Q) Transverse momentum dependent Collinear/ longitudinal PT ΛQCD << 9/9/2020 PT << Q Ji-Qiu-Vogelsang-Yuan, 2006 Yuan-Zhou, 2009 23
Collins-Soper-Sterman Resummation n Separate the singular and regular parts n TMD factorization in b-space 9/9/2020 Kang-Xiao-Yuan, 2011 24
Collinear divergence--splitting Similar to the weighted asymmetry, and the splitting Vogelsang-Yuan, 2009 n Sivers function 9/9/2020 25
Hard factor at one-loop order n Same as the spin-average case 9/9/2020 26
Final resum form n Sudakov the same 9/9/2020 27
Coefficients at one-loop order Together with A(2), this resum at Nextto-leading-logarithmic level n Phenomenological implementation is underway n ¨ Unpolarized, ¨ ALL, Nadolsky et al, 2001 Koike-Nagashima-Vogelsang 2006 9/9/2020 28
Directly working on TMDs Aybat-Collins-Qiu-Rogers, 2011 9/9/2020 29
Q 2 -dependence n Aybat-Prokudin-Rogers, 2011 Needs a cross check! 9/9/2020 30
TMD gluon distributions It is not easy, because gluon does not couple to photon directly n Can be studied in two-particle processes n Di-photon In pp Dijet In DIS Vogelsang-Yuan, 2007 Dominguez-Xiao-Yuan, 2010 Boer-Brodsky-Mulders-Pisano, 2010 9/9/2020 Qiu-Schlegel-Vogelsang, 2011 31
Summary Wonderful physics associated with TMDs: nucleon tomography; spin-orbital correlation; QCD dynamics; n We have learned something from HERMES, COMPASS, Jlab, BELLE n Electron-ion collider is the ultimate machine to study TMDs n 9/9/2020 32
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