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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
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Kinematics compared to previous machines
04/22/23 3Courtesy from Sichtermann-Vogelsang for EIC-White paper
Physics programs Spin and parton imaging of nucleon
Quark/gluon helicity distributions Spin puzzle
3-D imaging of partons (OAM) Transverse coordinate space (GPDs) Transverse momentum space (TMDs)
Gluon saturation in large nucleus at small-x Electroweak physics, new physics beyond SM Cross-links among the above, and …
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INT-Write-up, Boer, et al., arXive:1108.1713
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Wigner DistributionW(x,r,kt)
d3 r
Transverse Momentum
Dependent PDF f(x,kt)Generalized Parton Distr.
H(x,ξ,t)
d 2kt dzF.T.
d2k t
PDF f(x)
dx
Form Factors
F1(Q),F2(Q)
GPD
Transverse momentum dependent parton distribution Straightforward extension
Spin average, helicity, and transversity distributions
Transverse momentum-spin correlationsNontrivial distributions, STXPT In quark model, depends on S- and P-
wave interference
04/22/23 6Mulders and Qiu’s talks
Deformation when nucleon is transversely polarized
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Lattice Calculation of the IP density ofUp quark, QCDSF/UKQCD Coll., 2006
Quark Sivers function fit to the SIDISData, Anselmino, et al. 20009
k y
kx
-0.5
0.5
0.0
-0.5 0.0 0.5
Where can we learn TMDs Semi-inclusive hadron production in
deep inelastic scattering (SIDIS) Drell-Yan lepton pair, photon pair
productions in pp scattering Dijet correlation in DIS Relevant e+e- annihilation processes …
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9 04/22/23
Novel Single Spin Asymmetries
U: unpolarized beamT: transversely polarized target
Semi-inclusive DIS
Spin-orbital correlation Leading order TMDs
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All these TMDs can be probed through different azimuthalangle distributions
Two major contributions
Sivers effect in the distribution
Collins effect in the fragmentation
Other contributions…
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kTST
P
(zk+pT)~pTXsT
(k,sT)
ST (PXkT)
Universality of the Collins Fragmentation
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ep--> e Pi X e+e---> Pi Pi X pp--> jet(->Pi) XMetz 02, Collins-Metz 02,Yuan 07,Gamberg-Mukherjee-Mulders 08,10Meissner-Metz 0812.3783Yuan-Zhou, 0903.4680
Exps: BELLE, HERMES, STAR, COMPASS
Collins asymmetries in SIDIS
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Summarized in theEIC Write-up
Collins effects in e+e-
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BELLE Coll., 2008 Collins functions extracted from theData, Anselmino, et al., 2009
Sivers effect It is the final state interaction
providing the phase to a nonzero SSA Non-universality in general Only in special case, we have “Special Universality”
Brodsky,Hwang,Schmidt 02Collins, 02;Ji,Yuan,02;Belitsky,Ji,Yuan,02
Sivers asymmetries in SIDIS
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Non-zero Sivers effectsObserved in SIDIS
Jlab Hall A 3He
Great Potential at the EIC High precision, detailed study Wide range of Q2 coverage, QCD
dynamics Sea quark TMDs Gluon TMDs Large transverse momentum,
connecting to collinear factorization
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Electron-Ion Collider Projections: Impressive coverage on Q2, x, z, and PT
04/22/23 18√S=140,50,15 GeV
Quark Sivers function extracted from the data
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Alexei Prokudin, et al.
Leading order fit, simple Gaussian assumption for the Sivers function
There are still theoretical uncertaintiesIn the fit: scale dependence, highorder corrections, …
Inner band is the impact from the planed EIC kinematics
Sea quark:
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Large transverse momentum Only possible with the EIC QCD dynamics, evolution effects Q2 dependence Pt dependence Twist-three mechanism
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Qiu’s talk
EIC coverage
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120fb-1
A unified picture (leading pt/Q)
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QΛQCD PT
Collinear/longitudinal
<<<<
Transverse momentum dependent
Ji-Qiu-Vogelsang-Yuan,2006Yuan-Zhou, 2009
PT
Collins-Soper-Sterman Resummation
Separate the singular and regular parts
TMD factorization in b-space
04/22/23 24Kang-Xiao-Yuan, 2011
Collinear divergence--splitting
Sivers function
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Similar to the weighted asymmetry, and the splittingVogelsang-Yuan, 2009
Hard factor at one-loop order Same as the spin-average case
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Final resum form
Sudakov the same
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Coefficients at one-loop order
Together with A(2), this resum at Next-to-leading-logarithmic level
Phenomenological implementation is underway Unpolarized, Nadolsky et al, 2001 ALL, Koike-Nagashima-Vogelsang 2006
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Directly working on TMDs
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Aybat-Collins-Qiu-Rogers, 2011
Q2-dependence Aybat-Prokudin-Rogers, 2011
04/22/23 30Needs a cross check!
TMD gluon distributions It is not easy, because gluon does
not couple to photon directly Can be studied in two-particle
processes
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Dijet In DIS
Vogelsang-Yuan, 2007Dominguez-Xiao-Yuan, 2010Boer-Brodsky-Mulders-Pisano, 2010
Di-photon In pp
Qiu-Schlegel-Vogelsang, 2011
Summary Wonderful physics associated with
TMDs: nucleon tomography; spin-orbital correlation; QCD dynamics;
We have learned something from HERMES, COMPASS, Jlab, BELLE
Electron-ion collider is the ultimate machine to study TMDs
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