transverse momentum dependent parton distributions at an eic
DESCRIPTION
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. Kinematics compared to previous machines. Courtesy from Sichtermann-Vogelsang for EIC-White paper. - PowerPoint PPT PresentationTRANSCRIPT
04/22/23 1
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
04/22/23 2
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 …
04/22/23 4
INT-Write-up, Boer, et al., arXive:1108.1713
04/22/23 5
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
04/22/23 7
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
04/22/23 16
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
04/22/23 17
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
04/22/23 19
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:
04/22/23 20
Large transverse momentum Only possible with the EIC QCD dynamics, evolution effects Q2 dependence Pt dependence Twist-three mechanism
04/22/23 21
Qiu’s talk
EIC coverage
04/22/23 22
120fb-1
A unified picture (leading pt/Q)
04/22/23 23
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
04/22/23 28
Directly working on TMDs
04/22/23 29
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
04/22/23 31
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
04/22/23 32