Nucleon Tomography Feng Yuan Lawrence Berkeley National Laboratory
Nucleon Tomography Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory Thanks Kresimir Kumerick, Dieter Mueller, Alexei Prokudin for providing nice plots, and authors of TMD-charpter of the EIC Write-up 11/3/2020 1
Exploring the nucleon: Of fundamental importance in science 11/3/2020 2
Feynman Parton: one-dimension n Inclusive cross sections probe the momentum (longitudinal) distributions of partons inside nucleon Hadronic reactions 11/3/2020 3
Extension to transverse direction… n Semi-inclusive measurements ¨ Transverse momentum dependent (TMD) parton distributions n Deeply Virtual Compton Scattering and Exclusive processes ¨ Generalized n parton distributions (GPD) Recently, there have been very exciting developments in both fields 11/3/2020 4
Hope to highlight n Fruitful imaging from the GPDs and TMDs measurements ¨ Try to answer more detailed questions as Rutherford was doing 100 years ago n QCD dynamics involved in these processes ¨ In particular for the TMD part: universality, factorization, … 11/3/2020 5
Wigner function n Define as ¨ When Wigner 1933 integrated over x (p), one gets the momentum (probability) density ¨ Not positive definite in general, but is in classical limit ¨ Any dynamical variable can be calculated as
Wigner distribution for the quark n The quark operator n Wigner distributions Ji: PRL 91, 062001(2003) After integrating over r, one gets TMD After integrating over k, one gets Fourier transform of GPDs 7
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) 11/3/2020 8
TMD Parton Distributions n The definition contains explicitly the Collins-Soper 1981, gauge links Collins 2002, Belitsky-Ji-Yuan 2002 n The polarization and kt dependence provide rich structure in the quark and gluon distributions ¨ Mulders-Tangerman 95, Boer-Mulders 98 11/3/2020 9
Generalized Parton Distributions Mueller, et al. 1994; Ji, 1996, Radyushkin 1996 n n Off-diagonal matrix elements of the quark operator (along light-cone) It depends on quark momentum fraction x and skewness ξ, and nucleon momentum transfer t 11/3/2020 10
Impact parameter dependent parton distributions Soper 1977 Burkardt 2000, 2003 n Quark operator depends on bt n It is the F. T. of the GPD at ξ =0 11/3/2020 11
Transverse profile for the quark distribution: kt vs bt Quark distribution calculated from a saturation-inspired model A. Mueller 99, Mc. Lerran-Venugopalan 99 11/3/2020 GPD fit to the DVCS data from HERA, Kumerick-D. Mueller, 09, 10 12
Gluon distribution One of the TMD gluon distributions at small-x 11/3/2020 GPD fit to the DVCS data from HERA, Kumerick-Mueller, 09, 10 13
Deformation when nucleon is transversely polarized Burkardt 2002 -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 11/3/2020 Lattice Calculation of the IP density of Up quark, QCDSF/UKQCD Coll. , 2006 14
Access the GPDs n Deeply virtual Compton Scattering (DVCS) and deeply virtual exclusive meson production (DVEM) GPD In the Bjorken limit: Q 2>>(-t), ∧ 2 QCD, M 2 11/3/2020 15
DVCS kinematics Experiments measure the Compton Form Factors (CFF) 11/3/2020 16
Extract the GPDs n The theoretical framework has been well established ¨ Perturbative QCD corrections at NLO, some at NNLO n However, GPDs depend on x, ξ, t, it is much more difficult than PDFs (only depends on x) ¨ There will be model dependence at the beginning 11/3/2020 17
Great efforts have been made n Several groups have been working on extraction of the GPDs ¨ See some of these in the parallel sessions We do have a glimpse of the GPDs n Decisive answer shall be possible with future JLab 12 Ge. V and COMPASS, and the planed EIC n 11/3/2020 18
Highlights from Mueller et al. 09, 10 Sea quark and gluon GPDs parameterized in the conformal moment space, tchannel partial wave expansion n Valence quark GPDs parameterized on the η=x trajectory, dispersion relation to construct the real part n Muller’s parallel session talk 11/3/2020 19
HERA HERMES CLAS Jlab-Hall-A 11/3/2020 20
One example: H(x, x, t) D. Mueller, et al, 09, 10 Small-x range constrained by HERA, uncertainties at large-x shall be very much reduced with Jlab 12 Ge. V COMPASS, and the planed EIC Of course, there also other GPDs, in particular, the GPD E HERA HERMES 11/3/2020 JLab 21
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 11/3/2020 22
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 11/3/2020 23
Semi-inclusive DIS n Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 24 11/3/2020
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… 11/3/2020 25
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 11/3/2020 pp--> jet(->Pi) X Exps: BELLE, HERMES, STAR, parallel talks 26
Collins asymmetries in SIDIS Summarized in the EIC Write-up Details see the parallel Session talks 11/3/2020 27
Collins effects in e+e- BELLE Coll. , 2008 Collins functions extracted from the Data, Anselmino, et al. , 2009 11/3/2020 28
Sivers effect is different 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 Jlab Hall A 3 He data to appear Non-zero Sivers effects Observed in SIDIS Parallel sessions 11/3/2020 30
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 kiematics Alexei Prokudin, et al. 11/3/2020 31
DIS and Drell-Yan n Initial state vs. final state interactions * * Drell-Yan DIS HERMES n “Universality”: QCD prediction 32
RHIC predictions There have been proposals to Do this measurement at RHIC http: //spin. riken. bnl. gov/rsc/ Collider or fixed target modes There is also a COMPASS Proposal in the near future It is very important to test the sign change of the quark Sivers function Kang, Qiu, 2008 11/3/2020 33
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 11/3/2020 Qiu-Schlegel-Vogelsang, 2011 34
Dijet-correlation at RHIC n Initial state and/or final state interactions Jet 2 Jet 1 Boer-Vogelsang 03 P, ST Standard (naïve) Factorization breaks! Dominguez and Rogers’ talks in parallel sessions 35
Theoretical challenges in the TMD n Q 2 dependence and soft gluon resummation, in particular, for the SSA ¨ Parallel session talks by Global study at the Next-to-leading order n Relation to the Orbital angular momentum n Unified picture for GPDs and TMDs n… n 11/3/2020 36
2 d d 3 r Wigner Distribution W(x, r, kt) dz kt T. F. dz Transverse Momentum Dependent PDF f(x, kt) Generalized Parton Distr. H(x, ξ, t) W(x, kt, rt) PDF f(x) dx d 2 kt T-Wigner Distribution Form Factors F 1(Q), F 2(Q) 11/3/2020 37
Transverse Wigner Distributions n Integrate out z in the Wigner function ¨ Depends on x, kt, bt ¨ Also referred as GTMD in the literature n n See for example, Metz, et al. , 09; Pasquini, 10, 11 It has close connection to the small-x parton distributions in large nuclei e. g. , gluon number distr. Mueller, NPB 1999 Albacete’s talk this afternoon 11/3/2020 38
Further integrate out x AMO Exp. d-dbar rx kx Quark model calculation: Xiong, et al. Skovsen et al. (Denmark) PRL 91, 090604 11/3/2020 39
There is no known process can be used to measure the T-Wigner distribution n We have to either use a model (constrained by the GPD and TMDs) to calculate this function n ¨ n Muller and Pasquini’s talks in parallel sessions Or parameterize them and fit to GPDs and TMDs simultaneously 11/3/2020 40
Summary There have been great progresses in both experiment and theory for GPD and TMD physics n Challenges are still in both fields n Future Jlab 12 Ge. V upgrade, COMPASS, RHIC and the planed EIC experiments, will lead us a complete 3 D tomography of the nucleon n 11/3/2020 41
BACK-UP 11/3/2020 42
gluon distributions 11/3/2020 43
3 D image of quarks at fixed-x n GPDs can be used to picture quarks in the proton (Belitsky-Ji-Yuan, PRD 04) Beam direction z fm fm y x fm low x 44 moderate x high x
Transverse charge density in nucleon G. Miller, 2007; M. Burkardt 2008 11/3/2020 45
Polarized TMD Quark Distributions Nucleon Quark Unpol. Long. Trans. Unpol. Long. Trans. Boer, Mulders, Tangerman (96&98) 46
Three classes in the view of a quark model n S-wave ¨ Unpolarized, n helicity, transversity S-P interference ¨ g 1 T, h 1 L ¨ f 1 T┴, h 1┴ n P-P or S-D interference ¨ h 1 T┴ n Miller 07, Burkardt 07, Avakian et al 08. 11/3/2020 47
Phase-space Distribution? n n The state of a classical particle is specified by its coordinate and momentum (x, p): phase-space In quantum mechanics, Wigner introduced the first phase-space distribution in quantum mechanics (1932) ¨ Heavy-ion collisions, quantum molecular dynamics, signal analysis, quantum info, optics, image processing…
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