1. Zhongbo Kang Los Alamos National Laboratory Recent progress on TMD study and future perspective at the EIC Baryons 2016 Tallahassee, Florida May 16–20, 2016

2. Outline  Transverse momentum dependent distributions (TMDs): how they have challenged and greatly brought forward our understanding of the hadron structure and novel QCD dynamics  Sivers function is NOT universal: sign change from SIDIS to DY  Collins function is universal: same in SIDIS, e+e-, and pp  Global analysis: universality and TMD evolution  Moving forward: Electron Ion Collider (EIC)  Precision study of valence quark TMDs  First study of TMDs for sea quark and gluons  Summary 2

3. Hadron structure  Frontier science: to explore the partonic structure of the nucleon, and to understand the associated QCD dynamics  High energy scattering: to extract information on the nucleon structure, we send in a probe and measure the outcome of the collisions 3 Drell-Yan (DY) Deep Inelastic Scattering (DIS) Quantum many-body system Rutherfold’s experiment

4.  Perturbative QCD paradigm: Asymptotic freedom + QCD factorization How to trace back? 4 2004 Asymptotic freedom ↓ perturbation theory for quarks and gluons ↓ only hadrons are observed in experiments (confinement) calculablemeasuredextracted Parton distribution function quark

5. Recent advance in hadron structure  Hadron 3D structure: both longitudinal + transverse momentum dependent structure (confined motion in a nucleon)  Transversely polarized scattering provides new structure of proton 5 Transverse Momentum Dependent parton distribution (TMDs) Longitudinal motion only Longitudinal + transverse motion

6. TMDs: rich quantum correlations 6 Pion Quark Polarization U L T Quark Polarization U L T Collins TMD parton distribution TMD fragmentation function Transversal Helicity

7. Sivers function: non-universal  Sivers function: unpolarized quark distribution inside a transversely polarized proton 7 Spin - independent Spin-dependent Collins 02, Boer-Mulders-Pijlman 03, Collins, Metz 04, Kang Qiu, PRL 09, … 1990: introduced by D. Sivers, to describe the large single spin asymmetry measured in inclusive hadron production in p+p collisions at Fermilab 1993: J. Collins shows Sivers function has to vanish due to time-reversal invariance 2002: Brodsky, Hwang, Schmidt performed an explicit model calculation, showed the existence of the Sivers function 2002: Original proof missed the gauge link (needed to properly define gauge invariant distribution), once added, found Sivers function in SIDIS is opposite to that in Drell-Yan 1990: introduced by D. Sivers, to describe the large single spin asymmetry measured in inclusive hadron production in p+p collisions at Fermilab 1993: J. Collins shows Sivers function has to vanish due to time-reversal invariance 2002: Brodsky, Hwang, Schmidt performed an explicit model calculation, showed the existence of the Sivers function 2002: Original proof missed the gauge link (needed to properly define gauge invariant distribution), once added, found Sivers function in SIDIS is opposite to that in Drell-Yan

8. Collins function: universal  Collins function: unpolarized hadron from a transversely polarized quark 8 h Metz 02, Collins, Metz 04, Yuan 08, Yuan, Zhou 09, Boer, Kang, Vogelsang, Yuan, PRL 10, … Spin - independent Spin-dependent 2002: Metz studied the universality property of Collins function in a model-dependent way – very subtle – finally found it is universal between SIDIS and e+e- 2004: Collins and Metz have general arguments 2008: Yuan generalizes to pp 2010: perturbative tail calculation, demonstrate the gauge link does not contribute 2002: Metz studied the universality property of Collins function in a model-dependent way – very subtle – finally found it is universal between SIDIS and e+e- 2004: Collins and Metz have general arguments 2008: Yuan generalizes to pp 2010: perturbative tail calculation, demonstrate the gauge link does not contribute

9. TMD factorization in a nut-shell  Drell-Yan:  Factorized form and mimic “parton model” 9 Factorization of regions: (1) k//P 1, (2) k//P 2, (3) k soft, (4) k hard Factorization of regions: (1) k//P 1, (2) k//P 2, (3) k soft, (4) k hard mimic “parton model”

10. TMD evolves  Just like collinear PDFs, TMDs also depend on the scale of the probe = evolution 10 Collinear PDFs DGLAP evolution Resum Kernel: purely perturbative TMDs Collins-Soper/rapidity evolution equation Resum Kernel: can be non-perturbative when

11. TMD evolution in b-space  We have a TMD above measured at a scale Q. So far the evolution is written down in the Fourier transformed space (convolution → product)  In the small b region (1/b >> Λ QCD ), one can then compute the evolution to this TMD, which goes like 11 Collins-Sopoer-Sterman papers Kang, Xiao, Yuan, PRL 11, Aybat, Rogers, Collins, Qiu, 12, Aybat, Prokudin, Rogers, 12, Sun, Yuan, 13, Echevarria, Idilbi, Schafer, Scimemi, 13, Echevarria, Idilbi, Kang, Vitev, 14, Kang, Prokudin, Sun, Yuan, 15, 16, … Only valid for small b

12.  Fourier transform back to the momentum space, one needs the whole b region (large b): need some non-perturbative extrapolation  Many different methods/proposals to model this non-perturbative part  Eventually evolved TMDs in b-space TMD evolution contains non-perturbative component 12 Collins, Soper, Sterman 85, ResBos, Qiu, Zhang 99, Echevarria, Idilbi, Kang, Vitev, 14, Aidala, Field, Gamberg, Rogers, 14, Sun, Yuan 14, D’Alesio, Echevarria, Melis, Scimemi, 14, Rogers, Collins, 15, … longitudinal/collinear parttransverse part Non-perturbative: fitted from data The key ingredient – ln(Q) piece is spin-independent Since the polarized scattering data is still limited kinematics, we can use unpolarized data to constrain/extract the key ingredient for the non-perturbative part

13. TMD global analysis  Outline of a TMD global analysis: numerically more heavy 13 yes Model ansatz for TMDs with initial set of parameters Evolve TMDs to relevant scale with TMD evolution Model ansatz for non- perturbative evolution kernel calculate the cross section/asymmetry as well as χ 2 no χ 2 minimum? Fourier transform back to momentum space

14. Unpolarized TMDs: SIDIS  Comparison to COMPASS data 14 Echevarria, Idilbi, Kang, Vitev, 14

15. Drell-Yan and W/Z production  Comparison with DY, W/Z pt distribution 15  Works for SIDIS, DY, and W/Z in all the energy ranges DY Z W

16. QCD evolved unpolarized TMD  What evolution does  Spread out the distribution to much larger kt  At low kt, the distribution decreases due to this spread 16 Based on Echevarria, Idilbi, Kang, Vitev, 14

17. Sivers asymmetry from SIDIS  Sivers asymmetry has been measured in SIDIS process: HERMES, COMPASS, JLab 17 Sivers function

18. Sivers function with energy evolution  Example of the fit: JLab, HERMES, COMPASS 18 Echevarria, Idilbi, Kang, Vitev, 14

19. Extracted Sivers function and evolution  χ 2 /d.o.f. = 1.3, the collinear part is plotted: only u and d valence quark Sivers are constrained  Visualization: positive = more quark moves to the left (Q 2 =2 – 100 GeV 2 ) 19 D U

20. Sign change and predictions for W/Z  Sivers effect: still need DY/W/Z to verify the sign change, thus fully understand the mechanism of the SSAs  Reverse the sign of Sivers function from SIDIS, make predictions for W/Z at 510 GeV RHIC energy  Note: sea quark Sivers functions are not constrained from the current data, so the backward rapidity region has large uncertainty 20

21. Uncertainty in the evolution formalism  Even the evolution formalism itself has large room to improve – non- perturbative Sudakov needs further improvement 21 w/o TMD evolution Kang, 2015

22. Experimental evidence of sign change  STAR measurements: the data favors sign change  Both theory and experiment has large uncertainty: hope to be improved in the near future (2017 run) 22 STAR, PRL 16, arXiv:1511.06003 KQ = Kang, Qiu, PRL09 – w/o evolution

23. Sivers Transversal helicity Transverse W program  All the spin correlations in polarized p+p collisions 23 up down Huang, Kang, Xing, Vitev, PRD16

24. Collins asymmetry from SIDIS and e+e-  SIDIS and e+e-: combined global analysis 24 transversity Collins function

25. Collins asymmetry in SIDIS  Fitting of SIDIS data 25 HERMES COMPASS Kang, Prokudin, Sun, Yuan, PRD 15 & 16 JLab

26. Collins asymmetry in e+e-  Fitting of e+e- data from BaBar and Belle 26 BaBar Belle

27. Fitted TMDs  Fitted quark transversity and Collins function: x (z) -dependence  Collins function: pt-dependence 27

28.  Collins asymmetry can also be studied through the azimuthal distribution of hadrons inside a jet in p+p collisions  Such an asymmetry has been measured by STAR at RHIC  Could be used to test the universality of the Collins functions Collins asymmetry in p+p 28 h jet

29. Hadron azimuthal distribution in a jet  Indicate the universality of the Collins function in pp collisions  w/o TMD evolution 29 Collins function from a Gaussian fit: Anselmino, et.al., arXiv: 1510.05389 Kang, Prokudin, Ringer, Sun, Yuan, 16, in preparation STAR preliminary data

30. Future: what EIC can do  High precision quantitative measurements of all the quark TMDs in the valence region, with the ability to go to sufficiently large values of Q 2 in order to suppress potential higher twist contaminations  First-ever measurements of the TMDs for anti-quarks and gluons  Multi-dimensional representations of the observables leading to TMDs  Systematic studies of perturbative QCD techniques (for polarization observables) and studies of QCD evolution properties of TMDs 30

31. Wide kinematic coverage  (x, Q 2 ) coverage of EIC, HERMES, COMPASS, and Jlab 12  EIC: unique position – valence region at much larger Q 2  Accessing low-x down to 10 -5, where sea quarks and gluons can be studied in detail 31

32. Example: improvement for Sivers functions  Extraction of both valence and sea-quark Sivers function can be greatly improved (with high luminosity) 32

33. Gluon TMDs  Gluon correlation  Example: linear polarized gluon (gluon Boer-Mulders function) in unpolarized proton  Accessible through DIS dijet production: 33 Dumitru, Lappi, Skokov, PRL 15, also Mulders, Ridrigues, 01, Boer, Mulders, Pisano, 09, Metz, Qiu, 11, …

34. Summary: EIC  The EIC will be a unique facility to systematically investigate the transverse momentum dependent parton distribution comprehensively  While the measurements of quark TMDs have begun in fixed-target experiments, the gluon TMDs can only be studied at an EIC, and such studies would be unprecedented  The QCD dynamics associated with the transverse momentum dependence in hard processes can be rigorously studied at the EIC because of its wide kinematic coverage 34

35. Backup 35

36. Moving forward  Nobody is perfect: different approaches on TMD global analysis  Simple Gaussian model: describe all the asymmetry data equally well – But certainly cannot describe the absolute cross section at high energy  TMD evolutions in b-space with different non-perturbative models: doing much better in describing both low and high energy cross sections – but seems too strong suppression  How to move forward  Perform data analysis directly in b-space  Perform evolution directly in momentum space  Improve the current non-perturbative model  Concentrate more on the cross sections, not the asymmetries (ratios)  COMPASS and RHIC: DY/W data on spin asymmetry could really help constrain these ideas  Of course, it is time to move to gluon TMDs now 36 Boer, Gamberg, Prokudin, et.al. Collins, Rogers; Kang, Qiu; Prokudin, Yuan; … Kang, in preparation

37. Opportunities at LHC  TMD opportunities at the LHC 37 Z boson Hadron in a jet Photon + jet

38. TMD study  Study on TMDs are extremely active in the past few years, lots of progress have been made  With great excitement, we look forward to the future experimental results from COMPASS/RHIC, as well as Jefferson Lab, of course also LHC, most importantly, the EIC 38 Thank you!