Simonetta Liuti University of Virginia Structure of Nucleons and Nuclei Workshop

1. Generalized TMDs • SimonettaLiuti • University of Virginia • Structure of Nucleons and Nuclei Workshop • Como, June 10th-14th,2013 presented by Osvaldo Gonzalez Hernandez - Torino SimonettaLiuti

2. In collaboration with: Aurore Courtoy (Liege U.) Gary Goldstein (Tufts U.) Osvaldo Gonzalez Hernandez (INFN Torino since Fall 2012) Graduate Students Kunal Kathuria (U.Va.) Evan Askanazi (U.Va.) Abha Rajan (U.Va.) Simonetta Liuti

3. Question of what components do Lq and measure (Ji, Xiong, Yuan, 2011, 2012, Burkardt 2012) Simonetta Liuti

4. A Saga in Several Episodes: Developing a Sum Rule for Angular Momentum • A Sum Rule was constructed which identified components of the Energy Momentum Tensor (EMT) with the Angular Momentum carried by quarks and gluons. • (Jaffe&Manohar (JM)) 1990 Simonetta Liuti

5. Partonic picture: • work directly in A+=0 gauge • quark and gluon spin components are identified with the n=1 moments of spin dependent structure functions from DIS, ΔΣ and ΔG. ΔG ΔΣ Simonetta Liuti

6. 1997 New Relation (X.Ji) e q'=q+Δ New processes (DVCS …) were thought of, whose structure functions – the GPDs - admit n=2 moments that were identified with the (spin+OAM) quark and gluon components of the SR q p+q p’+= p –Δ p+ H,E P P’ Simonetta Liuti

7. Lots of work followed in a series of papers by Wakamatsu, Leader and collaborators, Chen et al., Hatta, and Burkardtto understand the origin of this discrepancy. Simonetta Liuti

8. We would like to do some phenomenology Conceptual issues: “What type of information can one obtain?” The goal is to give a partonic interpretation of the observables Once a scheme, whichever, is defined to connect with experiment, we stick to it. Corollary: If Lcan is not observable, does it exist? Practical issues: “how can one extract information from experiment”? Example: GPDs are hard to extract because they need to be “deconvoluted” from Compton Form Factors… Both points pose important theoretical problems. Simonetta Liuti

9. GPD x,kT x,kT’ bin bout p p’ Simonetta Liuti

10. TMD x,kT zT x,kT bin bout p p’ p’=p, kT’=kT Simonetta Liuti

11. What do we obtain (or wish to obtain) from experiment GPD Transverse coordinate density distributions Dirac Pauli d u d u (using constraints from Jlab flavor separated form factor data, G. Cates et al, 2011) Simonetta Liuti

12. What do we obtain (or wish to obtain) from experiment TMDs u Gonzalez et al. Bacchetta, Conti Radici Calculations done using reggeized diquark model, O. Gonzalez et al., arXiv:1206.1876 Qo2≈ 0.3 GeV2 d This needs to be evolved to the scale of the data (Collins, Rogers, Boglione, Prokudin, …) Simonetta Liuti

13. Unintegrated GPDs  GTMDs Fourier Transform wrt ΔTWigner Distributions Notice! Two transverse momenta, simultaneously present What partonic configurations do they correspond to? Simonetta Liuti

14. GTMD zT b p p’ average shift • GTMDs correlate partonic configurations with both: • a shift in transverse position from the initial to final state zT • an average transverse position  b. When can these configurations exist in the “impulse approximation”, and when do we need to introduce FSI? Simonetta Liuti

15. How would we observe GTMDs? q’=q+Δ, Λγ’ q, Λγ k’= k –Δ. λ’ k, λ p, Λ p’= k-Δ, Λ’ u-channel two body scattering k’= k –Δ. λ’ p, Λ ϑ k, λ Simonetta Liuti

16. Transverse Plane x p’CM= kCM-Δ, Λ’ k’CM= kCM –Δ. λ’ pCM, Λ ϑ This angle determined by ΔT kCM, λ CoM motion determined by z y Simonetta Liuti

17. In CoM the scattering happens in one plane therefore there is only one transverse direction defined by ΔT • In CoM frame ΔT and individual partons kT are parallel to one another • Average kT describes the motion of the CoM Simonetta Liuti

18. GTMDs in Cartesian Basis Meissner, Metz, Schlegel, JHEP 2009 λ λ' same as GPDs “New” terms can exist Simonetta Liuti

19. Spin(Helicity/Transversity) Basis Quark-proton helicity amplitude Simonetta Liuti

20. Chiral Even Sector Metz Us Helicity amps content F11 2F13-F11 G14 2G13-G14 Simonetta Liuti

21. Can the new GTMDs F14 and G11 be defined at leading twist? • In two-body scattering these terms are Parity violating • (valid in CM frame, demonstration in general frame hinges on • appropriate Lorentz Transformation) • In a quark-target model only H, H are present ~ Simonetta Liuti

22. Why are they important: the idea has been emerging that canonical OAM can be related to F14 Lorce and Pasquini, 2011 Ji, Xiong and Yuan, 2012 Simonetta Liuti

23. However F14 drops out of the observables Not because it contains “even more information on the structure of the proton than what can be measured”, but for a good reason… Simonetta Liuti

24. The demonstration is rather technical Out of all the functions that parameterize the generalized correlator (MMS’09)… … the matrix elements for the “type 3” ones transform the opposite way under Parity. These define F14 Simonetta Liuti

25. Summary so far… We confirm that canonical AM cannot be measured if defined as because it corresponds – in two body scattering – to a combination of helicity amplitudes that violates Parity Simonetta Liuti

26. Consider now the angular momentum sum rule including twist 3 contributions Belitsky and Mueller (2000), Polyakov et al. (2000), Hatta (2011) -Lq -Jq Sq Twist 3 decomposition of hadronic tensor OAM is a twist three contribution Simonetta Liuti

27. In order to describe GTMDs including partonic interactions, i.e.moving out of a 2 body scattering picture, we need a situation where even in the CoM, one can define two independent transverse vectors as if there were a third particle, so that the additional combinations giving rise to “LU”-type contributions can exist Simonetta Liuti

28. Twist 3 GTMDs MMS’09 spin non flip spin flip Simonetta Liuti

29. Simonetta Liuti

30. Finally…a prerequisite for all these calculations is that we use a model whose parameters are constrained by a quantitative fit to all data which are relevant for GPDs (Form Factors, DIS and DVCS) Simonetta Liuti

31. Sections of Wigner distributions: Completely Unpolarized Case kT u quark Simonetta Liuti

32. All together: integrated over x and kT (this is a fit to real data: DVCS+G.Cates et al) u quark d quark Simonetta Liuti

33. Sections of Wigner distributions: Transversely Polarized Case kT u quark Simonetta Liuti Simonetta Liuti 32 APS Denver 4/12/13

34. All together: integrated over x and kT Δ1Eu - Δ1Ed Simonetta Liuti

35. Twist 3 component  G2 Simonetta Liuti

36. Summary of this part and Open Questions • G2 can be measured directly, and it does have a partonic interpretation, if one views it as a twist 3 quantity. • We can distinguish in models a WW part defining OAM, and a genuine twist 3 part. • Canonical angular momentum cannot be measured directly, but it can be linked to G2 through M. Burkardt’s “force-type” correction • We need to devise experiments that are sensitive to this contributions (they might be already in the available data!) • Question of L vs. T interpretation • We focused mainly on quarks, question of gluon component One way to shed light on these questions is to look at deuteron Simonetta Liuti

37. Spin 1 systems, due to • The presence of additional L components (D-waves) • Isoscalarity • provide a crucial test the working of the angular momentum sum rules Simonetta Liuti

38. What are the quark and gluon angular momenta in the deuteron? z=pN+/P+D λq Nucleon DVCS λN Deuteron λ HISO=Hu+Hd EISO=Eu+Ed Simonetta Liuti

39. Sum Rules in Deuteron (K.Kathuria) Momentum Spin 1/2 OAM Spin 1/2 Form factors from the respective Energy Momentum tensors, Tμν Simonetta Liuti

40. If f++(z) = f+0(z)=δ(1-z) then H2=H+E Longitudinal Nucleon Deuteron F1+F2= GM GM Transverse Deuteron Differently from the nucleon, in the transverse case, we are not finding the same relation (other GPDs describing charge and tensor component enter…). More details later… Simonetta Liuti

41. How does Ji sum rule differ from JM in the deuteron? Effect of evolution Models are important Model calculations of L with w.f.s’ seem to lead to similar conclusions as M.Burkardt, more to explore here… avenue to compare different schemes? Using GPDs from Goldstein, Gonzalez, SL, PRD84 Simonetta Liuti

42. Nuclear effect much larger than in unpolarized scattering Needs to be treated systematically… Simonetta Liuti

43. Observables: DVCS from deuteron subleading Can the deuteron help us understand the role of gluon OAM? (Brodsky, Gardner, 2006) By connecting Lg to SSA in ≈ 0 Both L q and Lg contribute! Since Lq disappears because of isospin symmetry, if AUTπ is 0 then Lg is 0 Simonetta Liuti

44. Two ways to go beyond the two body scattering scenario: 3 2 Consider twist three terms (consistent with Polyakov’s sum rule, EPJC 37 (2004) Consider target fragmentation: generalized fracture functions 1 2 1 3

45. Our model for fracture functions (work in progress…) q-bar frag. h outgoing qqqq-bar B Initial proton A scattered quark

46. GG, S. Liuti and O. Gonzalez, GPDS, THEIR RELATIONSHIPS WITH TMDS & RELATED TOPICS Proceedings of QCD-N12, Bilbao, Spain - 2012 Simonetta Liuti

47. Conclusions We conclude that the distribution of an unpolarized quark in a longitudinally polarized nucleon does indeed measure OAM We provide a theoretical basis for the “simple moment” of Wigner distributions, connecting to twist 3 GPDs Belitsky, Mueller, Polyakov, Hatta,… Now one can think seriously of observables (DV processes including twist 3 GPDs) Our argument stresses the fact that in order to measure OAM one has to go beyond a two body scattering picture Transverse vs. Longitudinal sum rule? Gluon components?  we should look into Spin 1 systems also Simonetta Liuti

48. G. Goldstein, O. Gonzalez Hernandez, S.Liuti, J.Phys. G, 39 (2012) 11500 G. Goldstein, O. Gonzalez Hernandez, S.Liuti, Phys. Rev. D84, 034007 (2011) S.K. Taneja, K. Kathuria, S.Liuti, G. Goldstein, Phys. Rev. D86 (2012) G. Goldstein, O. Gonzalez Hernandez, S.Liuti, K. Kathuria, arXiv:1206.1876, subm. PRC G. Goldstein, O. Gonzalez Hernandez, S.Liuti, K. Kathuria, “Proceedings of 4th QCD Evolution Workshop”, Jefferson Lab, May (2012) Simonetta Liuti

49. Backup Simonetta Liuti

50. Sections of Wigner distributions: Mixed Transverse/Longitudinal Basis Simonetta Liuti