1. Simonetta Liuti University of Virginia “Garyfest 2010” Jefferson Lab October 29, 2010 Generalized Parton Distributions Interpretation of Exclusive Deep Inelastic Processes

5. Generalized Parton Distributions are a new way of interpreting a “growing” class of exclusive deep inelastic phenomena (X.Ji, D. Müller, A. Radyushkin) Prototype Process: “Deeply Virtual Compton Scattering” q k' + =(X- Δ)P +, k T - Δ T q'=q+Δ k + =XP +, k T P' + =(1- Δ )P +, - Δ T P+P+

6. Amplitude GPDs are embedded in soft matrix elements for deeply virtual Compton scattering p + =XP + p’ + =(X- Δ )P + P’ + =(1- Δ )P + P+P+ p+q q q’=q+ Δ

7. GPDs – using the fact that factorization works at the amplitude level - provide a key to interpreting a number of “exclusive” DIS processes, other than DVCS GPDs with Gary Transversity and Tensor Charge From exclusive DIS π o electro production Studies of strange and charm content of nucleon at Jlab/12 Gev and future ElectronIonCollider  transversity Deeply Virtual Neutrino Production of π o from Nucleon and Nuclear Targets Hyperon and charmed hyperon transverse polarization in unpolarized scattering

8. Re k - Im k - 3'1' 2' Re k - Im k - 2'3' 1' X>ζ X<ζ 3 1 2

9. P+P+ k’ + =(  -X)P + P’ + =(1-  )P + In ERBL region struck quark, k, is on-shell k + =XP + P+P+ k’ + =(X-  )P + P’ + =(1-  )P + P X + =(1-X)P + In DGLAP region spectator with diquark q. numbers is on-shell Analysis done for DIS/forward case by Jaffe NPB(1983)

10. P+P+ k’ + =(  -X)P + P’ + =(1-  )P + ERBL region corresponds to semi-disconnected diagrams: no partonic interpretation

11. (1) GPDs in ERBL region seem to be described within QCD, consistently with factorization theorems, only by multiparton configurations (2) Dispersion relations cannot be applied straighforwardly to DVCS. The “ridge” does not seem to contain all the information borrowed from D. Mueller

12. The next decade…role of QCD at the LHC LHC results from multi-TeV CM energy collisions will open new horizons but many “candidate theories” will provide similar signatures of a departure from SM predictions… Precision measurements require QCD input QCD: A background for “beyond the SM discovery” Interesting dynamical questions for QCD at untested high energies Measured x-section Parton distributions Hard process x-section σ ij P2P2 P1P1

13. Most important points for EIC 1) Our understanding of the structure of hadrons is … disconcertingly incomplete 2) Rich dynamics of hadrons can only be accessed and tested at the desired accuracy level in lepton DIS Uncertainties from different PDF evaluations/extractions ( Δ PDF ) are smaller than the differences between the evaluations ( Δ G ) Δ PDF < Δ G d-bar u-valenced-valence Gluon

14. Strange and charm components studied through hard exclusive processes Why exclusive processes? LHC processes are sensitive to charm content of the proton  Higgs production: SM Higgs, charged Higgs,  Precision physics (CKM matrix elements, V tb ….): single top production, … C.P.Yuan and collaborators IC Electroproduction

15. Data are at very low x where they cannot discriminate whether IC is there 10 -2 x 10 -3 IC/no-IC

16. - Λ c, D o, and D o exclusive production is governed by chiral-odd soft matrix elements (  Generalized Parton Distributions, GPDs) which cannot evolve from gluons! Λ c, D o, and D o used as triggers of “intrinsic charm content”! P+P+ p+q q q’=q+ γ Chiral-odd GPDs: H T,E T,.. Λ c, D o, … Focus e.g. on heavy flavor production at EIC kinematics -

17. Intrinsic Charm (IC) Gluon Fusion (GF) vs. IC content of proton can be large (up to 3 times earlier estimates) but PDF analyses are inconclusive (J.Pumplin, PRD75, 2007) Inclusive

18. Intrinsic Charm (IC) “Light Cone” based Processes Hadronic Processes Meson Cloud: Thomas, Melnichouk …Brodsky, Gunion, Hoyer, R.Vogt, …

19. strange γ *p  K + Λ  2H u - H d + H s γ*p  K o Σ +  H d – H s γ *n  K o Σ o  H u - H s (s) p H c c p u u p  u + ud  cud = Λ c p  ccuud  (u u) cud = Λ c -- ( 2 ) ( 1 ) What Observables? Spin Asymmetries from Exclusive Strange/Charm Quark Meson Production! charm γ *p  D o Λ c +  2H u - H d + H c γ*p  D o Σ c +  H d – H c γ *n  D o Σ c o  H u - H c SU(3) (SU(4) for charm) relations allow one to extract H s (H c ) (Λ)(Λ) (K + ) “di”quark“tetra”quark (s) (K + )

20. Slice SU(4) weight diagrams to obtain SU(3) subgroup weight diagrams This replaces u,d,s by u,d,c octet relations

21. Pseudoscalar Mesons Electroproduction and Chiral Odd GPDs (S. Ahmad, G. Goldstein and S.L., PRD (2008))

22. LAB e' e γ * Unpolarized Cross Section

23. Q 2 dependence in exclusive meson production Jlab Unexpected dominance of transverse components

24.  “Regge factorization” QCD factorization π o vertex is described by current operators: γ 5 or γ μ γ 5 chiral-even structure chiral-odd structure GPDs: H, E,… ~ ~ GPDs: H T, E T, H T, E T … ~ ~ J PC =1 -- J PC =1 +- ρ, ω,.. b 1, h 1 

25. t-channel exchange vertex modeled as pseudoscalar-meson transition form factor Islam Bedir’s talk ρ, ω b 1, h 1 ρ, ω, b 1, h 1 J PC =1 -- ( 3 S 1 ) J PC =1 +- ( 1 P 1 ) J PC =0 -+ mesons quark content: Q 2 dependence

26. Chiral Even Sector: M. Diehl and D. Ivanov (2008) Only combination good for π o production

27. GPDs: H, E, and Weak Form factors ~ ~ g P (t) = pseudoscalar form factor dominated by pion pole

28. E ~ Goeke et al. 1) For  o production the pion pole contribution is absent! 2) The non-pole contribution is very small! “non-pole” contribution pion pole contribution

29. π o, η c electroproduction happens mostly in the chiral-odd sector  it is governed by chiral-odd GPDs  issue overlooked in most recent literature on the subject Since chiral-odd GPDs cannot evolve from gluons we have proven that charmed mesons production uniquely single out the “intrinsic charm content”!

30. Helicity Amplitudes formalism from Goldstein and Owens photon initial proton final proton pion Factorized form P’,  ’ k’, ’ P,  k, “quark-proton helicity amp.”  quark scattering amp. 6 “f” helicity amps

31. Rewrite helicity amps. expressions using new GFFs Q 2 dependent pion vertex GFFs elementary subprocess

32. Standard approach (Goloskokov and Kroll, 2009)  leading twist contribution within OPE, leads to suppression of transverse vs. longitudinal terms  twist-3 contribution is possible However… suppression is not seen in experiments Need to devise method to go beyond the collinear OPE: consider a mechanism that takes into account the breaking of rotational symmetry by the scattering plane in helicity flip processes (transverse d.o.f.) See also

33. Distinction between ρ,ω (vector) and b 1,h 1 (axial-vector)exchanges J PC =1 -- J PC =1 +- transition from ρ,ω (S=1 L=0) to π o (S=0 L=0) L =0 transition from b 1,h 1 (S=0 L=1) to π o (S=0 L=0) L =1 “Vector” exchanges no change in OAM “Axial-vector” exchanges change 1 unit of OAM! This yields configurations of larger “radius” in b space (suppressed with Q 2 ) Because of OAM axial vector transition involves Bessel J 1

36. At this point we need a sensible parametrization…

37. In doing so … a large set of increasingly complicated and diverse observations is involved, from which PDFs, TMDs, GPDs, etc… are extracted and compared to patterns predicted theoretically What goes into a theoretically motivated parametrization for GPDs...? The name of the game: Devise an analytical form combining essential dynamical elements with a flexible model whose parameters can be tuned However…for a fully quantitative analysis that is constrained by the data it is fundamental to evaluate both the number and type of parameters Multi-dimensional phase space (Elliott Leader)

38. “Conventional” based on microscopic properties of the theory (two body interactions) “Neural Networks” study the behavior of multiparticle systems as they evolve from a large and varied number of initial conditions. Two main approaches “Regge” Quark-Diquark + Q 2 Evolution Proceed conventionally at first: Ahmad et al.,

39. LSS06 New GPDs “physically motivated” Parametrization G.Goldstein, O. Gonzalez Hernandez, S.L.

40. Predict J u and J d

41. Covariant quark diquark model Re k - Im k - 2'3' 1' X>ζ 3 1 2

42. Skip some neat details, derivation from helicity amps. and connection with Chiral Odd GPDs (Kubarovsky’s pi0 data)

43.  /2  H-H- H+H+ (H + + H - )/2=H q Q 2 dependent dominated by valence Implement Crossing Symmetries in ERBL region

44. ERBL Region Ahmad et al., EPJC (2009) Determined from lattice moments up to n=3

45. Recursive Fitting Procedure vs. Global Fits In global fits we apply constraints simultaneously  calculate χ 2 (and covariance matrix) once including all constraints  Need to find the solution for a system with n equations Everytime new data come in the fit needs to be repeated from scratch  In a recursive fitting procedure (Kalman) one applies constraints sequentially  Need to update solution after each constraint  Find solutions for < n systems, each one with fewer equations Better control at each stage Mandatory for GPDs (some of this is implicit in Moutarde’s approach)

46. 7 parameters per quark flavor per GPD, but we have not constrained the ζ dependence yet….. DVCS data

47. Hall A Hall B GGL’s prediction based on our choice of physical model, fixing parameters from “non-DVCS” data Hall A ζ=0.25 x Bj = ζ ζ=0.36 ζ=0.45 ζ=0.13

48. For strange and charm  Replace PDF used for light quarks GPDs with NP strange/charm based one

49. HAPPEx+E734 G0 + BNL E734  Replace FF used for light quarks GPDs with upper limit on charm based one Pate, McKee, Papavissiliou, PRC78(2008)

50. G.Goldstein, S.L. (preliminary) Ratio η c / π o

51. Problem of Transverse Polarization of Hyperons and Charmed Baryons in unpolarized pp collisions p Λ p What generates polarization?

52. Spin degrees of freedom in pp scattering Outstanding puzzle! Collinear Factorization  Polarizing Fragmentation Function Non Collinear Factorization D. Boer, DIS 2010 Set of all data compiled by K. Heller Go beyond collinear factorization, Insert k T and polarization dependent Fragmentation function

53. 1.Gluon fusion dominant mechanism for producing polarized massive quark pair 2. Low p T phenomenon 3. Recombination rules Model of hyperon polarization Dharmaratna & GRG (1990,96,99) PΛPΛ p T (GeV) 3/18/2016 p PΛPΛ p T (GeV)  +p  C +X Polzn(Λ C ) E791 Large mass scale

54. Hyperon and Charmed Hyperon Polarization work with G. Goldstein and P. Di Nezza (ALICE) udud anti-c ΛcΛc + Dharmaratna and Goldstein

55. Interpretation in new language of GPDs: Generalized Fracture Functions Next, new frontier….. H T hh p p See also work by F. Ceccopieri and L.Trentadue Phys.Lett.B (2006) D. Sivers, PRD81(2010) O.Teryaev, Acta Phys. Polonica (2002) A. Kotzinian, PLB (2003)

56. Finally, somewhat unrelated… Work in progress with K. Kathuria, and S.Taneja (BNL) What observables? A UT..... Taneja and S.L., arXiv:1008.1706

57. Conclusions and Outlook My own interaction with Gary has given me ”lots of courage” Together we keep on generating ideas, students are getting involved, more projects, collaborations….