Simonetta Liuti University of Virginia “ Garyfest 2010 ” Jefferson Lab October 29, 2010

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

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

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

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 Studies of strange and charm content of nucleon at Jlab/12 Gev and future ElectronIonCollider  transversity Transversity and Tensor Charge From exclusive DIS πo electroproduction GPDs with Gary Hyperon and charmed hyperon transverse polarization in unpolarized scattering Deeply Virtual Neutrino Production of πo from Nucleon and Nuclear Targets

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

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

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

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 P1 σij P2 Measured x-section Parton distributions Hard process x-section

13. Most important points for EIC1) Our understanding of the structure of hadrons is … disconcertingly incomplete Gluon d-bar 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 (ΔPDF) are smaller than the differences between the evaluations (ΔG) ΔPDF < ΔG u-valence d-valence

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

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

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

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

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

19. What Observables? Spin Asymmetries from Exclusive Strange/Charm Quark Meson Production! ( 2 ) ( 1 ) u (K+) (K+) (s) u c (s) Hc Hc p p (Λ) - - p  ccuud  (u u) cud = Λc p  u + ud  cud = Λc “tetra”quark “di”quark strange γ*p K+Λ2Hu - Hd + Hs γ*p  Ko Σ+Hd – Hs γ*n  Ko ΣoHu - Hs SU(3) (SU(4) for charm) relations allow one to extract Hs (Hc) charm γ*p DoΛc+2Hu - Hd + Hc γ*p  Do Σc+Hd – Hc γ*n  Do ΣcoHu - Hc

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. Unpolarized Cross Section LAB γ* e e'

23. Q2 dependence in exclusive meson production Jlab Unexpected dominance of transverse components

24.   ρ, ω, .. JPC=1-- JPC=1+- b1, h1 QCD factorization “Regge factorization” chiral-even structure ~ ~ π o vertex is described by current operators: γ5 or γμγ5 GPDs: H, E,… ~ ~ GPDs: HT, ET, HT, ET… chiral-odd structure

25. Q2 dependence t-channel exchange vertex modeled as pseudoscalar-meson transition form factor Islam Bedir’s talk ρ, ω, b1, h1 ρ, ω b1, h1 JPC=0-+ JPC=1-- (3S1) JPC=1+-(1P1) mesons quark content:

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

27. ~ ~ GPDs: H, E, and Weak Form factors gP(t) = pseudoscalar form factordominated by pion pole

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

29. πo,ηcelectroproduction 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-oddGPDs cannot evolve from gluonswe have proven that charmed mesons productionuniquely single out the “intrinsic charm content”!

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

31. Rewrite helicity amps. expressions using new GFFs elementary subprocess GFFs Q2 dependent pion vertex

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 betweenρ,ω(vector) andb1,h1(axial-vector)exchanges transition from ρ,ω(S=1 L=0) to πo(S=0 L=0)L =0 JPC=1-- transition from b1,h1(S=0 L=1) to πo(S=0 L=0) L =1 JPC=1+- “Vector” exchanges no change in OAM “Axial-vector” exchanges change 1 unit of OAM! Because of OAM axial vector transition involves Bessel J1 This yields configurations of larger “radius” in b space (suppressed with Q2)

36. At this point we need a sensible parametrization…

37. 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 modelwhose parameters can be tuned 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 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) Two main approaches “Neural Networks” study the behavior of multiparticle systems as they evolve from a large and varied number of initial conditions. Proceed conventionally at first: Quark-Diquark “Regge” + Q2 Evolution Ahmad et al.,

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

40. Predict Ju and Jd

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

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

43. Implement Crossing Symmetries in ERBL region H+ (H+ + H-)/2=Hq H- dominated by valence ζ ζ/2 Q2 dependent

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 χ2 (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 ζ=0.45 Hall B ζ=0.36 Hall A ζ=0.25 GGL’s prediction based on our choice of physical model, fixing parameters from “non-DVCS” data ζ=0.13 xBj=ζ

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

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

50. Ratio ηc/πo G.Goldstein, S.L. (preliminary)