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Strategies to extract GPDs from data

Simonetta Liuti University of Virginia & Gary Goldstein Tufts University INT, 14-19 September 2009 APS DNP Meeting Saturday, October 25th, 2008. Oakland, USA. Strategies to extract GPDs from data. Introduce a step by step analysis Step 1, Step 2, Step 3, Step 4

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Strategies to extract GPDs from data

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  1. Simonetta Liuti University of Virginia & Gary Goldstein Tufts University INT, 14-19 September 2009 APS DNP Meeting Saturday, October 25th, 2008. Oakland, USA Strategies to extract GPDs from data

  2. Introduce a step by step analysis Step 1, Step 2, Step 3, Step 4 Interesting applications: Access Chiral-Odd GPDs, Nuclei: DVCS and 0 electroproduction on 4He Conclusions/Outlook Outline

  3. With the new experimental analyses at HERMES, Jlab, Compass… we are entering a new, more advanced phase of extracting GPDs from data Many concerns have been raised recently: No longer simple parametrizations (K. Kumericki, D. Muller) Q2 dependence (M. Diehl et al.) What type of information and accuracy from simultaneous measurements of different observables? (M. Guidal, H. Moutarde) How can one use Lattice + Chiral Extrapolations (P. Hägler, S.L.) How can one connect various experiments, separate valence from sea, flavors separation (P. Kroll, T. Feldman)... Use of dispersion relation: is it only necessary to measure imaginary part of DVCS, DVMP? (Anikin & Teryaev, Diehl & Ivanov, Vanderhaeghen, Goldstein & S.L.) Global analysis exists for TMDs (simpler partonic interpretation than GPDs) see e.g. M. Anselmino and collaborators

  4. DVCS Cross Section (Belitsky, Kirchner, Muller, 2002) Amplitude Angle between transverse spin and final state plane Azimuthal angle between planes

  5. Comtpon Scattering and Bethe Heitler Processes Dynamics

  6. Look for instance at DVCS-BH Interference

  7. Off forward Parton Distributions (GPDs) are embedded in soft matrix elements for deeply virtual Compton scattering (DVCS) q q’=q+ p+q p’+=(X-)P+ p+=XP+ P’+=(1- )P+ P+ Amplitude

  8. What goes into a theoretically motivated parametrization...? The name of the game: Devise a form combining essential dynamical elements with a flexible model that allows for a fully quantitative analysis constrained by the data Hq(X, , t)= R(X, , t) G(X, , t) “Regge” Quark-Diquark + Q2 Evolution

  9. Quark-Diquark model: two different time orderings/pole structure! DGLAP: quark off shell, spectator on shell ERBL: quark on shell, spectator off-shell X> X< Quark anti-quark pair describes similar physics (dual to) Regge t-channel exchange (JPC quantum numbers)

  10. Vertex Structures  k’+=(X-)P+ k+=XP+  P’+=(1- )P+ P+ PX+=(1-X)P+ PX+=(1-X)P+ S=0 or 1 Focus e.g. on S=0 Vertex function  2 2 O. Gonzalez Hernandez, S.L.

  11. Fixed diquark mass formulation DGLAP region ERBL region

  12. Reggeized diquark mass formulation Diquark spectral function  (MX2-MX2)  (MX2) MX2 DIS  Brodsky, Close, Gunion ‘70s

  13. Fitting Procedure • Fit at=0, t=0  Hq(x,0,0)=q(X) • 3 parameters per quark flavor (MXq, q, q) + initial Qo2 • Fit at=0, t0  • 2 parameters per quark flavor (, p) • Fit at 0, t0 DVCS, DVMP,… data (convolutions of GPDs with Wilson coefficient functions) + lattice results (Mellin Moments of GPDs) • Note! This is a multivariable analysis  see e.g. Moutarde, Kumericki and D. Mueller, Guidal and Moutarde •  additional parameters (how many?) t Regge Quark-Diquark

  14. =0,t=0 Parton Distribution Functions Notice! GPD parametric form is given at Q2=Qo2 and evolved to Q2 of data. Notice! We provide a parametrization for GPDs that simultaneously fits the PDFs: Hq(X,,t)= R(X,,t) G(X,,t) Regge Quark-Diquark

  15. Nucleon Form Factors = 0, t0 S. Ahmad, H. Honkanen, S. L., S.K. Taneja, PRD75:094003,2007

  16. Parameters from PDFs Parameters from FFs

  17. Some results… Hu Hd S. Ahmad, H. Honkanen, S. L., S.K. Taneja, (AHLT), PRD75:094003,2007

  18. , t S. Ahmad et al., EPJC (2009)  we were able to extend the parametrization to  taking into account lattice results on n=2,3 moments of GPDs  the new parametrization is valid for valence quarks only (not expected to be extended sensibly, “as it is”, into HERA/HERMES region: need sea quarks + gluons)  it works fine at Jefferson Lab kinematics

  19. Use information from Lattice QCD: (1) Assume lattice results follow dipole behavior for n=1,2,3    Extract dipole masses from lattice data  Relate dipole mass to “radius” parameter  Chiral extrapolation of dip. mass

  20. Polynomiality from lattice results up to n=3 n=2 n=3

  21. Results of Chiral Extrapolations proton form factor  Ashley et al. (2003)  Ahmad et al. (2008) -t (GeV2)

  22. New Developments (H.Nguyen) We repeated the calculation with improved lattice results (Haegler et al., PRD 2007, arXiv:0705:4295)

  23. A20u-d Results are comparable (up to n=2) to our “phenomenological” extrapolation We are investigating the impact of different chiral extrapolation methods: “direct” extrapolation applicable up to n=2 only M. Dorati, T. Gail and T. Hemmert (NPA 798, 2008) (Also using P. Wang, A. Thomas et al. )

  24. New Results are more precise and compatible with other chiral extrapolations A20u-d vs. (-t) Nguyen, S.L. Dorati

  25. Lattice results are used to model/fit the ERBL Region… We know the area from n=1 moment + constrained DGLAP

  26. Reconstruction of GPDs from Bernstein moments Weighted Average Value Location of X-bin Dispersion (error in X) * * Algebra a bit more complicated for  to transformation, details in EPJC(2009)

  27. Test with known, previously evaluated GPD, at 0

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

  29. New Analysis • Results are more accurate one can see trends • both isovector and isoscalar terms

  30. Summary of first three steps towards parametrization 0 7 + 1 (Qo) parameters v1 10 + 1 (Qo) parameters v2 use v1 for DGLAP region(X >  ) 0 use lattice calculations for ERBL region(X <  )

  31. BSA data are predicted at this stage Munoz Camacho et al., PRL(2006)

  32. Hall B (one binning, 11 more)

  33. Comparison with Jlab Hall A data (neutron) Mazouz et al. (2007)

  34. 0 Fit to JLAB data: real part of CFF from d+ + d- Real Part(work with S.Ahmad, H. Nguyen)

  35. Schematically Fitted directly at Q2 of data Cusp from reggeized ERBL  (-X) either from phenom.“DA type” shape, or diquark model

  36. Behavior determined by Jlab data on Real Part and Q2 dependence • Consistent with lattice determination!

  37. Dispersion Relations (brief parenthesis…) Dispersion Direct Difference Direct Dispersion G.Goldstein and S.L.,arXiv:0905.4753 [hep-ph]

  38. Dispersion relations cannot be directly applied to DVCS because one misses a fundamental hypothesis: “all intermediate states need to be summed over” This happens because “t” is not zero  t-dependent threshold cuts out physical states It is not an issue in DIS (see your favorite textbook, LeBellac, Muta, Jaffe’s lectures…) because of optical theorem From DR to Mellin moments expansion

  39. DVCS One proceeds backwards, from polynomiality  analytic properties (Teryaev) But here one is forced to look into the nature of intermediate states because there is no optical theorem t-dependent thresholds are important: counter-intuitively as Q2 increases the DRs start failing because the physical threshold is farther away from the continuum one (from factorization) Is the mismatch between the limits obtained from factorization and the physical limits from DRs a signature of the “limits of standard kinematical approximations”? (Collins, Rogers, Stasto and Accardi, Qiu)

  40. Dispersion Relations (brief parenthesis…) Dispersion Direct Difference Direct Dispersion G.Goldstein and S.L.,

  41. Applications

  42. Transversity Simple Ansatz h1(x,Q2) = q f1(x,Q2)  u HT(x, , t,Q2) = q H(x, , t,Q2)   d ET(x,  , t,Q2) = TqHT(x, , t,Q2) Related to Boer-Mulders function

  43. Nuclei GPDs & hadron tensor for Spin 0 nuclear target(Liuti and Taneja, PRC 2005)Exclusive o production from 4He (with G. Goldstein) OAM sum rule in deuterium (with S.K. Taneja)

  44. Jefferson Lab approved experiment, H. Egiyan, F.X Girod, K. Hafidi, S.L. and E. Voutier

  45. Spatial structure of quarks and gluons in nuclei Burkardt-Soper impact parameter quark's position in nuclei

  46. New! Test OAM SR in Spin 1 system: Deuteron (S.L. and S. Taneja)

  47. Conclusions and Outlook • Approaching “Global Analysis” for GPDs is a more complex problem than for PDFs and TMDs: • combinations of GPDs enter simultaneously the physical observables • dependence on several kinematical variables: X,,t,Q2 of which… • …X always appears integrated over • Strategies to extract GPDs from data are based on multistep analyses: we propose one of such analyses using a physically motivated parametrization + lattice results • Focus of the present work was on H and E in “valence” region • Several applications and extensions: extraction of tensor charge and transverse anomalous moment from neutral pion production data, studies of spatial structure of nuclei… • …but analysis is underway that takes into account all GPDs • This analysis is possible thanks to the flexibility offered by our parametrization/model

  48. , , , .. b1, h1 JPC=1+- JPC=1--

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