Strategies to extract GPDs from data Simonetta Liuti University of Virginia & Gary Goldstein Tufts University INT, September 2009 APS DNP Meeting Saturday, October 25th, Oakland, USA Outline 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 4 He Conclusions/Outlook 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) Q 2 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. Hgler, 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 DVCS Cross Section (Belitsky, Kirchner, Muller, 2002) Amplitude Azimuthal angle between planes Angle between transverse spin and final state plane Comtpon Scattering and Bethe Heitler Processes Dynamics Look for instance at DVCS-BH Interference Amplitude Off forward Parton Distributions (GPDs) are embedded in soft matrix elements for deeply virtual Compton scattering (DVCS) p + =XP + p + =(X- )P + P + =(1- )P + P+P+ p+q q q=q+ 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 H q (X, , t)= R(X, , t) G(X, , t) Regge Quark-Diquark + Q 2 Evolution Quark-Diquark model: two different time orderings/pole structure! Quark anti-quark pair describes similar physics (dual to) Regge t-channel exchange (J PC quantum numbers) DGLAP: quark off shell, spectator on shellERBL: quark on shell, spectator off-shell X> X< k + =XP + k + =(X- )P + P + =(1- )P + P X + =(1-X)P + Vertex Structures P+P+ P X + =(1-X)P + S=0 or 1 Focus e.g. on S=0 Vertex function 2 O. Gonzalez Hernandez, S.L. Fixed diquark mass formulation ERBL region DGLAP region Reggeized diquark mass formulation DIS Brodsky, Close, Gunion 70s Diquark spectral function MX2MX2 (M X 2 ) (M X 2 -M X 2 ) Fitting Procedure Fit at =0, t=0 H q (x,0,0)=q(X) 3 parameters per quark flavor (M X q, q, q ) + initial Q o 2 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 Parton Distribution Functions Notice! GPD parametric form is given at Q 2 = Q o 2 and evolved to Q 2 of data. Notice! We provide a parametrization for GPDs that simultaneously fits the PDFs: H q (X, ,t)= R(X, ,t) G(X, ,t) Regge Quark-Diquark =0,t=0 S. Ahmad, H. Honkanen, S. L., S.K. Taneja, PRD75:094003,2007 = 0, t 0 Nucleon Form Factors Parameters from PDFs Parameters from FFs Some results S. Ahmad, H. Honkanen, S. L., S.K. Taneja, (AHLT), PRD75:094003,2007 HdHd HuHu , t S. Ahmad et al., EPJC (2009) w e 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 Use information from Lattice QCD: (1) Assume lattice results follow dipole behavior for n=1,2,3 Chiral extrapolation of dip. mass Extract dipole masses from lattice data Relate dipole mass to radius parameter Polynomiality from lattice results up to n=3 n=2 n=3 Results of Chiral Extrapolations Ahmad et al. (2008) -t (GeV 2 ) proton form factor Ashley et al. (2003) New Developments (H.Nguyen) (Haegler et al., PRD 2007, arXiv:0705:4295) We repeated the calculation with improved lattice results We are investigating the impact of different chiral extrapolation methods: direct extrapolation applicable up to n=2 only Results are comparable (up to n=2) to our phenomenological extrapolation M. Dorati, T. Gail and T. Hemmert (NPA 798, 2008) (Also using P. Wang, A. Thomas et al. ) A 20 u-d New Results are more precise and compatible with other chiral extrapolations A 20 u-d vs. (-t) Dorati Nguyen, S.L. Lattice results are used to model/fit the ERBL Region We know the area from n=1 moment + constrained DGLAP Weighted Average Value Location of X-bin Dispersion (error in X) Reconstruction of GPDs from Bernstein moments * Algebra a bit more complicated for to transformation, details in EPJC(2009) * Test with known, previously evaluated GPD, at 0 ERBL Region Ahmad et al., EPJC (2009) Determined from lattice moments up to n=3 New Analysis Results are more accurate one can see trends both isovector and isoscalar terms Summary of first three steps towards parametrization v1 v (Q o ) parameters (Q o ) parameters 0 use lattice calculations for ERBL region (X < ) 0 use v1 for DGLAP region (X > ) BSA data are predicted at this stage Munoz Camacho et al., PRL(2006) Hall B (one binning, 11 more) Comparison with Jlab Hall A data (neutron) Mazouz et al. (2007) Real Part (work with S.Ahmad, H. Nguyen) Fit to JLAB data: real part of CFF from d + + d - 0 Cusp from reggeized ERBL ( -X) Fitted directly at Q 2 of data either from phenom.DA type shape, or diquark model Schematically Behavior determined by Jlab data on Real Part and Q 2 dependence Consistent with lattice determination! Dispersion Relations (brief parenthesis) Difference Direct Dispersion G.Goldstein and S.L.,arXiv: [hep-ph ] Dispersion 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, Jaffes lectures) because of optical theorem From DR to Mellin moments expansion 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 Q 2 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) Dispersion Relations (brief parenthesis) Difference Direct Dispersion G.Goldstein and S.L., Dispersion Applications Transversity u d Related to Boer-Mulders function E T (x, , t,Q 2 ) = T q H T (x, , t,Q 2 ) h 1 (x,Q 2 ) = q f 1 (x,Q 2 ) H T (x, , t,Q 2 ) = q H(x, , t,Q 2 ) Simple Ansatz 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) Jefferson Lab approved experiment, H. Egiyan, F.X Girod, K. Hafidi, S.L. and E. Voutier Spatial structure of quarks and gluons in nuclei Burkardt-Soper impact parameter quark's position in nuclei New! Test OAM SR in Spin 1 system: Deuteron (S.L. and S. Taneja) 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,Q 2 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 J PC =1 -- J PC =1 +- , , ,.. b 1, h 1