Realistic parameterization of GPDs and its applications. Simonetta Liuti University of Virginia. Jlab Theory Group Seminar November 10th, 2008.

Transcription

1 Realistic parameterization of GPDs and its applications Simonetta Liuti University of Virginia Jlab Theory Group Seminar November 10th, 2008.

2 Collaborations Gary Goldstein (Tufts University) Leonard Gamberg (Penn State, Berks) Eric Voutier (Grenoble) AHLT: Saeed Ahmad (U. Wisconsin), Heli Honkanen (Iowa State), S.L., Swadhin Taneja Graduate Students: Osvaldo Gonzalez, Chuanzhe Lin, Huong Nguyen, Dan Perry

3 Outline Unpolarized GPDs from proton and neutron data sets New results using Jlab data constraints! Access to Chiral-Odd GPDs Practical method for the extraction of both tensor charge: q Burkardt's moment : T q Nuclei: DVCS and p0 electroproduction on 4He Conclusions/Outlook

4 1. Extraction from data needs a reliable GPD model

5 A more advanced phase of extracting GPDs from data (a bit of summary from ECT*, June'08, and Jlab Hall B meeting, Aug. 08) No longer simple models (D. Muller) Include Q 2 dependence (M. Diehl) Include all constraints from data DVCS, DVMP... (S.L.) Include new data as they become available... (S.L.) Use Lattice + Chiral Extrapolations (P. Hägler, A. Schaefer) Connect various experiments, separate valence from sea, flavors separation (T. Feldman)... New! Representation in terms of dispersion relation only necessary to measure imaginary part? Stronger polynomiality constraint (Anikin, Teryaev, Diehl, Ivanov, Vanderhaeghen) A similar program exists for TMDs (simpler partonic interpretation than GPDs) see e.g. M. Anselmino and collaborators

6 DVCS and Generalized Parton Distributions t= 2 Generalized Parton Distributions Correlator GPDs are hybrids of PDFs and FFs: describe simultaneously x and t-dependences! GPDs give access to spatial d.o.f. of partons! GPDs give access to orbital angular momentum of partons! X. Ji

7 DVCS Cross Section

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 H q (X, t)= R(X, t) G(X, t) Regge Quark-Diquark Q 2 Evolution is an essential element!! S. Ahmad, H. Honkanen, S. Liuti and S.K. Taneja, Phys. Rev. D 75, (2007)

9 Two different time orderings/pole structure! DGLAP ERBL X> X< Quark anti-quark pair describes similar physics (dual to) Regge t-channel exchange!!

10 In DGLAP region partonic picture q q+ Regge k P + X P + k' =k - k + =XP + k' + =(X- )P + P' + =(1- )P + Quark-Diquark t Formulae extended to >0 in AHLT2 (arxiv: ).

11 Constraints on parameters...

12 = 0 Nucleon Form Factors

13 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: q(x) = H q (x,0,0)

14 Polynomiality For higher moments (n=2,3,...) use lattice results (consistency with data can be checked J u vs. J d ) n=2 n=3

15 Use information from Lattice QCD: (1) lattice results follow dipole behavior for n=1,2,3 P. Haegler

16 Chiral Extrapolations Dorati, Gail and Hemmert (2007) Wang, Thomas, Young (2008) Ashley et al. (2003) -t (GeV 2 )

17 Sensible predictions for k T vs. x Bj

18 Sensible predictions for r 2 = b 2 /(1-x Bj ) vs. x Bj (M. Burkardt)

19 Dominance of large x Bj at large t

20 Summary of Constraints Constraints from Form Factors Dirac Pauli Constraints from Polynomiality Constraints from PDFs Further Theoretical Constraints: Sensible prediction for hadron shape at x 1 Sensible prediction for k T dependence (connection with TMDs!) (SL and Taneja, 2004)

21 On the connection between TMDs and GPDs Liuti and Taneja, PRD (2004)

22 AHLT Parameterization v (Q o ) parameters v (Q o ) parameters use v1 for DGLAP region (X > ) 0 More details in AHLT, PRD 2007

23 Comparison with similar parametrizations at =0 (Diehl et al.) H q (x,0,t) E q (x,0,t) u d u d

24 Comparison with similar parametrizations at =0 (Guidal et al.)

25 The ERBL Region partonic interpretation is not obvious We extract it from lattice QCD results Hybrid Model (Dieter Mueller) We know the area from n=1 moment + constrained DGLAP

26 Weighted Average Value Location of X-bin We know n 3 moments Reconstruct GPDs from Bernstein moments Dispersion (error in X)

27 Test with known, previously evaluated GPD, at 0

28 ERBL Region AHLT arxiv: Determined from lattice moments up to n=3

29 Comparison with Jlab Hall A data (proton) Munoz Camacho et al. (2006) Note!! Im H from asymmetry Re H from x-section

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

31 AHLT, PRD75: (2007) From fit to form factors From fit to PDFs

32 VGG: crisis or not? Cannot reproduce both! Im F Re F Guidal (2008) Polyakov and Vanderhaeghen (2008)

33 Are the exclusive data telling us something? Real Part (S.Ahmad, S.L., preliminary)

34 Fitted directly at Q of data cusp (X- ) DA type shape needed to fit t -dependence of Jlab data!!! vanishes at X=0 as X

35 S. Ahmad Behavior determined by Jlab data on Real Part and Q 2 dependence Consistent with lattice determination!

36 Orbital Angular Momentum AHLT includes only valence contribution! J q =( q +1)A 20 (0)

37 Dispersion Relations (Anikin, Teryaev, Diehl, Ivanov, ) Q 2 2 H(x,x,t) + C

38 Where is threshold? Viewed this way a quark + spectator cannot be on their mass shell but hadronic jets must have some threshold. This threshold ( physical threshold ) is much higher than what required for the dispersion relations to be valid 0 physical t phys ifmasses in the two-body scattering problem are different! Continuum starts at s =(M+m ) 2 lowest hadronic threshold. How to fill the gap? Analytic continuation?

39 Gaps in dispersion integrals Q 2 =1.0 GeV 2 Q 2 =2.0 GeV 2-1.1>t>-2.7 GeV 2 Physical region has no gap for Q 2 =2.0 GeV 2 -t -t -0.60>t>-1.34 GeV 2 Physical region has no gap for Q 2 =1.0 GeV 2 Q 2 =5.5 GeV 2-2.4>t>-7.4 GeV 2 Physical region has no gap for Q 2 =5.5 GeV 2 -t From Gary Goldstein, SPIN 2008

40 When deeply virtual processes involve directly final states - like in exclusive or semi-inclusive processes - standard kinematic approximations should be questioned (Collins, Rogers, Stasto, 2007)

41

42 h 1 Transversity Simple Ansatz h 1 (x,q 2 ) = q f 1 (x,q 2 ) u H T (x,, t,q 2 ) = q H(x,, t,q 2 ) d E T (x,, t,q 2 ) = Tq H T (x,, t,q 2 ) Related to Boer-Mulders function: h 1

43 2. Electroproduction Observables and GPDs * *S. Ahmad, Gary Goldstein, S.L., arxiv: hep-ph

44 Exclusive o electroproduction h 1 LAB e e'

45 Dual Representation? t= 2 helicity amps. Quark-Hadron Helicity Amplitudes (Marcus Diehl)

46 Comparison between Regge and Partonic approaches

47 Q 2 dependence at pion vertex q o q' cross section Chiral Odd Generalized Form Factors

48 Only chiral-odd GPDs!!! J PC =1 -- J PC =1 +- J PC =1 --, 1 +-,... H T, E T,... ~ ~ J PC =1 ++,... (a 1 -type exchange) H, E,...

49 What goes into the quark-hadron amplitudes? Generalized Form Factors H T (X,0,0) = h 1 (X) = transversity h 1 (X,Q 2 ) dx = q= tensor charge E 2 (X,0,0) dx = T = Burkardt's moment h 1 (X) dx d 2 k T ~ - T (A.Metz)

50 Observables are sensitive to both q and T!... and more...!!!

51 Q 2 dependence

52 t-channel exchange vertex modeled as F (pseudoscalarmeson transition form factor),, b 1, h 1 J PC =1 -- ( 3 S 1 ), b 1, h 1 J PC =1 +- ( 1 P 1 ) J PC =0 -+ quark content:

53 Distinction between and b 1, h 1 exchanges J PC =1 -- J PC =1 +- o : qqbar from S, L S=0, L L o : qqbar from (S=0, L=1) (S=0,L=0) L =1 Vector exchanges no change in OAM Axial-vector exchanges change 1 unit of OAM!

54

55 Main Result: Tensor Charge and Anomalous Transverse Moment treated as free parameters to be extracted from data Fixed u and d

56

57 3. Nuclei: Spin 0 and Spin 1

58 GPDs & hadron tensor for Spin 0 nuclear target (S.L. and SwadhinTaneja, PRC 2005) o production (with G. Goldstein)

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

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

61

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

63 o electro-production from 4He m quark =0 has to flip helicity for q +q and q q 0. o +1/2 4 He He +1/2 0-1/2 0 J PC = 1 +- exchange b 1, h 1 & J PC = exchange 0, o f 0,00(s,t,Q 2 ) = g +,0- A 0+,0 - +1,0 analogue of H T structure of p p A+i(p +p) B 2 invariant amps, 2 independent helicity amps 0 b 1 & h 1 0 & 0 4 He 4 He

64 Conclusions and Outlook Comparison between GPD models and data is indeed possible...gpd extraction is possible!!! Approaching Global Analysis Interesting connections between TMDs and GPDs Proposed extraction of tensor charge and transverse anomalous moment from neutral pion production data Spatial structure of Nuclei

65 J PC =1 --,,,.. J PC =1 +- b 1, h 1