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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

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


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 4He

Conclusions/Outlook

Outline


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


DVCS Cross Section (Belitsky, Kirchner, Muller, 2002) Compass… we are entering a new, more advanced phase of extracting GPDs from data

Amplitude

Angle between transverse spin and final state plane

Azimuthal angle between planes


Comtpon Scattering and Bethe Heitler Processes Compass… we are entering a new, more advanced phase of extracting GPDs from data

Dynamics


Look for instance at DVCS-BH Interference Compass… we are entering a new, more advanced phase of extracting GPDs from data


Off forward Parton Distributions (GPDs) are embedded in Compass… we are entering a new, more advanced phase of extracting GPDs from data

soft matrix elements for deeply virtual Compton scattering (DVCS)

q

q’=q+

p+q

p’+=(X-)P+

p+=XP+

P’+=(1- )P+

P+

Amplitude


What goes into a theoretically motivated parametrization...? Compass… we are entering a new, more advanced phase of extracting GPDs from data

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


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)


Vertex Structures structure!

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.


Fixed diquark mass formulation structure!

DGLAP region

ERBL region


Reggeized diquark mass formulation structure!

Diquark spectral function

(MX2-MX2)

 (MX2)

MX2

DIS  Brodsky, Close, Gunion ‘70s


  • Fitting Procedure structure!

  • 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


    =0,t=0 structure!

    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


    Nucleon Form Factors structure!

    = 0, t0

    S. Ahmad, H. Honkanen, S. L., S.K. Taneja, PRD75:094003,2007


    Parameters from PDFs structure!

    Parameters from FFs


    Some results… structure!

    Hu

    Hd

    S. Ahmad, H. Honkanen, S. L., S.K. Taneja, (AHLT), PRD75:094003,2007


    , t S. Ahmad et al., EPJC (2009) structure!

     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


    Use information from structure!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



    Results of Chiral Extrapolations structure!

    proton form factor

     Ashley et al. (2003)

     Ahmad et al. (2008)

    -t (GeV2)


    New Developments (H.Nguyen) structure!

    We repeated the calculation with improved lattice results

    (Haegler et al., PRD 2007, arXiv:0705:4295)


    A structure!20u-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. )


    New Results are more precise and compatible with other chiral extrapolations

    A20u-d vs. (-t)

    Nguyen, S.L.

    Dorati


    Lattice results are used to model/fit the ERBL Region… chiral extrapolations

    We know the area from n=1 moment + constrained DGLAP


    Reconstruction of GPDs from Bernstein moments chiral extrapolations

    Weighted Average Value

    Location of X-bin

    Dispersion (error in X)

    *

    * Algebra a bit more complicated for  to transformation, details in EPJC(2009)



    ERBL Region chiral extrapolations

    Ahmad et al., EPJC (2009)

    Determined from lattice moments up to n=3


    New Analysis chiral extrapolations

    • Results are more accurate one can see trends

    • both isovector and isoscalar terms


    Summary of first three steps towards parametrization chiral extrapolations

    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 <  )


    BSA data are predicted at this stage chiral extrapolations

    Munoz Camacho et al., PRL(2006)


    Hall B (one binning, 11 more) chiral extrapolations


    Comparison with Jlab Hall A data (neutron) chiral extrapolations

    Mazouz et al. (2007)


    0 chiral extrapolations

    Fit to JLAB data: real part of CFF from d+ + d-

    Real Part(work with S.Ahmad, H. Nguyen)


    Schematically chiral extrapolations

    Fitted directly at Q2 of data

    Cusp from reggeized ERBL  (-X)

    either from phenom.“DA type” shape, or diquark model


    • Consistent with lattice determination!


    Dispersion Relations (brief parenthesis…) chiral extrapolations

    Dispersion

    Direct

    Difference

    Direct

    Dispersion

    G.Goldstein and S.L.,arXiv:0905.4753 [hep-ph]


    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


    DVCS because one misses a

    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)


    Dispersion Relations (brief parenthesis…) because one misses a

    Dispersion

    Direct

    Difference

    Direct

    Dispersion

    G.Goldstein and S.L.,


    Applications because one misses a


    Transversity because one misses a

    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


    Nuclei because one misses a

    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)



    Spatial structure of quarks and gluons in nuclei Hafidi,

    Burkardt-Soper

    impact parameter

    quark's position

    in nuclei


    New! Test OAM SR in Spin 1 system: Deuteron Hafidi,

    (S.L. and S. Taneja)


    Conclusions and outlook
    Conclusions and Outlook Hafidi,

    • 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


    , , , .. Hafidi,

    b1, h1

    JPC=1+-

    JPC=1--


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