1. Generalized Parton Distributions and Deep Virtual Compton Scattering
PHOTON 2017, CERN, 24/05/2017
Generalized Parton Distributions
and Deep Virtual Compton Scattering
Michel Guidal (IPN Orsay)

2. y x z
ep a eX
(DIS)
(Parton Distribution
Functions: PDF)

3. ep a eX (DIS) ep a ep (elastic) y z (Parton Distribution x
Functions: PDF) y x z
ep a ep
(elastic)
(Form Factors: FFs)

4. ep a eX (DIS) ep a ep (elastic) ep a epg (DVCS) y z
(Parton Distribution
Functions: PDF) y x z
ep a ep
(elastic)
(Form Factors: FFs) x z
ep a epg
(DVCS)

5. ep a eX (DIS) ep a ep (elastic) ep a epg (DVCS) ep a epX (SIDIS) y z
(Parton Distribution
Functions: PDF) y x z
ep a ep
(elastic)
(Form Factors: FFs) x z
ep a epg
(DVCS)
(Generalized Parton
Distributions: GPDs)
ep a epX
(SIDIS) z
(Transverse Momentum
Dependent PDFs: TMDs) x

7. In the light-cone frame:
x+x : relative longitudinal momentum of initial quark
x-x : relative longitudinal momentum of final quark
t=D2 : total squared momentum transfer to the nucleon
(transverse component: )
(also Q2-dependence but LO and LT framework in the following)

8. GPDs or the tomography of the nucleonx b
(GeV-1)
Hu(x,b ) y x z
Ji’s sum rule
2Jq =  x(H+E)(x,ξ,0)dx

9. ~ Im{Hp, Hp, Ep} ~ ~ Im{Hp, Hp} Re{Hp, Hp} Im{Hp, Ep} f DVCSg f
leptonic plane
hadronic
plane N’ e’ e
DVCS
Bethe-Heitler
GPDs
F1,F2
CFFs
x= xB/(2-xB) k=-t/4M2
DsLU ~ sinf Im{F1H + x(F1+F2)H -kF2E}df ~
Polarized beam, unpolarized target (BSA) :
Im{Hp, Hp, Ep}
Unpolarized beam, longitudinal target (lTSA) :
DsUL ~ sinfIm{F1H+x(F1+F2)(H + xB/2E) –xkF2 E+…}df ~
Im{Hp, Hp}
nDVCS complements pDVCS for the different sensitivity to GPDs of the various observables
Polarized beam, longitudinal target (BlTSA) :
DsLL ~ (A+Bcosf)Re{F1H+x(F1+F2)(H + xB/2E)…}df ~
Re{Hp, Hp}
Unpolarized beam, transverse target (tTSA) :
DsUT ~ cosfIm{k(F2H – F1E) + ….. }df
Im{Hp, Ep}

10. Hq(x,x,t) but only x and t experimentally accessible

12. JLab Hall A JLab CLAS HERMES DVCS unpol. X-section DVCS
B-pol. X-section
JLab
CLAS
DVCS
BSA
DVCS
lTSA
DVCS unpol. and
B-pol. X-sections
HERMES
DVCS
BSA,lTSA,tTSA,BCA

13. From data to GPDs (CFFs):
Deconvolution/
Fitting algorithms
of CFFs from
(BH+DVCS) amplitudes

14. M.G., H. Moutarde,
M. Vanderhaeghen
Rept.Prog.Phys. 76 (2013)

15. New recent data from JLab:
CLAS coll.
PRL 115 (2015),
Hall A coll.
PRC92 (2015),
CLAS coll.
PRL 114 (2015),
CLAS coll.
PRD91 (2015),
R. Dupré, M.G., M. Vanderhaeghen
Phys.Rev. D95 (2017)

17. If Up to (model-dependent) « deskewing effects » (a few percent) :
this formula involves:
While we extract:
Need to estimate:
(assuming )

18. HERMES
JLab
« Integrated » radius from elastic form factor F1:

19. HERMES
JLab
« Integrated » radius from elastic form factor F1:

20. GPDs contain a wealth of information on nucleon structure
and dynamics: space-momentum quark correlation, orbital
momentum, pion cloud, pressure forces within the nucleon,…
Large flow of new observables being released and
new data expected soon (JLab6,JLab12,COMPASS)
(Other DVCS-related processes planned for JLab 12 GeV
(TCS, DVMP, DDVCS,…)
First new insights on nucleon structure already emerging
from current data with new fitting algorithms
Theory developments: higher twists, target mass corrections,
NLO corrections, …

21. BACK-UP

22. The Bethe-Heitler process

23. M. Boer, MG J.Phys. G42 (2015) 3,

24. M. Boer, MG J.Phys. G42 (2015) 3,

25. M. Boer, MG J.Phys. G42 (2015) 3,

26. M. Boer, MG J.Phys. G42 (2015) 3,

28. If However, this formula involves: While we extract: Need to estimate:
(M. Burkhardt) If
However, this formula involves:
While we extract:
Need to estimate:
(assuming )

29. for

31. Resultats pour HtildeIm
The axial charge (Him) appears to be more « concentrated » than the electromagnetic charge (Him) ~
Confirmed by CLAS A_UL and A_LL data: Phys.Rev. D91 (2015) 5,

32. Polarized beam, unpolarized target (BSA) :~
Examples of correlation between HIm and HIm
DsLU ~ sinf Im{F1H + x(F1+F2)H -kF2E}df ~
Polarized beam, unpolarized target (BSA) :

33. for