1. P I N P
Two Photon Exchange in elastic electron-proton scattering: QCD factorization approach
Nikolai Kivel
in collaboration with
M. Vanderhaeghen
DSPIN-09

2. Missing radiative corrections
Radiative correction at electron side:
well understood and taken care of
Box diagrams involve photons
of all wavelength
long wavelength (soft photon) is included in radiative correction (IR divergence is cancelled with electron proton brems- strahlung interference)
Soft bremsstrahlung involves long-wavelength photons
compositeness of the nucleon only enters through on-shell ff
Maximon, Tjon PRC62, 2000

3. Large Q2 asymptotic of the TPE contribution: motivation
Chen, Afanasev et al PRL93(2004)
partonic or GPD-model
Blunden Melnitchouk Tjon PRL91(2003)
hadronic-model
TPE is responsible
for the discrepancy in FF
extraction
? pQCD in TPE
Future
JLab Hall A/C PR / pol GE/GM Q2=6-14.8GeV2
JLab Hall A PR unpol Q2=7-17.5GeV2 , stat. err. < 1%

4. Guichon Vanderhaeghen PRL91(2003)
TPE contribution: theory
Guichon Vanderhaeghen PRL91(2003)
ep ep k k’
( ) p p’

5. ( ) TPE contribution: theory ep ep Form factors k k’ p p’ 1γ exch
( ) p p’
1γ exch
Form factors
2γ exch

6. ( ) TPE contribution: theory ep ep Form factors k k’ p p’ 1γ exch
( ) p p’
1γ exch
Form factors
Large Q2 asymptotic (pQCD)
2γ exch

7. TPE at large-Q2: QCD factorization approach
both photons have large virtualities
+ crossed
Breit frame -
n=(1,0,0,1) n=(1,0,0,-1)

8. TPE at large-Q2: QCD factorization approach
+ others
23 graphs
+ crossed =
Lowest order graphs to turn 3 collinear quarks
into 3 collinear quarks moving in opposite direction

9. TPE at large-Q2: QCD factorization approach
+ others
23 graphs
+ crossed =
Lowest order graphs to turn 3 collinear quarks
into 3 collinear quarks moving in opposite direction

10. TPE at large-Q2: QCD factorization approach
+ others
23 graphs
+ crossed =
Breit frame:

11. TPE at large-Q2: QCD factorization approach
+ others
23 graphs
+ crossed =
Nucleon DA

12. TPE at large-Q2: QCD factorization approach
+ others
23 graphs
+ crossed =
Hard subprocess * *

13. ( ) TPE contribution: theory ep ep Form factors k k’ p p’ 1γ exch
( ) p p’
1γ exch
Form factors
Large Q2 asymptotic (pQCD)
2γ exch
helicity flip suppressed

14. TPE at large-Q: QCD factorization approach
Form factors:
all integrals are IR-finite
pole ⇒ Im part !
NK, Vanderhaeghen, 2009
Borisyuk, Kobushkin, 2008
normalization is not computed, only the ratio to nucleon pQCD FF’s

15. TPE at large-Q: QCD factorization approach
Nucleon DA
assumption: drop the highest conformal moments
theor. uncertainties: renorm. scale (NLO)
helicity flip FF:
3 non-perturbative parameters
Models for DA :
QCD SR (1988), COZ
QCD LCSR (2006), BLW
Lattice (2006), QCDSF

16. Guichon Vanderhaeghen PRL91(2003)
Reduced cross section with TPE correction
Guichon Vanderhaeghen PRL91(2003)
Born app
Re part of TPE
Empirical fit for the ratio and form factor:
JLab Hall A, 2002
Brash, Kozlov, Li, Huber 2002

17. Reduced cross section with TPE correction
NK, Vanderhaeghen, 2009
1-γ pol
BLW
QCDSF
COZ
Data set SLAC NE11, 1994

18. Golden mode: e+p vs. e-p elastic scattering
JLab Class PR Q2= GeV2 ε=.1-.9
Future experiments:
VEPP-3 Novosibirsk Q2=1.6 GeV2 ε=.44, .92
Q2= GeV2 ε=.4-.9
pQCD estimate
COZ
Expected accuracy <2%
BLW
QCDSF

19. Polarized observables with TPE: test of ε-dependencePl Pt
μpGE/GM
Born
Pl/Pl
COZ
BLW
BLW
COZ

20. Polarized observables with TPE: test of ε-dependencePl Pt
JLab Hall C E completed, new preliminary Q2=2.5 GeV2 ε=.14,.63,.785
Pre li mi na ry
!!!
BLW
COZ
GPD

21. Target Normal Spin Asymmetry
Asymmetries related to absorptive part
Target Normal Spin Asymmetry
E Hall-C
prelimin
μnGE/GM ≃0.35
Elab= 4.8 GeV
GM ≃μnGD
CLASS, 2009
Q2= GeV2
COZ
PR Hall-A
Elab= 3.3, 5.3 GeV
Q2= 1.0, 2.5GeV2
BLW

22. Conclusions ☺
TPE is responsible for the discrepancy in FF extraction.
This can be determined experimentally (GE/GM, non-linearity of Rosenbluth plot, ratio e+p/e-p, asymmetries sensitive to Im part of TPE) ☺
Hard QCD contribution in TPE at large Q2 can be large and must be considered accurately ☺
TPE at large Q2 depends on the structure of target and can provide us information about nucleon DA ☺
Experiments at higher Q2 where the theory works better is a good opportunity to check pQCD predictions ☹
Large power corrections and/or NLO can change optimistic picture.