P I N P Two Photon Exchange in elastic electron-proton scattering: QCD factorization approach Nikolai Kivel in collaboration with M. Vanderhaeghen DSPIN-09
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
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-07-109/09-001 pol GE/GM Q2=6-14.8GeV2 JLab Hall A PR-07-108 unpol Q2=7-17.5GeV2 , stat. err. < 1%
Guichon Vanderhaeghen PRL91(2003) TPE contribution: theory Guichon Vanderhaeghen PRL91(2003) ep ep k k’ ( ) p p’
( ) TPE contribution: theory ep ep Form factors k k’ p p’ 1γ exch ( ) p p’ 1γ exch Form factors 2γ exch
( ) 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
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)
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
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
TPE at large-Q2: QCD factorization approach + others 23 graphs + crossed = Breit frame:
TPE at large-Q2: QCD factorization approach + others 23 graphs + crossed = Nucleon DA
TPE at large-Q2: QCD factorization approach + others 23 graphs + crossed = Hard subprocess * *
( ) 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
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
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
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
Reduced cross section with TPE correction NK, Vanderhaeghen, 2009 1-γ pol BLW QCDSF COZ Data set SLAC NE11, 1994
Golden mode: e+p vs. e-p elastic scattering JLab Class PR-07-005 Q2=.5-2.5 GeV2 ε=.1-.9 Future experiments: VEPP-3 Novosibirsk Q2=1.6 GeV2 ε=.44, .92 Olympus@Desy Q2=.8-4.5 GeV2 ε=.4-.9 pQCD estimate COZ Expected accuracy <2% BLW QCDSF
Polarized observables with TPE: test of ε-dependence Pl Pt μpGE/GM Born Pl/Pl COZ BLW BLW COZ
Polarized observables with TPE: test of ε-dependence Pl Pt JLab Hall C E-04-119 completed, new preliminary Q2=2.5 GeV2 ε=.14,.63,.785 Pre li mi na ry !!! BLW COZ GPD
Target Normal Spin Asymmetry Asymmetries related to absorptive part Target Normal Spin Asymmetry E-02-013 Hall-C prelimin μnGE/GM ≃0.35 Elab= 4.8 GeV GM ≃μnGD CLASS, 2009 Q2= 1.-4.5GeV2 COZ PR-05-015 Hall-A Elab= 3.3, 5.3 GeV Q2= 1.0, 2.5GeV2 BLW
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.