1. Experimental Probes of Two-Photon Exchange*
3rd Joint Meeting of the APS Division of Nuclear Physics and the Physical Society of Japan October 13-17, 2009, Waikoloa, Big Island, Hawaii, USA
Experimental Probes of Two-Photon Exchange*
Michael Kohl
Hampton University, VA and Jefferson Lab, VA 23606, USA
I’d like to thank the organizers for the possibility to talk here at HAW09.
* Supported by NSF grant PHY

2. Outline Form factors in the context of one-photon exchange (OPE)
The limit of OPE or:
What is GEp ?
What is the structure of lepton scattering?
Two-photon exchange (TPE): New observables
Current and future experiments to probe TPE
While they are interesting by themselves and ultimately determined by the quark structure and QCD, they are also used as input to nuclear structure and parity violation experiments, …, which brings me here.
After 50 years …

3. (Hadronic) Structure and (EW) Interaction
Factorization!
Structure
Interaction
s(structured object)
|Form factor|2 =
s(pointlike object)
→ Interference!
Probe
Object
→ Utilize spin dependence of electromagnetic interaction to achieve high precision
Born Approximation
Inelastic Elastic
Generally, Structure and interaction are unseparated aspects. However, in order to separate the different types of interactions, we can e.g. have leptons interact with hadrons. The interaction is purely electroweak (and well known), and the weakness allows to treat the process perturbatively, the hadronic system isn’t disturbed much, in turn opening the door to learn about the internal structure of the hadronic object. This is known as factorization, and the the hadronic structure is encoded in a quantity that we call form factor. Being the square of a scattering amplitude, quantum mechanics allows for interference phenomena. In particular, a well-known feature of the electromagnetic interaction is its spin dependence. Using spin-dependent electromagnetic (or electroweak) interaction is extremely powerful to obtain precision information on hadronic structure.
Structure
Electroweak probe
Hadronic object
Interaction
Lepton scattering
~|α|2 (α=1/137)

4. Form Factors in OPE General definition of the nucleon form factor
Sachs Form Factors
In one-photon exchange approximation above form factors are observables of elastic electron-nucleon scattering
Let me now turn to the physics.
From Rosenbluth it is hard to determine GM at very low Q2 and GE at very high Q2, fueling the idea to measure the ratio GE/GM through double polarization oberservables

5. Form Factors from Rosenbluth Method
tGM2
GE2
θ=180o
θ=0o
In One-photon exchange approximation above form factors are observables of elastic electron-nucleon scattering
 Determine
|GE/GM|
Let me now turn to the physics.
From Rosenbluth it is hard to determine GM at very low Q2 and GE at very high Q2, fueling the idea to measure the ratio GE/GM through double polarization oberservables

6. Nucleon Form Factors and Polarization
Double polarization in elastic ep scattering: Recoil polarization or (vector) polarized target
Polarized cross section
Double spin asymmetry = spin correlation
Asymmetry ratio (“Super ratio”) independent of polarization or analyzing power
1H(e,e’p), 1H(e,e’p)
Such double polarization observables can be measured in either recoil polarization or polarized target experiments. The polarized cross section section contains an asymmetry term that is related to the form factors through the dependence on the target or recoil polarization components. The polarization observable is an interference effect.

7. Proton Form Factor Ratio
Jefferson Lab 2000–
All Rosenbluth data from SLAC and Jlab in agreement
Dramatic discrepancy between Rosenbluth and recoil polarization technique
Multi-photon exchange considered best candidate
Dramatic discrepancy!
>800 citations 7

8. Proton Form Factor Ratio
Jefferson Lab 2000–
All Rosenbluth data from SLAC and Jlab in agreement
Dramatic discrepancy between Rosenbluth and recoil polarization technique
Multi-photon exchange considered best candidate
Even more dramatic with linear scale in Q2
Dramatic discrepancy!
>800 citations 8

9. Two-Photon Exchange: A Lot of Theory
Two-photon exchange theoretically suggested
Interference of one- and two-photon amplitudes
P.A.M. Guichon and M. Vanderhaeghen, PRL91 (2003) ; M.P. Rekalo and E. Tomasi-Gustafsson, EPJA22 (2004) 331: Formalism … TPE effect could be large
P.G. Blunden, W. Melnitchouk, and J.A. Tjon, PRC72 (2005) , PRL91 (2003) : Nucl. Theory … elastic ≈ half, Delta opposite
A.V. Afanasev and N.P. Merenkov, PRD70 (2004) : Large logarithms in normal beam asymmetry
Y.C. Chen et al., PRL93 (2004) : Partonic calculation (GPD), TPE large at high Q2
A.V. Afanasev, S.J. Brodsky, C.E. Carlson, Y.C. Chen, M. Vanderhaeghen, PRD72 (2005) : high Q2, small effect on asym., larger on x-sec., TPE on R small
M. Gorchtein, PLB644 (2007) 322: Fwd. angle, dispersion ansatz, TPE sizable
Y.C. Chen, C.W. Kao, S.N. Yang, PLB652 (2007) 269: Model-independent TPE large
D. Borisyuk, A. Kobushkin, PRC74 (2006) ; 78 (2008) : TPE effect sizable
Yu. M. Bystritskiy, E.A. Kuraev, E. Tomasi-Gustafsson, PRC75 (2007) : Importance of higher-order radiative effects, TPE effect rather small!
M. Kuhn, H. Weigel, EPJA38 (2008) 295: TPE in Skyrme Model
D.Y. Chen et al., PRC78 (2008) : TPE for timelike form factors
M. Gorchtein, C.J. Horowitz, PRL102 (2009) : gamma-Z box
D. Borisyuk, A. Kobushkin, PRD79 (2009) : pQCD, sizable
N. Kivel, M. Vanderhaeghen, PRL103 (2009) : pQCD, sizable

10. Kinematical invariants :
Elastic ep Scattering Beyond OPE k k’ p p’
s=1/2 lepton
s=1/2 proton
Kinematical invariants :
Next-to Born approximation:
(me = 0)
The T-matrix still factorizes, however a new response term F3 is generated by TPE Born-amplitudes are modified in presence of TPE
New amplitudes are complex!

11. Need positrons to identify Y2γ Beyond Born Approximation
Observables involving real part of TPE
E (Two-gamma)
e+/e- x-section ratio CLAS,VEPP3,OLYMPUS
Rosenbluth non-linearity E05-017
It is possible to use recoil pol and rosenbluth cross sec as functions of Q2 and epsilon to extract Y2g(Q2,eps) ASSUMING that
TPE is the accepted picture.
+Any Eps dependence of Pl or Pt/Pl is an indicator of Y2g, however absence is no disproof as Y2g can be eps-independent, too.
+Any non-linear eps dependence of xsec is an indicator of Y2g,
+RB plots are very linear in eps -> Y2g constant vs. eps?
+Pt/Pl constant vs. eps -> a+Y2g/(b+Y2g*2*eps/(1+eps)) constant ->Y2g=0?
+Y2g changes sign with the charge of the lepton, so the ONLY definitive test of the picture is to compare e+ with e- (cross sec).
Need positrons to identify Y2γ
Born Approximation
Beyond Born Approximation
P.A.M. Guichon and M.Vanderhaeghen, Phys.Rev.Lett. 91, (2003)
M.P. Rekalo and E. Tomasi-Gustafsson, E.P.J. A 22, 331 (2004)
Slide idea: L. Pentchev

12. Some remarks ~
Presence of TPE modifies GE and GM, AND generates new structure F3
Measurement of one type of observable (double polarization or Rosenbluth cross sections is insufficient to separately determine both GE/GM AND Y2γ.
Without positrons, it is possible to use double polarization observables AND Rosenbluth cross sections as functions of Q2 and ε to extract both GE/GM and Y2γ(Q2, ε) ASSUMING that TPE is the accepted picture.
Any change in the ε dependence of Pl or Pt/Pl is an indicator of non-zero Y2γ, however its absence is no disproof, as Y2γ can also be ε-independent. Small.
Any non-linear ε dependence of cross section is an indicator of non-zero Y2γ. Absence is no disproof, as Y2γ can also be ε-independent. Small effect.
RB plots ARE very linear in ε  Y2γ constant vs. ε ?
Pt/Pl constant vs. ε  (1–2εR/(1+ε)) Y2γ constant Y2γ = 0 ?
Positrons are needed to definitively establish TPE. The Y2γ terms change sign with the charge of the lepton, so the ONLY definitive test of the picture is to compare observables probed with e+ and e-

13. E04-019 (Two-gamma) PRELIMINARY GE/GM from Pt/Pl constant vs. ε
 (1–2εR/(1+ε)) Y2γ constant  with Y2γ = const.  Y2γ = 0?
PRELIMINARY
M. Meziane, BF-05 (Wed.)

14. OLYMPUS OLYMPUS Hera ZEUS Hermes pOsitron-proton and
eLectron-proton elastic scattering to test the
hYpothesis of
Multi-
Photon exchange
Using
DoriS
OLYMPUS
Hera
ZEUS
Hermes
2008 – Full proposal
2009 – Funding approval
2010/11 – Transfer of BLAST
2012 – OLYMPUS Running

15. OLYMPUS: BLAST@DESY/DORIS
One of the few places in this world providing e+ and e- beams of this energy could be the DORIS storage ring at DESY. We have recently documented this idea and established contact with DESY on this.
500 hours each
for e+ and e-
Lumi=2x1033 cm-2s-1

16. e+/e- cross section ratio to verify TPE
VEPP3
CLAS
VEPP3 scheduled to run in fall 2009
PR04-116: Engineering run in 2006, full proposal approved in January 2007, scheduled as last experiment in Hall B before shutdown
Experiment proposals to verify TPE hypothesis:
e+/e- ratio: CLAS/PR secondary e+/e- beam – 2011/ Novosibirsk/VEPP-3 storage ring / intern. target – 2009 storage ring / intern. target – 2012

17. New Proton Measurements at High Q2
High-Q2 measurements at Jefferson Lab
Hall C E05-017: Super-Rosenbluth Q2 = 0.9 – 6.6 (GeV/c)2 Completed in summer 2007
GEp-III /Hall C: E04-108/E Q2 = 2.5, 5.2, 6.8, 8.5 (GeV/c)2 Completed in spring 2008
SANE /Hall C E05-017: Polarized Target Q2 = 5 – 6 (GeV/c)2 Completed in spring 2009
BF-04 (Wed.)
BF-05 (Wed.)
LJ-06 (Sat.)
Proposed experiments
PAC32: PR /Hall A (GEp-IV) L. Pentchev, C.F. Perdrisat, E. Cisbani, V. Punjabi, B. Wojtskhowski, M. Khandaker et al. Q2=13,15 (GeV/c)2: Approved
PAC32: PR /Hall A (high-Q2 x-sec.) S. Gilad, B. Moffit, B. Wojtsekhowski, J. Arrington et al. Q2 = (GeV/c)2: Approved
PAC34: PR /Hall C (GEp-V) E.J. Brash, M. Jones, C.F. Perdrisat, V. Punjabi et al. Q2=6,10.5,13 (GeV/c)2: Conditionally approved
So let’s not put data points on it yet.
There have been additional high precision Super-Rosenbluth measurments in HallC up to 6.6 (still being analyzed)
And new proposals for recoil polarization in Hall A and C up to 15 GeV^2 have been approved, accompanied by new precision cross section experiment to also separate GE and GM.
CF-06 (Thu.)

18. spin of beam OR target NORMAL to scattering plane
Imaginary part of TPE: SSA’s
spin of beam OR target NORMAL to scattering plane
on-shell intermediate state (MX = W)
E.g. target normal spin asymmetry
Beam: PVES at Bates, MAMI and Jlab; Target: PR05-015, PR08-005
BF-06 (Wed.)
BF-07 (Wed.)

19. Transverse Beam Asymmetry
Plot: Courtesy of J. Mammei

20. Summary
The limits of OPE have been reached with available today’s precision  Nucleon elastic form factors, particularly GEp under doubt
The TPE hypothesis is suited to remove form factor discrepancy, however calculations of TPE are model-dependent
Experimental probes: Real part of TPE: Y2γ – Imaginary part: SSA’s
Need both positron and electron beams for a definitive test of TPE OLYMPUS, CLAS, VEPP-3
ε dependence of polarization transfer, ε-nonlinearity of cross sections transverse beam symmetries
Improved precision and extension of “standard” methods to high Q2
A comprehensive and rich program underway and/or proposed is expected to be conclusive within a few years
Broader Impact: gamma-Z box in PVES; TPE effects in DIS

21. Interpreting Electron Scattering …
“[…] most of what we know and everything we believe
about hadron structure [… is based on electron scattering]” (W. Turchinetz)
“The electromagnetic probe is well understood, hence …”
(a common phrase in many articles)
We have made big investments in lepton scattering facilities to explore hadron structure
The elastic form factors characterize the simplest process
in nuclear physics, namely elastic scattering
(straightforward, one should think)
We have to understand the elastic form factors before we can claim to have understood anything else

22. Backup slides

23. GpE and GpM from Unpolarized Data

24. GpE and GpM from Unpolarized Data
charge and magnetization density (Breit fr.)
Dipole form factor
within 10% for Q2 < 10 (GeV/c)2

25. Recoil Polarization Technique
Pioneered at MIT-Bates
Pursued in Halls A and C, and MAMI A1
In preparation for 12 GeV
V. Punjabi et al., Phys. Rev. C71 (2005) 05520
Focal-plane polarimeter
Secondary scattering of polarized proton from unpolarized analyzer
Spin transfer formalism to account for
spin precession through spectrometer

26. Polarized Targets
BLAST Internal Target:
Atomic Beam Source
UVA / “SLAC”-Target:
Dynamic Nuclear Polarization
Limited luminosity for polarized hydrogen/deuterium targets,
Very precise at low to moderately high Q2
from W. Meyer, SPIN2008

27. Nucleon Form Factors: Last Ten Years
5/18/2018
J. Arrington
PANIC08
GEn: 6, GMn: 6, GEp: GMp: L/T for 10-13
Magenta: underway or approved
Test

28. BLUE = CDR or PAC30 approved, GREEN = new ideas under development
Extensions with Jlab 12 GeV Upgrade
5/18/2018
J. Arrington
PANIC08
~8 GeV2
BLUE = CDR or PAC30 approved, GREEN = new ideas under development
Test

29. Two-Photon Exchange: Exp. Evidence
Two-photon exchange theoretically suggested
TPE can explain form factor discrepancy
J. Arrington, W. Melnitchouk, J.A. Tjon,
Phys. Rev. C 76 (2007)
Rosenbluth data with two-photon exchange correction
Polarization transfer data

30. Polarized Target Experiments at High Q2
Independent verification of recoil
polarization result is crucial
Polarized internal target / low Q2: BLAST Q2<0.65 (GeV/c)2 not high enough to see deviation from scaling
RSS /Hall C: Q2 ≈ 1.5 (GeV/c)2
SANE/Hall C: completed March 2009
BigCal electron detector
Recoil protons in HMS parasitically
Extract GE/GM to <5% at Q2≈5-6 (GeV/c)2
While it is exciting to see how the further Q2 evolution behaves (with a prospective node in the charge form factor around 8 (GeV/c)^2, it is also important to independently verify the case. In a recently published result from HallC at Q^2=1.5 (GeV/c)^2 the evidence is not confirmed without leaving doubts.
M.K. Jones et al., PRC74 (2006)

31. New Proton Measurements at High Q2
Extension to higher Q2 at Jefferson Lab
GEp-III /Hall C: PR04-108/PR Completed in spring 2008
Sign change of GE/GM observed (preliminary, C. PANIC08)
PRELIMINARY
Or maybe not (preliminary, CIPANP09)
Experiment Gep-III was carried out in in Hall C using a new FPP in the HMS
Preliminary data shown in fall 2008 indicated a linear continuation and hence a sign change of GE around 8 (Gev/c)^2
However further analysis has put doubts on this and the recently shown second set of preliminary data sees no longer a sign change
Ratio well described by VMD

32. spin of beam OR target NORMAL to scattering plane
Imaginary part of TPE: SSA’s
spin of beam OR target NORMAL to scattering plane
on-shell intermediate state (MX = W)
lepton
hadron
Beam: PVES at Bates, MAMI and Jlab; Target: PR05-015, PR08-005
BF-06 (Wed.)
BF-07 (Wed.)

33. Target normal spin asymmetry
general formula, of order e2
involves the imaginary part of two-photon exchange amplitudes