Two-photon Exchange

John Arrington

Argonne National Lab

International Workshop on Positrons at Jefferson Lab, Mar 25-27, 2009

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Unpolarized Elastic e-N Scattering

Early form factor measurements used Rosenbluth separation

R = d/d [(1+)/Mott] = GM2 + GE

2 in Born approx. ( = Q2/4M2)

GM2

GE2

=180o =0o

Reduced sensitivity to…

• GM if Q2 << 1

• GE if Q2 >> 1

• GE if GE2<<GM

2 (e.g. neutron)

Form factor extraction is very sensitive to angle-dependent corrections in these cases

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New techniques: Polarization and A(e,e’N) Mid ’90s brought measurements using improved techniques

– High luminosity, highly polarized electron beams

– Polarized targets (1H, 2H, 3He) or recoil polarimeters

– Large, efficient neutron detectors for 2H, 3He(e,e’n)

– Improved models for nuclear corrections

Polarized 3He targetBLAST at MIT-Bates

Focal plane polarimeter – Jefferson Lab

LT:GM2+GE

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PT:GE/GM

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Polarization vs. Rosenbluth: GE/GM

pGEp/GMp from Rosenbluth measurements

I. A. Qattan, et al, PRL 94, 142301 (2005)

JLab Hall A: M. Jones, et al.; O. Gayou, et al.

New data: Recoil polarization and p(e,p) “Super-Rosenbluth”

Slope from recoil polarization

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Two-photon exchange corrections

Clear discrepancy between LT, PT extractions

Two-photon exchange effects can explain discrepancy in GE

Requires ~3-6% -dependence, weekly dependent on Q2, roughly linear in

Guichon and Vanderhaeghen, PRL 91, 142303 (2003)

JA, PRC 69, 022201 (2004)

If this were the whole story, we would be done: L-T would give GM, PT gives GE

Still need to be careful when choosing form factors as, e.g. input to fits or data analysis

There are still issues to be addressedWhat about the constraints (~1%) from positron-electron comparisons?TPE effects on GM?TPE effects on polarization transfer?TPE effects on other measurements?

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Tests of Two-Photon Exchange (’50s and ’60s)

Secondary beams had low luminosity; data taken at high Q2 OR large , never both.

If correction is at large (small ), it would not have been clearly seen

JA, PRC 69, 032201 (2004)

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Aside: Rosenbluth separation for e+p

PT results LT (electron) LT (positron)

(GE/GM)2<1

Small (3-5%) -dependent TPE correction can yield large (>100%) corrections to GE, since GE contributes so little to cross section

Focus has been on how TPE impacts GEp at high Q2

Biggest issue, but not the only important one

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Low-Q2 behavior: Unpolarized, Polarizated

0.01-0.06 GeV2

0.1-0.61.0-6.0

0.1,0.2,0.3,0.6,1.0 GeV2

TPE effect does not approach zero as Q2 0

P. Blunden, W. Melnitchouk, and J. Tjon, PRC 72, 034612 (2005)

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GMp from inclusive measurements – data extend to 30 GeV2

Impact on GMp

Proton form factor measurements from Rosenbluth separations

– TPE correction to GE is large, so are (most) LT uncertainties

– Correction to GM much smaller, but large compared to uncertainties

GMp from inclusive measurements – data extend to 30 GeV2

With TPE corrections (Blunden, et al.), GMp shifts by up to 2-3 sigma

pGEp/GMp from Rosenbluth measurementspGEp/GMp from Rosenbluth measurements

New data: Recoil polarization

pGEp/GMp from Rosenbluth measurements

New data: Recoil polarization and p(e,p) “Super-Rosenbluth”

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“Indirect” impact: Parity Measurements Neglect TPE in calculating APV small

effect (top)

– Especially for small angles (large ) where most data is taken

– Missing -Z box, which is typically the largest correction, but is still small

Neglect TPE in extracting EM FFs much larger effect (bottom)

– Corrections largest at large – Note: form factor uncertainties typically

taken as <1%, but TPE corrections can be significantly larger (and correlated)

JA and Ingo Sick, PRC 76, 035201 (2007)

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Effect on Rosenbluth (L-T) Extractions

LTPT

LT + BMTPT

• Hadronic calculation resolves the discrepancy up to 2-3 GeV2

• Note: TPE effects of ~same size for cross section and polarizations

Effect on GE amplified in high-Q2 Rosenbluth measurements

Most polarization (and cross section) measurements at large , smaller TPE

P. Blunden, W. Melnitchouk, and J. Tjon, PRC 72, 034612 (2005)

• Note: Limited direct evidence for TPE, other RC issues to be addressed

Extraction of proton form factors not too sensitive to details, but does assume entire effect is TPE (e.g. no correction at = 1)

J. Arrington, W. Melnitchouk, and J. Tjon, PRC76, 035205 (2007)

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TPE Beyond the Elastic Cross Section

TPE Calculations sufficient for extracting proton form factor

– Additional uncertainty at high Q2

Precise experimental tests of TPE calculations possible for the proton

– Important for validating calculations used for other reactions

– Hadronic, partonic calculations yield different sign for recoil polarization Important direct and indirect consequences on other experiments

• High-precision quasi-elastic expts.

• - N scattering measurements

• Proton charge radius, hyperfine splitting

• Strangeness from parity violation

• Neutron, Nuclear form factors

• Transition form factors

• Bethe-Heitler, Coulomb Distortion,…

D.Dutta, et al., PRC 68, 064603 (2003)

JA, PRC 69, 022201(R) (2004)

H.Budd, A.Bodek, and JA hep-ex/0308005

P.Blunden and I.Sick, PRC 72, 057601 (2005)

S.Brodsky, et al., PRL 94, 022001 (2005)

A.Afanasev and C.Carlson, PRL 94, 212301 (2005)

JA and I.Sick, nucl-th/0612079

P.Blunden, W.Melnitchouk, and J.Tjon, PRC72, 034612 (2005)

A.Afanasev, et al., PRD 72, 013008 (2005)

S. Kondratyuk and P. Blunden, NPA778 (2006)

V. Pasculutsa, C. Carlson, M. Vanderhaeghen, PRL96, 012301 (2006)

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TPE measurements in e-p scattering

Precise e-p elastic cross sections (JLab,Mainz) - dependence of cross section

Polarization transfer: Pl/Pt (Jlab) - dependence of polarization ratio

Positron-electron comparisons (VEPP, JLab, DESY) - Clean extraction of two-photon terms - Map out Q2 and dependence of TPE

Can test TPE explanationMap out TPE up to Q2 ~ 2 GeV

Map out TPE for Q2 > 1-2 GeV2

Longer term (test calculations for e-p, other reactions)

Short term (verify TPE, determine proton form factors)

Born-forbidden observables in p(e,e’p) – imaginary part of TPE amplitude - Beam single-spin asymmetries (SAMPLE, A4, G0, HAPPEX) - Normal polarization transfer, normal target spin asymmetriesMeasurements to constrain TPE in other reactions - Elastic form factors for neutron or light nuclei - Other exclusive processes (e.g. N form factors)

- Experimentally, very little can be done without positron beams - Need well tested, well constrained calculations

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Benefits of improved LT separations

Compare precise LT and PT to constrain linear part of TPE corrections

– Limiting factor in constraining TPE from PT-LT difference is precision of LT data

At high Q2, almost all -dependence comes from TPE

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Nonlinearity Tests

Born approx R linear in ε, TPE can have nonlinearity

SLAC NE11, JLab E01-001: quadratic terms consistent with zero

Global fit, averaged over all Q2 yields P2 = 0.019±0.027

E05-007: Project P2 ≈ ±0.020 for both linearity scans, with global P2

≈ ±0.011

Set meaningful limits over a wide Q2 range

NE11: L. Andivahis, et al, PRD 50, 5491 (1994)

E01-001: I. A. Qattan, et al, PRL 94, 142301 (2005)

Global linearity limits: V.Tvaskis, et al., PRC 73, 025206 (2006)

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E04-019: dependence in polarization transfer

Experiment ran in early 2008 Preliminary results suggest Preliminary results suggest

little or no little or no -dependence-dependence

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Two-Photon Exchange Measurements

Comparisons of e+-p, e--p scattering [VEPP-III, Hall B, DESY-Olympus proposal]

World’s dataNovosibirsk

Previous comparisons limited to low Q2 or small scattering angle (large )

Examination of angular dependence yields evidence (3 level) for TPE in existing data

J. Arrington, PRC 69, 032201(R) (2004)

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Test run at Novosibirsk

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Two-Photon Exchange Measurements

Comparisons of e+-p, e--p scattering [VEPP-III, Hall B, DESY-Olympus]

dependence of polarization transfer and unpolarized e-p [Hall C]

World’s dataNovosibirskJLab – Hall B

Previous comparisons limited to low Q2 or small scattering angle (large )

Examination of angular dependence yields evidence (3 level) for TPE in existing data

J. Arrington, PRC 69, 032201(R) (2004)

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Two-Photon Exchange Measurements

Comparisons of e+-p, e--p scattering [VEPP-III, Hall B, DESY-Olympus]

dependence of polarization transfer and unpolarized e-p [Hall C]

– More quantitative measure of the discrepancy

– Test against models of TPE at both low and high Q2

TPE effects in Born-forbidden observables [Hall A, Hall C, Mainz]

– Target single spin asymmetry, Ay in e-n scattering

– Induced polarization, py, in e-p scattering

– Vector analyzing power, AN, in e-p scattering (beam normal spin asymmetry)

World’s dataNovosibirskJLab – Hall B

Previous comparisons limited to low Q2 or small scattering angle (large )

Examination of angular dependence yields evidence (3 level) for TPE in existing data

J. Arrington, PRC 69, 032201(R) (2004)

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Why do we need more?

The proposed e+/e- experiments are very limited (but very important)

– Verify TPE as source of discrepancy

– First quantitative measure of TPE effect on cross section

– Begin to test , Q2 dependence of calculations

No plans to study polarization observables Nothing proposed to look at other reactions

– Very limited tests might be possible with CLAS or Olympus

To thoroughly test calculations, need other measurements:

– Polarization, Born-forbidden observables

– Range of positron/electron comparisons (polarization, other reactions…)

A “real” positron beam, e.g. 1A, would be a huge improvement

– Great coverage for elastic, many other reaction channels

– Higher current or polarization TPE in polarization observables

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Fin…

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Radiative Corrections: Beyond the Born Approximation

Additional two-photon contributions expected to be small (~EM)Theoretical estimates generally indicated ~1% correctionsLinearity of Rosenbluth plot taken as evidence of small TPEComparison of positron to electron scattering was the “definitive” test

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JLab E01-001: Test of Radiative Corrections RC terms largely -independent except for electron brem.

Form factor ratios for Q2 of 2.5-2.64 GeV2, before and after RC - Andivahis, Qattan, and Walker (solid = after RC)

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E05-017: Extended “Super-Rosenbluth”

102 Kinematics points

Q2 0.40-5.76 GeV2

13 points at Q2=0.983

10 points at Q2=2.284

Ran summer 2007 in Hall C at Jefferson Lab Extremely high precision LT separations over large kinematic range

– Improved measurement of TPE effects over large Q2 range

– Very precise linearity tests at Q2= 0.983, 2.284 GeV2

– Nearly all dependence is TPE for Q2 > 5 GeV2

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Positron-electron comparison in CLAS@JLab

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Positron-electron comparison in CLAS@JLab

1%

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CLAS TPE Test Run

Focus was on background issues Clearly identified e-p and e+p elastic events

rati

o of

yie

ld e

- p/e

+p

lepton scattering lab angle

• Leptons in sector 5 only: 1/6 of data• Red for negative torus polarity, Black for positive.

• Only crude CLAS calibrations

Q2<0.5 GeV2

0.4<<0.95

ratio ~1

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OLYMPUS: BLAST@DORIS

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The BLAST Detector

Left-right symmetric

Large acceptance:0.1 < Q2/(GeV/c)2 < 0.820o < < 80o, -15o < < 15o

COILS Bmax = 3.8 kG

DRIFT CHAMBERSTracking, PID (charge)p/p=3%, = 0.5o

CERENKOV COUNTERSe/ separation

SCINTILLATORSTrigger, ToF, PID (/p)

NEUTRON COUNTERSNeutron tracking (ToF)

DRIFT CHAMBERS

CERENKOVCOUNTERS

SCINTILLATORS

NEUTRON COUNTERS

TARGET

BEAM

BEAM

COILS

All the advantages of VEPP-3 expt.– Pure beam, well defined energy

Q2, coverage close to CLAS

Coincidence measurement– Could do (e,e’n), other reactions