Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Two-Photon Exchange

Andrei Afanasev, JLab Users Workshop, 6/22/05Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Two-Photon Exchange for Elastic Electron-Nucleon Scattering

Andrei Afanasev

Jefferson Lab

JLab Users Workshop

June 22, 2005


Plan of talk

Two-photon exchange effects in the process e+p→e+p

. Models for two-photon exchange

. Cross sections

. Polarization transfer

. Single-spin asymmetries

. Parity-violating asymmetry

. Refined bremsstrahlung calculations


Elastic Nucleon Form Factors

pm

q

peefi

fifi

utFtFuuueM

MM

))()(( 22121

1

•Based on one-photon exchange approximation

)0(

,

:1

)1(2

:)(

2121

2

220

y

ME

M

E

z

x

z

x

EM

P

FFGFFG

techniqueonPolarizatiG

G

A

A

P

P

techniqueRosenbluthGG

•Two techniques to measure

Latter due to: Akhiezer, Rekalo; Arnold, Carlson, Gross


Do the techniques agree?

. Both early SLAC and Recent JLab experiments on (super)Rosenbluth separations followed Ge/Gm~const

. JLab measurements using polarization transfer technique give different results (Jones’00, Gayou’02)

Radiative corrections, in particular, a short-range part of 2-photon exchange is a likely origin of the discrepancy

SLAC/Rosenbluth

JLab/Polarization

~5% difference in cross-section


Electron Scattering: LO and NLO in αem

Radiative Corrections:• Electron vertex correction (a)• Vacuum polarization (b)• Electron bremsstrahlung (c,d)• Two-photon exchange (e,f)• Proton vertex and VCS (g,h)• Corrections (e-h) depend on the nucleon structure

•Guichon&Vanderhaeghen’03:Can (e-f) account for the Rosenbluth vs. polarization experimental discrepancy? Look for ~3% ...

Main issue: Corrections dependent on nucleon structureModel calculations: •Blunden, Melnitchuk,Tjon, Phys.Rev.Lett.91:142304,2003•Chen, AA, Brodsky, Carlson, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004


Separating soft photon exchange. Tsai; Maximon & Tjon

. We used Grammer &Yennie prescription PRD 8, 4332 (1973) (also applied in QCD calculations)

. Shown is the resulting (soft) QED correction to cross section

. NB: Corresponding effect to polarization transfer and/or asymmetry is zero

ε

δSoftQ2= 6 GeV2


Lorentz Structure of 2-γ amplitude

pAppeee

pm

q

ppeee

pepefi

pm

q

peefi

fififi

uusGuAuuA

uusFusFuVuuV

AAVVM

utFtFuuuM

MMM

55

221

2

2211

21

),(,

)),('),('(,

))()((

Generalized form factors are functions of two Mandelstam invariants;Specific dependence is determined by nucleon structure


New Expressions for Observables

AMEM

AEMEy

AMM

AEME

z

x

AMEM

GGGG

GGGGP

GGG

GGGG

P

P

GGGG

*222

**

*22

**

*2220

Re)1)(1(2||||

)1(21)Im()1(2)Im(

)1(2)Re(1||

)1(21)Re()1(2)Re(

)Re)1)(1(2|||(|

We can formally define ep-scattering observables in terms of the new form factors:

For the target asymmetries: Ax=Px, Ay=Py, Az=-Pz


Calculations using Generalized

Parton Distributions

Hard interaction with a quark

Model schematics: • Hard eq-interaction•GPDs describe quark emission/absorption •Soft/hard separation

•Use Grammer-Yennie prescription

AA, Brodsky, Carlson, Chen, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004; hep-ph/0502013


Short-range effects; on-mass-shell quark(AA, Brodsky, Carlson, Chen,Vanderhaeghen)

Two-photon probe directly interacts with a (massless) quarkEmission/reabsorption of the quark is described by GPDs

su

tii

t

s

t

s

ut

u

s

su

t

s

ui

t

u

s

tf

su

suii

t

s

t

s

ut

u

s

su

t

s

ui

t

u

s

tti

s

uf

uuAuuV

fAAfVVt

eA

A

V

qeqeqe

qeqeqe

Aqe

Vqeemq

eqeq

2)]2))(log(log(

1))((log

1[

4

)(

)]log(1

))(log(1

[2

2)]2))(log(log(

1))((log

1[

4

)(

)]log(1

))(log(1

[2

)log(])[log(2

,

),(2

2

222

2

22

22

222

2

22

2

,5,,

,,,

22

Note the additional effective (axial-vector)2 interaction; absence of mass terms


`Hard’ contributions to generalizedform factors

GPD integrals

Two-photon-exchange form factors from GPDs


Two-Photon Effect for Rosenbluth Cross Sections

. Data shown are from Andivahis et al, PRD 50, 5491 (1994)

. Included GPD calculation of two-photon-exchange effect

. Qualitative agreement with data:

. Discrepancy likely reconciled


Two-Photon Effect for Rosenbluth Cross Sections. Blunden, Melnitchouk, Tjon, Phys.Rev.Lett.91:142304,2003; nucl-

th/0506039


Updated Ge/Gm plot

AA, Brodsky, Carlson, Chen, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004; hep-ph/0502013


Polarization transfer

. Also corrected by two-photon exchange, but with little impact on Gep/Gmp extracted ratio


Charge asymmetry

. Cross sections of electron-proton scattering and positron-proton scattering are equal in one-photon exchange approximation

. Different for two- or more photon exchange

To be measured in JLab Experiment 04-116, Spokepersons W. Brooks et al.


Quark+Nucleon Contributions to An

. Single-spin asymmetry or polarization normal to the scattering plane

. Handbag mechanism prediction for single-spin asymmetry/polarization of elastic ep-scattering on a polarized proton target

HGPDondependenceNo

BGAGA MER

n

~

)Im(2

1)Im(

1)1(2

Only minor role of quark mass


Parity Violating elastic e-N scattering

Longitudinally polarized electrons,

unpolarized target

2

e e pp

unpol

AMEF

LR

LR AAAQGA

224

2

sRFGQG

GGRGRQGe

AZA

eA

sME

nME

nA

pME

pAW

ZME

)()(

)1()1)(sin41()(2

,,,22

,

45.3

sin41

282

W

MeAWA

MZMM

EZEE

GGA

GGA

GGA

)sin41(

)(

2

Neutral weak form factors contain explicit contributions from strange sea

GZA(0) = 1.2673 ± 0.0035 (from decay)

= Q2/4M2

= [1+2(1+)tan2(/2)]-1

’= [(+1)(1-2)]1/2


2γ-exchange Correction to Parity-ViolatingElectron Scattering

. New parity violating terms due to (2gamma)x(Z0) interference should be added:

xγ γ Z0

Electromagnetic Neutral Weak

eZAAW

ZVAAA

eZMA

ZAVAA

GGAA

GGAA

)Re()1)(sin41(Re

)Re()1)(1()(Re2

21

221


GPD Calculation of 2γ×Z-interference. Can be used at higher Q2, but points at a

problem of additional systematic corrections for parity-violating electron scattering. The effect evaluated in GPD formalism is the largest for backward angles:

AA & Carlson, hep-ph/0502128, Phys. Rev. Lett. 94, 212301 (2005): measurements of strange-quark content of the nucleon are affected, Δs may shift by ~10%

Important note: (nonsoft) 2γ-exchange amplitude has no 1/Q2 singularity;1γ-exchange is 1/Q2 singular => At low Q2, 2γ-corrections is suppressed as Q2 P. Blunden used this formalism and evaluated correction of 0.16% for Qweak


Proton Mott Asymmetry at Higher Energies

. Due to absorptive part of two-photon exchange amplitude (elastic contribution: dotted, elastic+inelastic: solid curve for target case)

. Nonzero effect observed by SAMPLE Collab for beam asymmetry (S.Wells et al., PRC63:064001,2001) for 200 MeV electrons

Transverse beam SSA, note (α me/Ebeam) suppression, units are

parts per million calculation by AA et al, hep-ph/0208260

Spin-orbit interaction of electron moving in a Coulomb field N.F. Mott, Proc. Roy. Soc. London, Set. A 135, 429 (1932).


MAMI data on Mott Asymmetry

. F. Maas et al., Phys.Rev.Lett.94:082001, 2005

. Pasquini, Vanderhaeghen:

Surprising result: Dominance of inelastic intermediate excitations

Elastic intermediatestate

Inelastic excitationsdominate


Beam Normal Asymmetry(AA, Merenkov)

0

ˆ

)ˆ1)(ˆ()ˆ(4

1

)ˆ()ˆ1)(ˆ()ˆ(4

1

2Im

),(

1212

512

512

22

210

3

22

2

qHqHqHqLqLqL

aa

TMpMpTrH

mkmkmkTrL

QQ

HL

k

kd

QsD

QA

p

eeee

en

Gauge invariance essential in cancellation of infra-red singularity:

0/0 22

21 QorandQifHL

Feature of the normal beam asymmetry: After me is factored out, the remaining expression is singular when virtuality of the photons reach zero in the loop integral!But why are the expressions regular for the target SSA?!Also available calculations by Gorshtein, Guichon, Vanderhaeghen, Pasquini;Confirm quasi-real photon exchange enhancement in the nucleon resonance region


Phase Space Contributing to the absorptivepart of 2γ-exchange amplitude

. 2-dimensional integration (Q12, Q2

2) for the elastic intermediate state

. 3-dimensional integration (Q12, Q2

2,W2) for inelastic excitations

Example: MAMI A4E= 855 MeVΘcm= 57 deg

`Soft’ intermediate electron;Both photons are hard collinear

One photon is Hard collinear


Special property of normal beam asymmetry

. Reason for the unexpected behavior: hard collinear quasi-real photons

. Intermediate photon is collinear to the parent electron

. It generates a dynamical pole and logarithmic enhancement of inelastic excitations of the intermediate hadronic state

. For s>>-t and above the resonance region, the asymmetry is given by:

)2)(log(8

)(2

2

22

21

212

2

e

ep

en m

Q

FF

FFQmA

Also suppressed by a standard diffractive factor exp(-BQ2), where B=3.5-4 GeV-2 Compare with no-structure asymmetry at small θ:

AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004;

+Erratum (2005)

3s

mA ee

n


Input parameters

. Used σγp from parameterization by N. Bianchi at al., Phys.Rev.C54 (1996)1688

(resonance region) and Block&Halzen, Phys.Rev. D70 (2004) 091901


Predictions for normal beam asymmetry

Use fit to experimental data on σγp and exact 3-dimensional integration over phase space of intermediate 2 photons

HAPPEX

Data expected from HAPPEX, G0


No suppression for beam asymmetry with energyat fixed Q2

x10-6 x10-9

Parts-per-million vs. parts-per billion scales: a consequence ofsoft Pomeron exchange, and hard collinear photon exchange

SLAC E158 kinematics


Beam SSA in the resonance region


Trouble with `Handbag’ for beam normal asymmetry Model schematics:

• Hard eq-interaction•GPDs describe quark emission/absorption •Soft/hard photon separation

•Use Grammer-Yennie prescription

•Hard interaction with a quark•Applied for BSSA by Gorshtein, Guichon, Vanderhaeghen, NP A741, 234 (2004)

•Exchange of hard collinear photons is kinematically forbidden if one assumesa handbag approximation (placing quarks on mass shell) , BUT…•Collinear-photon-exchange enhancement (up to two orders of magnitude) is allowed for off-mass-shell quarks (higher twists) and Regge-like contributions=> If the handbag approximation is violated at ≈ 0.5% level, It would result in (0.5%)log2(Q2/me

2) ≈100% level correction to beam asymmetryBut target asymmetry, TPE corrections to Rosenbluth and polarization transfer predictions will be violated at the same 0.5% level


Lessons from SSA in Elastic ep-Scattering

. Collinear photon exchange present in (light particle) beam SSA

. (Electromagnetic) gauge invariance of is essential for cancellation of collinear-photon exchange contribution for a (heavy) target SSA

. Unitarity is very helpful in reducing model dependence of calculations at small scattering angles, in particular for beam asymmetry


Mott Asymmetry Promoted to High Energies. Excitation of inelastic hadronic intermediate states by the consecutive

exchange of two photons leads to logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons for the beam normal asymmetry

. The strongest enhancement has a form: log2(Q2/me2) => two orders of

magnitude+unsuppressed angular dependence

. Can be generalized to transverse asymmetries in light spin-1/2 particle scattering via massless gauge boson exchange

. Beam asymmetry at high energies is strongly affected by effects beyond pure Coulomb distortion

. Supports Qiu-Sterman twist-3 picture of SSA in QCD

. What else can we learn from elastic beam SSA?

. Check implications of elastic hadron scattering in QCD

(Can large An,t in pp elastic be due to onset of collinear multi-gluon exchange + inelastic excitations?)

. Large SSA in deep-inelastic collisions due to hard collinear gluon exchange; in pQCD need NNLO to obtain unsupressed collinear gluons


Full Calculation of Bethe-Heitler Contribution

212

2

1

1

212

2

1

1

152

2

ˆ

2

ˆ

2

ˆ

2

ˆ

)ˆ)(ˆ1()ˆ(2

1

kk

k

kk

k

kk

k

kk

k

kk

k

kk

k

kk

k

kk

k

mkmkTrL er

Radiative leptonic tensor in full formAA et al, PLB 514, 269 (2001)

Additional effect of full soft+hard brem → +1.2% correction to ε-slopeResolves additional ~25% of Rosenbluth/polarization discrepancy!

Additional work by AA at al., using MASCARAD (Phys.Rev.D64:113009,2001) Full calculation including soft and hard bremsstrahlung


Bethe-Heitler corrections to polarization transfer and cross sectionsAA, Akushevich, Merenkov Phys.Rev.D64:113009,2001;AA, Akushevich, Ilychev, Merenkov, PL B514, 269 (2001)

Pion threshold: um=mπ2

In kinematic of elastic ep-scattering measurements, cross sections are more sensitive to RC


. Quark-level short-range contributions are substantial (3-4%) ; correspond to J=0 fixed pole (Brodsky-Close-Gunion, PRD 5, 1384 (1972)).

. Structure-dependent radiative corrections calculated using GPDs bring into agreement the results of polarization transfer and Rosenbluth techniques for Gep measurements

. Full treatment of brem corrections removed ~25% of R/P discrepancy in addition to 2γ

. Collinear photon exchange + inelastic excitations dominance for beam asymmetry

. Experimental tests of multi-photon exchange. Comparison between electron and positron elastic scattering (JLab E04-116). Measurement of nonlinearity of Rosenbluth plot (JLab E05-017). Search for deviation of angular dependence of polarization and/or asymmetries

from Born behavior at fixed Q2 (JLab E04-019)

. Elastic single-spin asymmetry or induced polarization (JLab E05-015)

. 2γ add-ons for parity-violating measurements (HAPPEX, G0)

Through active theoretical support emerged JLab research program of

Testing precision of the electromagnetic probeDouble-virtual VCS studies with two spacelike photons

Two-photon exchange for electron-proton scattering

Documents

Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Two-Photon Exchange