Two-photon physics Two-photon physics in in

hadronic processeshadronic processes

Marc VanderhaeghenCollege of William & Mary / Jefferson Lab

PPP7 workshop, Taipei, June 7 - 10, 2007

OutlineOutline Elastic eN scattering beyond the one-photon exchange

approximation puzzle of different results extracted for GE/GM

in Rosenbluth vs polarization experiments two-photon exchange processes

Beam (target) normal spin asymmetry in elastic eN scattering new observable : absorptive part of double Virtual Compton Scattering (VCS)

amplitude resonance region, diffractive region, partonic estimate (GPDs)

in coll. with A.Afanasev, S. Brodsky, C. Carlson, Y.C. Chen, M. Gorchtein, P.A.M. Guichon, V. Pascalutsa, B. Pasquini

Carlson, Vdh : Ann. Rev. Nucl. Part. Sci. 57 (2007) 171-204

Early Measurements of GEarly Measurements of GEEpp

• relied on Rosenbluth separation• measure d/d at constant Q2

• GEp inversely weighted with Q2, increasing the systematic error

above Q2 ~ 1 GeV2

At 6 GeV2 R changes by only 8% from =0 to =1 if GE

p=GMp/µp

Hence, measurement of GEp with 10% accuracy

requires 1.6% cross-section measurement

Method : at fixed Q2, vary angle (or equivalently ) and plot reduced cross section versus

Spin Transfer Reaction Spin Transfer Reaction 11H(e,e’p)H(e,e’p)

Pn 0

hPt h2 (1 )GEpGM

p tane

2

/ I0

hPl h Ee Ee' GMp 2

(1 )tan2 e

2

/ M / I0

I0 GEp Q2 2

GMp Q2 2

1 2(1 )tan2 e

2

GEp

GMp

Pt

Pl

Ee Ee'

2Mtan

e

2

No error contributions from• analyzing power• beam polarimetry

Rosenbluth vs polarization transfer measurements of GE/GM of proton

Jlab/Hall A Polarization

data

Jones et al. (2000)

Gayou et al. (2002)

SLAC, Jlab

Rosenbluth data

Puzzle Puzzle : two methods, : two methods, two different results !two different results !

Speculation : missing radiative Speculation : missing radiative correctionscorrections

Speculation : there are radiative corrections to Rosenbluth

experiments that are important and are not included missing correction : linear in not strongly Q

2 dependent

GE term is proportionally smaller at large Q2

if both FF scale in same wayeffect more visible at large Q2

Q2 = 6 GeV2

Radiative correction diagramsRadiative correction diagrams

bremsstrahlung

vertex

corrections

2 photon

exchange box

diagrams

Status of radiative correctionsStatus of radiative corrections

Tsai (1961), Mo & Tsai (1968) box diagram calculated using only nucleon intermediate state

and using q1 ¼ 0 or q2 ¼ 0 in both numerator and

denominator (calculate 3-point function) -> gives correct IR divergent terms

Maximon & Tjon (2000)

same as above, but make the above approximation only in numerator (calculate 4-point function)

+ use on-shell nucleon form factors in loop integral Blunden, Melnitchouk, Tjon (2003)

further improvement by keeping the full numerator

N

Elastic eN scattering Elastic eN scattering beyond beyond one-photonone-photon exchange exchange

approximationapproximation

equivalently, introduce

Kinematical invariants :

(me = 0)

Observables including two-photon exchangeObservables including two-photon exchange

Real parts Real parts of two-photon amplitudesof two-photon amplitudes

Phenomenological analysisPhenomenological analysis

Guichon, Vdh (2003)

2-photon exchange corrections

can become large on the

Rosenbluth extraction,and are

of different size for both

observables

relevance when extracting

form factors at large Q2

Two-photon exchange calculation : Two-photon exchange calculation : elastic contributionelastic contribution

Blunden, Tjon, Melnitchouk (2003, 2005)

N

world Rosenbluth data

Polarization Transfer

hard scattering

amplitude

electron helicity quark helicity

Calculation for eecan be found in literature

(e.g. van Nieuwenhuizen (1971) ), which we verified explicitly IR divergences of boxes must disappear or cancel in the end,

regularize through photon mass

Two-photon exchange : Two-photon exchange : partonic partonic calculationcalculation

kinematics partonic subprocess :

Separation soft-hard parts in electron-quark Separation soft-hard parts in electron-quark boxbox

Follow the decomposition of Grammer and Yennie (1973) :

soft part calculated as 3-point function

reproduces Low Energy Theorem

hard scattering

amplitude

Two-photon exchange : Two-photon exchange : partonic partonic calculationcalculation

GPD integrals

“magnetic” GPD

“electric” GPD

“axial” GPD

Two-photon exchange : Two-photon exchange : partonic calculationpartonic calculation

GPDs

Chen, Afanasev, Brodsky, Carlson, Vdh

(2004)

Experimental Experimental verification verification

of TPE contributionsof TPE contributionsExperimental verification (will be

performed in next couple of years ! )

• non-linearity in -dependence (test of model calculations)

• transverse single-spin asymmetry (imaginary part of two-photon amplitude)

• ratio of e+p and e-p cross section (direct measurement of two-photon contributions)

• CLAS experiment E04-116 aims at a measurement of the -dependence of the e+/e- ratio for Q2-values up to 2.0 GeV2

• At the VEPP-3 ring that ratio will be measured at two and Q2-values

εε - - dependence of TPE contributions (I)dependence of TPE contributions (I)

Chen, Kao, Yang (2007)

Polynomial fit

“log” fit

1γ only : Rosenbluth1γ + 2γ : log fit

1γ + 2γ : polynomial fit

Q2 (GeV2)

ε

0 10.2 0.4 0.6 0.8

1.75

3.25

5.00

e+ p / e- p

1.00

1.10

1.12

ε

0 0.4 10.2 0.80.6

e+ p / e- p

1.02

1.10

1.14

Chen, Kao, Yang (2007)

polynomial fit

log fit

εε - - dependence of TPE contributions (II)dependence of TPE contributions (II)

Polarization transfer observablesPolarization transfer observables

12

2 correction

on is small

2 correction on

can be tested at small

proton proton Dirac & Pauli Dirac & Pauli FFs :FFs :

modified Regge GPD model

PQCD

Belitsky, Ji, Yuan (2003)

GPD framework

Guidal, Polyakov, Radyushkin, Vdh (2005)

data : SLAC

data : JLab/HallAdata : JLab/HallA

Normal spin asymmetries in Normal spin asymmetries in elastic eN scatteringelastic eN scattering

on-shell intermediate state

spin of beam OR target

NORMAL to scattering

plane

directly proportional to the imaginary part of 2-photon exchange amplitudes

OR

order of magnitude estimates :

target :

beam :

time reversed states

momenta and spins reversed

rotation over 180o around axis ? to plane

phase

SSA in elastic eN scatteringSSA in elastic eN scattering

Unitarity

with

Time reversal invariance :

Perturbation theory in em

to

to

1 exchange gives no contribution to spin asymmetries

spin asymmetries arise from interference between

1 exchange and absorptive part of 2 exchange

2 exchange

1 exchange

function of elastic nucleon form factors

absorptive part of double

virtual Compton scattering

toDe Rujula et al.

(1971)

elastic contribution

on-shell nucleon intermediate nucleon

inelastic contribution

resonant and non-resonant N intermediate states calculated with MAID2003 : unitary isobar model

X= N

all 13 **** resonances below 2 GeV included

Drechsel, Hanstein, Kamalov, Tiator (1999)

Beam Beam normal spin normal spin asymmetryasymmetry

N (elastic)

N (inelastic)

total (N + N)

MAMI dataF. Maas et al., PRL 94 (2005)

New measurements at MAMI at backward angles :

Pasquini & Vdh (2004)

for E Eee = 0.570 GeV = 0.570 GeV

Bn = -8.59±0.89 ppm measurement of resonance

form factors over range in Q2

no suppression of Bn with energy at fixed

Q2

x10-6

ps (GeV)

QQ2 2 = 0.05 GeV= 0.05 GeV22

BBn n in in

diffractive regiondiffractive region

Afanasev & Merenkov

BBn n

σγp

E158 : Bn = -3.5 -> -2.5 ppm (K. Kumar, prelim.)

Note on SLAC E158 :

30% inelastic events included

Expt. E(GeV) θe Q2 GeV2 Bn(ppm)

SAMPLE 0.192 146 0.10 -16.4±5.9

A4 0.570 35 0.11 -8.59±0.89

A4 0.855 35 0.23 -8.52±2.31

HAPPEX 3.0 16 0.11 -6.7 ± 1.5

G0 3.0 19 0.15 -4.06± 1.62

G0 3.0 37 0.25 -4.82 ± 2.85

E-158(ep) 46.0 ~3.0 0.06 -3.5 -> -2.5

E-158(ee) 46.0 ~100 0.03

Beam Beam normal spin asymmetry : normal spin asymmetry : experimentsexperiments

Elastic electron-nucleon amplitudes Elastic electron-nucleon amplitudes with electron helicity flipwith electron helicity flip

In Born approximation :

Elastic electron-quark amplitudes Elastic electron-quark amplitudes

with electron helicity flipwith electron helicity flip

lepton mass new amplitude

BeamBeam normal spin asymmetry : partonic normal spin asymmetry : partonic calculationcalculation

“magnetic” GPD

“magnetic” GPD

“electric” GPD

“electric” GPD

Beam normal spin asymmetry : Beam normal spin asymmetry : protonproton resultsresults

Future PV experimental set-ups (0.1 ppm precision) :

challenge to measure this asymmetry

Results of GPD

calculation

Note : elastic contribution to

Bn is negligibly small

SummarySummary

Normal spin asymmetries (NSA) in elastic electron-nucleon scattering : unique new tool to access the imaginary part of 2 exchange amplitudes

-> Imaginary part of 2 amplitude absorptive part of non-forward doubly VCS tensor-> Unitarity to relate the absorptive part of doubly VCS tensor to pion-electroproduction amplitudes beam NSA in the resonance region as a new tool to extract resonance transition form factors -> In hard scattering region : use handbag approach to relate beam

and target NSA to moments of GPDs

difference Rosenbluth vs polarization data-> GE

p /GMp : now mainly understood as due to two-photon exchange

effects -> quantitative theoretical calculations needed-> precision test : several new expt. planned