Charge asymmetry and symmetry properties

Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO3-IX-2009 1

Charge asymmetry and

symmetry properties

Egle Tomasi-GustafssonIRFU, SPhN-Saclay,

and IN2P3-IPNO France

DUBNA, September 1-5, 2009


Scattering and annihilationScattering and annihilation

__

q2<0

e-e-

p p

q2>0

e-

e+ p

p

q2q2=4mp2

Unp

hysi

cal r

egio

n

Space-like

Time-like

Asymptotics- QCD- analyticity

p+p ↔ e++e-e+p e+p

p+p

↔ e

++

e- +

(+)(+)


Crossing SymmetryCrossing Symmetry

Scattering and annihilation channels:

- Described by the same amplitude :

- function of two kinematical variables, s and t

p2 → – k2 → – k2

- which scan different kinematical regions

p2


1{g

1-2 interference

{ 21 {

M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999)


•Differential cross section at complementary angles:

Symmetry relations (annihilation)

The DIFFERENCE enhances the 2contribution:

The SUM cancels the 2contribution:


Radiative Return (ISR)

.s

m,

x

sin

xx

x),x,s(W

,s

m

s

Ex),m)(ppee(),x,s(W

s

m

cosddm

)ppee(d

e

2

22

122

2

2

2

2

e+ +e- p + p +

B. Aubert ( BABAR Collaboration) Phys Rev. D73, 012005 (2006)


1.877÷1.950

Angular distribution

Eve

nts

/0.2

vs.

cos

2.400÷3.0002.200÷2.4002.100÷2.200

2.025÷2.1001.950÷2.025

2exchange?


Mpp=1.877-1.9Mpp=1.877-1.9

A=0.01A=0.01±±0.020.02

Mpp=2.4-3Mpp=2.4-3

E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008)


Linearity of the Rosenbluth fit


From the data:

deviation from linearity

<< 1%!

Parametrization of 2-contribution for e+p

E. T.-G., G. Gakh, Phys. Rev. C 72, 015209 (2005)

)(1

1),( 2)(2 QfQF a

2222

22

]1[ a

Dγ(a)

/m[GeV]Q

GC)(Qf


2γ-Gamma Models and Data

12

The inclusion of hard 2γ exchange: Chen et al (2003) with GPDs, Blunden et al (2003) in hadronic model

04/22/23

Expt. Jlab 04-019 measuredRatio PL/PT for Q2=2.49 GeV2

at 3 values of ε

PRELIMINARY

C. Perdrisat,L. Pentchev

NO ε-dependence at 0.01 level

NO evidence of 2 contribution

Bystriskyi et al., LSFPR C75, 015207 (2007)


Linear fit to e+4He scattering


Electron/Positron scattering

•What about data: electron positron scattering (elastic or inelastic) in the same experimental conditions?

•If R ≠1 is there any other source of asymmetry?

•Any evidence of two photon exchange (real part of hard box diagram)?



2

1

2*

1 )Re(41

1

1

)(

)(

M

MM

A

A

pe

peR

Born approximation

Two photon exchange:

The effect is enhanced in the ratio

222

11 MMM

2 exchange:2

2*

12

1

2

21

2

2Re2

MMMMMMM

2

1

21Re2

)()(

)()(

M

MM

pepe

pepeA

Asymmetry


World data e+e- scattering


Elastic scattering

R=(-0.071 ± 0.016 )+(1.058 ±0.014)

q2 =1, 3, 5 GeV2 =0.2, 0.5, 0.8



Soft photon emission 2 exchange

C=0.97,0.99

q2=3 GeV2

=0.4

E.A. Kuraev, V.V.Bytev, S.Bakmaev and E.T-G, PRC 78, 015295 (2008).


=1.1

=4.

Simulation with PANDA


p+p e++ e-


2 0.02

2 0.05 2 0.2

1

q2=5.4 GeV2

N=a0+a2cossin2+a1 cos2, a2~2


Conclusions Determination of the validity of one photon exchange approximation: basic question for deriving information on the hadron structure

in annihilation processes all information is contained in a precise measurement of the angular distribution

Comparison of scattering and annihilation channels: model

independent statements

No evidence of two photon exchange (real part) in the data.

Precise calculation of radiative corrections


Simulations

Approximations:•Neglect contributions to GE,GM•Consider only real part

Main effect: odd cos- distribution

20.0/3 MGF

02.0/3 MGF

0/3 MGF

05.0/3 MGF

q2=5.4,8.2,13.8 GeV2


N=a0+a2cossin2+a1 cos2, a2~2

2 visible from F3/GM ~ 0.05


Fitting the angular distributions..

E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)

Cross section at 900 Angular asymmetry

The form of the differential cross section:

is equivalent to:


Angular asymmetry and

Charge asymmetry


Inelastic e+e- scatteringR=1.002±0.002

R=(-0.0009 ± 0.001 )q2

+(1.005 ±0.003)

R=(0.005 ± 0.014 )XBj

+(1.002 ±0.004) =0.84


Elastic e -4He scattering ( L.J. Kaufman)

Ayexp(4He) =-13.51 ± 1.34 (stat) ± 0.37(syst) ppm

=6°, Q2=0.077 GeV2

Im F1 (s,q2) ~ F(q2)

1~ 2 term !

If Im F1 (s,q2) ~ Re F1 (s,q2)


Matrix element: spins 0 and 1/2

Two helicity amplitudes, functions of s and t

q1+q2~m

F(0)=Ze Electromagnetic He form factor

Holds for crossed channel,

q1→ -q1 q2→ -q2


Two photon exchange•The calculation of the box amplitude requires

thedescription of intermediate nucleon excitation

and of their FFs at any Q2

•Different calculations give quantitatively different results

Theory not enough constrained!

Model independent statements



In presence of 2 exchange :

- Non linearity in the Rosenbluth fit- charge asymmetry (and/or odd powers of cos in the crossed channel

- Non vanishing odd polarization observables

- Different cross section for electron/positron – proton elastic(inelastic) scatteringM. P. Rekalo, E. T.-G. , EPJA (2004), Nucl. Phys. A (2003)


Two photon exchange

Unpolarized cross section

F1~m, F~0, f~

p1

p2

Lab system


Transversal Beam asymmetry(2 exchange)

Spin vector of e beam

Normal component

T-odd ,~m, imaginary part of the spin flip 2 amplitude

If ground state He, predicted: Ayth~10 -10

E.D. Cooper, C.J. Horowitz, PRC72,034602 (2005)


Elastic e -4He scattering ( L.J. Kaufman)

Ayexp(4He) =-13.51 ± 1.34 (stat) ± 0.37(syst) ppm

=6°, Q2=0.077 GeV2

→ contibution from excited states…


Two photon exchange•The calculation of the box amplitude requires

thedescription of intermediate nucleon excitation

and of their FFs at any Q2

•Different calculations give quantitatively different results

Theory not enough constrained!



How to proceed?

Our Suggestion:

•Search for model independent statements•Exact calculation in frame of QED (p~)•Prove that QED box is upper limit of QCD box

diagram

Our Conclusion

•Two photon contribution is negligible (real part)•Radiative corrections are huge: take into account

higher order effects (Structure Functions method)E.A. Kuraev, Yu. Bystritsky, V. Bytev, E. T.-G. , (2006-2008)


11-2-2 interference (e-d) interference (e-d)

M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, 042202 (1999)

C/A D/A


Unpolarized cross section

•Induces four new terms•Odd function of •Does not contribute at =90°

Two Photon Exchange:

Charge asymmetry and symmetry properties

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