Hadron form factor measurements at large momentum transfer Egle Tomasi-Gustafsson IRFU, SPhN- Saclay, and IN2P3- IPN Orsay France Kolomna, 11-VI-2010 1

Hadron form factor measurements at large momentum transfer

Egle Tomasi-GustafssonIRFU, SPhN-Saclay, and

IN2P3- IPN Orsay France

Kolomna, 11-VI-2010 1Egle Tomasi-Gustafsson

Egle Tomasi-Gustafsson 2

PLAN

•Introduction

•What is new?•Space-like region : new data at JLab

• Rosenbluth separation (unpolarized scattering)•Recoil proton polarization

(A.I. Akhiezer and M.P. Rekalo in 1968)•Time-like region

•Plans at PANDA

•Global description in a wide kinematical region• Asymptotics• Counting rules• Two photon exchange

Kolomna, 11-VI-2010


Hadron Electromagnetic Form factors

Characterize the internal structure of a particle ( point-like)

Elastic form factors contain information on the hadron ground state.

In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors.

Neutron and proton form factors are different.

Deuteron: 2 structure functions, but 3 form factors.

Playground for theory and experiment at low q2 probe the size of the

nucleus, at high q2 test QCD scaling

Kolomna, 11-VI-2010

4Kolomna, 11-VI-2010

The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1,F2

Electromagnetic Interaction

q2<0

e-e-

p p

)2q(2FM2

qi)2q(1F

or in terms of Sachs FFs:GE=F1- t F2, GM=F1+F2, t=-q2/4M2

The electron vertex is known,gm

The interaction is carried by a virtual photon of mass q2

What about high order

radiative corrections?

Egle Tomasi-Gustafsson

Egle Tomasi-Gustafsson Kolomna, 11-VI-20105

Crossing Symmetry

Scattering and annihilation channels:

- Described by the same amplitude :

- function of two kinematical variables, s and t

k2 → – k2

- which scan different kinematical regions

p2 → – p2


Analyticity

__

q2<0

e-e-

p p

q2>0

e-

e+ p

p

q2q2=4mp2

FFs are complexFFs are real

Unp

hysi

cal r

egio

n

GE=GM

Space-like

Time-likeGE(0)=1

GM(0)=mp

Asymptotics- QCD- analyticity

p+p ↔ e++e-e+p e+p

p+p

↔ e

++

e- +

p



Proton Form Factors ...before

Rosenbluth separation/ Polarization observables

Dipole approximation: GD=(1+Q2/0.71 GeV2)-2

Kolomna, 11-VI-2010


Dipole Approximation

• Classical approach– Nucleon FF (in the Breit

system) are Fourier transform of the charge or magnetic distribution.

•The dipole approximation corresponds to an exponential density distribution.

– ρ = ρ0 exp(-r/r0),

– r02= (0.24 fm)2, <r2> ~(0.81 fm) 2

m2D =0.71 GeV2

Dipole approximation: GD=(1+Q2/0.71 GeV2)-2

Kolomna, 11-VI-2010


Dipole Approximation and pQCD

V. A. Matveev, R. M. Muradian, and A. N. Tavkhelidze (1973), Brodsky and Farrar (1973), Politzer (1974), Chernyak & Zhitnisky (1984), Efremov & Radyuskin (1980)…

Dimensional scaling

– Fn (Q2)= Cn [1/( 1+Q2/mn) n-1],• mn=n2 , <quark momentum squared>• n is the number of constituent quarks

– Setting 2 =(0.471±.010) GeV2 (fitting pion data)

• pion: F (Q2)= C [1/ (1+Q2/0.471 GeV2)1],

• nucleon: FN (Q2)= CN [1/( 1+Q2/0.71 GeV2)2],• deuteron: Fd (Q2)= Cd [1/( 1+Q2/1.41GeV2)5]

Kolomna, 11-VI-2010


The Rosenbluth separation

)2(2)2(2

)1(1 QMGQEG

Mottd

ddd

2M4

2Q,1

2e2)tan1(21

2MG2

EGR

®Holds for 1 g exchange only

Linearity of the reduced cross section

PRL 94, 142301 (2005)

®tan2qe dependencee

Q2 f

ixed

Kolomna, 11-VI-2010


Rosenbluth separation

=0.5=0.2

=0.8

Contribution of the electric term

…to be compared to the absolute value of the error on s and to the size and e dependence of RC

Kolomna, 11-VI-2010


The polarization induces a term in the cross section proportional to GE GM

Polarized beam and target or

polarized beam and recoil proton polarization

The polarization method (1967)

Kolomna, 11-VI-2010


The simultaneous measurement of Pt and Pl reduces the systematic errors

The polarization method (exp)

Kolomna, 11-VI-2010

C. Perdrisat et al, JLab-GEp collaboration

Polarization experiments - JlabA.I. Akhiezer and M.P. Rekalo, 1967

GEp collaboration1) "standard" dipole function

for the nucleon magnetic FFs GMp and GMn

2) linear deviation from the dipole function for the electric proton FF Gep

3) QCD scaling not reached3) Zero crossing of Gep?4) contradiction between

polarized and unpolarized measurements

Kolomna, 11-VI-2010 14Egle Tomasi-Gustafsson

A.J.R. Puckett et al, PRL (2010)


Issues•Some models (IJL 73, Di-quark, soliton..) predicted such behavior before the data appeared

•Simultaneous description of the four nucleon form factors...•...in the space-like and in the time-

like regions•Consequences for the light ions

description•When pQCD starts to apply?•Source of the discrepancy

BUT

Kolomna, 11-VI-2010

Egle Tomasi-GustafssonGDR 25/XI/2010 16

Neutron/proton form factors ratio GEn (Hall A)

Egle Tomasi-Gustafsson17

The IA deuteron structure: S=1, T=0

2) The S (u) and D (w) deuteron wave function

1) The nucleon form factors:

GDR 25/XI/2010

Egle Tomasi-Gustafsson18

GEn from the deuteron

E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001)

GDR 25/XI/2010

•GEn > GEp starting from 2-3 GeV2 !

Egle Tomasi-Gustafsson 19Kolomna, 11-VI-2010

Iachello, Jakson and Landé (1973)

Isoscalar and isovector FFs* ,ρ,


The nucleon form factors

VDM : IJLF. Iachello..PLB 43, 191 (1973)

Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002)

HohlerNPB 114, 505 (1976)

BostedPRC 51, 409 (1995)

Electric Magneticne

utro

npr

oton

E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA (2005)

Kolomna, 11-VI-2010


Time-like observables: | GE| 2 and | GM| 2 .

As in SL region:- Dependence on q2 contained in FFs- Even dependence on cos2 q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term

but TL form factors are complex!

A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il Nuovo Cimento XXIV, 170 (1962)B. Bilenkii, C. Giunti, V. Wataghin, Z. Phys. C 59, 475 (1993).G. Gakh, E.T-G., Nucl. Phys. A761,120 (2005).



Models in T.L. region

E. T-G., F. Lacroix, C. Duterte, G.I. Gakh EPJA 2005

VDM : IJLF. Iachello..PLB43 191 (1973)

Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002)

‘QCD inspired’

proton

neutron

Kolomna, 11-VI-2010


Spin Observables

Analyzing power, A

Double spin observables

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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:


Models in T.L. Region (polarization)

VDM : IJL

Ext. VDM

‘QCD inspired’

AngularAsymmetry

Ay Axx Ayy

AxzAzz

E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 2005

Kolomna, 11-VI-2010


SIS

HESR

PANDA

http://www-panda.gsi.de/Parameters of HESR

• Injection of p at 3.7 GeV• Slow synchrotron (1.5-14.5 GeV/c)• Storage ring for internal target operation• Luminosity up to L~ 2x1032 cm-2s-1• Beam cooling (stochastic & electron)

need of • highest rates• good resolution• Good Particle

Identification

Proton-Antiproton Annihilation

Kolomna, 11-VI-2010

27Kolomna, 11-VI-2010 27

• 3 body reactions kinematical constraints

PID

• 2 body reactions (hadrons)

π+π-, K+K-

610~

ee

It is possible to discriminate e+e- from π+ π-

High statistics GEANT4 simulations • < few 0/00 misidentified events / cosCM bin

• < 1% on the total cross section up to 16 GeV2

Physical BackgroundM. Sudol et al, arXiv:0907.4478 [nucl-ex]



Individual determination of GE and GM up to large Q2

Expected Results

R=GE/GM

BaBAR

PS170 PANDA sim

L = 2 10 32 cm-2 s-1

100 jours

M. Sudol et al, EPJA 2010, arXiv:0907.4478 [nucl-ex]



Phragmèn-Lindelöf theorem

Asymptotic properties for analytical functions

E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005)

D=0.05, 0.1

If f(z) a as z along a straight line, and f(z) b as zalong another straight line, and f(z) is regular and bounded in the angle between, then a=b and f(z) a

uniformly in the angle.



Phragmèn-Lindelöf theorem


Applies to NN and NNInteraction (Pomeranchuk theorem)t=0 : not a QCD regime!

Connection with QCD asymptotics?


E. T-G. e-Print: arXiv:0907.4442 [nucl-th]

Egle Tomasi-Gustafsson31GSI 1/XII/2010

Radiative Corrections (ep)

RC to the cross section:- large (may reach 40%)- e and Q2 dependent- calculated at first order

May change the slope of sR

(and even the sign !!!)

Q2=5 GeV2

Q2=3.75 GeV2

Q2=1.75 GeV2

E. T.-G., G. Gakh, PRC 72, 015209 (2005)

Andivahis et al., PRD50, 5491 (1994)

2MG2

EGR

Egle Tomasi-GustafssonGSI 1/XII/2010 32

Scattered electron energy

All orders of PT needed beyond Mo & Tsai approximation!

Initial state emission

final state emission

Quasi-elastic scattering

3%

Y0

Not so small!

Shift to LOWER Q2


Short history (I)

Schwinger: corrections to cross section for electron scattering in external field

s=s0(1+d) (1)

Yennie, Frauchi, Suura: cross section of any pure process (without real photon emission) is zero.

Kessler, Ericsson, Baier, Fadin, Khoze, Y. Tsai : quasi real electron method. Emission of hard photon is described in terms of a convolution of a radiative function with Born cross section.

(1) Not adequate


The Structure Function Method

Distinguish: -leading contributions of higher order

-non leading ones

E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985)

The SF method is based on: • Renormalization group evolution equation• Drell-Yan parton picture of the cross section in QCD

Electron SF: probability to ‘find’ electron in the initial electron, with energy fraction x and virtuality up to Q2


LSF: ‰ precision

2e

2

m

QlnL,1L

%2.0400

1L

E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985)

LLA (Leading Logarithm Approximation)

Precision of LLA

%01.0L2

Even when corrections in first order PT are d~100%, the accuracy of higher order RC (LSF) is / a p d1% !

Including K-factor


The LSF cross section (for ep )

•If the electron is detected in a calorimeter: the cross section is integrated over the scattered electron energy fraction:

•The K-factor includes all non leading contributions:

1),z(Ddz1

0

QED Radiative Corrections and DVCS


V.V. Bytev, E.A. Kuraev, E.T.G., Phys.Rev.C77:055205,2008.

Helicity asymmetry Q2=2.3 GeV2

xBj=0.36

Charge asymmetry

RCBorn

39Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

12-XII-2008

Unpolarized cross section

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

Two Photon Exchange:

M.P. Rekalo and E. T.-G., EPJA 22, 331 (2004)G.I. Gakh and E. T.-G., NPA761, 120 (2005)


12-XII-2008

•Properties of the TPE amplitudes with respect to the transformation: cos = - cos i.e., -

(equivalent to non-linearity in Rosenbluth fit)

•Based on these properties one can remove or single out TPE contribution

Symmetry relations

E. T.-G., G. Gakh, NPA (2007)

Egle Tomasi-Gustafsson Kolomna, 11-VI-2010 41

•Differential cross section at complementary angles:

Symmetry relations (annihilation)

The DIFFERENCE enhances the 2 contribution:

The SUM cancels the 2 contribution:


12-XII-2008

Simulations

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

Main effect: odd cos -qdistribution

20.0/3 MGF

02.0/3 MGF

0/3 MGF

05.0/3 MGF

q2=5.4,8.2,13.8 GeV2


12-XII-2008

Fitting the angular distributions...


Cross section at 900 Angular asymmetry

The form of the differential cross section:

is equivalent to:


12-XII-2008



1 g exchange:

Linear Fit in cos2q

2 g exchange Quadratic Fit in x=cosq


12-XII-2008

q2=5.4 GeV2

2 g 0



12-XII-2008

q2=5.4 GeV2

2 g 0.02



12-XII-2008

q2=5.4 GeV2

2 g 0.05



12-XII-2008

q2=5.4 GeV2

2 g 0.20

Fitting the angular distributions…


12-XII-2008

0.02

q2=5.4 GeV2

q2= 8.2 GeV2

q2=13.8 GeV2

0.05 0.201g 2g


12-XII-2008

N=a0+a2cos q sinq +a1 cos2q, a2~2g

Gep III results (2010)


Bystritskiy SF

No radiative corrections applied to the data

No evidence of two photon effects


12-XII-2008

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)


12-XII-2008

1.877÷1.950

Angular distribution

Eve

nts

/0.2

vs.

cos

q

2.400÷3.0002.200÷2.4002.100÷2.200

2.025÷2.1001.950÷2.025

2 -g exchange?


12-XII-2008

Angular Asymmetry

Mpp=1.877-1.9

A=0.01±0.02

Mpp=2.4-3

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

Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 55GSI, 8-XII-2009

Structure Function method

e+ +e- p + p + DE=0.05

• Virtual and soft photon emission

• Hard photon emission

• LLA- Structure Functions Kuraev,Fadin (1985) Egle Tomasi-GustafssonGSI 1/XII/2010 56

Differential cross section (SF)


• The structure function of the lepton

Energy fractions of the leptons

Partition function

Odd term

K-factor


K-factor (hard)

1. of the order of one2. from the even part of the cross section

cos q

Charge Asymmetry


Radiative correction factor


s=10 GeV2

cos q

Ncorr=Nraw(1+ )d

d

Integrated in all phase space for gProton structureless

Dalitz-plot p+p →e++e- (+ )g


x+=Ee+

x-=Ee-

s=10 GeV2

Conclusions Comparison of scattering and annihilation channels:

model independent statements

Study of the validity of one photon exchange approximation: basic question for deriving information on the hadron structure : in annihilation processes all FFs information is contained in a precise measurement of the angular distribution.

Determination of time-like form factors up to large q2 Tests of validity of pQCD and analiticity. Polarization

observables?basic program with anti-proton beams: Panda Physics Performance Report e-Print: arXiv:0903.3905 [hep-ex] Kolomna, 11-VI-2010 62


Documents

Hadron form factor measurements at large momentum transfer Egle Tomasi-Gustafsson IRFU, SPhN- Saclay, and IN2P3- IPN Orsay France Kolomna, 11-VI-2010 1