Recent developments in Electromagnetic Hadron Form Factors

Recent developments in

Electromagnetic Hadron Form Factors

„

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are Form Factors?

„

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to measure?

„

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to measure?

„

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„

Consequences,

Conclusions

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Hadron Electromagnetic Form factors

„

Characterize the internal structure of a particle (

≠

point-like)

„

FFs are

real

in

space-like

region

(scattering)

and

imaginary

in

time-like

region

(annihilation

).

„

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.

027,9$7,216

„

In the traditional view, the atom’s

nucleus appears as a cluster of

nucleons - protons and neutrons. A

deeper view reveals quarks and

gluons inside the nucleons.

„

CEBAF’s continuous, energetic beams of probing

electrons let physicists examine how the two view fit

together. Ultimately, the process of bridging the views will

yield a complete understanding of nuclear matter….

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.

exp(-r/r

),

r

_{= (0.24 fm)}

_{, <r}

_{> ~(0.81 fm)}

↔

m

=0.71 GeV

G

=1/(1+Q

_{/0.71 GeV}

₎

Dipole Approximation and pQCD

‰

Dimensional scaling

F

_n

(Q

2

_{)= C}

n

[1/( 1+Q

2

/m

n

)

n-1

],

„

m

_n

=

n

β

2

, <quark momentum squared>

„

n is the number of constituent quarks

Setting

β

2

_{=(0.471±.010) GeV}

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„

pion

:

F

_π

(Q

2

)= C

_π

[1/ (1+Q

2

/

0.471

GeV

2

₎

1

_],

„

nucleon

: F

₁

(Q

2

_{)= C}

1

[1/( 1+Q

2

/

0.71

GeV

2

)

2

],

The Pauli and Dirac Form Factors

„

The electromagnetic current in terms of the Pauli and Dirac FFs:

•

Normalization:

F

(0)=1, F

•

Normalization:

G

(0)=1, G

=2.79

Proton Form Factors

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F2

F2

F1

F1

Q

Q

_{=1 GeV}

_{=1 GeV}

The Rosenbluth separation

„

Elastic

HS

cross section (1-

H[FKDQJH

•

point-like particle:

σ

Mott

The Rosenbluth data (SLAC)

Proton Form Factors ...before

Dipole approximation:

G

=1/(1+Q

_{/0.71 GeV}

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The polarization induces a term in the cross section proportional to G

G

Polarized beam and target

or

polarized beam and recoil proton polarization

Proton polarimeter

Inclusive reaction p+C

1 Charged particle+X

•

•

Analyzing powers:

Analyzing powers:

•

The experimental set-up(JLab-E99007)

-Trigger on proton: background, target walls and pion electroproduction

-The solid angle is defined by the proton

The polarization method (exp)

The HALL A-calorimeter

• Assembled a 1.35 x 2.55 m

_calorimeter

• 17 rows and 9 columns of 15x15

lead-glass blocks

Azymuthal distribution

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•Linear deviation from dipole

•G

_Ep

≠

G

_Mp

Scaling?

pQCD: F

₁

→

1/Q

4

, F

₂

→

1/Q

6

F

₁

/ F

₂

→

Q

2

Models, models, models...

„

Skyrme Models (Soliton)

„

Vector Dominance Models (G-K, IJL…)

„

Perturbative QCD

„

(Relativistic) Constituent Quark Model

„

Di-quark models

Issues

„

When pQCD starts to apply?

„

Simultaneous description of the four nucleon

form factors...

„

...in the space-like and in the time-like regions

The proton magnetic form factor

The new results induce

3% global effect

Radiative corrections on

σ

(ep)

up to 30%!

The nucleon form factors

proton

The deuteron

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2

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The deuteron

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The IA deuteron structure:

S=1

,

T=0

1) The nucleon form factors:

2) The S

X

and D

Z

G

_En

from the deuteron

„

G

_En

>

G

_Ep

starting from 2 GeV

2

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The IA deuteron structure

The reaction d(e,e’n)p - A

_x

- The Impulse Approximation

- The deuteron structure

- Kinematics: proton spectator

- Polarization observables

The reaction d(e,e’n)p - A

_x

Select the quasi-elastic

Kinematics

Large dependence of the

asymmetry on Gen!

Polarized electron beam,

polarized target or neutron

polarimeter

The neutron electric form factor

„

Polarization

method

„

Nuclear effects

When G

_E

p

=0?

„

Jlab E01-109

approved 07/2001

scheduled 2005

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„

Hall A => Hall C

„

New polarimeter

„

New calorimeter

„

G

_e

p

IV

: up to 12 GeV

2

_,

after the upgrade of Cebaf

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Time-like and space-like regions

„

Form factors are

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and

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.

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-

+ h => e

-

+ h

_e

+

_{+ e}

-

_{=> h + h}

_

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_

Time-like and space-like regions

„

T-L

→

|

G

|

„

Asymptotic properties from the

Phragmèn-Lindelöf theorem

Possible corrections

„

2-

H[FKDQJH"

„

Radiative corrections?

„

P-violating terms?

Complete calculations in progress

Estimations give effects of the order of few

percent

Conclusions

„

New precise results on proton

electric form factor

„

Recoil polarization method

Polarimetry

„

Jlab polarized electron beam

„

The electric and the magnetic

distributions of the proton are

different!

„

The asymptotic region is far.

„

The nucleon and light hadrons

models have to be revisited.