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Nucleon Electromagnetic Form Factors:Introduction and Overview
Diego Bettoni Istituto Nazionale di Fisica Nucleare, Ferrara
Scattering and Annihilation Electromagnetic Processes Trento, 18-22 February 2013
Diego Bettoni Nucleon Form Factors 2
Outline • Introduction
– definitions – main properties
• Space-like Form Factors – Rosenbluth separation – Polarization transfer – Experimental situation – Summary and outlook
• Time-like Form Factors – Main properties and predictions – Experimental situation – Open issues – Summary and outlook
• Conclusions
Diego Bettoni Nucleon Form Factors 3
Introduction
( ) ( ) ⎥⎦⎤
⎢⎣⎡ += ν
µνµµ σκγ qiQFM
QFeJ 22
21 2
p0 p
k k
q = p0 - p
1)0(0)0(1)0(1)0(
21
21====
nn
pp
FFFF Dirac and Pauli
Form Factors
M nucleon mass Q2 = -q2
21
22
2
1 4FFG
FMqFG
M
E
κ
κ
+≡
+≡ Electric form factor
Magnetic form factor
Sachs Form Factors
( ) ( )22 qGGqGG MMEE == ( ) ( )( ) ( ) 91.1079.20
0010−=+=
==nM
pM
nE
pE
GGGG
GE and GM are Fourier transforms of nucleon charge and magnetization density distributions (in the Breit Frame). q2 < 0 space-like form factors (elastic eN scattering) q2 > 0 time-like form factors (creation or annihilation of an NN pair)
Diego Bettoni Nucleon Form Factors 4
Diego Bettoni Nucleon Form Factors 5
• Spacelike form factors are real, timelike are complex.
• The analytic structure of the timelike form factors is connected by dispersion relations to the spacelike regime. • By definition they do not interfere in the expression of the cross section, therefore, in the timelike case, only polarization observables allow to get the relative phase.
Form Factors Properties
Space-like Form Factors
• Rosenbluth separation • Polarization transfer
• Experimental Situation • Two-photon contribution
• Future experiments
( ) ⎥⎦
⎤⎢⎣
⎡+−⎟
⎠⎞⎜
⎝⎛ −×⎟
⎠⎞⎜
⎝⎛
Ω=⎟
⎠⎞⎜
⎝⎛
Ω 2sin
22cos
422
212
222
22
2221
θκθκσσ FFMqF
MqF
dd
dd
Rutherford
⎥⎦⎤
⎢⎣⎡ +
++×⎟
⎠⎞⎜
⎝⎛
Ω=⎟
⎠⎞⎜
⎝⎛
Ω 2sin2
2cos
1222
22 θτθττσσ
MME
Rutherford
GGGdd
dd
⎥⎦⎤
⎢⎣⎡ +
++×⎟
⎠⎞⎜
⎝⎛
Ω=⎟
⎠⎞⎜
⎝⎛
Ω 2tan2
122
22 θτττσσ
MME
Mott
GGGdd
dd
2
2
4Mq=τ
eN Elastic Scattering The experimental determination of the nucleon form factors in the space-like region (q2 < 0) is carried out by studying eN elastic scattering
dedepepe
+→+
+→+−−
−−
Diego Bettoni Nucleon Form Factors 7 Rosenbluth Formula
( ) ( )2
tan222 θσ
σ
qBqA
dd
dd
Mott
+=⎟⎠⎞⎜
⎝⎛
Ω
⎟⎠⎞⎜
⎝⎛
Ω
Rosenbluth Plot
Rosenbluth Separation Method
Diego Bettoni Nucleon Form Factors 8
Early Measurements
Diego Bettoni Nucleon Form Factors 9
p
pMG
µpEG
n
nMGµ
( ) ( ) ( ) ( )
( ) 02
222
2
=
===
qG
qGqGqGqG
nE
n
nM
p
pMp
E µµ
Scaling laws for the form factors:
( ) ( )22
1qG
baqG n
nE τ
τµ+
−=
Proton Charge Radius
Dipole formula: ( ) 2
2
2
2
1
1
⎟⎟⎠
⎞⎜⎜⎝
⎛ +
=
VMq
qG22 )84.0( GeVMV =
RMVeR −= 0)( ρρ
2
0
30
0
320
2 12VRM
RM
MRde
RdReR
V
V
==∫
∫∞
−
∞−
ρ
ρ
fmM
RV
80.0122 ==
The dipole form corresponds to an exponential charge distribution
with an rms radius
For the proton: Diego Bettoni Nucleon Form Factors 10
Polarization Transfer Method
Diego Bettoni Nucleon Form Factors 14
pepe +→+
2tan
2θ
MEE
PP
GG ee
L
T
M
E ′+−=
( )( ) ( )29.013.01 22
2
−−≈= QQGQG
RM
Epp
µ
1≈pR
Diego Bettoni Nucleon Form Factors 23 Mark Jones – Nucleon05
Two-Photon Exchange
Diego Bettoni Nucleon Form Factors 26
• Investigated both experimentally and theoretically for the past 50 years. • Radiative corrections to Rosebluth tecnique normally ignore terms with two hard photons. • Can be studied experimentally by measuring the ratio of electron and positron elastic scattering off a proton.
Space-like FF Outlook
• Explain discrepancy between Rosenbluth separation method and polarization transfer.
• Two-photon contribution. • Main player will be JLAB at 12 GeV.
Diego Bettoni Nucleon Form Factors 27
Time-like Form Factors
• Measurement method • Main properties and predictions
• Experimental Situation • Open issues
• Future prospects
Diego Bettoni Nucleon Form Factors 29
NNee +→+ −+
⎥⎦
⎤⎢⎣
⎡++= *22
2*22
2sin)(4)cos1()(
4θθβα
Ωσ sG
smsG
sC
dd
EN
M
⎥⎦
⎤⎢⎣
⎡+= 2
22
2)(2)(
34 sG
smsG
sC
EN
Mπβασ
02 >= Qsp
p
e+ e-
*
Diego Bettoni Nucleon Form Factors 30
)(GeVs
C is the Coulomb correction factor, taking into account the QED coulomb interaction. Important at threshold.
yeC −−
=11
sMy N
βπα2=
β1
24⎯⎯⎯ →⎯
→ NMsC finite
( ) nbMGM
M NEN
N 1.0)4(4
422
2
322 ≈= απσ
There is no Coulomb correction in the neutron case.
Diego Bettoni Nucleon Form Factors 31
Form Factor Properties
• At threshold GE=GM by definition, if F1 and F2 are analytic functions with a continuous behaviour through threshold.
GE (4mp2) = GM (4mp
2) • Timelike GE and GM are the analytical continuation of non spin flip
and, respectively, spin flip spacelike form factors. Since timelike form factors are complex functions, this continuity requirement imposes theoretical constraints.
• Two-photon contribution can be measured from asymmetry in angular distribution.
Diego Bettoni Nucleon Form Factors 32
Form Factor Properties
• Perturbative QCD and analyticity relate timelike and spacelike form factors, predicting a continuous transition and spacelike-timelike equalitity at high Q2.
• At high Q2 PQCD predicts:
• Naïve prediction for the neutron:
6
222
24
222
1)()()()(
QQQF
QQQF ss αα ∝∝
25.022
=⎟⎟⎠
⎞⎜⎜⎝
⎛≈
u
dpM
nM
GG
Diego Bettoni Nucleon Form Factors 33
Proton Form Factors
• The moduli of the Form Factors can be derived from measurements of the cross sections for e+e- pp
• Due to the low value of the cross sections and the consequent limited statistics, most experiments could not determine |GM| and |GE| separately from the analysis of the angular distributions, but extracted |GM| using the (arbitrary) assumption |GE| = |GM|.
• The magnetic form factor has been derived in this way by many e+e- and pp experiments. The timelike electric form factor is basically unknown.
• Recently BaBar has attempted to measure |GM|/ |GE| by means of ISR, but the final result is quoted using |GE| = |GM|.
Diego Bettoni Nucleon Form Factors 34
The first experiment to produce a positive result
for the proton timelike form factor was carried
out at ADONE in Frascati e+e- pp
The measurement was based on 0.2 pb-1 of data
at 4.4 GeV2 yielding 25 events.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 35
The first measurement of the timelike form factors at
threshold is due to the ELPAR experiment at CERN. They observed
34 events of pp annihilation at rest in a liquid H2 target.
The measurement assumes |GE|=|GM|
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 36
Various measurements of the proton form factors were carried out at DCI
in Orsay using e+e- pp
The first experiment was DM1 which recorded
63 events in 4 data points.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 37
At DCI in ORSAY the DM2 collected data in three data taking runs
for a total of 0.7 pb-1. With a total of 112 events in 6 points they attempted to measure the angular
distribution, from which they could fit |GM|/|GE|=0.34,
but |GE|=|GM| was still allowed.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 38
The first high-statistics measurement of the timelike form factors was carried out
at LEAR by the PS 170 collaboration. They recorded
a total of 3667 pp e+e-
events in 9 data points. The angular distribution is compatible with |GE|=|GM|.
First indication of steep rise near threshold.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 39
The E760 experiment at Fermilab produced the first measurement of the form
factors at high Q2
pp e+e- Very difficult measurement
due to very small cross section. They recorded
29 events. The measurement assumes |GE|=|GM|.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 40
The FENICE experiment at ADONE, primarily devoted to the measurement of the neutron form factor, produced also a measurement of the proton magnetic form factor with 69 events in 4 points.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 41
E835 at FNAL, continuation of E760, made further measurements at high Q2 with a total of 206 events in 2 data taking runs.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 42
A new measurement at high Q2 was recently made by the CLEO at CESR in e+e- pp. It assumes |GE|=|GM|. The measurement is based on 14 events.
Proton Magnetic Form Factor |GM|
Diego Bettoni Nucleon Form Factors 43
Proton Magnetic Form Factor |GM|
Another measurement of the proton timelike form factors has been reported by BES. The measurement covers 9 data points from (2.0 GeV)2 to (3.07 GeV)2 using the hypothesis |GE|=|GM|.
Diego Bettoni Nucleon Form Factors 44
Proton Magnetic Form Factor |GM|
BaBar measurement using Initial State Radiation (ISR)
e+e- pp Advantages: • All energies at the same
time fewer systematics
• CMS boost easier measurement at threshold
Disadvantages • Luminosity proportional to
invariant mass bin L s
• More background
Diego Bettoni Nucleon Form Factors 45
⎟⎠⎞⎜
⎝⎛Λ
=
222 ln ss
CG
p
M
µ
Asymptotic Behavior
The dashed line is a fit to the PQCD prediction
The expected Q2 behaviour is reached quite early, however ...
Diego Bettoni Nucleon Form Factors 46
Asymptotic Behavior
The dashed line is a fit to the PQCD prediction
⎟⎠⎞⎜
⎝⎛Λ
=
222 ln ss
CG
p
M
µ
The expected Q2 behaviour is reached quite early, however ... ... there is still a factor of 2 between timelike and spacelike.
The ratio |GE|/|GM|
Diego Bettoni Nucleon Form Factors 48
So far only two experiments have collected enough statistics to analyze the angular distribution and attempt to extract |GE| and |GM| independently.
The present accuracy in the ratio |GE| and |GM| is of the order of 50 %.
Diego Bettoni Nucleon Form Factors 49
Threshold Q2 Dependence
Steep behavior near threshold observed by PS 170 at LEAR (2000 events).
Diego Bettoni Nucleon Form Factors 50
BaBar Measurement using ISR
BaBar measurement very near threshold confirms steep rise of Form Factor
Diego Bettoni Nucleon Form Factors 51
Resonant Structures
The dip in the total multihadronic cross section and the steep variation of the proton form factor near threshold may be fitted with
a narrow vector meson resonance, with a mass
M 1.87 GeV and a width 10-20 MeV,
consistent with an NN bound state.
Diego Bettoni Nucleon Form Factors 52
14.0 −=∫ p bL d t 80 events
The neutron form factor is bigger than that of the proton !!!
Neutron Timelike Form Factor
G eVs 5 5.29.1 <<
Diego Bettoni Nucleon Form Factors 53
Measuring the Phase between GE and GM
MEMEN
EN
M
y GGsm
sGsmsG
P δθθ
θ sin4
sin)(4)cos1()(
2sin 2
*222
*22
*
⎥⎦
⎤⎢⎣
⎡++
=
ez
MEex
PPPP
∝∝ δcos
The relative phase ME between GM and GE can only be measured by means of single- or double-polarization experiments.
It takes the maximum value near scattering angles of 450 and 1350 and vanishes at 900. Once this phase is known, by measuring the ratio of the two components of the nucleon polarizations in the scattering plane with longitudinally polarized beams, the ratio |GM|/|GE| can be obtained with small systematic uncertainties.
Diego Bettoni Nucleon Form Factors 54
Summary and Outlook In spite of more than forty years of measurements our knowledge of the timelike nucleon form factors is far from complete. • Proton Form Factors
– Only “effective” |GM| has been measured. Almost no information on |GE| and phases.
– Steep behavior near threshold poses interesting challenge (baryonium, dips in hadronic cross sections ...).
– Asymptotic Q2 regime reached quite early, but still far from spacelike. – BaBar data suggest steps rather than smooth behavior.
• Neutron Form Factor, measured by a single (low statistics) experiment – |GM
n| > |GMp| contrary to expectations
– |GMn|>> |GE
n| • Future prospects: BES III, Belle II, VEPP, PANDA.
Diego Bettoni Nucleon Form Factors 55
Conclusions
These considerations strongly support the importance of new measurements of the neutron and proton form factors with much higher statistics than previous work and with the capability of separately determining the electric and magnetic form factors (timelike) and to understand the discrepancy between Rosenbluth separation and polarization transfer measurements. We can look forward to many more years of exciting
Form Factor Physics !
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