From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions
Hadron electromagnetic form factors contain information on the intrinsic structure of the hadrons. The pioneering work developed at the Kharkov Physical-Technical Institute in the 60's on the relation between the polarized cross section and the proton form factors triggered a number of experime...
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nasplib_isofts_kiev_ua-123456789-1109352025-02-23T17:39:55Z From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions Від теорії до експерименту: електромагнітні формфактори адронів у просторово- та часоподібних областях От теории к эксперименту: электромагнитные формфакторы адронов в пространственно- и времениподобных областях Tomasi-Gustafsson, E. Gakh, G.I. Rekalo, A.P. Elementary particle theory Hadron electromagnetic form factors contain information on the intrinsic structure of the hadrons. The pioneering work developed at the Kharkov Physical-Technical Institute in the 60's on the relation between the polarized cross section and the proton form factors triggered a number of experiments. Such experiments could be performed only recently, due to the progress in accelerator and polarimetry techniques. The principle of these measurements is recalled and surprise and very precise results obtained on proton are presented. The actual status of nucleon electromagnetic form factors is reviewed, with special attention to the basic work done in Kharkov Physical-Technical Institute. This paper is devoted to the memory of Prof. M.P. Rekalo. Електромагнітні формфактори адронів містять інформацію про внутрішню структуру адронів. Піонерська робота, виконана у 60-ті роки у Харківському фізико-технічному інституті, яка була присвячена зв’язку протонних формфакторів з перерізом розсіювання поляризованих частинок, ініціювала низку експериментів. Такі експерименти стали можливими зовсім недавно завдяки прогресу у конструюванні прискорювачів та поляриметрів. Наведені умови цих вимірювань та прецизійні результати дослідів з протонами. Представлений сучасний стан електромагнітних формфакторів нуклонів, особлива увага приділена основоположній роботі, яка була виконана у Харківському фізико-технічному інституті. Стаття присвячена пам’яті професора М.П. Рекала. Электромагнитные формфакторы адронов содержат информацию о внутренней структуре адронов. Пионерская работа, выполненная в 60-е годы в Харьковском физико-техническом институте, посвященная связи протонных формфакторов с сечением рассеяния поляризованных частиц, инициировала ряд экспериментов. Такие эксперименты стали возможны совсем недавно благодаря прогрессу в конструировании ускорителей и поляриметров. Приведены условия этих измерений и прецизионные результаты опытов с протонами. Представлен современный статус электромагнитных формфакторов нуклонов, особое внимание уделено основополагающей работе, выполненной в Харьковском физико-техническом институте. Статья посвящена памяти профессора М.П. Рекало. 2007 Article From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions / E. Tomasi-Gustafsson, G.I. Gakh, A.P. Rekalo // Вопросы атомной науки и техники. — 2007. — № 3. — С. 142-148. — Бібліогр.: 39 назв. — англ. 1562-6016 PACS: 13.40.-f, 13.60.-r, 13.88.+e https://nasplib.isofts.kiev.ua/handle/123456789/110935 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Elementary particle theory Elementary particle theory Tomasi-Gustafsson, E. Gakh, G.I. Rekalo, A.P. From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions Вопросы атомной науки и техники |
| description |
Hadron electromagnetic form factors contain information on the intrinsic structure of the hadrons. The pioneering work developed at the Kharkov Physical-Technical Institute in the 60's on the relation between the polarized cross section and the proton form factors triggered a number of experiments. Such experiments could be performed only recently, due to the progress in accelerator and polarimetry techniques. The principle of these measurements is recalled and surprise and very precise results obtained on proton are presented. The actual status of nucleon electromagnetic form factors is reviewed, with special attention to the basic work done in Kharkov Physical-Technical Institute. This paper is devoted to the memory of Prof. M.P. Rekalo. |
| format |
Article |
| author |
Tomasi-Gustafsson, E. Gakh, G.I. Rekalo, A.P. |
| author_facet |
Tomasi-Gustafsson, E. Gakh, G.I. Rekalo, A.P. |
| author_sort |
Tomasi-Gustafsson, E. |
| title |
From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions |
| title_short |
From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions |
| title_full |
From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions |
| title_fullStr |
From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions |
| title_full_unstemmed |
From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions |
| title_sort |
from theory to experiment: hadron electromagnetic form factors in space-like and time-like regions |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2007 |
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Elementary particle theory |
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https://nasplib.isofts.kiev.ua/handle/123456789/110935 |
| citation_txt |
From theory to experiment: hadron electromagnetic form factors in space-like and time-like regions / E. Tomasi-Gustafsson, G.I. Gakh, A.P. Rekalo // Вопросы атомной науки и техники. — 2007. — № 3. — С. 142-148. — Бібліогр.: 39 назв. — англ. |
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FROM THEORY TO EXPERIMENT: HADRON ELECTROMAGNETIC
FORM FACTORS IN SPACE-LIKE AND TIME-LIKE REGIONS
E. Tomasi-Gustafsson1, G.I. Gakh2, and A.P. Rekalo2
1DAPNIA/SPhN, CEA/SACLAY, 91191 Gif-sur-Yvette Cedex, France;
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
Hadron electromagnetic form factors contain information on the intrinsic structure of the hadrons. The pioneer-
ing work developed at the Kharkov Physical-Technical Institute in the 60's on the relation between the polarized
cross section and the proton form factors triggered a number of experiments. Such experiments could be performed
only recently, due to the progress in accelerator and polarimetry techniques. The principle of these measurements is
recalled and surprise and very precise results obtained on proton are presented. The actual status of nucleon elec-
tromagnetic form factors is reviewed, with special attention to the basic work done in Kharkov Physical-Technical
Institute. This paper is devoted to the memory of Prof. M.P. Rekalo.
PACS: 13.40.-f, 13.60.-r, 13.88.+e
1. INTRODUCTION
Electromagnetic form factors (FFs) are fundamental
quantities which describe the internal structure of com-
posite particles. Hadron FFs contain dynamical
information about charge and magnetic currents and are
calculated in frame of hadron models. Elastic hadron
FFs can be studied through elastic electron hadron
scattering , or through annihilation
reaction
heh +→+e
−+ + ee→+ pp , where the momentum q is
transferred by the exchange of one photon. Assuming
this reaction mechanism, FFs enter in the expression of
hadron electromagnetic vertex, and can be directly
accessible from experiment, measuring the differential
cross section and polarization observables.
Polarization observables, indeed, is the key word of
this talk, which is dedicated to the fundamental contri-
bution of the “Kharkov theoretical school”, leaded by
Academician A. I. Akhiezer, whose memory we honour
today. Basic papers, in collaboration with Prof.
M. P. Rekalo [1-2], were written in the late 60's, which
indicated the way to get precise data on FFs at large
values of the four-momentum transfer squared, .
Such experiments have been realized only recently, due
to the progress achieved in building high intensity po-
larized beams, spectrometers, hadron polarimeters in the
GeV range. The model independent derivation of the
necessary observables, the ideas and the suggestions
made in Kharkov almost 40 years ago, represent a re-
markable advance of the theory on experiment. At that
time it was difficult to conceive that an intense high
polarized beam could be accelerated, and the calcula-
tions were done for polarized target, which seemed
more realistic.
2
µ− q
Nowadays higher transfer momenta are reached with
polarized beam and hadron polarimeters which can
measure the polarization of the scattered hadron, proton
[3-5] or deuteron [6-7], but polarized targets are also
currently used.
In this presentation, we briefly present the main
lines of the theoretical background, describe the ex-
perimental set up and focus on the results and their im-
plications.
2. ELECTRON - HADRON ELASTIC
SCATTERING-THEORETICAL FRAMEWORK
2.1. THEORETICAL FRAMEWORK
The Feynman diagram for elastic electron-nucleon
scattering is shown in Fig. 1, assuming the one-photon
exchange, together with the notations of the particle
four-momenta.
γ∗(q)
N(p1) N(p2)
e(k1) e(k2)
Fig. 1. Feynman diagram for elastic scattering
NeNe +→+ −−
The most convenient frame for the analysis of elas-
tic scattering is the Breit frame, which is defined as
the system where the initial and final nucleon energies
are the same. As a consequence, the energy of the vir-
tual photon vanishes and its four-momentum square,
coincides with its three-momentum square (in modulus).
Therefore, the derivation of the formalism in Breit sys-
tem is more simple and has some analogy with a non-
relativistic description of the nucleon electromagnetic
structure. We choose the -axis parallel to the virtual
photon three-momentum in the Breit frame and the
-plane as the scattering plane. An useful kinematical
relation can be derived between the electron scattering
angle in the Lab system and in the Breit system θ :
eN
z
q
e
xz
θ B
τ+
θ
=
θ
1
2cot
2
cot
2
2 eB , 2
2
m
qµ−=τ , (1)
where is the nucleon mass and . m 21 kkq −=
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2007, N3 (1), p. 142-148. 142
The matrix element corresponding to the diagram of
Fig. 1 is:
αα
µ
Jl
q
e
2
2
=Μ , )()( 12 kukul αα γ= , (2)
where is the electromagnetic current of electron,
is the nucleon electromagnetic current, is the
proton charge.
αl
αJ e
The nucleon electromagnetic current can be written
in terms of Pauli and Dirac nucleon FFs and
:
)( 2
1 qF
)( 2
2 qF
)(
2
)(
)()( 1
2
22
12 puq
m
qF
qFpuJ
σ−γ= νµνµµ , (3)
where )(
2
1
µννµµν γγ−γγ=σ .
Note that for any values of and
, i.e. the current is conserved.
0=µµJq )( 2
1 qF
)( 2
2 qF µJ
The expressions for the different components of the
current in the Breit frame are: αJ
;)(2 12210 χχτ +−= FFmJ
,)( 1221 χ×σχ+= +
BqiFFJ
and allow to introduce in a straightforward way the
Sachs nucleon electromagnetic FFs, electric and mag-
netic, which are written as:
);()()( 22212 qFqFqGE τ−=
.)()()( 2
2
2
1
2 qFqFqGM += (4)
Such identification can be easily understood, if one
takes into account that the time component of the cur-
rent , describes the interaction of the nucleon with
Coulomb potential. Correspondingly, the space compo-
nent describes the interaction with the magnetic
field.
0J
J
The differential cross section in the Lab system is
written as
2
1
2
22
2
64
ε
ε
π
Μ
=
Ω
σ
md
d
e
, (5) )( 22 ε+=
where is the energy of initial (final) electron,
is the element of the final electron solid angle in
the Lab frame.
)( 21 εε
edΩ
From Eq. (2) we can obtain the following representa-
tion for 2Μ
;
2
2
22
µνµν WL
q
e
=Μ
∗
νµµν = llL , W , ∗
νµµν = JJ
where is the lepton tensor and W is the nucleon
tensor.
µνL µν
The product of the tensors and W is a rela-
tivistic invariant, therefore it can be calculated in any
reference system. For comparison with experiment it is
more convenient to use the differential cross section in
Lab system (the Rosenbluth formula [8])
µνL µν
τ+
τ+
+
θ
τσ=
Ω
σ
12
tan2
22
22 MEe
MM
e
GGG
d
d (6)
with
,
)2(sin)2(1
)2(cos
)(
4
2
cos
)(
4
2
1
22
2
22
2
2
1
3
2
22
2
e
e
e
M
mq
q
θε+
θε
−
α
=
=
θ
ε
ε
−
α
=σ
where , is the Mott cross-
section, describing a scattering of relativistic electrons
by a point particle (with charge e and spin ½).
137/14/2 ≈π=α e Mσ
Note that the very specific )2(cot2
eθ dependence
of the reduced cross-section eM dd Ωσσ−1 for elastic
scattering ( ) results from the assumption
of one-photon-exchange mechanism for the considered
reaction. This can be easily proved, by cross-symmetry
considerations, looking to the annihilation channel,
Ne npN ,=
p
θ2
pe +→−
cos
e ++ [9-10]. In the CMS of such reaction,
the one-photon-exchange mechanism induces a simple
and evident -dependence of the corresponding
differential cross section ( is the angle of the emitted
nucleon in center of mass system), due to the C-
invariance of the hadron electromagnetic interaction,
and unit value of the photon spin. The particular
θ
)2( eθcot2 - dependence of the differential cross sec-
tion (6) is at the basis of the method to determine both
nucleon electromagnetic FFs, G and , using
the ε linearity of the reduced cross section:
E GM
=
Ω
σ
θ
θ
α
ε
θ
ε
+τ+ε=
=τθσ
ee
e
e
e
Born
red
d
d
m )2(cos
)2(sin4
)2(sin
2
1)1(
),(
2
4
2
2
121
)( 22 QGQG EMτ , (7)
[ ] 12 )2(tan)1(21
−
θτ++=ε e ,
where is polarization parameter of the virtual photon
(we use the common notation Q for the value of the
four-momentum transfer squared, Q ) .
ε
2
22
µ−= q
Measurements of the elastic differential cross-
section as a function of , at different angles for a
fixed value of Q allow and to be deter-
mined as the slope and the intercept, respectively, from
the linear dependence (7) (Rosenbluth fit) [6].
ε
G
eθ
2 2
E
2
MGτ
ε
143
One can see that the backward scattering
( θ ) is determined by the magnetic FF only, and
that the slope for is sensitive to . At
large , (such that τ ), the differential cross sec-
tion
eN
(GE
π=e
2Q
redσ
>>
)2Q
1
eΩ
E
ddσ (with nonpolarized particles) is unsensi-
tive to G : the corresponding combination of the nu-
cleon FFs, ( )2
MGτ+2
EGε is dominated by the G
contribution, due to the following reasons:
2
M
1) pEpMp QGQGR µ≥=µ )()( 22
2 ≈µR
2
, where is
the proton magnetic moment, so ;
pµ
8
2) The factor increases the contribution at
large momentum transfer, where >>1.
τ MG
τ
Therefore electron-proton scattering (with unpolar-
ized particles) is dominated by the magnetic FF, at large
values of momentum transfer. The same holds for elec-
tron-neutron scattering, even at relatively small values
of , due to the smaller values of the neutron electric
FF.
2Q
As a result, for the exact determination of the proton
electric FF, in the region of large momentum transfer,
and for the neutron electric FF — at any value of ,
polarization measurements are strongly required and in
particular those polarization observables which are de-
termined by the product , and are,
therefore, more sensitive to [1]. Both experiments
(with polarized electron beam) have been realized:
for the determination of the proton FF [3-
5] and, for the determination of the neutron FF ,
[11] and [12].
2Q
Ep
EnG
)()( 22 QGQG ME
EG
pn)
epep ),(
need ),( ′
G
p eed ,( ′
In general the hadronic tensor W for elastic
( en ) scattering, contains four terms, related to the 4
possibilities of polarizing the initial and final protons
(neutrons):
µν ep
),()()()0( 2121 PPWPWPWWW µνµνµνµνµν +++= ,
where and are the polarization vectors of the
initial and final protons (neutrons).
1P 2P
The first term corresponds to the unpolarized case,
the second (third) term corresponds to the case when the
initial (final) nucleon is polarized, and the last term de-
scribes the reaction when both nucleons (initial and
final) are polarized.
One can show that the polarization of the final pro-
ton (neutron) vanishes, if the electrons are unpolarized:
unpolarized electrons can not induce polarization of the
scattered proton (neutron). This is a property of the one-
photon mechanism for elastic e scattering ( )
and of the hermiticity of the Hamiltonian for the hadron
electromagnetic interaction. Namely the hermiticity
condition allows to prove that the hadron electromag-
netic FFs are real functions of the momentum transfer
squared in the space-like region < 0. On the other
hand, in the time-like region, which is scanned by the
annihilation process
N npN ,=
2q
ppe +→+ −+
2q 2 ≥q
e , the nucleon FFs
are complex functions of if , where
is the pion mass.
24 πm πm
ppee +→+ −+
(Im *
MEGG
α
+∞→2
2)( )(lim
q
qF TL
xP2
)
α
zP2
xz
MGG
τ+
τ
)2G
τ
D
The complexity of nucleon FF's (in the time-like re-
gion) results in specific polarization phenomena, for the
annihilation process , which are dif-
ferent from the case of elastic electron - proton scatter-
ing. For example, the polarization of the final proton (or
antiproton) is different from zero, even in the case of
annihilation of unpolarized leptons: this polarization is
determined by the product (and, therefore,
vanishes in the case of elastic electron - proton scatter-
ing, where FFs are real functions).
Note that the two-photon exchange in elastic
scattering is also generating complex amplitudes. So
the interference between one and two-photon ampli-
tudes induces nonzero proton polarization, but small in
absolute value, as it is proportional to .
ep
Numerous experiments have been done with the aim
to detect such polarization at the momentum transfers
1 GeV≤2Q 2, but with negative result, at a percent
level.
Only recently the above mentioned interference was
experimentally detected, measuring the asymmetry in the
scattering of transversally polarized electrons by an unpo-
larized proton target [13], which contains information on
the imaginary part of the two–photon contribution.
Note that at very large momentum transfer, the rela-
tive role of two-photon exchange amplitudes may be
increased (violating the counting in ), due to the steep
decreasing of hadronic electromagnetic FFs. 2Q
Note also that the analytical properties of the nu-
cleon FFs, considered as functions of the complex vari-
able , result in a specific asymptotic behavior, as
they obey to the Phragmen-Lindeloef theorem:
2qz =
−∞→
=
2
2)( )(lim
q
qF SL
. (8)
The existing experimental data about the proton FFs
in time-like region up to 15 GeV2, seem to contradict
this theorem [14], showing that the asymptotic region is
more far than expected.
Let us define a coordinate system where -axis is
parallel to the virtual photon three-momentum and
is the scattering plane. One can find the following ex-
pressions for the components and of the pro-
ton polarization vector (in the scattering plane) - in
terms of the proton electromagnetic FFs [1-2]:
z
E
e
xDP θ
λ−=
12
cot22 ,
(21
2 1 Mz m
DP
+
τε+ε
λ= , (9)
where is the electron helicity, which takes values
, corresponding to the direction of spin parallel or
antiparallel to the electron three-momentum, and is
λ
1±
144
proportional to the differential cross section with
unpolarized particles:
2
cot
1
2 2
22
2 eME
M
GGGD
θ
τ+
τ+
+τ= . (10)
So, for the ratio of these components one can find
the following formula:
)(
)(
2
cot2 2
2
212
2
qG
qGm
P
P
P
P
M
Ee
l
t
z
x
ε+ε
θ
−== . (11)
A measurement of the ratio of the transverse and the
longitudinal polarization of the recoil proton is directly
related to the ratio (11) of electric and magnetic FFs,
)()( 22 qGqG ME .
In the same way it is possible to calculate the de-
pendence of the differential cross section for the elastic
scattering of the longitudinally polarized electrons by a
polarized proton target, with polarization : 1P
( xxzz
ee
APAP
d
dP
d
d
11
0
1 1)( λ+λ+
Ω
σ
=
Ω
σ ) , (12)
where the asymmetries and (or the correspond-
ing analyzing powers) are related in a simple and direct
way, to the components of the final proton polarization:
xA zA
xx PA 2= , (13) zz PA 2−= ) =R
This holds in the framework of the one-photon-
exchange mechanism for elastic scattering. Note that
the quantities and have the same sign and ab-
solute value, but the components and being
equal in absolute value, have opposite sign.
ep
xA xP2
zA zP2
In the framework of the one-photon-exchange
mechanism, there are at least two different sources of
corrections to these relations:
- the standard radiative corrections;
- the electroweak corrrections.
2.2. EXPERIMENTAL RESULTS
Highly polarized electron beams are available at dif-
ferent accelerators, MAMI (Mainz), MIT (Bates), JLab
(Virginia). At JLab, where the G experiment was
done [3-5], electron energies are available up to 6 GeV,
the typical intensity about 30 µ and the polarization
from 60 to 80%. The (longitudinal) electron polariza-
tion is obtained by photoemission from a semiconductor
cathode using polarized laser light from a pulsed diode
laser. Beam polarimeters based on Mott, Moeller or
Compton scattering measure the electron beam polariza-
tion with an error of the order of percent.
Ep
A
Measurements of elastic scattering require coinci-
dence experiments in order to eliminate the background,
even if in a binary process, in principle, the detection of
one particle allows to reconstruct fully the kinematics.
ep
The momentum of the scattered proton is analyzed
by a high resolution spectrometer which focal plane
detection constitutes also the front detection of the focal
polarimeter.
Proton polarimeters in the GeV range are based on
inclusive scattering on a graphite or polyethylene target,
where one charged particle is detected. The azymuthal
asymmetry of the scattered particle contains the infor-
mation on the polarization of the proton at the focal
plane.
The optimization of the figure of merit (efficiency
and analyzing powers) in the GeV range was carefully
studied at Saturne accelerator [15] and at JINR-LHE
accelerator complex in Dubna, where polarized proton
beams are available in the GeV range [16]. In particular
it has been shown that the thickness of the target is a
very important parameter, and depends on the proton
energy. For proton momenta over 3 GeV/c, very thick
targets (larger than the collision length) do not improve
the polarimeter performances.
After that a good elastic ep event is identified by
energy and angular correlation of the two outgoing par-
ticles, and its polarization measured, the ratio of the
longitudinal and transverse polarization is directly re-
lated to the ratio MGEGR µ= (µ is the proton mag-
netic moment), by Eq. (11).
The ratio is shown in Fig. 2. These data show two
remarkable features: high precision of the polarization
data, compared to the Rosenbluth data, and monotonical
decrease with Q which can be parametrized as:
R
2
( ))09.004.0(/)005.0130.0(1
(
22
2
±−±−= GeVQ
Q
(14)
2.3. IMPLICATIONS
This means that the charge and magnetic currents in
the nucleon are different, contrary to what had been
previously assumed. Indeed, a commonly used pa-
rametrization was a dipole approximation for both FFs,
which was compatible with an exponential distribution
of the charge, in non-relativistic approximation, and
agreed with predictions from quark counting rules [22-
23].
Fig. 2. -dependence for the proton form factor ra-
tio. Selected data from Rosenbluth measurements are
plotted: from [17] (solid triangles); from [18] (solid cir-
cles); from [19] (open circles); from [20] (solid squares)
from [21] (open triangles). Polarization data (solid stars)
are shown together with the fit from Eq. (14)
2Q
145
QCD predicts a )()( 2
1
2
2
2 qFqFq scaling, because
carries an extra factor )( 2
2 qF 2q
2
1 as it requires a spin
flip. Such scaling was approximately in agreement with
the previous data, and it was argued that asymptotic
predictions were reached already at Q . 25....2 GeV≈
When logarithmic corrections are added, pQCD pa-
rametrizations may reproduce the polarization data
(which scale as )()( 2
1
2
2
2 qFqFq−
2
) . However ana-
lytical properties of FFs, which should satisfy Phrag-
men-Lindeloff theorem, are fulfilled by such parametri-
zations only at much larger value of Q [24].
Another important issue concerns the light nuclei
structure, 2H, 3He. A good description of the electro-
magnetic properties of these nuclei requires the knowl-
edge of nucleon FFs. A modification of the proton FFs
requires either another prescription for the neutron FFs,
or a revision of other ingredients of the models, such as
wave functions or meson exchange currents, relativistic
effects etc [25].
Data in time-like region are also necessary for a
complete understanding of the nucleon structure. The
separation of individual electromagnetic FFs has not
been done, yet. As electromagnetic FFs are complex
functions of in time-like region, polarization ex-
periments are necessary. The present understanding is
poor, and few phenomenological models can describe
all data in the full kinematical region [26]. Experiments
are planned in future, at Novosibirsk, Frascati, FAIR.
2q
Reasons of the discrepancy between the two meth-
ods have been indicated in the two-photon exchange
[27]. However this is incompatible with model inde-
pendent considerations, which require non-linearity of
the Rosenbluth fit as a function of and the experi-
ments do not give evidence for the presence of such
mechanism [28-31].
ε
Recent calculations of the box diagram prove that
this contribution is small [32-33]. A more realistic ex-
planation relies on the method used to calculate and to
apply standard radiative corrections, as a multiplicative
factor to the measured cross section. Such factor con-
tains a large and dependence, which are the rele-
vant variables. Therefore, this procedure induces large
correlations between the parameters of the Rosenbluth
fit [34]. A recent suggestion to apply higher order cor-
rections, through the structure function method, proves
to be successful in bringing into agreement the two sets
of data [35].
ε 2Q
3. CONCLUSIONS
The pioneering work [1] is at the origin of a series
of experiments and programs at different world accel-
erators. The unexpected results which were obtained
changed our view on the nucleon structure.
Although an English translation of the original pa-
pers [1-2] was soon available, these papers did not re-
ceive the consideration they deserve and are not prop-
erly quoted. Only recently these papers have been added
to the High-Energy Physics Literature Database [37]
and appear very little quoted in comparison with later
works. From this database, it appears today that works,
which essentially reproduce the same result are more
widely quoted, as for example Ref. [38] which appeared
at least one year later and Ref. [39] published in 1981.
This situation is not new, and unfortunately not ade-
quate citation of appropriate references is a current
problem. Efforts and concernment of scientific authori-
ties at the level of Editorial board of journals, Confer-
ence Committees, representatives and individuals are
necessary in order to have a proper appreciation of these
achievements.
We would like to conclude with a citation from [1]:
“Thus, there exist a number of polarization experiments
which are more effective for determining the proton
charge FF than is the measurement of the differential
cross section for unpolarized particles”.
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147
ОТ ТЕОРИИ К ЭКСПЕРИМЕНТУ: ЭЛЕКТРОМАГНИТНЫЕ ФОРМФАКТОРЫ АДРОНОВ В
ПРОСТРАНСТВЕННО- И ВРЕМЕНИПОДОБНЫХ ОБЛАСТЯХ
Е. Томаси-Густафссон, Г.И. Гах, А.П. Рекало
Электромагнитные формфакторы адронов содержат информацию о внутренней структуре адронов. Пио-
нерская работа, выполненная в 60-е годы в Харьковском физико-техническом институте, посвященная связи
протонных формфакторов с сечением рассеяния поляризованных частиц, инициировала ряд экспериментов.
Такие эксперименты стали возможны совсем недавно благодаря прогрессу в конструировании ускорителей
и поляриметров. Приведены условия этих измерений и прецизионные результаты опытов с протонами.
Представлен современный статус электромагнитных формфакторов нуклонов, особое внимание уделено
основополагающей работе, выполненной в Харьковском физико-техническом институте. Статья посвящена
памяти профессора М.П. Рекало.
ВІД ТЕОРІЇ ДО ЕКСПЕРИМЕНТУ: ЕЛЕКТРОМАГНІТНІ ФОРМФАКТОРИ АДРОНІВ У
ПРОСТОРОВО- ТА ЧАСОПОДІБНИХ ОБЛАСТЯХ
Е. Томасі-Густафссон, Г.І. Гах, О.П. Рекало
Електромагнітні формфактори адронів містять інформацію про внутрішню структуру адронів. Піонерсь-
ка робота, виконана у 60-ті роки у Харківському фізико-технічному інституті, яка була присвячена зв’язку
протонних формфакторів з перерізом розсіювання поляризованих частинок, ініціювала низку експеримен-
тів. Такі експерименти стали можливими зовсім недавно завдяки прогресу у конструюванні прискорювачів
та поляриметрів. Наведені умови цих вимірювань та прецизійні результати дослідів з протонами. Представ-
лений сучасний стан електромагнітних формфакторів нуклонів, особлива увага приділена основоположній
роботі, яка була виконана у Харківському фізико-технічному інституті. Стаття присвячена пам’яті професо-
ра М.П. Рекала.
148
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