Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections
The single–spin target asymmetries in the hard electroproduction process e⁻ + p → e⁻ + γ + p and in the e⁺e⁻-pair photoproduction γ + p → e⁺ + e⁻ + p, induced by the loop radiative corrections to the vertex part of lepton interaction are considered. The physical reason to appearance such a kind of a...
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irk-123456789-1109432017-01-08T03:02:34Z Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections Afanasev, A.V. Konchatnij, M.I. Merenkov, N.P. Elementary particle theory The single–spin target asymmetries in the hard electroproduction process e⁻ + p → e⁻ + γ + p and in the e⁺e⁻-pair photoproduction γ + p → e⁺ + e⁻ + p, induced by the loop radiative corrections to the vertex part of lepton interaction are considered. The physical reason to appearance such a kind of asymmetries is the nonzero imaginary part of the respective Bethe-Heitler amplitudes (on the level of radiative correction). The single–spin target asym-metries at unpolarized ingoing electron or photon beams and at arbitrary polarizations of the target proton for condi-tions of CLAS (Jefferson Lab, USA) and HERMES (DESY) experiments are calculated. Досліджені односпінові асиметрії мішені в процесах “жорсткого” електронародження e⁻ + p → e⁻ + γ + p і в фотонародженні e⁺e⁻--пар γ + p → e⁺ + e⁻ + p, індуковані петлевими радіаційними поправками в лептон-ній частині взаємодії. Фізичною причиною, що обумовлює такого виду асиметрії, є ненульова уявна частина Бете-Гайтлерівської амплітуди, яка з’являється на рівні радіаційної поправки. Односпінові асиметрії мішені у випадку неполяризованого електронного (чи фотонного) пучків та довільної поляризації протона-мішені обчислені в кінематичних умовах експериментів по електронародженню CLAS (Jefferson Lab, USA) і HERMES (DESY). Исследованы односпиновые асимметрии мишени в процессах “жесткого” электророждения e⁻ + p → e⁻ + γ + p и в фоторождении e⁺e⁻--пар γ + p → e⁺ + e⁻ + p, индуцированные петлевыми радиационными поправками в лептонной части взаимодействия. Физической причиной, обуславливающей такого вида асимметрии, является ненулевая мнимая часть Бете-Гайтлеровской амплитуды, которая появляется на уровне радиационной поправки. Односпиновые асимметрии мишени в случае неполяризованного электронного (или фотонного) пучка и произвольной поляризации протона-мишени вычислены в кинематических условиях экспериментов по электророждению CLAS (Jefferson Lab, USA) и HERMES (DESY). 2007 Article Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections/ A.V. Afanasev, M.I. Konchatnij, and N.P. Merenkov // Вопросы атомной науки и техники. — 2007. — № 3. — С. 93-97. — Бібліогр.: 5 назв. — рос. 1562-6016 PACS: 12.20.-m, 13.60.-r http://dspace.nbuv.gov.ua/handle/123456789/110943 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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English |
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Elementary particle theory Elementary particle theory |
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Elementary particle theory Elementary particle theory Afanasev, A.V. Konchatnij, M.I. Merenkov, N.P. Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections Вопросы атомной науки и техники |
| description |
The single–spin target asymmetries in the hard electroproduction process e⁻ + p → e⁻ + γ + p and in the e⁺e⁻-pair photoproduction γ + p → e⁺ + e⁻ + p, induced by the loop radiative corrections to the vertex part of lepton interaction are considered. The physical reason to appearance such a kind of asymmetries is the nonzero imaginary part of the respective Bethe-Heitler amplitudes (on the level of radiative correction). The single–spin target asym-metries at unpolarized ingoing electron or photon beams and at arbitrary polarizations of the target proton for condi-tions of CLAS (Jefferson Lab, USA) and HERMES (DESY) experiments are calculated. |
| format |
Article |
| author |
Afanasev, A.V. Konchatnij, M.I. Merenkov, N.P. |
| author_facet |
Afanasev, A.V. Konchatnij, M.I. Merenkov, N.P. |
| author_sort |
Afanasev, A.V. |
| title |
Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections |
| title_short |
Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections |
| title_full |
Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections |
| title_fullStr |
Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections |
| title_full_unstemmed |
Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections |
| title_sort |
single–spin asymmetries in electron–proton and photon-proton scattering in the bethe–heitler processes induced by loop corrections |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2007 |
| topic_facet |
Elementary particle theory |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/110943 |
| citation_txt |
Single–spin asymmetries in electron–proton and photon-proton scattering in the Bethe–Heitler processes induced by loop corrections/ A.V. Afanasev, M.I. Konchatnij, and N.P. Merenkov // Вопросы атомной науки и техники. — 2007. — № 3. — С. 93-97. — Бібліогр.: 5 назв. — рос. |
| series |
Вопросы атомной науки и техники |
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| first_indexed |
2025-07-08T01:23:02Z |
| last_indexed |
2025-07-08T01:23:02Z |
| _version_ |
1837039912688287744 |
| fulltext |
Section B. ELEMENTARY PARTICLE THEORY
SINGLE–SPIN ASYMMETRIES IN ELECTRON–PROTON
AND PHOTON-PROTON SCATTERING IN THE BETHE–HEITLER
PROCESSES INDUCED BY LOOP CORRECTIONS
A.V. Afanasev1, M.I. Konchatnij2, and N.P. Merenkov2
1Jefferson Lab, Newport News, VA 23606, USA;
e-mail: afanas@jlab.org;
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
e-mail: konchatnij@kipt.kharkov.ua; merenkov@kipt.kharkov.ua
The single–spin target asymmetries in the hard electroproduction process and in the e e -
pair photoproduction , induced by the loop radiative corrections to the vertex part of lepton
interaction are considered. The physical reason to appearance such a kind of asymmetries is the nonzero imaginary
part of the respective Bethe-Heitler amplitudes (on the level of radiative correction). The single–spin target asym-
metries at unpolarized ingoing electron or photon beams and at arbitrary polarizations of the target proton for condi-
tions of CLAS (Jefferson Lab, USA) and HERMES (DESY) experiments are calculated.
e p e γ− −+ → + + p
p
2 .
+ −
p e eγ + −+ → + +
PACS: 12.20.-m, 13.60.-r
1. INTRODUCTION
The parity–conserving single–spin beam and target
correlations in elastic electron–proton scattering and
radiative reaction are used to extract information about
virtual Compton scattering (VCS) amplitude. This last
is very important physical quantity which has triggered
a significant experimental and theoretical activity.
In elastic scattering the VCS amplitude enters
through the two–photon exchange diagram (TPE) with
two off-shell photons. The cross section and parity-
conserved spin–spin correlations in this case are sensi-
tive only to the real part of this diagram and, therefore,
to the real part of the double off-shell VCS amplitude.
Contrary, the single–spin normal asymmetry probes
only the imaginary part of TPE amplitude for both beam
and target normal polarizations.
If the electron beam or the target proton is polarized
in the reaction plane, the parity–conserving single–spin
asymmetry for elastic scattering is strictly zero. Never-
theless, the nonzero such kind asymmetry can manifest
itself in the process with three (and more) final particles
provided that all the final–particle 3–momenta do not
belong to single (the same) plane. The simplest such
type process that probes VCS amplitude is the hard
electroproduction ( reaction )ee γ′
1 1 2( ) ( ) ( ) ( ) ( )e k p p e k k p pγ− −+ → + + (1)
The whole amplitude of this process can be repre-
sented as a sum of they real Bethe–Heitler amplitude
and VCS one, that has both the real and imaginary
parts.
In present paper we want to pay attention that the
one–loop correction to the lepton part of the Bethe–
Heitler amplitude with radiation of a photon by the out-
going electron can generate the non–zero imaginary
part, and, consequently, an additional contribution to
the single-spin asymmetries, which has the status of
radiative correction to main effect caused by imaginary
part of VCS amplitude.
2. KINEMATICAL VARIABLES
To describe the physical observables in the process
(1) usually used three dimensionless variables
2
1 2 1 1 2
1 1 2
( ) 2 (
2 ( )
k k p k k
x y
p k k V
− −
= − , = ,
−
)
2
1 2
1 1
( )
2
p p
V p k
V
ρ
−
= − , = ,
(2)
and azimuth angle in the target proton rest frame
that is simply the angle between leptonic and hadronic
planes as shown in Fig. 1 for two different choices of
-axis: opposite to direction (Fig. 1,a)
and along direction of (Fig. 1,b).
Φ
k
Z 1 1= −q k k 2
1
Fig. 1. Definition of angles in laboratory frame
The energies and the 3–momentum modules of the
particles do not depend on the choice of Z–axis and
neglecting the electron mass read
1 2 10(1 )y q yε β ε β β= , = − , = ,
2 2(2 ) (4 )E β τ ρ β ρ τ ρ= + , | |= +p , (3)
2
2
1 4
4
V My xy
V
β τ β τ
τ
| |= + , = , =q ,
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2007, N3 (1), p. 93-97. 93
where is the energy of ingoing (outgoing) elec-
tron, is the energy (3–momentum) of the recoil
proton.
1 2( )ε ε
2 2( )E p
In contrast with the energies, the scattering angles
depend on the choice of Z–axis direction. For the sys-
tem (Fig.1,a) one has K
2
(1 2 )cos
(1 ) 4
e
y y x
y y xy
τθ
τ
− −
= − ,
− +
2
2 ( )cos
(4 )( 4 )
p
y xy
y xy
ρ τ ρθ
ρ τ ρ τ
+ +
= − ,
+ +
(4)
whereas in the case of system (Fig.1,b): K̂
1 2 2ˆ ˆcos cos
1 (4 )e p
y xy z
y
τ ρθ θ
ρ τ ρ
− − +
= , =
− +
τ
,
1 22
1
k p
z
V
= − , (5) )iB + =
where is the electron and proton scattering an-
gles in system , is the same but in system
and we introduced for a convenience new dimensionless
quantity that has to be expressed through azimuth
angle and invariant variables Eq. (2) in the final results.
( )e pθ θ
z
K ˆ ˆ(e pθ θ ) K̂
In what follows we will present the analytical for-
mulae only for -system. Usually the photon is not
recorded experimentally and therefore we have to ex-
clude the photon 4–momentum from the phase space of
final particles by means of the overall –function.
Thus, we have to define
K
(4)δ
3 3
22 2
2 2
( )
d k d p
dF k
E
δ
ε
= . (6) T u
Elimination of is trivial in system 2( )kδ K
2
1 2
1( ) cos
2pk dδ θ = ,
| || |q p
that leads to
22 4
V ydF dxdyd d
y xy
π ρ
τ
=
+
Φ. (7)
The invariant variable can be expressed through
and c namely (see also Ref. [1])
z
x y ρ, , osΦ,
1
4
z
y xτ
=
+
2 cosK× Φ[ ]2 ( ) (1 2 ) ;x xy xy xy xτ ρ ρ+ + + + + − (8)
( )( )( )( )2 1x y xy y xy
K
y
τ τ ρ ρ ρ+− − − + − −
= .
ρ−
Quantities in the last expression have a sense of the
minimum and maximum value of at fixed and
ρ±
ρ x y
( )( )21 4
2[ (1 ) ]
y x y y xy x
y x
ρ τ
τ±
= − ± + − +
(9) 2+ .τ (1) 1 2
[ ] [ ]
4 (
( )(
M F F
H B
V z z xyµν µν
π ρ
ρ
+
= −
− −
)
)
3. THE SINGLE–SPIN TARGET
ASYMMETRY IN ELECTROPRODUCTION
In this paper we will concentrate on the single–spin
target asymmetries. They can be written in terms of
contraction of leptonic and hadronic tensors. For the
hard electroproduction process (1) we have [2]
(1)
[ ] [ ]
( ) ( )4t
H B
A
H B
µν µν
µν µν
α
π
= − , (10)
where and are the symmetrical and anti-
symmetrical parts of hadronic tensor. They can be ex-
pressed through the proton electromagnetic form factors
(see Ref. [2]). Tensor is the leptonic tensor in the
Born approximation and ] is antisymmetrical imagi-
nary part of leptonic tensor that generated by the loop
radiative correction. Here we bear in mind that the lep-
ton beam is unpolarized and the target proton has an
arbitrary polarization. We use the result of Ref. [3] and
write one–loop corrected unpolarized leptonic tensor in
the form
( )H µν [ ]H µν
B( )µν
(1
[B )
µν
(1 (1)
[ ] ( ) 11 11 1 1( ) ( )g gB T T T Tg k kµν µν µ νµν
∗ ∗+ + +
22 22 12 212 2 1 2
21 12 2 1
( ) ( )
( ) .
T T T Tk k k k
T T k k
µ ν µ ν
µ ν
∗ ∗
∗
+ + + +
+ +
It is easy to divide the right-hand side of above
equation by its symmetrical and antisymmetrical pieces
and we arrive at
(1)
[ ] 12 21 1 2( )[ ]B T T k kµν µν= ℑ − . (11)
Quantities and T are found in Ref. [3], and the
extraction of the respective imaginary part leads to re-
sult
12T 21
( )(1)
[ ] 1 2 1 22 ;B Tk k k kµν µ ν ν µπ= −
2
2
2 1 14 lnq st u t
st t u cc
+= + −
(12) ,
t
where we used the same variables as in Ref. [3]
2
1 2 2 12 2 2u k k s kk t kk q s t u c u= − , = , = − , = + + , = + .
Note that quantity T does not have singularity at t
and goes to zero when q
0→
2 0→ .
The denominator in Eq. (10) in terms of invariant
variables reads
( ) ( )H Bµν µν
2 2 2
1 1 2 2 1 2( ) 2 ( )
( )( ) 4
V F F F F
z z xy
ρχ χ
ρ τ
= − + + + − −
;
)
,
,
(13)
2
1 2 ( ) ( ) ;z z xy xyχ ρ ρ ρ = − − − + +
( )[ ]2 2 (1z xy z yχ ρ τ ρ= − − + −
( )2 21 (1 )xy z yτ ρ ρ + + − − + −
where we used also and
is the Dirac (Pauli) proton form factor.
( ) ( )s V z t V z xyρ= − , = − −
1 2( )F F
The numerator in Eq. (10) is expressed via the tar-
get–proton polarization 4-vector S
2
21 s
xy xy xy z G
z z xy xyz
ρ ρ −
× − + + + −
ln ; (14)
1 2 1 2
1 2 1 2 2
( )( )
2( ) ,
4s
k k qp p S
G k k qS F F F
V
ρ
τ τ
= − +
94
where δ . ( )abcd a b c dα β γ
αβγδε=
In general the one-loop correction to the leptonic
part of interaction generates the three types of target
single-spin asymmetries when the target proton has
three different directions of its polarization 3-vector in
laboratory system.
If the longitudinal (L) target proton polarization in
laboratory system is chosen along direction of the
transverse (T) polarization belongs to plane
and the normal (N) one – along direction the
respective polarization 4-vectors can be ex-
pressed through the particles 4-momenta as Ref. [4].
1,k
1( ,k k
2×k
2
1 ,
)
k
)(
1
L T NS , ,
Fig. 2. The target single-spin asymmetries that are suit-
able for choice (16) of the target-proton polarizations
as a function of angle Φ
1 1 1 2 1
1 1 3
2 2( )
(1 )
L Nk p k k p
S S
V V xy y xy
µ µ
µ µ
τ µ
τ τ
−
= , = −
− −
, (15)
2 1
1
(1 2 )
(1 )
T k y xy k xyp
S
Vxy y xy
µ µ
µ
τ
τ
− − − −
= ,
− −
1µ
.
where and
For this choice of the target polarization we have
1 1( )I J
IJS S δ= − 1 1( ) 0;IS p I J L T N= , = , ,
(1 2 1
1 1
( )
2L
s
k k qp
G F
Vτ
= − + ,)2zF (16) G L
1 2 1
1
( )
(1 )
T
s
k k qp
G
Vxy y xyτ
= ×
− −
2
12 ( (1 2
2
F
xyF xy yz xρ
τ
− + + − +
)) ;τ (17)
3
1 1
1
2 (1 ) 4
N
s
V xyG F
y xy
ρ
τ τ
= − × − − −
2F
[ ]
2
2 1 2 1
4
4 ( )
(2 ) (1 )
F k k qp
z y xy
V xy
ρ ρ
τ
× − − − − −
, (18)
where the proton form factors depend on
The target single-spin asymmetries
corresponding to above choice of polarizations are
shown on Fig. 2.
2 2q Q Vρ= − = − .
In principle, one can choose other directions to de-
fine polarizations of the target proton. The case when
the longitudinal direction is along the 3-momentum of
the recoil proton and the transverse one – in the plane
were considered in [2]. 1 2( ,Ρk )
2
2
+
4. SINGLE-SPIN TARGET ASYMMETRIES
IN PAIR PRODUCTION
The amplitudes of the BH-processes (1) and the
electron-positron pair production
1 1 2( ) ( ) ( ) ( ) ( )k p p e k e k p pγ + −+ → + + (19)
are connected each others by well known substitution
law [5].
By means of this substitution law one can calculate
both, the symmetrical and antisymmetrical parts of lep-
tonic tensor in process (19), using the known re-
sults for leptonic tensor in process Eq. (1), namely
Lγµν
1 1 2( )L L k k k k k kγ
µν µν= − → − , → − , → . (20)
In one-loop approximation we have
(1) (1)
[ ] ( ) 11 11 1 1( ) ( )g giB B T T T Tg k k
γ γ γ γ γ γ
µν µν µ νµν
∗ ∗+ = + + +
22 22 12 212 2 1 2
21 12 2 1
( ) ( )
( ) ;
T T T Tk k k k
T T k k
γ γ γ γ
µ ν µ ν
γ γ
µ ν
∗ ∗
∗
+ + + +
+ +
(1)
[ ] 12 21 1 2( )[ ]B T T k kγ γ γ
µν µν= ℑ − ,
and the interesting for us term T has the following
form
12
γ
2 2 2
12 2 2
2 ( ) ( )aq s u G q sq ut GT
ut u t
γ γ
γ
− −
= +
2
2 2 22 8qs
sq s u t usq L s t
ut c a
− +
− + + + − +
3 u
2 2 2 2
2 2
4( )( ) (2 )( )qs
qu
s au q L c q a t ut sq L
c a t
− − + −
− +
2 (2 ) ;qt
q a s u L
bu
−
−
(21)
2
( 2 )
3qs q s tL L Lγ π
= + − −
2
2 2 22 (1 ) 2 (1 )q tLi Li
s q
− − + − ,
95
( )G G t uγ γ= → ,
2
0
( ) (1 )
x dyLi x ln y
y
= − −∫
,
where and
also
2
1 2 1 2( ) 2 2s k k t kk u kk= + , = − , = −
, , .a s t b s u c u t= + = + = +
,
The quantities in Eq. (21) are defined in the follow-
ing way
ikL
2, , , , ,ik i kL L L i k s t u q= − = , 2lni
iL
m
−
= .
Quantity can be obtained from T by change
.
21T γ
12
γ
t u↔
The extraction of imaginary part leads to
12 21
2
2
( )
8 ln ln
( )
T T
q s u t s u t q u t
ut t t u u u t
γ γ
π
ℑ − =
+ + −
= − + +
2 ( )
.
(22)
It is convenient also to introduce the appropriate for the
process (19) dimensionless variables
2 2
2 1 2 1
1 2
( ) 2 ( ) ( )
2 ( )
k k p k k p p
x y
p k k V V
ρ
− −
= − , = , = − ,
−
2− (23)
2
1
2
1 2
kp
z V
V
= − , =
p k.
In terms of these variables we have
(1) 1 2
[ ] [ ]
8 (
( )
M F FH B
Vxy z xy
γ
µν µν
πρ +
=
−
)
2
( 2 )ln ln ;s
z z z z z xy G
xy xy z xy z xy z
γρ ρ ρ − − −
× − − − −
( ) ( ) ( )
VH B
xy z xy
γ
µν µν = − ×
−
2 2
1 1 2 2 1 2( ) 2 (
4
F F F Fγ γ ρχ χ
τ
+ + +
2 ) ,
) ;
)
.
where
2 2
1 ( ) (z xy xyχ ρ ρ ρ = − − − + −
1 2 3 4 5 6
-0.03
-0.02
-0.01
0.01
0.02
0.03
1 2 3 4
-0.006
-0.004
-0.002
0.002
0.004
0.006
1 2 3 4 5 6
0.002
0.004
0.006
0.008
8 2.9 3.1 3.2 3.3 3.4 3.5
0.005
0.01
0.015
0.02
2 2
2 ( ) (z xy xyχ τ ρ ρ = − − + −
21 (1 ) (1 )( )y xy z z xyρ ρ ρ − + − + − − − − −
The function , that depends on the target polari-
zations, has the same form in terms of variables of
Eq. (23) as function in Eq. (14) in terms of variables
Eq. (2).
sGγ
sG
The single–spin target asymmetry in the photopro-
duction process (19) is
(1)
[ ] [ ]
( ) ( )4t
H B
A
H B
γ
µν µνγ
γ
µν µν
α
π
= − . (24)
In our numerical evaluations we use the parameteriza-
tion Eq. (15) of the target proton polarizations in which
changed by . The results are shown on Fig. 3 for
CLAS1 experimental condition.
1k k
5. CONCLUSIONS
In present paper we studied the single-spin parity
conserving target asymmetries in the Bethe-Heitler
processes of hard electroproduction (1) and electron-
positron pair photoproduction (19). Effect arises due to
appearance of non zero imaginary part of the amplitudes
on the level of radiative corrections. During the calcula-
tions we used the substitution law to obtain the one-loop
corrected leptonic tensor in process (19) using corre-
sponding and known tensor for the process (1). The
numerical estimations in conditions of current experi-
ments CLAS (JLab) and HERMES (DESY) indicate
very small values of any kind asymmetry in process (1).
Fig. 3. The -dependence of target asymmetries in
photoproduction for clas1 conditions. From top:
angle Φ is given in radians
Φ
,Tγ,LAγ A ;NAγ
In fact, in this reaction there is additional suppres-
sion due to used kinematical restrictions: small values
of invariants and .This suppression leads to asym-
metries which do not exceed 10 . At the same kine-
matics the asymmetries in process (19) can reach for
about two order more values. Such situation, in princi-
t 2q
4−
96
ple, gives the possibility to use process of pair photo-
production to determine the polarization states of the
proton and even for independent measurement of the
proton electromagnetic form factors.
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ess induced by loop correc-
tions //J. Exp. Theor. Phys. 2006, v. 102, p. 220-
233.
e p e γ− −+ → + +
3. E.A. Kuraev, N.P. Merenkov, V. S. Fadin. The
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ep
p
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p
p
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ОДНОСПИНОВЫЕ АСИММЕТРИИ В ЭЛЕКТРОН-ПРОТОННОМ И ФОТОН-ПРОТОННОМ
РАССЕИВАНИИ В ПРОЦЕССАХ БЕТЕ-ГАЙТЛЕРА, ИНДУЦИРОВАННЫЕ ПЕТЛЕВЫМИ
ПОПРАВКАМИ
А.В. Афанасьев, М.И. Кончатный, Н.П. Меренков
Исследованы односпиновые асимметрии мишени в процессах “жесткого” электророждения
и в фоторождении -пар , индуцированные петлевыми радиаци-
онными поправками в лептонной части взаимодействия. Физической причиной, обуславливающей такого
вида асимметрии, является ненулевая мнимая часть Бете-Гайтлеровской амплитуды, которая появляется на
уровне радиационной поправки. Односпиновые асимметрии мишени в случае неполяризованного электрон-
ного (или фотонного) пучка и произвольной поляризации протона-мишени вычислены в кинематических
условиях экспериментов по электророждению CLAS (Jefferson Lab, USA) и HERMES (DESY).
e p e γ− −+ → + + e e+ − p e eγ + −+ → + +
ОДНОСПІНОВІ АСИМЕТРІЇ В EЛЕКТРОН-ПРОТОННОМУ І ФОТОН-ПРОТОННОМУ
РОЗСІЮВАННІ В ПРОЦЕСАХ БЕТЕ-ГАЙТЛЕРА, ІНДУКОВАНІ ПЕТЛЕВИМИ ПОПРАВКАМИ
А.В. Афанас’єв, М.І. Кончатний, М.П. Меренков
Досліджені односпінові асиметрії мішені в процесах “жорсткого” електронародження
і в фотонародженні -пар , індуковані петлевими радіаційними поправками в лептон-
ній частині взаємодії. Фізичною причиною, що обумовлює такого виду асиметрії, є ненульова уявна частина
Бете-Гайтлерівської амплітуди, яка з’являється на рівні радіаційної поправки. Односпінові асиметрії мішені
у випадку неполяризованого електронного (чи фотонного) пучків та довільної поляризації протона-мішені
обчислені в кінематичних умовах експериментів по електронародженню CLAS (Jefferson Lab, USA) і
HERMES (DESY).
e p e γ− −+ → + +
e e+ − p e eγ + −+ → + +
97
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