Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters
We present the analytic review of π⁺ and π⁰ mesons photoproduction off the proton target as the only source of information about the Δ⁺(1232) resonance parameters. The review focuses at the estimation of the influence of different contributions to the experimental database on determination of the E2...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1105992017-01-06T03:02:33Z Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters Omelaenko, A.S. Nuclear reactions We present the analytic review of π⁺ and π⁰ mesons photoproduction off the proton target as the only source of information about the Δ⁺(1232) resonance parameters. The review focuses at the estimation of the influence of different contributions to the experimental database on determination of the E2/M1 ratio for γp→Δ⁺ transition and the resonance parameters, with discussion of the previous Kharkov results. Представлено аналітичний огляд фотонародження π⁺ та π⁰ мезонів на протонній мішені як єдиного джерела інформації про параметри Δ⁺(1232)-разонанса. Огляд фокусується на оцінці впливу різних вкладів в экспериментальну базу даних на визначення E2/M1-відношення для γp→Δ⁺ переходу і параметрів резонанса, з обговоренням отриманих раніше в Харкові результатів. Представлен аналитический обзор фоторождения π⁺ и π⁰ мезонов на протонной мишени как единственный источник информации о параметрах Δ⁺(1232)-разонанса. Обзор фокусируется на оценке влияния различных вкладов в экспериментальную базу данных на определение E2/M1-отношения для γp→Δ⁺ перехода и параметров резонанса, с обсуждением полученных ранее в Харькове результатов. 2003 Article Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters / A.S. Omelaenko // Вопросы атомной науки и техники. — 2003. — № 2. — С. 39-44. — Бібліогр.: 29 назв. — англ. 1562-6016 PACS: 13.75Gx http://dspace.nbuv.gov.ua/handle/123456789/110599 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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We present the analytic review of π⁺ and π⁰ mesons photoproduction off the proton target as the only source of information about the Δ⁺(1232) resonance parameters. The review focuses at the estimation of the influence of different contributions to the experimental database on determination of the E2/M1 ratio for γp→Δ⁺ transition and the resonance parameters, with discussion of the previous Kharkov results. |
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Omelaenko, A.S. |
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Omelaenko, A.S. |
| author_sort |
Omelaenko, A.S. |
| title |
Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters |
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Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters |
| title_full |
Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters |
| title_fullStr |
Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters |
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Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters |
| title_sort |
kharkov data on pion photoproduction and δ⁺(1232) resonance parameters |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2003 |
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Nuclear reactions |
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http://dspace.nbuv.gov.ua/handle/123456789/110599 |
| citation_txt |
Kharkov data on pion photoproduction and Δ⁺(1232) resonance parameters / A.S. Omelaenko // Вопросы атомной науки и техники. — 2003. — № 2. — С. 39-44. — Бібліогр.: 29 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-08T00:50:05Z |
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2025-07-08T00:50:05Z |
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1837037839284436992 |
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KHARKOV DATA ON PION PHOTOPRODUCTION AND
∆+(1232) RESONANCE PARAMETERS
A.S. Omelaenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
We present the analytic review of π+ and π0 mesons photoproduction off the proton target as the only source of
information about the ∆+(1232) resonance parameters. The review focuses at the estimation of the influence of
different contributions to the experimental database on determination of the E2/M1 ratio for γp→∆+ transition and
the resonance parameters, with discussion of the previous Kharkov results.
PACS: 13.75Gx
1. INTRODUCTION
The successful experiment on lithium splitting on
10 October 1932 was the initiating event followed by
the entire chain of long-term developments in the
atomic science in Kharkov and Former Soviet Union.
As one of the consequences, 33 years later the 2 GeV
electron linac was built in Kharkov, under direction of
K.D. Sinel’nikov and A.K. Val’ter − two participants of
the “high-voltage brigade” which had split up the
lithium nuclei. Unfortunately the following pulse
stretcher ring project left unrealized and performing the
coincidence experiments turned out to be very compli-
cated. As the result the single pion photoproduction on
proton happened to be practically the only one
elementary process thoroughly studied in Kharkov. In
particular, in the region of excitement of the first
nucleon resonance there were carried out numerous
measurements of asymmetry Σ in reactions with linearly
polarized photons [1,2]. The first round of successful
experiments using the polarized proton target in
addition [3,4] (see also article [5] in this issue) was the
most important result of these measurements. The new
information obtained in these experiments made it
possible to solve problem of the unique solution in the
energy independent multipole analysis using some
plausible stabilization procedure [6], and next without
any additional conditions [7].
The most interesting and theoretically important
result of such a multipole analyses is determination of
the resonance radiative decay amplitudes, in particular
the ratio EMR of the electric quadroupole E2 and
magnetic dipole M1 amplitudes. The deviation of EMR
from 0 is evidence in favor of the existence of color
magnetism due to the gluon exchange between quarks.
The EMR value plays a role of the litmus paper for
hadron models that predict this ratio to be quite small
with values ranging between –0.5% and –6% [8]. From
the Kharkov data EMR was obtained with the range of −
(1.2 ... 1.3)% [9].
However, later on and especially in the last decade
the database has considerably expanded. In addition, the
EMR happened to be very sensitive to some inconsis-
tencies in the database [10]. The present-day EMR value
is determined in many works [11], approximately with
the results being at least twice-larger then those
obtained in [9] (in recent work [12] EMR = =−
[3.07 ± 0.26(stat + syst) ± 0.24(model)]%). The reason
of this contradiction can be understood from article [10]
where the model dependence and the influence of
choice of database in extracting the ∆(1232) electro-
magnetic transition amplitudes were investigated. In
particular, the crucial correlation between the Bonn π0
cross section data [13] and the EMR was demonstrated.
The strong influence of this data on the extracted EMR
has also been confirmed by the LEGS group [14,12].
The mass splitting of the different ∆ charge states is
another problem associated with the Kharkov data.
Indeed, the πN scattering analyses has given the ∆0 and
∆++ masses, characteristic values being 1233.6±0.5 MeV
and 1230.9±0.3 MeV respectively [11] (PDG)). The
missing ∆+ mass can be obtained only from the single
pion photoproduction reactions on proton, by the
resonance fitting of the multipoles leading to the final π
N state with isotopic spin T = 3/2 and total momentum
J=3 /2 at condition that the Watson’s theorem is not
used. The ∆+ mass value 1234.9±1.4 MeV was obtained
by authors of work [15] (MIROSHNIC 79 in PDG)
from the results of their preceding energy independent
analysis with ‘free’ imaginary part of the magnetic
dipole resonant amplitude [16]. But it has been a
concern that this ∆+ mass is inconsistent with ∆++ and ∆0
masses cited above. In particular, this issue was the
subject of a special publication [17], where it has also
been emphasized that a similar problem arises in any
analysis starting from multipoles determined in a
separate analysis.
The purpose of this mini-review is to shed some
light on the problems with both the Kharkov EMR and ∆
+ mass value, with paying a special attention to the
Kharkov data. We have invoked a realistic resonance
model approbated in our contribution to [18] and
fulfilled a series of retrospective fits beginning from the
data since 1990 and scaling down by degrees the year of
the data involved. It turned out that the Bonn’s cross
sections mentioned above have a strong influence not
only on the EMR, but also on the ∆+ mass.
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2003, № 2.
Series: Nuclear Physics Investigations (41), p. 39-44. 39
2. REMARKS ON THE DATABASE
Several years ago the full collection of the Kharkov
data on single pion photoproduction was uploaded to the
public-available compilation SAID [19,20]. In connec-
tion with this we have ceased replenishment of our own
database using the results of the vast work undertaken
by the authors of SAID. Now the Kharkov data are well
accessible and up to this time they are used in the
multipole analyses, for example, [12,21]. An essential
feature of the SAID compilation is that it contains all
accumulated data being verified by direct contacts with
numerous authors, without any preliminary selection
according to somebody’s preferences. As a result, the
database contains some conflicting measurements, but
there is a possibility to investigate the influence of these
discrepancies on the results of any specific multipole
analysis.
3. FORMALISM IN THE ∆(1232) REGION
Our analysis was carried out in terms of the
Walker’s helicity multipoles BAM I
l
I
l
I
l ±±≡± , with the
following isospin structure of the π0 and π+ photo-
production on proton [22]:
A1/2 = 1/3 A(π0) + √2/3 A(π+), (1)
A3/2 = A(π0) − 1/√2 A(π+). (2)
The starting point of the model used is the following
expression for the resonant multipoles obtained in the
K-matrix approach [23] as result of the unitary merging
of the background and the ‘pure’ resonance:
.sincos 3333
3333
2/3
1 eReBM iRPURE
M
iBORN
M
δ+δ= δδ+ (3)
In Eq. (3) BBORN
M is the background function (in [23] this
is the Born contribution to the resonant multipole),
RPURE
M is responsible for the resonance photoexcitation.
The full phase shift δ33 for the P33 wave in the πN
scattering is the sum of the background δ B
33 and the
‘pure’ resonance phase shift δ R
33 :
δδδ += RB
333333 . (4)
To fully demonstrate the dependence on δ33, which is
the main focus of our interest, Eq. (1) can be written as
eReBM i
M
i
M
δδ+δδ=+
3333
3333
2/3
1 sincos , (5)
with
,sin
33δ−= BPURE
M
BORN
MM RBB (6)
.cos 33δ= BPURE
MM RR (7)
Eq. (5) is the base of our treatment of the resonant
multipoles. The elastic background phase shift appears
not only as a component part of δ33 but also has an
additional influence on the redefined excitation func-
tions (6,7). These corrections are expected be small and
smooth, keeping in mind evaluations of the background
phase shift for the mixed charge δ33. There is no
possibility to determinate the elastic background phase
shift by using Eqs. (6,7) because the corresponding
trigonometric functions are multiplied by other
unknown smooth functions. So, the whole function BM
was parameterized through the Lagrange interpolation
formula (Eγ being the laboratory photon energy):
,)()()()( )()(
4
)(1
)(
4
1
)( ji
j
ijj
j
i
i
i EEEEEBEB γγ
=
≠=
γγ
=
=
γγ −−= ∏∑ (8)
with four knot energies and with coefficients being the
knot values of the function. In a special test it has been
compared to the relevant cubic spline without the first
derivatives specified at the ends, and Eq. (8) happened
to be preferable for extrapolating out of the energy
interval restricted by the extreme knots.
The full phase shift δ33 in (5) is chosen in accordance
with the standard Breit-Wigner formula:
WW
WWtg 22
0
0
33
)(
−
Γ=δ (9)
with
22
2
0
23
0
0)(
qX
qX
q
qW
+
+
Γ=Γ , (10)
where q is the c.m. momenta of the pion, q0 is the
corresponding quantities at W0. Here W0 (the mass) is
the value of the total c.m. energy W at which δ33 passes
though 90°, and the width is Γ0 = 2/(dδ33/dW)W=M0
(‘experimental’ values). Eq. (9) corresponds to the
approach without introduction the explicit background
at all, and a precaution about BM seems to be excessive,
as well. Accordingly, these definitions are the same as
in πN phase shift analysis [24] (KH80) at determination
of the ∆++ and ∆0 parameters, where “some guess for
uncertainty due to the non-resonant background are
simply added to the quoted errors”.
The last term in Eq. (5) corresponds the to resonance
contribution. It is introduced according to Walker [22]:
Γ−−
ΓΓ
=
γ
+
WiWW
W
kq
qkWCWM M
R
0
22
0
000
0
,2/3
1 )()( .
(11)
Here )(Im 0
,2/3
1 WM RC M +≡ is the resonance constant,
22
2
0
23
0
0)(
kX
kX
k
kW
+
+
Γ=Γ λ , (12)
where k is the c.m. momenta of the photon, k0 is the
corresponding quantities at W0.
Expression (8) is used also to describe the real parts
of the variable non-resonant multipoles, other
background multipoles up to l=3 are taken as full Born
approximation, and the corresponding imaginary parts
are calculated according to the Watson’s theorem:
).(ReIm )(2,2δ= ±±± lI
I
l
I
l tgMM (13)
The resonance constant in Eq. (11) refers to the ex-
perimental resonance in the meaning discussed above.
For parameterization with some realistic non-zero back-
ground phase shift the arguments can be provided in
such a way that the resonance constant would be very
close to the ‘pure’ one (see [9] and discussion of this
40
work in [25]). Especially, we can expect that for the
resonance ratio E2/M1 where reduction of the energy
dependence is also expected.
4. RETROSPECTIVE MULTIPOLE ANALYSIS
To concentrate calculations in the ∆+ region we have
treated the data at the photon energy interval 260-
420 MeV. The energies 280, 320, 360, and 400 MeV
were taken as knot energies in Eq. (8). The necessary
for Eq. (13) πN scattering phase shifts were calculated
according the recent πN analyses [26] (SM02 in SAID).
The data were fitted by minimizing the standard χ2
without introducing rating factors for any type of
observable. The main set of independent variables
included the ∆+ mass M0 and width Γ0 (parameter X was
fixed at the Walker’s value 185 MeV) and the knot
values from Eq. (8) used for the following functions: (a)
the background functions BA, BB in Eq. (5) for the
resonant multipoles; (b) the real parts of the non-
resonant multipoles A0+, A1- with isotopic I = 1/2,3/2,
A1+, B1+ with I = 1/2 (s,p waves), and A2-, B2- with
I = 1/2 to account the possible ‘tail’ of the second
resonance. The results obtained for several series of fits
with the data from different years are presented in
Table 1. The first fit was obtained using the new data
obtained from 1990. This data set practically corres-
ponds to the BRAG low energy set [18]. As in [18] we
were unlucky to describe the preliminary π0 cross
section HA97MA* from Mainz (our data labels contain
two letters of the first author and the laboratory name
being separated by the reduced year). In addition, there
is a problem with the LEGS differential cross sections
(BL01LE, π0 and π+ production). The corresponding χ
2
dp ≡ χ2/N (N is the number of points) are too large, and
that needs special consideration. In preliminary calcu-
lations the normalization factors being introduced as
additional free parameters for the both LEGS cross
sections were about 0.9, but only for the π0 production it
was possible to get reasonable χ2
dp ≈ 2.6. Consequently
we have omitted these data in the initial data set (group
I in Table 2, χ2 in this table are calculated according to
our final solution discussed below).
Table 1. ∆+ Parameters for different variants of the resonance model
№ Vari-
ants Year Excluded
data EMR, % M0, MeV Γ0, MeV N χ2
df
1
2
3
4
5
6
7
8
9
1
0
Main
set
1990 I -2.2 ± 0.2 1232.3 ± 0.8 117.1 ± 2.9 1339 1.59
1985 I -2.2 ± 0.2 1232.7 ± 0.8 117.2 ± 2.9 1343 1.60
1980 I -2.2 ± 0.1 1231.5 ± 0.6 113.5 ± 2.1 1762 1.80
1980 I,II -2.2 ± 0.1 1232.0 ± 0.6 114.1 ± 2.2 1758 1.78
1975 I,II -2.7 ± 0.1 1232.0 ± 0.5 111.3 ± 1.9 2152 2.35
1975 I-III -2.6 ± 0.1 1231.7 ± 0.5 112.1 ± 2.0 2113 2.15
1970 I-III -1.6 ± 0.1 1234.7 ± 0.4 117.3 ± 1.7 2997 2.30
1970 I-IV -1.6 ± 0.1 1234.7 ± 0.4 117.5 ± 1.7 2992 2.28
1970 I-V -2.5 ± 0.1 1232.0 ± 0.5 111.6 ± 1.7 2660 2.05
1960 I-VI -2.5 ± 0.1 1232.1 ± 0.4 113.0 ± 1.7 3225
2.24
1
1 s,p 1960 I-VI -2.2 ± 0.1 1232.4 ± 0.5 117.7 ± 1.8 3225 2.41
1
2 s,p,d 1960 I-VI -2.6 ± 0.1 1233.0 ± 0.5 113.0 ± 2.1 3225 2.13
Table 2. Characteristics of the deleted data
G. R O Label N Eγ, MeV ϑ, deg χ2
dp
I
π0 σ HA97MA
* 51 283-402 10.0-170.0 13.5
π+ σ BL01LE 48 265-322 20.0-170.0 25.7
π0 σ BL01LE 49 265-334 70.0-130.0 12.5
II π+ G BL84KH 4 320-380 65.0-80.0 9.9
III
π+ Σ GN76KH 32 280-420 25.0-140.0 10.2
π0 Σ GB77KH1 4 280-400 75.0-120.0 43.5
π0 σ JU76BO 2 373-416 89.4-90.9 7.6
IV π+ Σ ZD72ST 2 390-408 135.0 19.3
π0 σ HE73TO 3 350-420 4.4-6.1 7.8
V π0 σ GZ74BO1 332 260-420 10.0-160.0 6.9
VI π+ σ KN63UC 23 260-290 0-160 8.5
π+ Σ LU64ST 3 330 45-135 34.4
Note: R − reaction, O − observable value
Table 3. χ2 per point for different values for fit 10
Reaction dσ/d
Ω
Σ T P
γp→π+n 2.26 1.82 1.66 1.35
γp→πop 2.55 2.47 3.31 1.93
By decreasing the initial year down to 1975 we
exclude some other non-numerous data (groups II-IV in
Table 2) with per degree of freedom exceeding 9. There
were observed rather stable values of the resonance
parameters with acceptable values of χ2
df. But appearing
in the current compilation of the numerous π0 cross
section data resulting from some experimental setups at
Bonn [13] (GZ74BO) caused the striking effect. In
particular the ∆+ mass exceeding the ∆0 value known
from scattering has yielded (rows 7,8 in Table 1).
Because of this we have omitted this old Bonn data and
a subsequent involvement of the pioneer’s photo-
41
production measurements has given our final solution,
which seems to be the most realistic one (row 10).
Corresponding values of χ2
dp are placed in the last
column of Table 2 (rejected data), in Table 3 (π+ and π0
production separately for cross section, Σ, P, and T), and
in Table 4 for the Kharkov data from the final data set.
In two last fits we have restricted the background
variable parameters by the s, p waves and (row 11 in
Table 1) and increased to vary the full set of the
background d waves (row 12).
Table 4. Characteristics of the Kharkov data
R O Label Eγ, MeV ϑ, deg N χ2
dp
π+
Σ GE81KH 280-420 30-150 56 3.6
P GE81KH 280-420 30-150 54 1.4
T GE81KH 280-420 30-150 53 1.9
T GE80KH 340-340 30-150 7 2.2
H BL86KH 320-320 90-120 4 5.2
H BL84KH 320-380 65-80 4 1.0
π0
Σ BL83KH 280-420 60-135 38 3.6
Σ GN76KH1 300-420 60-135 35 4.7
Σ GB78KH 360-400 140 2 4.6
P BL83KH 280-420 60-135 38 1.4
P GB78KH 360-400 140 2 2.6
T BL83KH 280-420 60-135 38 3.9
T GB78KH 360-400 140 2 1.0
Note: R − reaction, O − observable value
5. DISCUSSION
By going back from the last decade into the past and
involving older data we observe a rather smooth and
plausible variations of the ∆+ mass and ratio EMR until
stumbling at the old Bonn data on π0 differential cross
sections. As to the EMR the relevant jump corroborates
the known effect discussed in the Introduction, but the
rapid increase of M0 and Γ0 on about 2 and 4 MeV
correspondingly is unexpected. For example, in our
previous calculations [27] all fits were fulfilled with the
data [13], but ‘small’ EMR = (−1.43±0.08)%
accompanied by the mass of M0
= 1232 ± 0.71 MeV
appeared only in row 8 of Table 1 for the data up to
maximal year 1984, and some comment seems to be
necessary. The expression for the resonant multipoles
used in [27] can be obtained from present Eq. (5):
eRM iS
M
δ= δ+
33
33
2/3
1 sin , (14)
with some function to parameterize the function
RBR MM
S
M += δ 33cot . (15)
Evident shortage of such a parameterization is that it has
to describe the cot δ33 being a sufficiently strong
function of independent resonance parameters. Used in
[27] rigid parameterization was not relevant to
reproduce this feather and that has influenced the
resonance parameters.
Concerning the ∆+ mass from [15] first of all one has
to take into account the difference in definitions. With
reference to the Olsson’s work [28] the full magnetic
resonant multipole is there proportional to the following
construction (electric quadroupole was not treated):
))()(exp())()((sin WWWW RR β+ϕα+ϕ , (16)
where the manifest notation of [15] are conserved. This
block corresponds to one from Eq. (8) in [28], namely
)sin( eP
ie δ−δ+δδ , (17)
supposing the phase shift addition (our Eq. (4)). That is
quite correct, as Eq. (8) in [28] is derived without any
assumption about the low of the unitary merging of the
resonance and background in scattering. (By the way, in
[28] Olsson has been advocated the low with approxi-
mate subtraction of the resonance and the background
phase shifts). However, the important point is that by
introducing the background phase shift in parameterized
form the authors of [15] are dealing with ‘pure’
resonance, with parameters being different from the
“experimental’ one discussed in Sect. 3. For example,
the mass of the latter coincides with the energy at which
the resonant photomultipole passes through zero. For
involved in [15] analysis ([16], 1977, s,p waves are
fitted) this is about 1240 MeV (Eγ ≈ 340 MeV). As we
have previously seen to some extent that could be
caused by to the Bonn data [13] already included in this
analysis. It should be stressed that the main Kharkov
data were absent yet and in any case could not have
influence on this mass.
As to the old Bonn data it is not possible yet to reject
them coming from the χ2
df value. We prefer the solution
obtained with more recent data and taking into account
location of the ∆+ mass relatively to the masses of the ∆
++ and ∆0 [24]. All these values can be compared using
Table 5 (we only take from PDG the data with errors).
Table 5. The charge splitting of the ∆(1232)
State Mass,
MeV
Width,
MeV Source
∆++
1230.5±0.2 ABAEV 95
1230.9±0.3 111.0±1.0 KOCH 80B
1231.1±0.2 111.3±0.5 PEDRONI 78
∆+ 1231.9±0.4 112.5±1.7 Table 1, row 10
∆0
1233.1±0.3 ABAEV 95
1233.6±0.5 113.0±1.5 KOCH 80B
1233.8±0.2 117.9±0.9 PEDRONI 78
Some of the Kharkov data have got into groups II, III of
rejected data. As it is clear now, the main reason is
underestimation of the systematic errors. Nevertheless
the overwhelming majority of this data has good or
acceptable χ2
dp. But time is coming, and now the
polarization data T, Σ and P from Kharkov are
considering as having the large statistical and systematic
errors, especially for the γp→π0p process [29]. In
addition, the combined experiments with linearly
polarized photons and polarized proton have not been
repeated yet and remain to be unique. General situation
with the polarization data in the both reaction at
consideration is demonstrated in the figure below,
where the Σ, P, T angle dependencies are presented at
some energies convenient to compare with the up-to-
42
date polarization measurements at Bonn, Mainz, and
Brookhaven. New points have appeared mostly for
linear asymmetry, and the situation for T asymmetry
and polarization P in the reaction γp→π0p continue to
be rather unambiguous. It is also easy to see that our
final fit is in an excellent agreement with the last GWU
solution [21] (SM02 in SAID) for the observables with
looking reliable measurements. Some differences are
seen only for two mentioned before P and T.
0,0
0,1
0,2
0,3
0,4
0,5
π +n, 320 MeV
Σ our fit
BE00MA
BL01LE
GE81KH
GN76KH
SM02
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
π +n, 340 MeV
P
our fit
GE81KH
SM02
0 20 40 60 80 100 120 140 160 180
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
θ , deg
π +n, 340 MeV
T our fit
AA72TO
GE80KH
GE81KH
SM02
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
our fit
BE97MA
BJ69FR
BL01LE
BL83KH
BP70FR
DR64ST
GB78KH
GN76KH
SM02
π 0p, 320 MeV
Σ
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
π 0p
350, 360 MeV
P
our fit, 350
our fit, 360
AL66BO
AL68BO
BL83KH
BM69BO
GB78KH
SM02
0 20 40 60 80 100 120 140 160 180
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6 π 0p, 320 MeV
T
θ , deg
our fit
BL83KH
BO98BO
GB78KH
SM02
The Σ, P, and T vs pion c.m. angle θ for γp→π+n and γp→π0p reactions at Eγ = 320,...,360 MeV, with
predictions according to the final solution (row 10 in Table 1, our fit) and GWU (SAID) solution SM02 [21]
6. SUMMARY
The basic points of the present analytical mini-
review and its conclusions can be briefly formulated as
follows:
• Our parameterization of the resonant photo-
multipoles is the downright corollary of the
expression obtained in the framework of the K-
matrix formalism with multichannel two-particle
unitarity [23], with using the Walker’s model for
the resonance term. The reliable presentation of
the background multipoles was reached via the
cubic polynomials for the real parts with using
the Watson theorem for imaginary ones.
• The undertaken retrospective analysis reveals the
significant influence of the Bonn π0 differential
cross sections [13] on the ∆+ parameters: increase
by ~ 3 MeV for the ∆+ mass and about 2 MeV for
the width. Such an effect for the EMR is the
43
same as in the analyses using the Watson
theorem [10] (approximately dividing by 2). That
fully explains the small value of the EMR
obtained in [9] by using the Kharkov analysis
and also can be a reason for observing very large
∆+ mass in [15].
• The withdrawal of the Bonn data [13] allows to
obtain the ∆+ mass and width being in a
reasonable accordance with the corresponding
values for the ∆++ and the ∆0 known from the πN
scattering.
• Despite some criticism the overwhelming
majority of the Kharkov data on pion
photoproduction in the first resonance region
preserve its scientific signifi
cance and in some cases even the monopoly
position.
As to the Bonn data the question is not so simple.
They systematically cover the whole resonance region
including the small and the large angles, where the new
measurements yet are rather seldom and spread.
Besides, coming from multipole analyses one can
observe some ‘suspicious’ points and “derivations” in
measurements of several laboratories, first of all at the
edges of the energy or the angle intervals with
measurements. Hence, the general conclusion is that the
region of the first resonance needs to be explored more
thoroughly. The systematic precision measurements of
the differential cross section and polarization parameters
using the relevant modern facilities would be an actual
item in the program of a new modern middle energy
accelerator.
REFERENCES
1. V.B. Ganenko et al. The asymmetry
measurement of positive pion photoproduction by
protons with using linearly polarized photons in the
250-500 MeV energy range // Yad. Phys. 1976,
v. 23, p. 100-106 (in Russian).
2. V.B. Ganenko, V.G. Gorbenko,
L.M. Derkach et al. The angular distributions of
asymmetry of γp→pπo reaction at energies between
250 and 650 MeV // Yad. Phys. 1976, v. 23, p. 310-
322 (in Russian).
3. V.A. Get’man, V.G. Gorbenko,
A.Ya. Derkach et al. Positive pion production from
polarized protons by linearly polarized photons in
the 280-420 MeV energy range // Nucl. Phys.
1981, v. B 188, p. 319-413.
4. A.A. Belyaev et al. Experimental studies of
the Σ, T, P polarization parameters and the γp→pπo
reaction multipole analysis in the first resonance
region // Nucl. Phys. B. 1983, v. 213, p. 201-222.
5. V.G. Gorbenko, L.Ya. Kolesnikov.
Experiments on electromagnetic interaction of
linearly polarized photons with nucleons and nuclei
// Problems of atomic science and technology.
Series: Nuclear physics investigations. 2002,
№2(41), p. 30-38 (this issue).
6. I.I. Miroshnichenko, V.I. Nikiforov,
V.M. Sanin, P.V. Sorokin, Yu.N. Telegin, S.V.
Shalatsky. Multipole analysis of the reaction γp→
Nπ applying the regularization method // Yad. Fiz.
1983, v. 32, p. 656-666 (in Russsian).
7. V.A. Get’man, V.M. Sanin, Yu.N. Telegin,
S.V. Shalatsky. Energy-independent multipole
analysis of single-pion photoproduction processes
on protons // Yad. Fiz. 1983, v. 38, p. 385-389 (in
Russsian).
8. N.C. Mukhopadhyay. Topical Workshop on
Excited Baryons 1988. Troy, New York, edited by
G. Adams, N. Mukhopadhyay, and P. Stoler.
Singapure: “World Scientific”, 1989, p. 205.
9. A.S. Omelaenko, P.V. Sorokin. Ratio of the
quadrupole and dipole ∆→Nγ transition amplitudes
from multipole analysis of the raction γp→nπ+(pπ0) //
Yad. Fiz.. 1983, v. 38, p. 668-673 [Sov. J. Nucl. Phys.
1983, v. 38, p. 398-403].
10. R.M. Davidson, N.C. Mukhopadhyay,
M.S. Pierce, R.A. Arndt, I.I. Strakovsky,
R.L. Workman. Electromagnetic amplitudes:
implication of the choice of data base vs. methods of
analysis // Phys Rev. 1999, v. C 59, p. 1059-1063.
11. D.E. Groom at al. (Particle Data Group) //
Eur. Phys. J. 2000, v. C 15, p. 1-878.
12. G. Blanpied et al. (The LEGS
Collaboration). N→∆ transition and proton
polarizabilities from measurements of p( γγ , ), p(
,γ π0), and p( ,γ π+) // Phys. Rev. C. 2001, v. 64,
025003, 57 p.
13. H. Genzel et all. Photoproduction of neutral
pions on hydrogen below 500 MeV.
IV. Combination of the cross section data of all
Bonn experiments on π0 photoproduction //
Z. Physik. 1974, v. 268, p. 43-50.
14. G. Blanpied et al. (The LEGS Collaboration). N
→∆ transition from simultaneous measurements of
p( ,γ π) and p( γγ , ) // Phys. Rev. Lett. 1997, v. 79,
p. 4337-4340.
15. I.I. Miroshnichenko, V.I. Nikiforov, V.M. Sanin,
P.V. Sorokin, and S.V. Shalatsky. Position and residue
of the pole in the M(3/2)
1+
amplitude of the reaction γp→
Nπ // Yad. Fiz. 1979, v. 29, p. 188-193 [Sov. J. Nucl.
Phys. 1979, v. 29, p. 94-99].
16. I.I. Miroshnichenko, V.I. Nikiforov, V.M. Sanin,
P.V. Sorokin, and S.V. Shalatsky. Multipole analysis of
single pion photoproduction in region of the P33
resonance // Yad. Fiz. 1977, v. 26, p. 99-108.
17. R. Workman. Remarks on the ∆+(1232) mass //
Phys. Rev. 1997, v. C 56, p. 1645-1646.
18. R.A. Arndt et all. Multipole analysis of a
benchmark data set for pion photoproduction.
Proceedings of the Workshop on The Physics of
Excited Nucleons (NSTAR 2001). Ed.
D. Drechsel, L. Tiator (World Scientific, London,
2001), p. 467; nucl-th/0106059.
19. R.A. Arndt, I.I. Strakovsky, and
R.L. Workman. Updated resonance photo-decay
amplitudes to 2 GeV // Phys. Rev. 1996, v. С 53,
p. 430-440.
44
20. The George Washington University, Center for
Nuclear Studies, Data Analysis Center.
http://gwdac.phys.gwu.edu
21. R.A. Arndt, W.J. Briscoe, I.I. Strakovsky,
R.L. Workman. Analysis of pion photoproduction
data. Phys. Rev. 2002, v. С 66, 055213, 17 p.
22. R.L. Walker. Phenomenological analysis of
single-pion photoproduction // Phys. Rev. 1969, v. 182,
p. 1729-1748.
23. P. Noelle. Baryon resonances and electro-
magnetic couplings // Prog. Theor. Phys. 1978, v. 60,
p. 778-793.
24. R. Koch, E. Pietarinen. Low-energy πN partial
wave analysis // Nucl. Phys. 1980, v. A 336, p. 331-345.
25. P. Christillin and G. Dillon. On the γN∆
coupling constants and on the ratio of quadrupole
to magnetic transitions // J. Phys. G: Nucl. Part.
Phys. 1989, v. 15, p. 967-975.
26. A. Arndt, R.L. Workman, I.I. Strakovsky,
M. Pavan. Partial-wave analysis of πN-scattering.
Eprint nucl-th/9807087 (submitted to Phys.
Rev. C).
27. A.S. Omelaenko. On the experimental value
of the ∆+ mass from γp→(pπ0) // Problems of
Atomic Science and Technology. Series: Nuclear
Physics Investigations. 2002, №2 (40), p. 3-6.
28. M.G. Olsson. Does the ∆(3,3) resonance
factorize? // Phys. Rev. 1976, v. D 13, p. 2502-2507.
29. R. Beck, H.P. Krahn, J. Ahrens et al.
Determination of the E2/M1 ratio in the γN→∆
(1232) transition from a simultaneous
measurement of p( ,γ
p)π0 and p( ,γ
π+)n // Phys.
Rev. 2000, v. C 61, 035204, 14 p.
45
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