The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method
The possibility of high precision measurement of the total hadronic cross-section in electron-positron annihilation process by analysis of the initial-state radiative events is discussed. Different experimental setups are discussed. The main attention is dedicated to measurement of hadronic cross-se...
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| Zitieren: | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method / M.I. Konchatnij, N.P. Merenkov, O.N. Shekhovtsova // Вопросы атомной науки и техники. — 2001. — № 6. — С. 30-34. — Бібліогр.: 12 назв. — англ. |
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| author | Konchatnij, M.I. Merenkov, N.P. Shekhovtsova, O.N. |
| author_facet | Konchatnij, M.I. Merenkov, N.P. Shekhovtsova, O.N. |
| citation_txt | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method / M.I. Konchatnij, N.P. Merenkov, O.N. Shekhovtsova // Вопросы атомной науки и техники. — 2001. — № 6. — С. 30-34. — Бібліогр.: 12 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The possibility of high precision measurement of the total hadronic cross-section in electron-positron annihilation process by analysis of the initial-state radiative events is discussed. Different experimental setups are discussed. The main attention is dedicated to measurement of hadronic cross-section at DAPhNE, where the final hadronic state π⁺π⁻ dominates due to radiative return on ρ-resonance. Radiative corrections at one percent level accuracy are calculated taking into account real experimental constraints on event selection.
|
| first_indexed | 2025-11-30T10:00:56Z |
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THE SCANNING OF HADRONIC CROSS-SECTION
IN e e+ − -ANNIHILATION BY RADIATIVE RETURN METHOD
M.I. Konchatnij, N.P. Merenkov, O.N. Shekhovtsova
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The possibility of high precision measurement of the total hadronic cross-section in electron-positron annihilation
process by analysis of the initial-state radiative events is discussed. Different experimental setups are discussed. The
main attention is dedicated to measurement of hadronic cross-section at DAPhNE, where the final hadronic state
π π+ − dominates due to radiative return on ρ -resonance. Radiative corrections at one percent level accuracy are
calculated taking into account real experimental constraints on event selection.
PACS: 29.27.Hj, 29.90. +r
In the interpretation of the recent high precision
measurement of muon anomalous magnetic moment [1]
the large uncertainty arouse in determine the contribu-
tion of hadron vacuum polarization contribution in (g−2)
µ [2,3].
The problem of hadron vacuum polarization
contribution is that it cannot be calculated analytically
because QCD loses its predictable force at low and
intermediate energies, where effect must be
considerable. Therefore, the only possibility to calculate
it is the utilization of the measured total hadronic cross
section in electron-positron annihilation, which
connected with hadron vacuum polarization by
dispersive relation. The necessary condition for such
calculation is the knowledge of total hadronic cross
section with one per cent accuracy and even better.
In the works [4,5] the radiative return method of the
scanning of the total hadronic cross section in --
annihilation discussed just in connection with
considered problem. For energies below 1 GeV
DAPhNE machine is ideal to use this method due to its
high luminosity and effect of radiative return on ρ -
resonance. In [6] the analysis initial state radiation (IRS)
events, has been performed for DAPhNE condition
when both the energy fraction of photon inside
calorimeter and the invariant mass of π π+ − -system are
measured.
Because of geometry of the used at DAPhNE KLOE
detector the most of ISR events, when photon belong to
the blind zone, are inaccessible for detection and cannot
be recorded by KLOE calorimeters. This circumstance
decreases the event statistics and, respectively, the
measurement precision. To avoid this problem G.
Venanzoni suggested to use inclusive event selection
(IES) method, when only invariant mass of the final
pions is measured. The main advantage of IES is the
increase of the corresponding cross section due to
ln(E2/m2) enhancement (here E is the beam energy and
m is the electron mass). To avoid uncertainties in
interpretation of IES approach, some additional rules for
event selection must be established.
Now to calculate analytically the Born cross-section
of ISR process
( ) ( ) ( ) ( ) ( )1 2e p e p k p pγ π π− + +
+ −+ → + +
and the QED radiative corrections (RC) to it for IES
experimental setup, taking into account appropriate
additional constraints for event selection, which can be
realized at DAPhNE accelerator.
1. IES SELECTION RULES
The main condition for IES approach is the precise
measurement of pion invariant mass. It can be done by
means of selection events with small difference between
the lost (undetected) energy and the lost 3-momentum
modulus in process (1).
2 , 1,E E E P p p Eη η+ − Φ + −− − − − − < < <
r r r
E± is the energy of π ± , and PΦ
r
is the total initial-
state 3-momentum which appears because laboratory
system at DAPhNE does not coincides with the center
mass system, 12.5PΦ =
r
MeV. The constraint (2)
avoids undetected 0π and keeps only undetected nγ
system. The inequality (2) can be rewritten in terms of
the total energy Ω and total 3-momentum modulus K
r
of all photons in reaction e e nπ π γ+ − + −+ → + + as
K EηΩ − <
r
The optimal value η =0.02 decreases also FSR
background. The next constraint (collinear) selects
events when at n=1 undetected photon is belongs to the
narrow cone along the electron beam direction.
1 0 0 0, cosK p K E c c θ> =
r rr
,
where 0θ can be chosen for about 5 6o o− . Due to this
constraint the collinear photon radiated by the initial
electron contributes into observed IES cross section and
exhibits itself by 22 2
0ln( / )E mθ enhancement.
Because of existence of the blind zone, KLOE
detector picks out events with pion polar angles in
diapason m mθ θ π θ±< < − . As show the Monte Carlo
calculations [5] the choice of mθ influences also on the
value of FRS background. The optimal value of mθ for
DAPhNe conditions is 20o . Ordinary the reduced pion
30 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 30-34.
phase space can be taken into account by introduction of
respective acceptance factor ( )mA θ .
2. BORN APPROXIMATION
To lowest order in α , the differential cross section
of the process(1) can be written in terms of contraction
of leptonic Lµ ν and hadronic H µ ν tensors as
2 2
1 24
3 33
2 2
8 ( , , )
( )
4 16
Bd L p p k H
sq
d p d pd k q p p
E E
γ
µ ν µ ν
π ασ
α δ
ωπ π
+ −
+ −
+ −
= Ч
− −
,
where ω is the energy of photon and
224 ( )H F q p pµ ν π µ ν− −= − % % ,
1
2
p p qµ µ µ− −= −% ,
1 2q p p k p p+ −= + − = +
The pion electromagnetic form factor defines the
total cross section 2( )qσ of the process
e e π π+ − + −+ → + , that is the subject of experimental
investigation, by means of relation
2 222
2
3 ( )( ) q qF qπ
σ
π α ς
= ,
2 3
2
2
4
(1 )
m
q
πς = − .
The leptonic tensor for the case of collinear ISR
along the electron beam direction is well known [7]:
( ) ( )2 22 2 2 2
1 2
1 2 2
1 2 1
2 2 2
1 1 2 22
1 2 1 2 1
2( , , )
4 4 8 ,
q t q t m qL p p k g
t t t
q q mp p p p
t t t t t
γ
µ ν µ ν
µ ν µ ν
й щ− + −
к ъ= −
к ъ
л ы
ж ц
+ + −з ч
и ш
%
% % % %
where 1 1 2 2 1 22 , 2 , 2 .t kp t kp s p p= − = − =
Then, we derive the distribution over pion squared
invariant mass 2q for non- cut pion phase space
( )2 24 2
0
02 2 2 2
0
1
2 84 2 4
[
B
F
qd Pq q L
E Edq E E E
σ ωσ α
π ω
Φж цж ц
= + + + −з чз ч з чи ши ш
r
22 4 2
0 0
2
0 0
2
2 6 8 2
].q q q
E E EE
θ ω
ω ω
ж ц
+ + −з ч
и ш
To guarantee only one percent accuracy one can
remove terms proportional to 2 2/ 4P EΦ
r
and 2
0 / 6θ :
( ) ( )
2
02 2 , ,
24
B
F
qd P z L
dq E
σσ α
π
=
22
0
0 2ln ,
EL
m
θж ц
= з чз ч
и ш
( )
2
0 0
1 2, ,
1 1
z zP z L L
z z
+= −
− −
2
2 .
4
qz
E
=
In the case of reduced pion phase space the form of
distribution is more complicated. But the result is also
simplified essentially if to neglect terms of the order
2 2/ 4P EΦ
r
and use QRE approximation,
( ) ( ) ( )
2
02 2 , , ,
24
B
R
m
qd P z L A z c
dq E
σσ α
π
=
where ( ), mA z c - acceptance factor
( ) ( ) ( )
( ) ( )
max
2
22 2 2
1 112, .
1 1m
c
m
c
z z K z c
A z c dc U
K z z cς
−
−
−
−
+ − −й щл ы=
й щ+ − −л ы
т
Here the notations are introduced
22
1 1
2 4 2 ,
4 16 4
mU
E E zE
πχ χ= − −
( ) ( )
2
2 2 2
21 1 1K z z c
z
δ
−
й щ= − + − −л ы ,
( )
( ) ( )
2
1
2 2 2
1 2 1
4 1 1
z z Kc z c
E z z c
χ − −
−
й щ+ − + −л ы=
+ − −
,
2
2
2 ,
4
m
E
πδ =
( ) ( )
( )( ) ( )
max 2 2 2
1
, ,
1 1
m
z g
c z c
z z g z δ
+
=
− − − +
( ) ( ) ( )
( ) ( )2 2 2
1 1 1 .
21 1
m m m
m
zc z K c z c zg
z z c
+ + −й щ −л ы= −
+ − −
The acceptance factor as a function of pion squared
invariant mass is shown on Fig. 1 for 10 ,20o o
mθ = .
Fig. 1. Acceptance factor defined by Eq. (8) for
different mc
3. RADIATIVE CORRECTIONS
If events with e e π π+ − + − final state are rejected,
only photonic RC have to be taken into account. These
corrections include contributions due to virtual and real
soft and hard photon emission. The soft and virtual
corrections are the same for non-cut and reduced pion
phase
( )2 2
2 2 ,
24
S V
S VF
qd C
dq E
σσ α
π
+
+ж ц= з ч
и ш
( )2 2 , ,
S V S V
R F
m
d d A z c
dq dq
σ σ+ +
=
( ) ( ) ( )0 0, , ,S V
sC P z L D L L z N zρ+ = + + .
All logarithmic strengthen contributions in
expression for S VC + are concentrated in first two terms
[4]. The third term is responsible for non-logarithmic
contribution [8].
As concerns contribution into RC due to additional
hard photon emission, we divide it by three parts. The
first one is responsible for radiation of additional photon
with the energy 2ω along the positron beam direction
(provided that collinear photon with the energy 1ω is
emitted along the electron beam direction).
( ) ( ) ( )
2 2
'1
0 02 2 , 2 1 ln ,
2 24
H
F
qd P z L L
dq E
σσ α η
π
ж ц ж ц= −з ч з ч∆и ш и ш
31
( )1 1
2 2 , .
H H
R F
m
d d A z c
dq dq
σ σ
= (10)
The second part of contribution into RC caused by
additional hard photon emission is responsible for
radiation of two hard collinear photons (every with the
energy more than E∆ ) by the electron, provided that
both belongs to narrow cone with the opening angle 02θ
along the electron beam direction.
( )2 2
2
2 2 ,
24
H
HF
qd C
dq E
σσ α
π
ж ц= з ч
и ш
( )2 2
2 2 , ,
H H
R F
m
d d A z c
dq dq
σ σ
=
( ) ( ) ( )2
1 0 2 0 3, , , .HC B z L B z L B z= ∆ + ∆ + ∆ (11)
Functions ( )1 ,B z ∆ , ( )2 ,B z ∆ and ( )3 ,B z ∆ were
calculated in [8,9].
The third, most non-trivial for calculation, part of
contribution into RC caused by two hard photon
emission is connected with events when photon with the
energy 1ω is collinear and the other one (with the
energy 2ω ) covers angles between '
0π θ− and 0 .θ The
respective contribution into RC destroys the acceptance
factor as given by Eq. (8).
To use QRE approach for description of collinear
photon it is necessary to take into consideration the
restrictions for event selection and the inequalities
'
0 2 0 ,c c c− < < 1 1 ,E Eω∆ < < Ω − ∆ ''
0 0cosc θ= (12)
for possible angles of the non-collinear photon and
energies of the collinear one.
Fig. 2. The integration region with respect to 1ω and Ω
as given by inequalities (3,4,12)
From these restrictions we can determine the
integration region for 1ω and Ω , see Fig. 2. Here
( ) ( )0
min
1
1 1 ,
2
c
E z
∆ −ж ц
Ω = − +з ч
и ш
( ) ( )1 1 ,E z∆Ω = − + ∆ ( )max 1 1 ,
2
E z ηж цΩ = − +з ч
и ш
( ) ( ) ( )01 1
1 1 ,
8c
c z
E z
− −ж ц
Ω = − +з ч
и ш
(13)
2
min
0
2 , 4 ,z
z
E K E
K c
ω Ω= = Ω − Ω
Ω −
r
r
'
0
2
14
1 1 1 ,
2 2
z cE
ω ±
й щж ц−ΩΩ к ъ= ± − +з чΩк ъи шл ы
( )2
0
8
1 1 .
2 1
zE
c
ω ±
й щΩΩ= ± −к ъ
Ω −к ъл ы
( )1z E zΩ = Ω − −
To executed the integration with respect to 1ω and
Ω over region (13) we can write
( ) ( )
2 2
3
0 1 0 2 32 2 2 , ,
24
H
F
qd P z L G L G G
dq E
σσ α
π
ж ц= + +й щз ч л ыи ш
( ) ( )'2
0 02 20
1
1 111 ln ln ln ln ,
2 2 2 2 4
c ccG π η ξ
− −−
= + − −
∆
( ) ( )0
,
1 1c z
ηξ =
− −
( ) ( ) ( ) ( ) ( )2 2
1 1
1 ln 2 1 1 ln ln[z
G z z z
ξ ξ
ξ
ξ
+ +й щ
= − − + + +к ъ
л ы
( ) ( ) ( )2 2 2 2
1 1 ,]zLi z Li Li Li z
z
ξ ξ−ж ц+ − + − − − − −з ч
и ш
( ) ( )
2
2
3 21 ln 2
3
G z Liπ ξ ξ
ж ц
= − − − + − +з ч
и ш
( ) ( )2 2 2
12 1 .zz Li z Li z Li
z
ξ −й щж ц− − − − −з чк ъи шл ы
(14)
Unfortunately, the calculations in the case of reduced
pion phase space cannot be performed analytically.
Nevertheless, the dependence on unphysical auxiliary
parameters ∆ and '
0θ , which have to vanish in final
result for total RC, can be extracted.
To extract ∆ -dependence it is enough investigate
limit 2 0.ω → The cross section we rewrite as the sum
of its hard and soft parts
3 3 3
2 2 2 ,
h sH HH
R R Rd d d
dq dq dq
σ σ σ
= + 3 3 3
2 2 2 ,
h sH HH
R R Rd d d
dq dq dq
σ σ σ
= −
The hard part of the cross section is not singular at
2 0ω → , whereas just integration of the soft one over
the region (47) extracts all ∆ − dependence.
( ) ( ) ( )
2 2
3
0 12 2 , , ,
24
sH
R
m
qd P z L G A z c
dq E
σσ α
π
ж ц= з ч
и ш
(15)
This soft part absorbs also all dependence on angular
auxiliary parameter '
0θ . That is why the hard part of the
cross section depends on physical parameters only and
can be computed numerically.
4. TOTAL RADIATIVE CORRECTIONS
The total RC to the Born cross section in the case of
non-cut and reduced pion phase space is represented by
1 , 2 , 3 ,, ,
2 2 2 2 2 ,
H H HRC S V
F R F R F RF R F R d d dd d
dq dq dq dq dq
σ σ σσ σ +
= + + + (16)
Since both auxiliary parameters, infrared ∆ and
collinear angular '
0θ , are canceled in Eq. (16), the total
RC depends only on physical parameters and can be
written in the case of non-cut phase space as
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.
Серия: Ядерно-физические исследования (36), с. 3-6.
32
( ) ( )
2
02 2 , ,
24
RC
RCF
F
qd P z L
dq E
σσ α δ
π
= (17)
( )
0 0 1 2
0
,
2 ,
RC
F
F L F F
P z L
αδ
π
+ +
=
( ) ( )2
0 0 2 0
2
2
2
00
1 3, [ 2ln
2 2 2
4 3 5 9ln ln 2 ln 2ln 3ln ],
2 2 3 2
sF L P z P z L L
z
z
θ
η
η η πξ
θθ
ж ц= + + +з ч
и ш
ж ц
+ − − + + −з ч
и ш
( )
( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
22
1
2
2 2
2 2
2 13 8 ln 1
2 1 1
4 11 1 ln ln 1 ln
1 2
1 11 2 1 ln
1 3
zz zF z
z z
z z z z z
z
zz Li z z
z
ξ
ξ ξπ
ξ
+− += − − +
− −
й щ+ + + + + +к ъ−л ы
+ +ж ц+ − + − +з ч− и ш
( ) ( ) ( ) ( )2 2 2 2
11 1 ,zz Li z Li Li Li z
z
ξ ξ−й щж ц+ − + − − − − −з чк ъи шл ы
( ) ( ) ( )2
2
3 4 41 ln ln 1
3 1 1
z zF z z
z z
ξ += − − + − +
− −
( )
( )
2
2
2
3 18 72 ln ln 2 ln 1
3 1
z zz z z z
z
ξ
й щ− +− + + − +к ъ
−к ъл ы
( )
2 3 4 2
2
3
3 12 30 36 7 14 5ln 4
6 3 16 1
z z z z zz
zz
π− + − + ж ц+ + −з ч−и ш−
( ) ( )2 2
54 6 1 1
1 3
zLi z z Li z
z
ж ц ж ц+ − + + − − +з ч з ч−и ш и ш
( ) ( )2 2 2
12 2 ,zLi z Li z Li J
z
ξ ξ −й щж ц− − − + − +з чк ъи шл ы
here ( )2P zθ is θ − term of second order electron
structure function [10].
0.0 0.2 0.4 0.6 0.8 1.0
-0.18
-0.16
-0.14
-0.12
-0.10
-0.08
δ
F
RC
z
Fig. 3. The full first order radiative correction to the
Born cross section (7) for the case of non-cut pion
phase space, that is defined by Eq. (17)
So the IES Born cross section and RC to it have a
factorized form: the low energy pion pair production
cross-section ( )2qσ , which is the object of precise
measurement, enters into right side of Eq. (17) as
factorized multiplier. The other multiplier has pure
electrodynamical origin and is not connected with strong
interaction of pions.
The z − dependence of RC
Fδ , that is the total
radiative correction to the Born cross section (7), is
shown on Fig. 3. Note that the contribution of non-
logarithmic terms in RC
Fδ parametrically equals to
( )0/ 2 Lα π that is of the order 410− . This order is the
same as relative contribution of terms proportional to
2 2/ 4P EΦ
r
and 2
0 / 6θ in the Born cross section (see
Eq. (6)). That is why the exact account of the Born IES
cross section requires with necessity the calculation of
RC with inclusion of non-logarithmic contribution.
By analogy with (17) we can write the total RC in
the case of reduced pion phase space in the following
form
( ) ( ) ( )
2
3
02 2 2, , ,
24
hHRC
RC RR
m R
q dd P z L A z c
dq E dq
σ σσ α δ
π
= + (18)
where
( )
0 0 1 2
0
,
2 ,
RC R R
R
F L F F
P z L
αδ
π
+ +
=
1 1 2 2 2 3, .R F R FF F G F F G= − = −
Because the multiplier ( )2 2/ 4q Eσ enters into last
term on the right side of Eq. (18) too, the total RC in
this case has as well factorized form.
5. PAIR PRODUCTION CONTRIBUTION
INTO IES CROSS SECTION
If e e π π+ − + − final state is not rejected from analysis,
there is an additional contribution caused by initial-state
hard e e+ − pair production [4]. The main part of this
contribution arises due to collinear kinematics. In
framework of NLO approximation keeping only
logarithmically strengthen terms, the corresponding
cross section can be written as
( ) ( ) ( ) ( )
2 2
2
1 0 2 02 2 ,
24
e e c
F
qd P z L P z L
dq E
σσ α
π
+ −
ж ц й щ= +з ч л ыи ш
( ) ( )
( )2 2 , ,
e e c e e c
R F
m
d d A z c
dq dq
σ σ
+ − + −
= (19)
where functions ( )1,2P z given in [11].
Within NLO accuracy one has to compute also the
contribution caused by semicollinear kinematics of pair
production when created electron belong to narrow cone
along the electron beam direction and created positron
does not. In the case of non-cut pion phase space the
respective differential cross section [12] we can
integrate over region on Fig. 2 with substitution
/ E xω → , here x is the energy fraction of created
collinear electron.
( ) ( ) ( )
2 2
02 2 , ,
24
e e s
F
qd L S z
dq E
σσ α ξ
π
+ −
ж ц= з ч
и ш
(20)
( ) ( ), 1S z zξ = − Ч
33
( )
( )
( )2 2
2
2 112 1ln 1 ln
1 3 1
z zz z
zz
ξξ ξ
ξ ξξ
м ьй щ+ +− +п пк ъ− + + +н э+ +к ъп пл ыо ю
( ) ( )222 1 ln 1 ln
3
[z z z z
z
ξж ц+ − − + +з ч
и ш
( ) ( ) ( )2 2 2 2
1 1 .]zLi z Li Li z Li
z
ξ ξ−ж ц− + − − − − −з ч
и ш
So, the contribution of the pair production into IES
cross section for the case of non-cut pion phase space is
( ) ( )
2
02 2 , ,
24
e e
e eF
F
qd P z L
dq E
σσ α δ
π
+ −
+ −ж ц= з ч
и ш
( ) ( ) ( )( )
( )
2
1 0 2 0
0
,
.
2 ,
e e
F
P z L P z S z L
P z L
ξαδ
π
+ −
+ +
= (21)
Function e e
Fδ
+ −
is shown in Fig. 4.
0.0 0.2 0.4 0.6 0.8 1 .0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
δ F
e
+
e
-
z
Fig. 4. The radiative correction to the IES Born cross
section caused by e e+ − -pair production
The total contribution of e e+ − − pair production into
IES cross section for the case of reduced pion phase
spacehas not any singularity and can be calculated
numerically.
As DAPhNE conditions allow select and detect also
the same events when collinear particles are emitted by
the initial positron, all derived cross sections have to be
doubled.
CONCLUSION
We compute the corresponding ISR Born cross
section and radiative corrections to it in the framework
of QRE approximation. The cases of non-cut and
reduced pion phase space are considered. In the first one
the photonic contribution into RC is calculated
analytically with NNLO accuracy and the contribution
caused by e e+ − -pair production with NLO one.
The photonic RC is large and negative in wide
diapason of the pion invariant mass. The RC caused by
pair production is positive and small as compared with
absolute value of photonic one. Only in the region near
the threshold (small z ), where cross section is very
small, it has approximately the same value. So, we
conclude that RC due to pair production must be taken
into account to guarantee one percent accuracy.
In the case of reduced pion phase space we derived
the analytical form of acceptance factor for the Born
cross section and the part of RC which includes
contributions due to virtual and real collinear photons
and e e+ − − pair. As concerns the contribution into IES
cross section caused by semicollinear kinematics for
double photon emission and pair production, the
respective acceptance factor cannot be calculated
analytically. In this case formulae suitable for numerical
calculation are derived.
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34
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35
M.I. Konchatnij, N.P. Merenkov, O.N. Shekhovtsova
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
PACS: 29.27.Hj, 29.90. +r
1. IES SELECTION RULES
2. BORN APPROXIMATION
3. RADIATIVE CORRECTIONS
4. TOTAL RADIATIVE CORRECTIONS
5. PAIR PRODUCTION CONTRIBUTION
INTO IES CROSS SECTION
CONCLUSION
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-79417 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-30T10:00:56Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Konchatnij, M.I. Merenkov, N.P. Shekhovtsova, O.N. 2015-04-01T19:09:27Z 2015-04-01T19:09:27Z 2001 The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method / M.I. Konchatnij, N.P. Merenkov, O.N. Shekhovtsova // Вопросы атомной науки и техники. — 2001. — № 6. — С. 30-34. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 29.27.Hj, 29.90. +r https://nasplib.isofts.kiev.ua/handle/123456789/79417 The possibility of high precision measurement of the total hadronic cross-section in electron-positron annihilation process by analysis of the initial-state radiative events is discussed. Different experimental setups are discussed. The main attention is dedicated to measurement of hadronic cross-section at DAPhNE, where the final hadronic state π⁺π⁻ dominates due to radiative return on ρ-resonance. Radiative corrections at one percent level accuracy are calculated taking into account real experimental constraints on event selection. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Quantum electrodynamics The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method Сканирование адронного сечения в e⁺e⁻-аннигиляции методом радиационного возврата Article published earlier |
| spellingShingle | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method Konchatnij, M.I. Merenkov, N.P. Shekhovtsova, O.N. Quantum electrodynamics |
| title | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method |
| title_alt | Сканирование адронного сечения в e⁺e⁻-аннигиляции методом радиационного возврата |
| title_full | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method |
| title_fullStr | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method |
| title_full_unstemmed | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method |
| title_short | The scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method |
| title_sort | scanning of hadronic cross-section in e⁺e⁻-annihilation by radiative return method |
| topic | Quantum electrodynamics |
| topic_facet | Quantum electrodynamics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79417 |
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