Classification of p¯+ p induced reactions
Annihilation cross sections of antiproton-proton into hadronic channels are studied and related experimental data are compiled. These channels constitute a high source of background to the annihilation reactions p¯+ p → l⁺ + l⁻, p¯+p → l⁺ + l⁻ + π⁰, used for the measurement of proton form factors in...
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CNRS/IN2P3, IPNO, UMR 8608, Univ. Paris-Sud
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irk-123456789-1070012016-10-11T03:02:26Z Classification of p¯+ p induced reactions Dbeyssi, A. Tomasi-Gustafsson, E. Section B. QED Processes at High Energies Annihilation cross sections of antiproton-proton into hadronic channels are studied and related experimental data are compiled. These channels constitute a high source of background to the annihilation reactions p¯+ p → l⁺ + l⁻, p¯+p → l⁺ + l⁻ + π⁰, used for the measurement of proton form factors in Time-like region. Pion multiplicity in final state is also analysed, since the 2 neutral or charged pion production is expected to be an important issue in the detection of the leptons pair. Изучены сечения аннигиляции протонов с антипротонами в адронные каналы и выполнена компиляция соответствующих экспериментальных данных. Эти каналы представляют источник большого фона для реакций аннигиляции, p¯+ p → l⁺ + l⁻, p¯+p → l⁺ + l⁻ + π⁰ которые используются для измерения протонных формфакторов во времениподобной области. Проанализирована также множественность пионов в конечном состоянии, так как ожидается, что образование двух нейтральных или заряженных пионов будет серьезной проблемой при детектировании лептонной пары. Вивчено перерізи анігіляції протонів та антипротонів у адронні канали і виконано компіляцію відповіднних експериментальних даних. Ці канали являють собою джерело великого фону для реакцій анігіляції, p¯+ p → l⁺ + l⁻, p¯+p → l⁺ + l⁻ + π⁰ які використовуються для вимірювання протонних формфакторів у часоподібній області. Проаналізовано також множинність піонів у кінцевому стані, тому що очікується, що утворення двох нейтральних або зарядженних піонів буде серйозною проблемою при детектуванні лептонної пари. 2012 Article Classification of p¯+ p induced reactions / A. Dbeyssi, E. Tomasi-Gustafsson // Вопросы атомной науки и техники. — 2012. — № 1. — С. 84-87. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 03.65.Pm, 03.65.Ge, 61.80.Mk http://dspace.nbuv.gov.ua/handle/123456789/107001 en Вопросы атомной науки и техники CNRS/IN2P3, IPNO, UMR 8608, Univ. Paris-Sud |
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Section B. QED Processes at High Energies Section B. QED Processes at High Energies |
| spellingShingle |
Section B. QED Processes at High Energies Section B. QED Processes at High Energies Dbeyssi, A. Tomasi-Gustafsson, E. Classification of p¯+ p induced reactions Вопросы атомной науки и техники |
| description |
Annihilation cross sections of antiproton-proton into hadronic channels are studied and related experimental data are compiled. These channels constitute a high source of background to the annihilation reactions p¯+ p → l⁺ + l⁻, p¯+p → l⁺ + l⁻ + π⁰, used for the measurement of proton form factors in Time-like region. Pion multiplicity in final state is also analysed, since the 2 neutral or charged pion production is expected to be an important issue in the detection of the leptons pair. |
| format |
Article |
| author |
Dbeyssi, A. Tomasi-Gustafsson, E. |
| author_facet |
Dbeyssi, A. Tomasi-Gustafsson, E. |
| author_sort |
Dbeyssi, A. |
| title |
Classification of p¯+ p induced reactions |
| title_short |
Classification of p¯+ p induced reactions |
| title_full |
Classification of p¯+ p induced reactions |
| title_fullStr |
Classification of p¯+ p induced reactions |
| title_full_unstemmed |
Classification of p¯+ p induced reactions |
| title_sort |
classification of p¯+ p induced reactions |
| publisher |
CNRS/IN2P3, IPNO, UMR 8608, Univ. Paris-Sud |
| publishDate |
2012 |
| topic_facet |
Section B. QED Processes at High Energies |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/107001 |
| citation_txt |
Classification of p¯+ p induced reactions / A. Dbeyssi, E. Tomasi-Gustafsson // Вопросы атомной науки и техники. — 2012. — № 1. — С. 84-87. — Бібліогр.: 5 назв. — англ. |
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Вопросы атомной науки и техники |
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| fulltext |
CLASSIFICATION OF p̄ + p INDUCED REACTIONS
A. Dbeyssi 1∗and Egle Tomasi-Gustafsson 1,2
1CNRS/IN2P3, IPNO, UMR 8608, Univ. Paris-Sud, 91405 Orsay, France
2CEA,IRFU,SPhN, Saclay, 91191 Gif-sur-Yvette Cedex, France
(Received October 18, 2011)
Annihilation cross sections of antiproton-proton into hadronic channels are studied and related experimental data are
compiled. These channels constitute a high source of background to the annihilation reactions p̄+p → �++�−, p̄+p →
�+ + �− + π0, used for the measurement of proton form factors in Time-like region. Pion multiplicity in final state is
also analysed, since the 2 neutral or charged pion production is expected to be an important issue in the detection
of the leptons pair.
PACS: 03.65.Pm, 03.65.Ge, 61.80.Mk
1. INTRODUCTION
The PANDA experiment will be one of the key experi-
ments at the Facility for Antiproton and Ion Research
(FAIR) which is currently being built on the area of
the GSI Helmholtzzentrum für Schwerionenforschung
in Darmstadt. One of the aims of this experiment is
to access the electromagnetic structure of the proton
by the annihilation reaction p̄ + p into leptons.
The reactions involving hadrons in final state are
orders of magnitude larger than the reaction of inter-
est and constitute the source of physical background.
They are also interesting by themselves as they con-
tain information on QCD subprocesses.
We illustrate the total cross sections of the known
reactions induced by p̄ + p, involving hadrons in final
state, for which experimental data (even partial) ex-
ist and are at [mb] level. We give the parametrization
for the total, elastic and inelastic cross sections and
we study the pions multiplicity in the final state.
This analysis may be used for evaluating count-
ing rates and as a base for selection methods,
at trigger level, too, of the reaction of interest
(p̄+ p → �+ + �−, p̄+ p → �+ + �− +π0) which cross
section is of the order of [nb].
2. TOTAL AND ELASTIC CROSS
SECTION
The world data for the total and elastic cross sec-
tions for the p̄ + p induced reactions are illustrated
in Fig. 1 as function of the laboratory antiproton mo-
mentum pp̄ expressed in [GeV/c]. The references of
the experimental measurements can be found in [1].
The lines are the results from a new parametrization
which describes the global structure of pp̄ total cross
sections and includes a low energy extension of the
Regge theory based on three-body forces in relativis-
tic quantum theory [2].
From the Fig. 1 we see that σel
p̄p/σtot
p̄p � 1/3, in
agreement with the quasi-eikonal approach of the
reggeon field theory [3].
This fit which reproduces the experimental data,
allows us to calculate the contribution for the inelas-
tic channels. The difference between the total and
elastic cross section parametrizations (green line) rep-
resents the contribution of inelastic events. It is of the
order of 40 mb for pp̄ >10 GeV/c.
[GeV/c]
p
p
-110 1 10
210
3
10 410
[m
b
]
�
1
10
210
Pbar+P
Elastic
Inelastic
Total
Fig. 1. Total (black) and elastic (red) cross section
for the p̄ + p reaction, as function of the antiproton
beam momentum. The contribution of inelastic
events is also shown (green line)
∗Boursier du CNRS libanais/LNCSR Scholar, E-mail address: dbeyssi@ipno.in2p3.fr
84 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1.
Series: Nuclear Physics Investigations (57), p. 84-87.
3. INDIVIDUAL CONTRIBUTION OF
(SOME) INELASTIC CHANNELS
The reactions of interest for form factor measure-
ments in the Time-like region involve two leptons
in final state and no hadrons (p̄ + p → �+ + �−),
or two leptons and a pion if one wants to investi-
gate the near threshold and the unphysical kinemat-
ical regions (p̄ + p → �+ + �− + π0). Experimen-
tal data on cross sections and angular distributions
concerning 230 final channels involving hadrons have
been classified [1]. Based on this compilation, various
cross sections are shown for selected processes in the
[0.01... 10 mb] range, in Figs. 2 and 3.
[GeV/c]
p
p1 10
[m
b
]
σ
-310
-210
-110
1
10
0π-π2+π2
0π2-π2+π2
-π2+π2
0π-π+π
0π3-π2+π2
ω-π+π
0ρ-π+π
0π-π3+π3
-π3+π3
0π5-π2+π2
0π4-π2+π2
-π+π
-k+k
0π0π
Fig. 2. Cross sections for different inelastic chan-
nels in the p̄ + p reaction as a function of pp̄
[GeV/c]
p
p
1 10 210
[m
b
]
σ
-310
-210
-110
1
10
nn
-π+πpp
0πpp
0π-π+πpp
+πnp
-πnp
-π+πn2p
-π2+πp2p
-π3+π3pp
-k+kpp
0π-π2+πp2p
-π2+πnp
-π4+π4pp
Fig. 3. Cross sections for different inelastic chan-
nels (pions with nucleons) in the p̄ + p reaction as a
function of pp̄
Let us focus our interest to the production of pi-
ons alone and pions accompanied by nucleons. Fig. 2
shows that the most probable reaction involving pi-
ons, corresponds to more than three pions in the final
state. We parametrize the cross section for the reac-
tions given in Fig. 2 as:
σ = ae−bpp̄ +
c
pp̄
, (1)
where pp̄ and σ are expressed in [GeV/c] and [mb]
respectively. The coefficients a, b and c of the para-
metrization (1) are given in the Table 1 for some re-
actions.
Table 1. Coefficients for the parametrization,
Eq. (1), of selected inelastic channel cross sections
Final state a [mb] b [GeV/c]−1 c [mbGeV/c]
π0π0 3.88 4.04 0.012
π+π−π0 6.1 1.99 1.41
2π+2π− 7.05 0.727 0.24
3π+3π− -10.58 1.949 2.654
2π+2π−π0 26.14 0.599 0.26
Table 2. Threshold kinetic, total energies and
momentum for p̄ + p annihilation into the final
states illustrated in Fig. 3
Final state Tthr[GeV] Ep̄[GeV] pp̄[GeV/c]
n̄n 0.005 0.943447 0.0986851
p̄pπ+π− 0.599 1.53808 1.21874
p̄pπ0 0.279 1.21793 0.776536
p̄pπ+π−π0 0.919 1.85789 1.60356
p̄p2π+2π− 1.283 2.22092 2.013
p̄p3π+3π− 2.049 2.98682 2.83562
p̄p2π+2π−π0 1.643 2.5809 2.40431
p̄p4π+4π− 2.897 3.83576 3.71923
In Fig. 3 we illustrate the cross sections for the
production of proton-antiprotons (neutrons) with a
different number of charged and neutral pions (the
other reactions with a larger number of pions are less
probable). We see that the cross sections increase
from threshold with the incident energy until a cer-
tain value of pp̄, except the charge exchange reaction
(p̄+ p → n̄+n) which has a sizeable cross section for
pp̄ < 3 GeV.
Over the corresponding threshold, the production
of any number of pions accompanied by a proton-
antiproton pair is more (less) probable for a large
(small) incident energy, than when they are produced
alone. Consequently, the most probable reactions are
the (4,5) pions production, or the charge exchange
reaction, but when the incident momentum increases
it is necessary to evaluate, either the production of a
larger number of pions (6,7, see following paragraph),
or of a lower number (2,3) but accompanied by a
proton-antiproton pair.
85
The difference between the behavior of the cross
sections can be explained at small incident energy re-
gion by the effect of threshold. The threshold is de-
fined by the condition that the emitted particles are
at rest, which corresponds to zero three-momentum.
We have calculated the threshold kinetic energy Tthr
from the equality of the invariant s in center of
mass and laboratory system slab = scm with slab =
(pp̄ + pp)2 = (2M)2 + 2MT and scm = (
∑
mf )2,
where
∑
mf is the sum of the masses of the final
particles:
Tthr =
(
∑
mf )2 − 4M2
2M
. (2)
The pion final states can be obtained by the proton-
antiproton annihilation at rest, but their production
with nucleon requires a certain threshold, which is
different from zero (Table 2). In the considered kine-
matical region, we see that the most important reac-
tions are those which have smaller threshold energy.
4. PROBABILITY OF n PION
PRODUCTION
Two (or three) pion production is the reaction that
constitutes the background which is most difficult to
eliminate for the reaction of interest : p̄+p → �++�−
(p̄ + p → �+ + �− + π0) [4]. However, the production
of a larger number of pions is more probable, which
might be a problem at the trigger level. A detailed
description and relative references can be found in
Ref. [5].
In the statistical bootstrap model [5], the average
pion multiplicity from p̄+p annihilation depends lin-
early on
√
s. The dependence on pp̄ [GeV/c] can be
parametrized as
〈nπ〉 = 2.6 + 1.3
(
1.76 + 1.88
√
0.88 + p2
p̄
)0.5
. (3)
A similar parametrization which applies to the range
s1/2 ≤ 30 GeV can be found in [5]:
〈nπ〉 = 2.65 + 1.78 log
(
1.76 + 1.88
√
0.88 + p2
p̄
)
.
(4)
These two parametrization reproduce the experimen-
tal data where we can see that the average pion mul-
tiplicity for e+e− and p̄p at the same CM energy is
essentially the same, for energies above the threshold.
The emission probability as a function of the pion
multiplicity can be parametrized as:
P (nπ) =
1√
2πD
exp
−(nπ − 〈nπ〉)2
2D2
,
D2
〈nπ〉 = 0.174
(
1.76 + 1.88
√
0.88 + p2
p̄
)0.2
. (5)
where 〈nπ〉 is the pion multiplicity and P (nπ) is the
probability for the n-pions emission, obtained from
Eq. (3), which is consistent with the existing experi-
mental values. The standard deviation D2 increases
with 〈nπ〉 and with pp̄. From numerical application
of the previous equations, it is seen that the contribu-
tion of six and seven pions (any charge state) in the
final state is larger than the five pion contribution for
pp̄ > 5 GeV/c. At lower momenta, five pion emission
has the largest contribution.
5. CONCLUSIONS
We have reported the world data and recalled a re-
cent physical parametrization for the total and elastic
p+ p̄ cross section. The elastic contribution amounts
to 1/3 of the total contribution.
We have classified the cross section data corre-
sponding to a number of interesting reactions with
cross section in the [mb] region, and illustrated as a
function of the incident momentum pp̄. These reac-
tions are more probable by orders of magnitude than
the ones which provide access to the electromagnetic
form factors of the proton.
We have shown that the pion multiplicity in the
final state of the p̄+p annihilation depends on the in-
cident energy. The annihilation at rest is dominated
by five pion emission. When the energy increases the
probability for a larger number of pions increases.
We have given useful parametrizations for selected
distributions using simple analytical formulas.
References
1. A. Dbeyssi, E. Tomasi-Gustafsson. Classifica-
tion of p̄ + p induced reactions // Rap-
port de recherche HAL in2p3-00600348, 2011,
http://hal.in2p3.fr/in2p3-00600348/fr/, 11 p.
2. A.A. Arkhipov. On global structure of hadronic
total cross-sections // arXiv : 9911533 [hep-ph].
2001, 10 p.
3. A.B. Kaidalov and K. A. Ter-Martirosyan. Mul-
tihadron production at high energies in the model
of quark gluon strings // Sov. J. Nucl. Phys.
1984, v. 40, p. 135-140.
4. M. Sudol et al. Feasibility studies of the time-
like proton electromagnetic form factor measure-
ments with PANDA at FAIR // Eur. Phys. J.
2010, v. A44, p. 373-384;
5. C.B. Dover, T. Gutsche, M. Maruyama, and
A. Faessler. The Physics of nucleon – anti-
nucleon annihilation // Prog. Part. Nucl. Phys.
1992, v. 29, p. 87-174.
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