arXiv:1203.2549v1 [nucl-ex] 12 Mar 2012
Inclusive dielectron production in proton-proton collisions at 2.2 GeV beam energy
G. Agakishiev5, H. Alvarez-Pol15, A. Balanda2, R. Bassini10, M. B¨ ohmer8, H. Bokemeyer3, J. L. Boyard13,
P. Cabanelas15, S. Chernenko5, T. Christ8, M. Destefanis9, F. Dohrmann4, A. Dybczak2, T. Eberl8, L. Fabbietti7,
O. Fateev5, P. Finocchiaro1, J. Friese8, I. Fr¨ ohlich6, T. Galatyuk6,b, J. A. Garz´ on15, R. Gernh¨ auser8, C. Gilardi9,
M. Golubeva11, D. Gonz´ alez-D´ ıazc, F. Guber11, M. Gumberidze13,∗, T. Hennino13, R. Holzmann3,
A. Ierusalimov5, I. Iori10,e, A. Ivashkin11, M. Jurkovic8, B. K¨ ampfer4,d, K. Kanaki4, T. Karavicheva11, I. Koenig3,
W. Koenig3, B. W. Kolb3, R. Kotte4, A. Kozuch2,f, F. Krizek14, W. K¨ uhn9, A. Kugler14, A. Kurepin11,
S. Lang3, K. Lapidus7, T. Liu13, L. Maier8, J. Markert6, V. Metag9, B. Michalska2, E. Morini` ere13,
J. Mousa12, C. M¨ unch3, C. M¨ untz6, L. Naumann4, J. Otwinowski2, Y. C. Pachmayer6, V. Pechenov3,
O. Pechenova6,T. Perez Cavalcanti9, J. Pietraszko6, V. Posp´ ısil14, W. Przygoda2, B. Ramstein13,
A. Reshetin11, M. Roy-Stephan13, A. Rustamov3, A. Sadovsky11, B. Sailer8, P. Salabura2, M. S´ anchez15,
A. Schmaha, E. Schwab3, Yu.G. Sobolev14, S. Spatarog, B. Spruck9, H. Str¨ obele6, J. Stroth6,3,
C. Sturm3, A. Tarantola6, K. Teilab6, P. Tlusty14, A. Toia9, M. Traxler3, R. Trebacz2, H. Tsertos12,
V. Wagner14, M. Wisniowski2, T. Wojcik2, J. W¨ ustenfeld4, S. Yurevich3, Y. Zanevsky5, P. Zumbruch3
1Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali del Sud, 95125 Catania, Italy
2Smoluchowski Institute of Physics, Jagiellonian University of Cracow, 30-059 Krak´ ow, Poland
3GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany
4Institut f¨ ur Strahlenphysik, Helmholtzzentrum Dresden-Rossendorf, 01314 Dresden, Germany
5Joint Institute of Nuclear Research, 141980 Dubna, Russia
6Institut f¨ ur Kernphysik, Goethe-Universit¨ at, 60438 Frankfurt, Germany
7Excellence Cluster ’Origin and Structure of the Universe’ , 85748 Garching, Germany
8Physik Department E12, Technische Universit¨ at M¨ unchen, 85748 Garching, Germany
9II.Physikalisches Institut, Justus Liebig Universit¨ at Giessen, 35392 Giessen, Germany
10Istituto Nazionale di Fisica Nucleare, Sezione di Milano, 20133 Milano, Italy
11Institute for Nuclear Research, Russian Academy of Science, 117312 Moscow, Russia
12Department of Physics, University of Cyprus, 1678 Nicosia, Cyprus
13Institut de Physique Nucl´ eaire (UMR 8608), CNRS/IN2P3 - Universit´ e Paris Sud, F-91406 Orsay Cedex, France
14Nuclear Physics Institute, Academy of Sciences of Czech Republic, 25068 Rez, Czech Republic
15Departamento de F´ ısica de Part´ ıculas, Univ. de Santiago de Compostela, 15706 Santiago de Compostela, Spain
∗Corresponding author. Email: email@example.com
aalso at Lawrence Berkeley National Laboratory, Berkeley, USA
balso at ExtreMe Matter Institute EMMI, 64291 Darmstadt, Germany
calso at Technische Universit¨ at Darmstadt, Darmstadt, Germany
dalso at Technische Universit¨ at Dresden, 01062 Dresden, Germany
ealso at Dipartimento di Fisica, Universit` a di Milano, 20133 Milano, Italy
falso at Panstwowa Wyzsza Szkola Zawodowa , 33-300 Nowy Sacz, Poland
galso at Dipartimento di Fisica Generale and INFN, Universit` a di Torino, 10125 Torino, Italy
(Dated: March 13, 2012)
Data on inclusive dielectron production are presented for the reaction p+p at 2.2 GeV measured
with the High Acceptance DiElectron Spectrometer (HADES). Our results supplement data obtained
earlier in this bombarding energy regime by DLS and HADES. The comparison with the 2.09 GeV
DLS data is discussed. The reconstructed e+e−distributions are confronted with simulated pair
cocktails, revealing an excess yield at invariant masses around 0.5 GeV/c2. Inclusive cross sections
of neutral pion and eta production are obtained.
PACS numbers: 25.40Ep, 13.40.Hq
The spectroscopy of e+e−pairs offers a new approach
to the study of baryon resonances excited in nucleon-
nucleon reactions. Dilepton (that is e+e−or µ+µ−) ob-
servables provide indeed information on the electromag-
netic structure of the resonances and, in the context of
vector meson dominance, their coupling to the light vec-
tor mesons . Furthermore, dilepton spectroscopy al-
lows to study the properties of hadrons produced and
decayed in a strongly interacting medium. This is be-
cause leptons do not themselves interact strongly when
propagating through hadronic matter, that is, their kine-
matics remains basically undistorted. For that reason
they are used to probe medium modifications of hadrons
intensively searched for in photon and proton-induced
reactions on nuclei as well as in heavy-ion collisions
. Transport models are commonly employed to de-
scribe particle production and propagation through the
medium, in particular when dealing with the complex
dynamics of nucleus-nucleus reactions [3–5]. The proper
modeling of lepton pair production mechanisms requires
a solid understanding of the underlying elementary pro-
cesses, be it in terms of resonance excitations or in terms
of a string fragmentation picture .
The HADES experiment pursues a comprehensive pro-
gram of dielectron emission studies in N + N [7, 8], in
p+A , as well as in A+A collisions [10–12]. Inclusive
e+e−production in p+p and p+d reactions had formerly
been studied in the range of 1 - 5 GeV by the DLS exper-
iment at the Bevalac , and more recently by HADES
at 1.25 GeV  and 3.5 GeV . In particular, the com-
parison of the latter data sets with various model cal-
culations demonstrated a need for improved theoretical
descriptions. In this paper we supplement the available
body of experimental results with data obtained on in-
clusive e+e−production in the p+p → p+p+e++e−+X
reaction at 2.2 GeV. A direct comparison with DLS data
measured at 2.09 GeV  is presented. Furthermore,
through the comparison with a calculated e+e−cock-
tail, we extract the inclusive production cross sections
of π0and η mesons at 2.2 GeV. Our paper is organized
as follows: Section 2 describes the experiment and the
data analysis. In Sec. 3 e+e−pair spectra are presented
and confronted with results from DLS. In Sec. 4 the pair
spectra are compared to calculated dielectron cocktails.
In Sec. 5 we discuss inclusive meson production cross sec-
tions and, finally, in Sec. 6 we summarize our findings.
The six-sector High-Acceptance DiElectron Spectrom-
eter (HADES) operates at the GSI Helmholtzzentrum f¨ ur
Schwerionenforschung in Darmstadt taking beams from
the heavy-ion synchrotron SIS18. Technical aspects of
the detector are described in . Its main component
serving for electron and positron selection is a hadron-
blind Ring-Imaging Cherenkov detector (RICH). Further
particle identification power is provided by the time of
flight measured in a plastic scintillator wall (TOF), the
electromagnetic shower characteristics observed in a pre-
shower detector, and the energy-loss signals from the
scintillators of the TOF wall.
In the experiment discussed here  a proton beam
with a kinetic energy of Tp = 2.2 GeV (corresponding
to a c.m. energy√sNN = 2.765 GeV) and an intensity
of about 107particles per second impinged on a 5 cm
long liquid hydrogen cell with a total areal thickness of
0.35 g/cm2. The online event selection was done in two
steps: (1) a 1st-level trigger (LVL1) selected events with
an overall multiplicity of at least four charged hits in the
TOF wall with additional topological conditions (two op-
posite sectors hit, two hits at polar angles < 45◦), and
(2) a 2nd-level trigger (LVL2) required an electron or
positron candidate. This trigger scheme was in fact op-
timized for measuring exclusive e+e−production in the
p + p → p + p + η reaction with a subsequent η Dalitz
decay . Note that such a trigger condition still al-
lows to study, albeit with a bias, inclusive e+e−emis-
sion. Indeed, because of overall charge conservation in
the p + p reaction, the dielectron is always accompanied
by at least two more charged particles. The resulting
trigger bias has been studied in simulations as a function
of various pair observables, in particular pair mass and
pair transverse momentum, providing a correction as well
as an estimate of the resulting systematic error (of order
20%). For normalization purposes, p + p elastic scatter-
ing events were recorded concurrently with an additional
scaled-down (by a factor 32) LVL1 trigger condition re-
quiring only two charged hits in opposite HADES sec-
tors. Thus, in total 2.7×108LVL1 events were recorded,
4.1 × 107of which fulfilled the LVL2 condition.
Dielectrons (that is e+e−pairs) were reconstructed
following the procedures described in detail in [11, 14]:
(1) leptons were identified based on various detector ob-
servables, (2) an efficiency correction was applied, (3)
opposite-sign leptons were combined into pairs, (4) the
background of uncorrelated (and partially correlated)
pairs representing the combinatorial background (CB)
was subtracted using the same-event geometric mean of
like-sign pairs, (5) the correction for the LVL1 trigger
bias was applied, and finally (6) the resulting inclusive
e+e−distributions were normalized to the reconstructed
yield of elastically scattered protons into the HADES ge-
ometric acceptance (see  for details). As no dedicated
start detector was present in this experimental run, the
start time for the time-of-flight measurement was recon-
structed event-by-event from the most optimal fit of dif-
ferent event hypotheses to the global event data .
A. Invariant mass spectra
Figure 1 shows the differential e+e−cross section
dσ/dMeeobtained after correcting the reconstructed pair
yield for efficiency, combinatorial background, and trig-
ger bias. As explained above, the absolute normalization
was done using the known p + p elastic scattering cross
section with the help of the concurrently measured yield
of elastic events . The data are presented with anal-
ysis cuts on single-lepton momentum, pe > 0.1 GeV/c,
and on pair opening angle, θee > 9◦. The total num-
ber of e+e−signal pairs contributing to this spectrum is
around 19,000 from which 2,000 pairs are located above
the π0Dalitz region (Mee> 0.15 GeV/c2). To illustrate
the significance of the reconstructed dielectron signal, the
signal-over-CB ratio is also shown as an inset in Fig. 1.
Note that the kinematic cutoff corresponding to the beam
energy of 2.2 GeV is at a pair mass of 0.89 GeV/c2.
00 2000.2 4000.46000.68000.810001
dσ/dMee measured in the 2.2 GeV p + p reaction within the
HADES acceptance (including pe > 0.1 GeV/c and θee > 9◦
cuts). The data are efficiency corrected and CB subtracted;
the insert shows the signal-over-CB ratio (S/CB). Point-to-
point statistical and systematic errors are indicated by (black)
vertical bars and (red) horizontal ticks, respectively.
(Color online) Differential e+e−
The obtained cross section is combined in Fig. 2 with
inclusive data from other HADES p + p runs done at
1.25  and 3.5 GeV  bombarding energy, respectively.
While the 3.5 GeV data were recorded in the same detec-
tor acceptance as the present 2.2 GeV data, the 1.25 GeV
data were adjusted for differences in the magnetic field
strengths and analysis cuts used. This way the three data
sets are compared within the same instrumental accep-
tance, revealing the strong beam energy dependence of
dielectron production, particularly at large pair masses.
Note, however, that between the three beam energies
the average momentum of the involved single lepton dis-
tributions differs significantly, resulting in substantially
different fractions of accepted pairs, particularly for low
B.Comparison with DLS
As the former DLS experiment provided e+e−data for
the p+p reaction at 2.09 GeV , we can make a direct
comparison along the line already used to confront the
DLS and HADES C+C data obtained at 1A GeV [10, 17].
As the HADES geometrical acceptance is substantially
broader than the DLS one such a comparison can be done
by projecting the reconstructed HADES dielectron yields
d3N/dMeedP⊥dY through the DLS acceptance filter 
(here P⊥and Y are the e+e−pair transverse momentum
0 0.20.40.6 0.81
= 3.5 GeV
= 2.2 GeV
= 1.25 GeV
0 0.2 0.40.60.81
FIG. 2: (Color online) Systematics of e+e−differential pro-
duction cross sections dσ/dMee measured in p + p reactions
at 1.25 GeV (squares), 2.2 GeV (circles), and 3.5 GeV (trian-
gles), all obtained within the HADES acceptance, efficiency
corrected, and CB subtracted (including pe > 0.1 GeV/c and
θee > 9◦cuts). The 1.25 GeV data, taken from , are ad-
justed for the present, more restrictive detector acceptance
(i.e. stronger magnetic field and explicit lepton momentum
cut of 0.1 GeV/c); the 3.5 GeV data are taken from . Only
statistical error bars are shown.
and rapidity, respectively). In fact, as DLS applied to
their p + p data additional cleaning cuts [13, 18] – 0.1 <
Mee < 1.25 GeV/c2, P⊥ < 1.2 GeV/c, 0.5 < Y < 1.7,
and θe> 21.5◦– an extrapolation of the HADES yield to
rapidities above 1.9, as applied in , is not needed here.
The result of this filtering procedure is shown in Fig. 3(a)
for the pair mass distributions dσ/dMeeand in (b) for the
pair transverse momentum spectrum 1/(2πP⊥) dσ/dP⊥,
the latter one with the condition Mee> 0.15 GeV/c2.
It is apparent that, within statistical and systematic
uncertainties, the HADES and the DLS data are in good
agreement. This result suggests that our result, together
with the data obtained by the DLS energy scan ,
can be used to constrain the various models aimed at
describing dielectron production in few-GeV elementary
IV.COMPARISON WITH A SIMULATED
The experimental pair distributions are next compared
to a calculated e+e−cocktail. For this, p + p reactions
were simulated with the event generator Pluto [19, 20]
and filtered through the HADES acceptance. The sim-
HADES 2.2 GeV
DLS 2.09 GeV
> 0.15 GeV/c
FIG. 3: (Color online) Direct comparison within the DLS
acceptance (see text for details) of the e+e−cross sections
measured by HADES in p+p at 2.2 GeV (closed circles) and
by DLS at 2.09 GeV (open crosses, taken from ). The
pair mass distributions (a) and pair transverse-momentum
distributions (b) are confronted.
only; additional systematic errors (not shown) are 23% for
DLS  and 29% for HADES.
Error bars are statistical
ulation included the following e+e−pair sources: (1)
π0→ γe+e−, (2) η → γe+e−, (3) ∆(1232) → Ne+e−,
(4) ω → π0e+e−, (5) ω → e+e−, and (6) ρ0→ e+e−with
dielectron branching ratios of mesons taken from  and
that of the ∆(1232) as calculated in . At the present
bombarding energy the production of π0and η mesons
is known to proceed mostly via resonance excitation
(e.g. R = ∆(1232),N∗(1440),N∗(1520),N∗(1535), etc.)
and is dominated by one-meson and two-meson channels
[16, 22–24]. For ρ0and ω production we have, however,
assumed phase-space population in the pp → ppX reac-
tions (X = ρ0or ω) with no further attempt at a more
refined description of the high-mass region. Note that
some of the excited resonances R, mostly the ∆, con-
tribute also directly to the dielectron yield via their elec-
tromagnetic Dalitz decay R → Ne+e−. In our cocktail
calculation we have only taken into account the ∆0and
∆+contributions following the prescription from Ref. .
The production cross sections used in the simulation were
taken as follows:
1. Inclusive π0production – 14 mb (adding all ob-
served inelastic channels contributing to π0pro-
duction from Ref.  gives a lower limit of about
12 mb, whereas 14 mb are needed to fully exhaust
the measured Dalitz yield).
2. Inclusive η production – in the range of 0.26 -
0.35 mb; a lower limit of 0.14 mb is given by the
known exclusive η production [16, 26].
3. Vector meson production – 0.01 mb exclusive ω pro-
duction  and assuming likewise for the ρ0, but
no φ contribution.
4. Inclusive ∆0,+(1232) excitation – in the range 10 -
The extremes of the cross section range used for ∆ pro-
duction correspond to the following two scenarios: (I)
assumes that pion production is mediated completely by
single ∆ excitation only, that is σ∆ = 3/2σπ0 (from
isospin addition rules), resulting in the upper value of
21 mb; scenario (II) sums explicitly the ∆ contributions
from one-pion and two-pion production channels. In the
latter the one-pion part of 3.6 mb is taken from a res-
onance model fit to exclusive pion production data 
whereas the two-pion part of 6.4 mb is taken from the
effective Lagrangian model of two-pion production pre-
sented in Ref. . Under the assumption and as sug-
gested indeed by various calculations [3–5] that dielec-
tron production is dominated in the mass range 0.15 -
0.45 GeV/c2by the ∆ and η contributions, the total
yield measured for these masses can be used to constrain
the η contribution for any assumed ∆ cross section. In
other words, the η and ∆ contributions are complemen-
tary. The extracted η cross section will evidently have a
model dependence which, however, turns out to be small.
The resulting e+e−cocktails, filtered with the HADES
acceptance, are overlayed in Figs. 4 and 5 with the data.
Up to masses of ≃ 0.45 GeV/c2the agreement is good in
both observables, Meeand P⊥, although at higher masses
the measured yield is not matched. Integrating up to
0.15 GeV/c2the low-mass region, dominated evidently
by the π0Dalitz contribution, and correcting for the de-
tector acceptance, allows to fix the inclusive π0produc-
tion cross section at σπ0 = 14±3.5 mb. The quoted 25%
error is determined mostly by systematic effects (normal-
ization, trigger bias correction, acceptance correction).
In a similar way, the integrated yield from the mass re-
gion of 0.15 - 0.45 GeV/c2has been used to extract the
cross section of inclusive η production after correcting,
as stated above, for the ∆ contribution. The range of
assumed ∆ cross sections used in the simulation leads
consequently to a corresponding range of η production
cross sections, indicated by the hatched bands shown in
the two figures. In scenario (I), where all π0production
goes through ∆ excitation and decay, σ∆= 21 mb and
ση = 0.26 mb. In scenario (II), based on the model of
, various nucleon resonances contribute to pion pro-
duction, such that σ∆= 10 mb and ση= 0.35 mb. We
feel that this model dependence is relatively small and
propose to use the average of the two results, namely
ση= 0.31±0.08±0.05 mb, where the first error is again
mostly ruled by systematic effects (normalization, trig-
ger bias and acceptance corrections) while the second one
covers the model dependence.
In the pair mass range 0.45 - 0.60 GeV/c2our simu-
lation underestimates grossly the observed yield. This
is also visible in the comparison of transverse momen-
tum distributions shown on Fig. 5. Clearly additional
dielectron sources are needed, among which one has to
consider the decays of N∗resonances, e.g. the N∗(1520)
and N∗(1720) known to couple strongly to the ρ, as well
as a possible general enhancement due to vector meson
dominance form factors of the nucleon resonances .
0 0.2 0.40.6 0.81
FIG. 4: (Color online) Pair mass distribution dσ/dMee mea-
sured in 2.2 GeV p + p reactions (full circles) compared with
simulated Pluto [19, 20] cocktails of dielectron sources filtered
through the HADES acceptance. The shaded bands delimit
the range of modeled ∆ and η contributions – as discussed in
the text – with the dashed delimiters corresponding to sce-
nario (I) and the solid ones to scenario (II). Only statistical
errors are shown.
V. INCLUSIVE MESON PRODUCTION
The inclusive π0and η production cross sections ob-
tained in the present analysis can be combined with the
result from our p + p runs at 1.25 and 3.5 GeV to in-
vestigate the excitation function of meson production in
the few-GeV regime. Figure 6 shows these cross sections
as function of√sNN together with exclusive data. A
wealth of information on exclusive pion production in
nucleon-nucleon reactions has indeed been accumulated
over the past 50 years (see [22, 23] for reviews and 
for a compilation). Fits to exclusive π0production cross
sections in one-pion and two-pion channels from  are
shown in Fig. 6. These processes are quite well under-
stood in terms of nucleon resonance excitations within
the resonance models [22, 24]. Data on π0production in-
volving three or more pions in the final state is, however,
still scarce and incomplete, although such processes can
be expected to contribute substantially at beam energies
above a few GeV. Indeed, from an extrapolation of three-
pion production data to Tp= 2.2 GeV published recently
 it is estimated that the contributions of the π+π−π0
and π0π0π0channels could add up to as much as 0.5 mb.
Figure 6 shows in fact very clearly that around 2.2 GeV
bombarding energy inclusive pion production stops to be
fully exhausted by the sum of one- and two-pion channels
Turning to η production we can do a similar compari-
son. Here, data has again been only available for the ex-
clusive channel. A compilation of exclusive η production
cross sections (from , extended with recent HADES
results ) is depicted in Fig. 6, as well as the corre-
sponding resonance model calculation of Teis et al. .
Assuming that η production is mediated solely by the
N∗(1535) resonance, the latter gives a reasonabledescrip-
tion of the data. Just like in the case of pion production,
our inclusive cross sections largely exceed the exclusive
ones in the energy range investigated here. Because a mi-
croscopic description of multi-particle production is not
yet at hand, transport models often make use of cross
section parameterizations based on the Lund string frag-
mentation model (LSM) .
tion of η production , based on the LSM and shown
as dot-dashed line in Fig. 6, turns out to be in reason-
able agreement with our inclusive result, although the
intended validity range of the LSM is in fact at much
higher beam energies.
To summarize, we have presented data on inclusive
e+e−production in the reaction p + p at 2.2 GeV beam
kinetic energy. The measured dielectron cross sections
are in good agreement with the DLS result obtained ear-
lier at 2.09 GeV. The employed cocktail of e+e−sources
does not saturate our data at invariant mass around
0.55 GeV/c2. Furthermore, inclusive π0and η produc-
00 2000.24000.4 6000.6800 0.8
002000.2 4000.46000.6800 0.8
00 2000.2 4000.46000.68000.8
FIG. 5: (Color online) Pair transverse momentum distributions dσ/dP⊥measured in 2.2 GeV p+p reactions within the HADES
acceptance. Three mass bins are shown: (a) Mee < 0.15, (b) 0.15 < Mee < 0.45, and (c) Mee > 0.45 GeV/c2. The simulated
Pluto cocktails are shown as well, with line styles as in Fig. 4.
FIG. 6: (Color online) π0and η production cross sections
in p + p reactions as a function of the c.m. energy√sNN
(bottom scale) and beam kinetic energy Tp(upper scale). The
present inclusive results are shown as full triangles and circles,
respectively, together with more HADES data obtained at
bombarding energies of 1.25 GeV  and 3.5 GeV . Fits
to a compilation of 1π and 1π + 2π cross sections  are
shown as solid and long-dashed curves, respectively. Open
squares are η exclusive cross sections taken from [23, 25]; the
solid square is the exclusive HADES point from . The
short-dashed curve corresponds to the resonance model ,
and the dot-dashed curve is the parametrization of inclusive
η production from .
tion coss sections were deduced, extending the world
body of meson production data. Such data, besides hav-
ing their own interest in the context of medium-energy
hadron reactions, represent valuable input for the analy-
sis and simulation of proton-nucleus and heavy-ion colli-
sions in the same energy regime.
The collaboration gratefully acknowledges the sup-
port by CNRS/IN2P3 and IPN Orsay (France), by SIP
JUC Cracow (Poland) (NN202 286038, NN202198639),
by HZDR, Dresden (Germany) (BMBF 06DR9059D),
by TU M¨ unchen, Garching (Germany) (MLL M¨ unchen,
DFG EClust 153, VH-NG-330, BMBF 06MT9156 TP5,
GSI TMKrue 1012), by Goethe-University, Frankfurt
(Germany) (HA216/EMMI, HIC for FAIR (LOEWE),
BMBF 06FY9100I, GSI F&E), by INFN (Italy), by
NPI AS CR, Rez (Czech Republic) (MSMT LC07050,
GAASCR IAA100480803), by USC - Santiago de Com-
postela (Spain) (CPAN:CSD2007-00042).
 M I. Krivoruchenko, B V. Martemyanov, A. Faessler, and
C. Fuchs, Ann. Phys. 296, 299 (2002).
 S. Leupold, V. Metag, and U. Mosel, Int. J. Mod. Phys.
E 19, 147 (2010).
 E. L. Bratkovskaya and W. Cassing, Nucl. Phys. A 807,
 K. Schmidt et al., Phys. Rev. C 79, 064908 (2009).
 O. Buss et al., arXiv:1106.1344v1 [hep-ph], submitted to
 B. Nilsson-Almqvist and E. Stenlund, Comp. Phys.
Comm. 43, 387 (1987).
 G. Agakishiev et al. (HADES Collaboration), Phys. Lett.
B 690, 118 (2010).
 G. Agakishiev
arXiv:1112.3607v2 [nucl-ex], submitted to Eur. Phys. J.
 M. Weber et al. (HADES Collaboration), J. Phys. Conf.
Ser. 316, 012007 (2011).
 G. Agakishiev et al. (HADES Collaboration), Phys. Lett.
B 663, 43 (2008).
 G. Agakishiev et al. (HADES Collaboration), Phys. Rev.
Lett. 98, 052302 (2007).
 G. Agakishiev et al. (HADES Collaboration), Phys. Rev.
C 84, 014902 (2011).
 W. Wilson et al. (DLS Collaboration), Phys. Rev. C 57,
 G. Agakishiev et al. (HADES Collaboration), Eur. Phys.
J. A 41, 243 (2009).
 B. Sailer, doctoral thesis, Technical University, M¨ unchen
 G. Agakishievet al.
arXiv:1203.1333v1 [nucl-ex], submitted to Eur. Phys. J.
 R. J. Porter et al. (DLS Collaboration), Phys. Rev. Lett.
79, 1229 (1997).
 H. Matis, LBNL, private communication.
 I. Fr¨ ohlich et al., Proceedings of the XI Interna-
tional Workshop on Advanced Computing and Analy-
sis Techniques, Amsterdam (The Netherlands) 2007, PoS
 F. Dohrmann et al., Eur. Phys. J. A 45, 401 (2010).
 K. Nakamura et al. (Particle Data Group), J. Phys. G
37, 075021 (2010).
 J. Bystricky et al., J. Physique 48, 1901 (1987).
 P. Moskal, M. Wolke, A. Khoukaz, and W. Oelert, Prog.
Part. Nucl. Phys. 49, 1 (2002) and refs. therein.
 X. Cao, B.-S. Zou, and H.-S. Xu, Phys. Rev. C 81, 065201
D. R. O. Morrison, in Landolt-B¨ ornstein, New Series
I/12b, (Springer 1988).
 F. Balestra et al. (DISTO Colaboration), Phys. Rev. C
69, 064003 (2004).
 M. Abdel-Bary et al. (COSY-TOF Collaboration), Phys.
Lett. B 647, 351 (2007).
 C. Pauly et al. (CELSIUS-WASA Collaboration), Phys.
Lett. B 649, 122 (2007).
 S. Teis et al., Z. Phys. A 356, 421 (1997).
 A. Sibirtsev, W. Cassing, and U. Mosel, Z. Phys. A 358,