arXiv:0912.1592v1 [nucl-ex] 8 Dec 2009
EPJ manuscript No.
(will be inserted by the editor)
Invariant mass distributions for the pp → ppη reaction at
Q = 10 MeV
P. Moskal1,2, R. Czy˙ zykiewicz1,3, E. Czerwi´ nski1,2, D. Gil1, D. Grzonka2, L. Jarczyk1, B. Kamys1, A. Khoukaz4,
J. Klaja1,2, P. Klaja1,2, W. Krzemie´ n1,2, W. Oelert2, J. Ritman2, T. Sefzick2, M. Siemaszko3, M. Silarski1,
J. Smyrski1, A. T¨ aschner4, M. Wolke5, P. W¨ ustner2, J. Zdebik1, M. J. Zieli´ nski1, and W. Zipper4
1Institute of Physics, Jagellonian University, PL-30-059 Cracow, Poland
2Nuclear Physics Institute, Research Center J¨ ulich, D-52425 J¨ ulich, Germany
3Institute of Physics, University of Silesia, PL-40-007 Katowice, Poland
4IKP, Westf¨ alische Wilhelms-Universit¨ at, D-48149 M¨ unster, Germany
5Department of Physics and Astronomy, Uppsala University, Sweden
Received: date / Revised version: date
Abstract. Proton-proton and proton-η invariant mass distributions and the total cross section for the pp →
ppη reaction have been determined near the threshold at an excess energy of Q = 10 MeV. The experiment
has been conducted using the COSY-11 detector setup and the cooler synchrotron COSY. The determined
invariant mass spectra reveal significant enhancements in the region of low proton-proton relative momenta,
similarly as observed previously at higher excess energies of Q = 15.5 MeV and Q = 40 MeV.
PACS. 13.60.Le Meson production – 13.85.Lg Total cross sections – 29.20.D- Cyclic accelerators and
The complexity of the structure of hadrons constitutes
the basic difficulty in the quantitative description of the
hadronic interaction in the medium energy regime. There-
fore, this interaction is not well understood especially in
the meson-nucleon and meson-meson sector, where an ad-
ditional difficulty is the relatively poor experimental data-
base. Particularly challenging are investigations of inter-
actions involving flavour-neutral mesons. This is due to
the short life-time of these mesons which can neither be
used as targets nor as beams. Thus, in practice such in-
teractions can be accessed only indirectly via observables
like excitation functions or invariant mass distributions.
Measurements of these observables are especially useful in
the close-to-threshold region where the final state parti-
cles are produced with low relative velocities. Among the
basic flavour neutral mesons the η is of particular interest
since its interaction with nucleons is strong enough to be
detectable with the presently achievable experimental pre-
cision , and since its interaction seems to be sufficently
strong to form an eta-mesic nucleus [2,3]. The existence
of such kind of nuclear matter is vividly discussed  and
there are ongoing experimental programs searching for a
signal of such a state .
The earlier high statistics measurements of the pp →
ppη reaction at an excess energy of Q = 15.5 MeV from
the COSY-11 collaboration , and also the measurements
of the TOF group  at Q = 15 and 41 MeV, revealed
that there exist significant enhancements in the invari-
ant mass distributions of pp and pη subsystems at higher
values of proton-proton invariant mass and lower values of
the proton-η invariant mass. One of the plausible explana-
tions for these enhancements could be an influence of the
proton-η interaction [1,8]. If this is the case one could use
such observables for the estimation of the strength of this
interaction. However, the observed invariant mass distri-
butions could be also plausibly explained by contributions
of higher partial waves [9,10] or by an energy dependence
of the primary production amplitude [11,12]. Therefore,
in order to verify the correctness of the proposed explana-
tions it is of importance to investigate the dependence of
the strength of the enhancements as a function of the ex-
cess energy. Qualitatively, with decreasing excess energy
the contribution from the higher partial waves should de-
crease whereas the influence of the interaction should be
Certainly, most effectively, contributions from higher
partial waves could be disentangled by the determination
of the analysing powers and spin transition coefficients [10,
13,14], yet such investigations are not planned in the near
future at COSY which is at present the only laboratory
where it can be conducted. This makes the determination
of the energy dependence of the distributions of the differ-
ential cross section for the pp → ppη reaction even more
important for studies of the proton-η hadronic interaction
and for studies of the properties of nucleon resonances [9,
2P. Moskal et al.: Invariant mass distributions for the pp → ppη reaction at Q = 10 MeV
In this article we present distributions of the proton-
proton and proton-η invariant masses at the excess energy
of Q = 10 MeV which is significantly closer to the thresh-
old with respect to the previous studies. Although the
original experiment at Q = 10 MeV has been devoted to
the investigations of the analysing power for the pp → ppη
reaction  and has been performed with a polarised pro-
ton beam, the data enable also the determination of the
spin averaged observables after appropriate offline ”depo-
larisation” of the beam explained in section 2.1. In Sec-
tion 2 we briefly describe the experimental set-up, present
the experimental principles of the measurement, and de-
scribe the method of the data analysis. In section 3 the
determined spectra are compared to the analogoues re-
sults determined at the excess energy of Q = 15.5 MeV,
and the final conclusions are drawn.
The measurement of the pp → ppη reaction has been per-
formed at the cooler synchrotron COSY  at the Re-
search Center J¨ ulich in Germany using the COSY-11 de-
tector setup , presented schematically in Figure 1.
Fig. 1. Schematic view of the COSY-11 detector setup .
D1 and D2 represent drift chambers. S1, S3, S4 denote scintil-
lator counters. Simon is the silicon strip detector used for the
detection of the elastically scattered protons. Superimposed
solid lines indicate final state protons from the pp → ppη reac-
tion. The size of detectors and their relative distances are not
The proton beam with a momentum of 2.010 GeV/c,
corresponding to an excess energy of Q = 10 MeV, has
been scattered on H2 molecules from an internal cluster
jet target [19,20], installed in front of the COSY magnet.
Reaction products carry lower momenta than the beam
protons, therefore are bent more in the magnetic field of
the dipole magnet. Positively charged ejectiles leave the
scattering chamber through a thin exit window reaching
the detection system operating under atmospheric pres-
sure. The hardware trigger was based on signals from
scintillator detectors only. It was adjusted to register all
events with at least two positively charged particles. For
this aim coincident signals in the S1 and S3 detectors were
required. In the case of the S1 detector only these events
were accepted for which either two separate segments were
hitted or an amplitude of the signal in a single module was
higher than the certain threshold value. Based on the data
analysis from the previous experiments, the threshold was
set high enough to reduce significantly the number of sin-
gle particle events, and at the same time to accept most
events (almost 100%) with two protons passing through
one segment. Next, in the off-line analysis it was required
that at least two tracks are reconstructed from signals
measured by means of two planar drift chambers D1 and
D2. The trajectories of the positively charged particles re-
constructed in drift chambers are further traced through
the magnetic field of the dipole back to the interaction
point. In this way the momenta of the particles can be
reconstructed with a precision of 6 MeV/c (standard de-
viation) . The time-of-flight measurement between the
scintillator hodoscope S1 and the scintillator wall S3, and
the independently reconstructed momentum enable a par-
ticle identification by means of the invariant mass tech-
nique. The COSY-11 mass resolution allows for a clear
seperation of groups of events with two protons, two pions,
proton and pion and also deutron and pion . Further on
the produced meson is identified using the missing mass
method. A more detailed description of the method and
results of the identification of the pp → ppη reaction can
be found in reference [1,6,21].
2.1 Off-line depolarisation of the beam
Originally the experiment was dedicated to the measure-
ment of the beam analysing power for the pp → ppη re-
action [16,21]. Therefore, the proton beam has been ver-
tically polarised. The vertical polarisation of the beam is
defined as an asymmetry of populations of particles in the
spin up (N+) and down (N−) states with respect to the
vertical axis, integrated over the whole period of measure-
In the discussed experiment the direction of the polarisa-
tion was being flipped from cycle to cycle. Hence, for the
so called ”spin up cycles” we define the spin up polarisa-
and analogously for ”spin down cycles” the spin down po-
P. Moskal et al.: Invariant mass distributions for the pp → ppη reaction at Q = 10 MeV3
where, n+,iand n−,idenote the number of protons in the
ithcycle, in spin up and down state, respectively. Please
note, that according to above definitions the following re-
lations are valid:
The beam can be effectively depolarized e.g. by assigning
to the events in spin up cycles the weights w which can
be derived from the requirement that the numerator of
Equation 1 has to vanish:
n−,i) = 0. (5)
Thus, combining Equations 2 and 3 with Equation 5 we
obtain the following formula for the value of w:
spin up and down cycles. Taking into account the numer-
ical values of P↑= 0.658±0.008, P↓= 0.702±0.008, and
Lrel = 0.98468 ± 0.00056 [16,21] one gets w = 1.083.
The weight w, assigned to events in spin up cycles,
does not change the absolute value of cross sections, as
the same weight has been applied in both: the calculation
of the number of events originating from the pp → ppη
reaction and the determination of the luminosity from the
pp → pp elastic scattering.
L↓ denotes the relative luminosity for the
2.2 Data analysis
The method applied to the determination of the differen-
tial cross sections follows the procedures described in ,
therefore for any details the reader is reffered to that pa-
per. Here we shall only briefly describe the main steps of
the data analysis and emphasize the differences between
the methods used in both studies.
After particle identification we continued the analy-
sis with the depolarization of the experimental data, ac-
cording to the procedure described in Section 2.1. Next,
we determined the covariance matrix and performed the
kinematical fitting [1,6].
For the description of the relative motion of the pro-
tons and the η meson, following reference , we have
chosen the squares of the invariant masses – sppand spη–
of the proton-proton and proton-η systems, respectively.
Optimizing the statistics we have divided the range of spp
and spη into 20 bins. For each bin of these variables we
have determined the spectrum of the square of the missing
mass. Analogoues spectra were simulated for the pp → ppη
reaction and for the background channels. The simulation
program, based on the GEANT3  code, accounts for
the geometry of the COSY-11 detector setup including the
conditions of the beam and target  and the resolution
and efficiency of the detectors . The simulated events
were analysed with the same program as the experimen-
tal data. Subsequently, functions of the type:
f(mm2) = α · fpp→pp2π(mm2) + β · fpp→pp3π(mm2) +
+γ · fpp→pp4π(mm2) + δ · fpp→ppη(mm2),
were fitted to the data, with α, β, γ, and δ treated as free
parameters responsible for the normalisation of the sim-
ulated missing mass spectra (f) of reactions indicated in
subscripts. In order to determine the background free in-
variant mass distributions the experimental missing mass
squared spectra were fitted separately for each bin of spp
and spη. As an example, the missing mass distributions
for arbitrarily chosen bins of sppand spηare presented in
0.28 0.285 0.29 0.295
0.3 0.305 0.31
spp = 3.542897 [GeV2/c4]
events / GeV2/c4
0.28 0.285 0.29 0.295
spη = 2.216543 [GeV2/c4]
events / GeV2/c4
spp = 3.552243 [GeV2/c4]
events / GeV2/c4
spη = 2.212101 [GeV2/c4]
events / GeV2/c4
spp = 3.557851 [GeV2/c4]
events / GeV2/c4
spη = 2.234312 [GeV2/c4]
events / GeV2/c4
Fig. 2. Missing mass squared distributions for arbitrarily cho-
sen bins of spp (left) and spη (right), as measured at the excess
energy of Q = 10 MeV. Dots represent the experimental data
points along with their statistical erros, whereas the solid line
is the best fit of the sum of the signal and background as ob-
tained in the Monte-Carlo simulations. The shaded part shows
the generated multi-pionic background.
4P. Moskal et al.: Invariant mass distributions for the pp → ppη reaction at Q = 10 MeV
The mumbers of η mesons Nηfor the individual inter-
vals of sppand spηhave been calculated as:
Nη= δ ·
and the statistical errors σ(Nη) have been estimated as:
σ(Nη) = σ(δ) ·
where σ(δ) are the estimates of the δ parameter uncer-
tainties (standard deviations) determined by means of the
MINUIT minimization package .
The systematic error of Nη has been estimated to be
not larger than 8%, based on the dependence of the re-
sults on different assumptions for i) background estima-
tion (∼2%), ii) description of the proton-proton final state
interaction (∼5%), and iii) inaccuracy in efficiency for re-
construction of both proton trajectories (∼6%). The un-
certainty in the number of the background events under
the peak of the η meson was estimated as differences be-
tween results obtained by fitting to the background a) the
first order polynomials, b) the second order polynomials,
c) the sum of two Gaussian functions, and d) the distri-
butions simulated for the multi-pion production [31,21].
The inaccuracy due to the model used for the description
of the proton-proton FSI was estimated conservatively as
a difference in results determined when using parameter-
ization of the proton-proton S-wave interaction  and
when neglecting the FSI and taking into account a homo-
geneous phase-space distribution of the momenta of final
The determination of the luminosity was based on the
comparison of the measured differential pp → pp elas-
tic scattering cross sections to the data of the EDDA
group . For the detailed method of the luminosity and
acceptance calculation the interested reader is referred
to [1,23]. The integrated luminosity was extracted to be
L = 58.53 ± 0.03 nb−1.
3 Results and conclusions
The total cross section evaluated as an integral of the spp
distribution equals to σ = 1.27±0.04±0.13 µb, where the
first error is the statistical and the second the systematic
one. The latter accounts for the quadratic sum of inde-
pendent contributions from 8% systematic error of Nη,
3% systematic error of the luminosity determination ,
and 6 % uncertainty in the acceptance estimation . The
determined total cross section is in line with the previous
measurements performed independently by various exper-
imental groups [6,27].
The results on the differential cross sections for the
pp → ppη reaction as a function of the square of the
proton-proton and proton-η invariant masses are given in
Table 1, and presented in the left part of Figure 3. They
are compared with the differential cross sections measured
at the excess energy of Q = 15.5 MeV , displayed in the
right part of Figure 3.
dσ/dspp [ µb/GeV2/c4 ]
dσ/dspp [ µb/GeV2/c4 ]
2.22.21 2.22 2.232.24
dσ/dspη [ µb/GeV2/c4 ]
dσ/dspη [ µb/GeV2/c4 ]
Fig. 3. Distributions of the square of the proton-proton and
proton-η invariant masses as measured at Q = 10 MeV (left)
and Q = 15.5 MeV (right). Solid lines represent the homo-
geneous phase-space distributions, while the dotted lines are
the theoretical predictions taking into account the1S0 proton-
proton final state interaction.
The homogeneous phase-space distributions, shown in
Figure 3 by solid lines, completely disagree with the ex-
perimental data for all distributions presented. The peak
observed at small values of spp is associated with strong
proton-proton final state interaction (FSI). On the other
hand the dotted lines, which represent the phase-space dis-
tribution convoluted with the proton-proton FSI describe
the data quite well in the range of small invariant masses
of the proton-proton system and in the range of large spη,
but for both excess energies there is a significant deviation
of the theoretical predictions from the experimental data
in the range of large values of sppand small values of spη.
In the calculations we have used the parameterization of
the proton-proton FSI given in reference . The curves
including the proton-proton FSI have been arbitrarily nor-
malized in the range of small values of sppand close to the
upper limit of the spηdistribution.
A preliminary result from a comparative analysis of
the ppη and ppη′system indicates that the observed en-
hancement is rather not due to the meson-proton interac-
tion [30,31]. Preliminary results show that the enhance-
ments in the invariant mass distributions are also present
in case of the pp → ppη′reaction [30,31]. Due to the fact
that the interaction between the η′meson and proton is
more than an order of magnitude weaker than the one be-
P. Moskal et al.: Invariant mass distributions for the pp → ppη reaction at Q = 10 MeV5
of the proton-proton and proton-η systems for the pp → ppη
reaction at the excess energy of Q = 10 MeV.
Distribution of the square of the invariant mass
33.6 ± 2.9
64.3 ± 4.4
58.8 ± 4.9
46.1 ± 4.8
38.6 ± 4.7
37.2 ± 4.9
40.3 ± 4.9
39.9 ± 5.0
35.8 ± 4.9
40.2 ± 5.3
31.3 ± 5.1
37.9 ± 5.6
26.2 ± 5.3
26.0 ± 5.4
30.8 ± 5.4
23.2 ± 5.4
26.6 ± 4.8
25.1 ± 4.7
9.8 ± 4.0
7.7 ± 1.9
11.0 ± 2.3
14.6 ± 3.2
24.0 ± 4.1
32.4 ± 4.8
32.0 ± 5.1
25.4 ± 5.1
51.5 ± 6.8
32.1 ± 6.0
50.7 ± 6.8
47.2 ± 6.7
57.1 ± 7.2
55.9 ± 7.2
60.1 ± 7.0
67.4 ± 7.4
67.4 ± 6.9
58.5 ± 6.3
56.6 ± 5.4
52.9 ± 4.6
41.8 ± 3.7
19.0 ± 2.0
tween the η meson and proton , the explanation that
the bump is caused by the proton-η final state interactions
is rather doubtious.
One plausible explanation for the bumps observed at
higher values of sppand lower values of spηis the presence
of higher partial waves in the final state proton-proton
system . Already the inclusion of the1S0→3P0s 
transition to the production amplitude of the pp → ppη re-
action leads to a quite well description of the experimental
data in the high values of sppand low values of spη, leaving
unaltered the description of the experimental data at low
values of sppand high values of spη, dominated mainly by
the3P0 →1S0s transition. However, to cope the P-wave
contribution with the flat angular distributions [6,7], it is
necessary that the amplitude1D2→3P2s vanishes or that
it interferes destructively with1S0→3P0s transition .
Moreover, the model calculations based on a significant
P-wave contribution underestimates the excitation func-
tion for the pp → ppη reaction below 20 MeV by a factor
of about two [1,6]. Although this deficit can be overcome
when assuming a relatively strong contribution to the pro-
duction amplitude from the nucleon resonances, such hy-
pothesis cannot be confirmed at the present stage of the in-
accuracies of the resonance parameters . The amount of
the P-wave contribution should decrease towards thresh-
old but the enhancement observed at Q = 10 MeV is
rather of the same order as the one at Q = 15.5 MeV,
however in view of the present experimental statistical
and systematic inaccuracies the hypothesis of the higher
partial wave contribution cannot be excluded.
Another explanation for the bumps observed at higher
values of sppwere put forward by Deloff  who explains
the observed spectra by allowing a linear energy depen-
dence of the leading3P0→1S0s partial wave amplitude.
Recently also Ceci,ˇSvarc and Zauner [12,32] have shown
that the excitation function and the enhancement in the
invariant mass spectra can be very well described by the
energy dependence of the production amplitude when the
negative interference between the π and the η meson ex-
change amplitudes is assumed. However, for the quanti-
tative confirmation of these hypotheses still more precise
data on the energy dependence of the enhancement in the
invariant mass spectra are required.
The work was partially supported by the European Co-
mmunity-Research Infrastructure Activity under the FP6
programme (Hadron Physics, RII3-CT-2004-506078), by
the Polish Ministry of Science and Higher Education under
grants No. 3240/H03/2006/31 and 1202/DFG/2007/03,
by the German Research Foundation (DFG), and by the
FFE grants from the Research Center J¨ ulich.
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