Hadronic interaction of the eta meson with two nucleons
ABSTRACT The COSY-11 collaboration has conducted experiments aiming at the determination of the excitation function and phase-space population of the p p --> p p eta reaction close to the kinematical threshold. The precise data obtained with the stochastically cooled proton beam of the cooler synchrotron COSY and the high resolution zero-degree magnetic spectrometer allowed for the observation of the significant deviations - in the shape of the excitation function and two-particle invariant masses - from the predictions based on the assumption that the reaction phase space is homogenously populated. Comparison of the shape of the excitation function for the p p --> p p eta and p p --> p p eta-prime reaction allows to distinquish in the model independent way an influence originating from the proton-proton and proton-eta interaction. For the comparison the full data set from experiments performed at COSY and other laboratories is used.
arXiv:hep-ex/0411052v1 16 Nov 2004
International Journal of Modern Physics A
c ? World Scientific Publishing Company
HADRONIC INTERACTION OF THE η MESON WITH TWO
P. MOSKAL∗,†, H.-H. ADAM‡, A. BUDZANOWSKI††, R. CZY˙ZYKIEWICZ∗,†,
D. GRZONKA†, M. JANUSZ∗, L. JARCZYK∗, B. KAMYS∗, A. KHOUKAZ‡, K. KILIAN†,
P. KLAJA∗, J. MAJEWSKI∗,†, W. OELERT†, C. PISKOR–IGNATOWICZ∗, J. PRZERWA∗,
T. RO˙ZEK⋆,†, T. SEFZICK†, M. SIEMASZKO⋆, J. SMYRSKI∗, A. T¨ASCHNER‡,
P. WINTER†, M. WOLKE†, P. W¨USTNER‡‡, W. ZIPPER⋆
∗Nuclear Physics Department, Jagellonian University, Cracow, 30-059, Poland
†Institut f¨ ur Kernphysik, Forschungszentrum J¨ ulich, J¨ ulich, 52425, Germany
‡Institut f¨ ur Kernphysik, Universit¨ at M¨ unster,M¨ unster, 48149, Germany
††Institute of Nuclear Physics, Cracow, 31-342, Poland
⋆Institute of Physics, University of Silesia, Katowice, 40-007, Poland
‡‡ZEL Forschungszentrum J¨ ulich, J¨ ulich, 52425, Germany
Received (Day Month Year)
Revised (Day Month Year)
The COSY-11 collaboration has conducted experiments aiming at the determination
of the excitation function and phase-space population of the pp → ppη reaction close to
the kinematical threshold. The precise data obtained with the stochastically cooled pro-
ton beam of the cooler synchrotron COSY and the high resolution zero-degree magnetic
spectrometer allowed for the observation of the significant deviations – in the shape of
the excitation function and two-particle invariant masses – from the predictions based on
the assumption that the reaction phase space is homogenously populated. Comparison
of the shape of the excitation function for the pp → ppη and pp → ppη′reaction allows
to distinquish in the model independent way an influence originating from the proton-
proton and proton-η interaction. For the comparison the full data set from experiments
performed at COSY and other laboratories is used.
Keywords: Meson-nucleon interaction, meson production
In analogy to the connection between electromagnetic and Van der Vaals potentials,
we may perceive the hadronic force as a residuum of the strong interaction that
occurs between quarks and gluons – the constituents of hadrons. Therefore, the
knowledge of the interaction of hadrons is interesting not only on its own account
but also since it delivers information about the structure of hadrons and the strong
The fact that fourty years after the discovery of the η and η′mesons1their
interactions with nucleons remain so weakly established, indicates that it is rather
challenging to conduct research which could deliver information about this inter-
Pawe? l Moskal et al.,
action. The scattering length – the very basic quantity describing the low energy
interaction potential – in the case of the η meson is poorly estimated, and in the
case of the η′meson it is entirely unknown. Estimated value of the real part of the
proton-η scattering length varies from 0.25 fm to 1.05 fm depending on the approach
employed for its determination2.
The main obstacle in the experimental studies involving any of neutral ground
state mesons is too short life–time which prohibits their utilization as secondary
beams. Therefore the study of their interaction with hadrons is accessible only via
observations of their influence on the cross section of the reactions in which they were
produced (eg. NN → NN Meson). The influence of the relatively weak nucleon-η
interaction may be magnified when producing the meson in the vicinity of two nu-
cleons. In this context the ppη system reveals to be particularly interesting since
neither the pp nor the pη interaction is strong enough to form a bound state and
so the ppη system may occur to be Borromean. It was pointed out by Wycech3
that the large enhancement in the excitation function of the pp → ppη reaction
observed close to the kinematical threshold can be described assuming that the
proton-proton pair is produced from a large object of a 4 fm radius. Yet, at present
it is still not established whether the low energy ppη system can really form a Bor-
romean or resonant state. Though the significant progress in the understanding of
the production mechanism on the hadronic level has been achieved4,5,6,7, the final
state system was always treated approximately utterly ignoring the η-proton final
state interaction. Only, very recently the rigorous three-body approach has been
applied for the description of the observed excitation function and two-particle in-
variant mass spectra of the pp → ppη reaction. Two independent approaches by
Deloff8and Fix & Arenh¨ ovel9revealed that the rigorous three body treatment of
the final state leads to the results significantly different from the two-body approach
even when the η-proton interaction is completely disregarded. Also a very impor-
tant conclusion drawn in reference9is that the role of the final state interaction
depends crucially on the range of the primary reaction dynamics, showing that the
inaccuracy of establishing contributions from the exchange of various mesons limits
the inferences about the interaction among the final state particles.
The data which stimulated the development of the abovementioned three body
formalism will be presented hereafter. For the better visualisation of the effects due
to the proton-η interaction we will compare the shape of the excitation functions
of the pp → ppη and pp → ppη′reactions and will discuss the observed differences.
In the next section which constitutes an extraction from the more comprehensive
treatise10we will present only the excitation function and for the details con-
cerning the differential distributions the reader is referred to the more exhaustive
experimental10,11,12and theoretical elaborations5,9,13,14.
Hadronic interaction of the η meson with two nucleons
2. Excitation function of the reactions pp → ppη and pp → ppη′
The determined energy dependences of the total cross section for η′ 15,16and
η11,16,17mesons production in proton-proton collisions are presented in figure 1.
Comparing the data to the arbitrarily normalized phase space integrals (dashed
lines) reveals that the ppη FSI enhances the total cross section by more than an
order of magnitude for low excess energies.
σ [ nb ]10
pp pp η
Q [ MeV]
ppη′(circles) and pp → ppη (squares) as a function
of the centre-of-mass excess energy Q. Data are from
refs.11,15,16,17The dashed lines indicate a phase
space integral normalized arbitrarily. The solid lines
show the phase space distribution with inclusion of the
1S0 proton-proton strong and Coulomb interactions.
In case of the pp → ppη reaction the solid line was
fitted to the data in the excess energy range between
15 and 40MeV. Additional inclusion of the proton-η in-
teraction is indicated by the dotted line. The scattering
length of apη = 0.7fm+i0.4fm and the effective range
parameter bpη = −1.50fm−i0.24fm18have been cho-
sen arbitrarily. The dashed-dotted line represents the
energy dependence taking into account the contribu-
tion from the3P0→1S0s,1S0→3P0s and1D2→3P2s
transitions13. Preliminary results for the3P0 →1S0s
transition with full treatment of three-body effects are
shown as a dashed-double-dotted line9. The absolute
scale of dashed-double-dotted line was arbitrary fitted
to demonstrate the energy dependence only.
Total cross section for the reactions pp →
One recognizes also that in the case of the η′meson the data are described very
well (solid line) assuming that the on-shell proton-proton amplitude exclusively
determines the phase space population. In the case of η meson production the
interaction between nucleons is evidently not sufficient to describe the increase of
the total cross section for very low and very high excess energies, as can be concluded
from the comparison of the data and the upper solid line in figure 1. This line was
normalized to the data at an excess energy range between 15MeV and 40MeV. The
enhancement of the total cross section for higher energies can be assigned to the
outset of higher partial waves, and the discrepancy visible closer to the threshold
can be plausibly explained by the influence of the attractive interaction between
the η meson and the proton. A similar effect close-to-threshold is also observed in
the data of photoproduction of η via the γd → pnη reaction19indicating to some
extent that the phenomenon is independent of the production process and rather is
related to the interaction among the η meson and nucleons.
The dotted–line in figure 1 corresponds to the simple phenomenological treat-
ment20based on the factorization of the transition amplitude into the constant
primary production and the on-shell incoherent pairwise interaction among outgo-
ing particles. Although it describes the enhancement close-to-threshold very well,
Pawe? l Moskal et al.,
it fails to describe the invariant mass distribution of the proton-proton and proton-
η subsystems determined recently at Q = 15 MeV by the COSY-TOF12and at
Q = 15.5 MeV by the COSY-1111collaborations. It was suggested in reference13
that the bump in the invariant mass spectra may be due to the contribution from
higher partial waves. However, the amount of the P-wave admixture derived from
the proton-proton invariant mass distribution spoils significantly the agreement with
the data at low values of Q (see dashed-dotted line in figure 1). Another explana-
tion proposed is based on the anticipation that the production amplitude may vary
with energy14. However, both listed approaches neglected the proton-η interaction
and only now the first calculations with the rigorous treatment of the three-body
final state including both proton-proton and proton-η interaction are available. And
although biased with neglection of the Coulomb effect9or imaginary part of the
proton-η scattering length8they herald a fully rigorous explanation of the observed
The work has been supported by the DAAD Exchange Programme (PPP-
Polen) and by the Polish State Committee for Scientific Research (grant No.
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