arXiv:0711.4998v2 [nucl-ex] 29 Jul 2008
EPJ manuscript No.
(will be inserted by the editor)
Dynamics of the near threshold η meson production in
R. Czy˙ zykiewicz1,2, P. Moskal1,2, H.-H. Adam3, A. Budzanowski4, E. Czerwi´ nski1, D. Gil1, D. Grzonka2,
M. Hodana1,2, M. Janusz1,2, L. Jarczyk1, B. Kamys1, A. Khoukaz3, K. Kilian2, P. Klaja1,2, B. Lorentz2, W. Oelert2,
C. Piskor-Ignatowicz1, J. Przerwa1,2, B. Rejdych1, J. Ritman2, T. Sefzick2, M. Siemaszko5, M. Silarski1, J. Smyrski1,
A. T¨ aschner3, K. Ulbrich6, P. Winter7, M. Wolke2, P. W¨ ustner2, M. J. Zieli´ nski1, W. Zipper5
1Institute of Physics, Jagellonian University, 30-059 Cracow, Poland
2IKP & ZEL, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany
3IKP, Westf¨ alische Wilhelms-Universit¨ at, 48149 M¨ unster, Germany
4Institute of Nuclear Physics, 31-342 Cracow, Poland
5Institute of Physics, University of Silesia, Katowice, Poland
6ISK, Rheinische Friedrich-Wilhelms-Universit¨ at, 53115 Bonn, Germany
7Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Received: date / Revised version: date
Abstract. We present the results of measurements of the analysing power for the pp → ppη reaction at
the excess energies of Q = 10 and 36 MeV, and interpret these results within the framework of the meson
exchange models. The determined values of the analysing power at both excess energies are consistent with
zero implying that the η meson is produced predominantly in s-wave.
PACS. 14.40.-n Mesons – 14.40.Aq π, K, and η mesons – 13.60.Le Meson production
From the precise measurements of the total cross section
for the η meson production in the pp → ppη reaction
in the close-to-threshold region [1,2,3,4,5,6,7,8] it was
concluded [9,10,11,12,13,14,15,16,17] that this process
proceeds through the excitation of one of the protons to
the S11(1535) state, which subsequently deexcites via the
emission of the η meson and a proton. However, there are
plenty of possible scenarios of the excitation of S11(1535)
resonance. In fact, exchange of any of the π,η,ω, or ρ
mesons may contribute to the resonance creation. Consid-
ering the cross sections itself doesn’t answer the question
which out of these mesons give the significant contribution
to the production amplitude.
Some constraints may be deduced from the investiga-
tions of the isospin dependence of the total cross section
for the NN → NNη reaction . The ratio of the to-
tal cross sections for the η meson production in proton-
neutron collisions to the analogouscross section with proton-
proton colliding in the initial state was found to be about
6.5 in the close-to-threshold region, which revealed strong
isospin dependence of the production process. This means
that the production of the η meson with the total isospin
I=0 in the initial channel exceeds the production with
the isospin I=1 by a factor of 12, suggesting  that the
isovector meson exchange - the π or ρ meson exchange -
is the dominant process leading to the excitation of the
S11resonance. However, the relative contributions of the
pseudoscalar π meson and vector ρ meson still remain to
Here, the measurements of the polarization observables
can assist, because the predictions of the one boson ex-
change models [16,17] with respect to the analysing power
are sensitive to the type of the exchanged meson.
COSY-11 collaboration performed two measurements
of the analysing power function at the beam momenta of
pbeam = 2.010 GeV/c and 2.085 GeV/c, which for the
pp → ppη reaction correspond to the excess energies of
Q=10 and 36 MeV, respectively. Here we would like to
briefly summarize the results of these measurements and
present the main conclusions we could have drawn from
In the measurements the COSY-11 detection setup [20,
21,22] has been used, along with the vertically polarized
proton beam, which polarization was flipped from cycle
to cycle in order to reduce the systematic uncertainties.
For the detailed description of the experimental apara-
tus, method of measurement and analysis, the reader is
referred to .
The tested predictions of the analysing power of ref-
erence  were based on the assumption of the ρ meson
2 R. Czy˙ zykiewicz, P. Moskal et al.: Dynamics of the near threshold η meson production in proton-proton interaction
exchange dominance and the proton asymmetries taken
from the photoproduction of the η meson . In the case
of the calculations of reference  the exchanges of all
mesons have been taken into account in the framework of
the relativistic meson exchange model of hadronic interac-
tions and it was found in this model that the contribution
from the pion exchange is the dominant one.
Fig. 1 shows the experimentally determined values of
the analysing power Ay for the pp → ppη reaction con-
fronted with the theoretical predictions of the pseudoscalar
and vector  meson exchange dominance models. The
χ2test of the correctness of these models have been per-
formed and the reduced values of the χ2were found to
be equal to 0.54 (corresponding to the significance level of
αpsc= 0.81) and 2.76 (αvec= 0.006), for pseudoscalar and
vector meson exchange dominance models, respectively.
Fig. 1. Analysing power Ay for the pp → ppη reaction as a
function of cosine of the polar angle of the η meson produc-
tion in the overall center-of-mass system for Q=10 MeV (left
panel) and Q=36 MeV (right panel). Full lines are the pre-
dictions based on the pseudoscalar meson exchange model 
whereas the dotted lines represent the calculations based on the
vector meson exchange . In the right panel the dotted line
is consistent with zero. Shown are the statistical uncertainties.
In the vector meson exchange dominance model 
the angular distribution of the analysing power is param-
eterized as a function of the polar angle of η meson pro-
duction in the center-of-mass system with the following
Ay(θη) = Amax,vec
where the amplitude Amax,vec
energy Q, shown as a dotted line in the left panel of Fig. 2.
We have estimated the values of Amax,vec
the experimental data with predicted shape utilizing a
χ2test [23,24,25]. Determined experimental values are
shown in Fig. 2 (left) along with the theoretical predic-
tions according to the vector meson exchange dominance
model . Analogously, the confrontation of the exper-
imentally determined amplitude Amax,psc
dictions of the pseudoscalar meson exchange dominance
model  are shown in Fig. 2 (right). Predictions of the
model based on the π mesons dominance are fairly consis-
tent with the data, whereas the calculations based on the
dominance of the ρ meson exchange differ from the data by
is a function of the excess
with the pre-
Q [ MeV ]
0 1020 30 40
Q [ MeV ]
Fig. 2. Theoretical predictions for the energy dependence of
the amplitude of Amax
confronted with the amplitudes deter-
mined experimentally at the excess energies of Q=10 and 37
MeV for the vector (left) and pseudoscalar (right) meson ex-
change dominance model.
more than four standard deviations. However, the latter
calculation used the proton asymmetry (T) in eta photo-
production , within the framework of the vector meson
dominance model , as the basis of their estimate. It
should be noted that it has proved hard to reconcile the
experimental value of T with the results of photoproduc-
tion amplitude analyses .
3 Conclusions and outlook
Taking into account the χ2analysis of the analysing power
for the pseudoscalar and vector meson exchange models
we have shown that the predictions of the pseudoscalar
meson exchange dominance  are in line with the ex-
perimental data at the significance level of 0.81. On the
other hand, the assumption that the η meson is produced
solely via the exchange of the ρ meson , leads to the
discrepancy between the theoretical predictions and ex-
perimental data larger than four standard deviations. It
must be stated, however, that the production amplitude
for the ρ meson exchange was determined based on the
vector meson dominance hypothesis and the photoproduc-
tion data . At this point it is also worth mentioning
that the recent calculations of the η meson production in
the NN collisions performed in the framework of the effec-
tive Lagrangian model  also indicate the dominance of
the pion exchange.
The analysing power values for both excess energies are
consistent with zero within one standard deviation. This
is in line with the results obtained by the DISTO  col-
laboration in the far-from-threshold energy region. Such
a result may indicate that the η meson is predominantly
produced in the s-wave.
4 Future perspectives
Recently, the proposal for the measurement of the analyz-
ing power function  with the WASA-at-COSY apara-
tus  has been presented and awaits recommendation
R. Czy˙ zykiewicz, P. Moskal et al.: Dynamics of the near threshold η meson production in proton-proton interaction3
of the COSY Programme Advisory Committee. Measure-
ments are planned with about 50 times better statistics
which should enable the error bars from Fig. 1 to be re-
duced of circa 7 times.
-1 -0.50 0.51
Fig. 3. Predictions of the dependence of the analyzing power
function on the intermediate resonance type .
Fig. 3 presents the dependence of the analyzing power
as a function of the cosine of the polar angle of the η
meson emission in the center-of-mass system on the inter-
mediate resonance type . Solid line are the calculations
of the pseudoscalar meson exchange model performed un-
der assumption that only S11(1535) resonance contributes
to the η meson production amplitude, whereas the dot-
ted line represent the predictions of the same model, in-
cluding D13(1520), S11(1535), S11(1650), and D13(1700)
resonances. Therefore, the improvement in the measure-
ment accuracy would enable to investigate the influence
of other-than-S11(1535) resonances upon the production
Measurements of the analysing power Ay with much
higher statistics may also allow the model independent
partial wave decomposition with an accuracy by far better
than resulting from the measurements of the distributions
of the spin averaged cross sections. This is because the
polarization observables can probe the interference terms
between various partial amplitudes, even if they are neg-
ligible for the spin averaged distributions. More impor-
tantly, in case of the pp → ppX reaction the interference
terms between the transition with odd and even values
of the angular momentum of the final state baryons are
bound to vanish for the cross sections [34,35]. This char-
acteristic is due to the invariance of all observables under
the exchange of identical nucleons in the final state. Due to
the same reason there is no interference between s and p-
waves of the η meson in the differential cross sections .
However, s-p interference does not vanish for the proton
analysing power, and thus the precise measurements of
Ay could provide the first determination of the compar-
atively small p-wave contribution , unreachable from
spin averaged observables.
We acknowledgethe support of the European Community-
ResearchInfrastructure Activity under the FP6 programme
(Hadron Physics, N4:EtaMesonNet, RII3-CT-2004-506078),
the support of the Polish Ministry of Science and Higher
Education under the grants No. PB1060/P03/2004/26,
3240/H03/2006/31and 1202/DFG/2007/03, and the sup-
port of the German Research Foundation (DFG) under the
grant No. GZ: 436 POL 113/117/0-1.
1. F. Hibou et al., Phys. Lett. B 438 (1998) 41;
2. J. Smyrski et al., Phys. Lett. B 474 (2000) 182;
3. A. M. Bergdolt et al., Phys. Rev. D 48 (1993) 2969;
4. E. Chiavassa et al., Phys. Lett. B 322 (1994) 270;
5. H. Cal´ en et al., Phys. Lett. B 366 (1996) 39;
6. H. Cal´ en et al., Phys. Rev. Lett. 79 (1997) 2642;
7. P. Moskal et al., Phys. Rev. C 69 (2004) 025203;
8. M. Abdel-Bary et al., Eur. Phys. J. A 16 (2003) 127.
9. A. Moalem et al., Nucl. Phys. A 600 (1996) 445.
10. M. Batini´ c et al., Phys. Scripta 56 (1997) 321.
11. J. F. Germond et al., Nucl. Phys. A 518 (1990) 308.
12. J. M. Laget et al., Phys. Lett. B 257 (1991) 254.
13. T. Vetter et al., Phys. Lett. B 263 (1991) 153.
14. B. L. Alvaredo et al., Phys. Lett. B 324 (1994) 125.
15. V. Bernard et al., Eur. Phys. J. A 4 (1999) 259.
16. G. F¨ aldt and C. Wilkin, Phys. Scripta 64 (2001) 427.
17. K. Nakayama et al., Phys. Rev. C 65 (2002) 045210.
18. H. Cal´ en et al., Phys. Rev. C 58 (1998) 2667.
19. C. Wilkin, Report No. TSL/ISV-96-0147 (1996).
20. S. Brauksiepe et al., Nucl. Instr. and Meth. A 376 (1996)
21. J. Smyrski et al., Nucl. Instr. and Meth. A 541 (2005)
22. P. Klaja et al., AIP Conf. Proc. 796 (2005) 160.
23. R. Czy˙ zykiewicz, nucl-ex/0702010, PhD. Dissertation,
Jagellonian University (2007).
24. R. Czy˙ zykiewicz et al., Phys. Rev. Lett. 98 (2007) 122003.
25. R. Czy˙ zykiewicz et al., Int. J. Mod. Phys. A22 (2007) 518.
26. A. Bock et al., Phys. Rev. Lett. 81 (1998) 534.
27. J. J. Sakurai, Annals Phys. 11 (1960) 1.
28. W.-T. Chiang, S.-N. Yang, L. Tiator, and D. Drechsel,
Nucl. Phys. A 700 (2002) 429.
29. R. Shyam, Phys. Rev. C 75 (2007) 055201.
30. F. Balestra et al., Phys. Rev. C 69 (2004) 064003.
31. P. Moskal, M. Hodana et al., COSY Proposal No. 185
32. H.-H. Adam etal.,Proposal
33. K. Nakayama, private communication (2007).
34. A. Deloff, Phys. Rev. C 69 (2004) 035206.
35. C. Wilkin, private communications (2007).