Photoproduction of meson pairs: First measurement of the polarization observable
The polarization observable , a feature exclusive to the acoplanar kinematics of multi-meson final states produced via linearly polarized photons, has been measured for the first time. Results for the reaction are presented for incoming photon energies between 970 MeV and 1650 MeV along with the beam asymmetry . The comparably large asymmetries demonstrate a high sensitivity of to the dynamics of the reaction. The sensitivity of these new polarization observables to the contributing partial waves is demonstrated by fits using the Bonn-Gatchina partial wave analysis.
PACS: 13.60.-r, 13.60.Le, 13.88.+e
111Corresponding authors. E-mail addresses:
firstname.lastname@example.org (E. Gutz)
email@example.com (U. Thoma), , , , , , , , , , , , , , , , , , , , , , , , , , , 222Present address: German Research School for Simulation Sciences, Jülich, Germany, , , , , , , , , , , , , , , , , , 333Present address: Institut für Kernphysik, Universität Mainz, Germany, 444On leave from: Nucl. Phys. Division, BARC, Mumbai, India, , , , 555On leave from: Department of Physics, IIT, Mumbai, India, , 666Present address: Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, Germany, , , , , , , , , 11footnotemark: 1, , 55footnotemark: 5, , 777Present address: Institut für Kernphysik, Universität Münster, Germany,
Baryons manifest the non-Abelian nature of the strong interaction. Thus, study of baryon excited states and production processes can provide insight into the dynamics and degrees of freedom relevant for non-perturbative quantum chromodynamics (QCD). At present, much of our limited understanding of these excited states comes from symmetric quark models [1, 2]. These models predict a number of states with masses above 1.8 GeV that have not been observed in the channel , the so-called missing resonances. Photoproduction of multi-meson final states avoids in the initial and the final state and gives the opportunity to probe the sequential decays of such high-lying resonances. Especially in the regime of excited states the final state is particularly attractive due to its isospin selectivity. Accordingly, the study of the photoproduction of multi-meson final states and in particular the reaction
has gained in importance over the past years, both from the
experimental side with the measurement of unpolarized total and
differential cross sections
[4, 5, 6, 7, 8]
and the beam asymmetry [5, 9], as well as
from the theoretical side. In the low-energy region, there have been attempts to
treat the as resonance that is dynamically generated from -
interactions , as well as attempts to understand
the rapidly rising cross section  by formation of
intermediate resonances. In the Bonn Gatchina partial wave analysis (BnGa-PWA),
described in [12, 13], evidence was
reported for the , an established (three-star) resonance
in the -wave and a not-well-known (one-star)
resonance with spin and parity [6, 7].
The two resonances seem to form a further parity doublet, possibly
indicating a restoration of chiral symmetry at high baryon
excitation masses . The mass of the -state
indicates a mild conflict with quark models [1, 2] and
is consistent with models describing QCD in terms of a dual gravitational
theory, AdS/QCD [15, 16].
Two-meson photoproduction is not - like two-body reactions - restricted to a single plane as seen in Fig. 1; two planes, a reaction and a decay plane enclosing an angle , occur. In contrast to single-meson production, here polarization asymmetries can also occur if e.g. only the target is longitudinally polarized or if only the beam is circularly polarized. The first measurements of the latter asymmetries in double-pion photoproduction [17, 18] have demonstrated their significant model sensitivity and revealed serious deficiencies of most available models.
For linearly polarized photons impinging on an unpolarized target two polarization observables and occur, for which so far no data has been published in any channel. The latter corresponds to the polarization observable if the dependence on the angle is integrated out. The cross section is written as
is the unpolarized cross section, is the
degree of linear photon polarization, and the azimuthal
angle of the reaction plane with respect to the normal on the polarization plane.
Since polarization observables are very sensitive to
interference effects in the amplitudes, they are
expected to significantly constrain reaction models, and hence make the extraction of resonance parameters much
more precise than unpolarized data alone would allow. Furthermore,
observables such as () can be expressed as the
imaginary (real) part of a linear combination of bilinears formed from the helicity or
transversity amplitudes that describe the process. They are therefore
not only particularly sensitive to interference effects, but also to
the relative phases of the amplitudes.
The data were obtained using the tagged photon beam of the ELectron Stretcher Accelerator (ELSA)  and the CBELSA/TAPS detector. The experimental setup consists of an arrangement of two electromagnetic calorimeters, the Crystal Barrel detector  comprising 1290 CsI(Tl) crystals and the TAPS detector [22, 23] in a forward wall setup consisting of 528 BaF modules in combination with plastic scintillators for charge information. Together these calorimeters cover the polar angular range from to and the full azimuthal range. For further charged particle identification a three layer scintillating fiber detector  surrounds the 5 cm long liquid hydrogen target .
The linearly polarized photons are produced via coherent bremsstrahlung of the initial 3.2 GeV electron beam off a diamond radiator. Electrons undergoing the bremsstrahlung process are then momentum analyzed using a tagging spectrometer consisting of a dipole magnet and a scintillator based detection system. For further details on the experimental setup, see .
For this analysis, two datasets were considered. Fig. 2 shows the degree of polarization as a function of the incident photon energy for two diamond radiator orientations. The systematic error of the polarization was determined to be .
The two datasets were subdivided into three energy ranges, MeV, MeV, and MeV respectively, as indicated by the vertical lines in Fig. 2. To guarantee a sufficiently high degree of polarization, the low energy range consists solely of data taken with the polarization setting A, the high energy range of data taken with setting B. For the intermediate energy range, both datasets were combined. To select the reaction (1), events with five distinct hits in the calorimeters were considered in further analysis. Events were retained if at least one combination of four out of the five clusters was consistent with a and an in the final state as determined by a 4 cut on the corresponding two-particle invariant mass distributions. To avoid possible systematic effects due to scintillator inefficiencies, charge information was not used to identify the proton. Instead, the direction of the fifth particle had to agree with the missing momentum of the supposed two-meson system; the angular difference had to be smaller than in and, depending on the angular resolution in the polar angle of the calorimeters, in for TAPS and for the Crystal Barrel, respectively. Additionally the missing mass needed to be consistent with the proton mass within 4. After applying the preselection, the data was subjected to a kinematic fit  imposing energy and momentum conservation, assuming that the interaction took place in the target center. Only events that exceeded, according to the respective distributions, a probability (CL) of 8% for the two-constraint hypothesis and of 6% for the three-constraint hypothesis, respectively, were retained. The proton direction resulting from the fit had to agree with the direction of the proton determined as stated above within 20. In addition, events compatible with for the hypothesis were rejected. The final event sample contains a total of 65431 events from reaction (1) with a maximum background contamination of 1% (Fig. 3).
To extract the polarization observables defined in Eq. (2), the distribution of the final state particles was fit with the expression
with being the polarization determined for each event individually and later averaged for each fitted bin. Fig. 4 shows an example of an according distribution. The effect of both beam asymmetries is clearly visible in the distinct superposition of a - () and a -modulation ().
When investigating asymmetries, the detection efficiency is usually
considered not to have an influence on the result. In the quotients
or this drops out as long as the bins in the 5-dimensional
phase space can be considered reasonably small compared to the
variation of efficiency. If on the other hand the 5-dimensional
phase space is not completely covered, which is true for most of the
experiments, the given distributions represent only the
polarization observable within the covered phase space. The
acceptance for the CBELSA/TAPS experiment determined from MC
simulations vanishes for forward protons leaving TAPS
through the forward hole, and for protons going backward in the
center-of-mass system, having very low laboratory momenta.
To study these effects on the shown distributions, different
MC datasets have been produced and analyzed.
First of all a phase space MC dataset has been produced and was analyzed using the same
analysis chain as for the data. A 2-dimensional acceptance and efficiency correction as function of the variables and
has been determined.
In addition, since effects due to the contributing physics amplitudes have to be considered, the result of the
PWA discussed below has been used to study the acceptance and efficiency. The systematic error shown in
Figs. 5 and 6 reflects the maximal effect determined
by these methods. Given the statistical uncertainties
of the data points the effects due to the acceptance and efficiency correction are
Symmetry properties allow for a further cross check of the data. has to vanish for coplanar kinematics () and the transition is equivalent to a mirror operation with respect to the reaction plane. In the case of linear polarization this leads to the transition and because to (see Eq. 2). These symmetry properties are clearly visible in the data with deviations consistent with statistics, which again shows the comparably small systematic uncertainties.
The sensitivity of the data to partial wave contributions is tested within the BnGa multi-channel partial wave analysis. The BnGa-PWA fits include a large number of reactions; a survey of the presently used datasets can be found elsewhere. Included in this fit were data on the reaction but without information on and . The fit [6, 7] had claimed evidence for contributions from negative- and positive-parity resonances with spin , the and the poorly established resonances with , and the established and resonances with . The result of a new fit including and is shown in Figs. 5 and 6 as solid curves. Removing the couplings of the -wave to p (which provides a small fraction of the total cross section only) results in a fit to and which is still acceptable; larger discrepancies are only observed in differential cross sections. However, removing the -wave which includes the above mentioned resonances and leads to noticeable discrepancies in the fits, shown as dashed curves in Figs. 5 and 6.
In addition to these fits within the BnGa-PWA, which demonstrate the sensitivity of and to the contributing partial waves, a preliminary comparison of the data with predictions using the chiral unitarity framework of  shows a significant relation between these new polarization observables and the production dynamics (1) . Furthermore, discrepancies between these predictions and the data at higher energies point towards the need for additional contributions to be included in the model. These observations underline the importance of polarization observables in general and demonstrates the significance of and as new polarization observables in particular.
We thank the technical staff of ELSA and the participating institutions for their invaluable contributions to the success of the experiment. We acknowledge financial support from the Deutsche Forschungsgemeinschaft (SFB/TR16) and Schweizerischer Nationalfonds.
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