Photoproduction of meson pairs: First measurement of the polarization observable I^{s}

Photoproduction of meson pairs: First measurement of the polarization observable

E. Gutz V. Sokhoyan H. van Pee A.V. Anisovich J.C.S. Bacelar B. Bantes O. Bartholomy D. Bayadilov R. Beck Yu. Beloglazov R. Castelijns V. Crede H. Dutz D. Elsner R. Ewald F. Frommberger M. Fuchs Ch. Funke R. Gregor A. Gridnev W. Hillert Ph. Hoffmeister I. Horn I. Jägle J. Junkersfeld H. Kalinowsky S. Kammer V. Kleber Frank Klein Friedrich Klein E. Klempt M. Kotulla B. Krusche M. Lang H. Löhner I. Lopatin S. Lugert D. Menze T. Mertens J.G. Messchendorp V. Metag M. Nanova V. Nikonov D. Novinski R. Novotny M. Ostrick L. Pant M. Pfeiffer D. Piontek W. Roberts A. Roy A. Sarantsev S. Schadmand Ch. Schmidt H. Schmieden B. Schoch S. Shende A. Süle V. Sumachev T. Szczepanek A. Thiel U. Thoma D. Trnka R. Varma D. Walther Ch. Weinheimer Ch. Wendel Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, Germany Petersburg Nuclear Physics Institute, Gatchina, Russia Kernfysisch Verseller Instituut, Groningen, The Netherlands Physikalisches Institut, Universität Bonn, Germany II. Physikalisches Institut, Universität Giessen, Germany Physikalisches Institut, Universität Basel, Switzerland Department of Physics, Florida State University, Tallahassee, FL 32306, USA
October 3, 2019

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: (E. Gutz) (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 [3], 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 [10], as well as attempts to understand the rapidly rising cross section [11] 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 [14]. 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.

Figure 1: Angle definitions in the center-of-momentum frame. is the angle between the reaction plane defined by the incoming photon and recoiling particle and the decay plane of two final state particles.

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


[19] where 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) [20] and the CBELSA/TAPS detector. The experimental setup consists of an arrangement of two electromagnetic calorimeters, the Crystal Barrel detector [21] 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 [24] surrounds the 5 cm long liquid hydrogen target [25].
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 [26].
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 [27].

Figure 2: Degree of linear polarization for the two settings. The largest polarizations were 49.2% at  MeV (A) and 38.7% at 1600 MeV (B), respectively (see [27] for details). Vertical lines indicate the chosen energy ranges.

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 [28] 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).

Figure 3: invariant mass distribution after cuts on the confidence levels of the ( ) and ( ) fits respectively. This yields a total number of 68514 events including the linear background (red line). An additional cut on the fit () rejects 3083 events, retaining 624 background events ().

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 ().

Figure 4: Example of a measured -distribution. Shown is the -distribution of the final state proton in the region for events in the energy range  MeV (y-axis with suppressed-zero scale).

From the fits to the according -distributions and have been extracted, as shown in Figs. 56.

Figure 5: Measured beam asymmetries in the reaction . Left to right: CMS energy ranges  MeV,  MeV,  MeV. Top to bottom: Beam asymmetries obtained treating the proton (top row), (center row) and (bottom row) as recoiling particle. Filled symbols: , open symbols: . Solid curve: Full BnGa-PWA fit, dashed curve: BnGa-PWA fit excluding -wave. Histograms below: Estimate of systematic errors due to acceptance and efficiency.
Figure 6: Measured beam asymmetries in the reaction . Notation as Fig. 5, except filled symbols: , open symbols: .

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 small.
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 [10] shows a significant relation between these new polarization observables and the production dynamics (1) [29]. 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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