First Measurement of $\Xi^-$ Polarization in Photoproduction

Despite decades of studies of the photoproduction of hyperons, both their production mechanisms and their spectra of excited states are still largely unknown. While the parity-violating weak decay of hyperons offers a means of measuring their polarization, which could help discern their production mechanisms and identify their excitation spectra, no such study has been possible for doubly strange baryons in photoproduction, due to low production cross sections. However, by making use of the reaction $\gamma p \to K^+ K^+ \Xi^-$, we have measured, for the first time, the induced polarization, $P$, and the transferred polarization from circularly polarized real photons, characterized by $C_x$ and $C_z$, to recoiling $\Xi^-$s. The data were obtained using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab for photon energies from just over threshold (2.4 GeV) to 5.45 GeV. These first-time measurements are compared, and are shown to broadly agree, with model predictions in which cascade photoproduction proceeds through the decay of intermediate hyperon resonances that are produced via relativistic meson exchange, offering a new step forward in the understanding of the production and polarization of doubly-strange baryons.

The CLAS collaboration has reported cross-section measurements for cascade photoproduction [26,27]. In these data, a strong back-angle peaking in the center-of-momentum cascade angular distribution (cos θ Ξ ) was observed, which along with the invariant mass distributions of the K + Ξ − system, suggested the significant role that intermediate hyperon resonances with masses of about 2 GeV play in cascade photoproduction. These results generated theoretical interest in understanding the production mechanism behind S = −2 states. In particular, Refs. [28,29] found it is necessary to include the contributions from the decay of high-mass hyperons (up to Λ(1890)) that are predominately produced in t-channel K/K * exchange, as illustrated in Fig. 1, to explain the CLAS cross-section measurements [27]. Furthermore, Ref. [29] investigated the role of the addition of high-spin hyperon states around 2 GeV and found significant contributions from spin/parity J P = These earlier photoproduction data from CLAS did not have either beam or target polarization, and no study on induced polarization was carried out. But as pointed out in Ref. [29], both the induced and transferred polarization of the cascade ground state are sensitive to the production mechanism, particularly, the mass, spin and parity of intermediate hyperon resonances, as well as to the mesonic exchange mechanisms.
The majority of early data for hyperon and cascade spectroscopy was generated using K − beams on nuclear targets. However, the significance of the Y * → KΞ decay has never been firmly established except for the small branching ratios and branching-ratio upper limits reported for Λ(2100) 7 2 − and Σ(2030) 7 2 + [30][31][32][33] in the 1960's and 1970's. In general, the excitation spectrum for S = −1 hyperons also remains under-explored, particularly in the high mass (> 2 GeV) region. When compared with model predictions, cascade polarization measurements can build on the evidence for or against intermediate hyperon resonances as the dominant production mode, discriminate among the candidate exchange mechanisms, and even point to the existence of higher mass/spin hyperons.
The understanding of the ground state cascade production mechanism is not limited to its connection to the intermediate hyperon resonances. The current spectrum of experimentally established excited cascade states has remained virtually unchanged in the past thirty years [34]. At present, just six states are considered to have solid experimental evidence, and only half of these have established spin and parity. Furthermore, the number of cascade (as well as hyperon) states that appear in the most recent lattice QCD calculations [35] are nearly as numerous as predicted by early constituent quark models [36]. Understanding the production of excited cascades cannot be fully achieved without a better understanding of the ground state production, including polarization measurements. This manuscript reports the first measurements of both induced and transferred polarization of cascade baryons in photoproduction.

Experimental Details
A large-statistics dataset with an integrated luminosity of 68 pb −1 was collected with CLAS [37] using a circularly polarized, tagged photon beam [38] of energy range 1.1 to 5.4 GeV incident on a liquid hydrogen target [39]. The photon beam was produced from a longitudinally polarized primary electron beam of energy 5.7 GeV, incident on a gold radiator. The electronbeam's helicity was flipped pseudo-randomly at a rate of 30 Hz and was measured periodically by a Møller polarimeter, yielding a degree of polarization of 0.68, Figure 1: A possible Feynman diagram of Ξ − photoproduction via the decay of intermediate hyperon resonances in t-channel K/K * exchange, which is a major component in the production models of Nakayama [28,29]. averaged over the entire run period. The degree of circular photon polarization was calculated and is known to be proportional to the electron beam polarization, and to increase as a function of the ratio of photon energy to the energy of the primary electron beam [40]. The target consisted of a 40-cm-long cylindrical cell containing liquid hydrogen. Momentum information for charged particles were obtained via tracking through three regions of multiwire drift chambers [41], with the regiontwo drift chambers inside a toroidal magnetic field that was generated by six superconducting coils. Scintillators [42] outside of the drift chambers were used to measure time-of-flight (TOF) information, which, when combined with the momentum information, provided charged-particle identification.

Analysis
Initial event selection required timing coincidences between the photon tagger and the passage of two charged particles through the CLAS detector. The photons that produced the event were selected using vertex information obtained from tracking, and the timing information from a start counter [43], which surrounded the target. The time that an event occurred at its vertex, as measured by the start counter, was required to be within ±1 ns of the photon time provided by the accelerator radio-frequency signal. Furthermore, the vertex time determined from the TOF system was required to be within ±1 ns of the photon time for all detected charged particles. The next step in the identification of the γp → K + K + Ξ − reaction with the subsequent decay of Ξ − → Λπ − was selecting events with three charged mesons, Figure 2: Mass distributions for all events passing cuts on timing, detected particle mass, and vertex location are shown by the data points with error bars. Top left: Missing mass spectrum of the K + K + system; Top right: Missing mass spectrum of the K + K + π − system; Bottom left: Invariant mass spectrum of the Λπ − system; Bottom right: Invariant mass spectrum as reconstructed from the four-momentum difference of the Ξ − and π − system. In all plots, a Gaussian is fit to the signal over a polynomial background (dashed red line). The same distributions after applying the hypersphere cuts are shown by the filled histograms. The vertical lines represents the known Λ or Ξ − masses. Detection of the π − originating the Λ decay, rather than the Ξ − decay, is evident in the left and right of the signal region, in the bottom left and bottom right plots, respectively. K + , K + , and π − , detected. Their momentum was corrected for the energy loss in the target region, as well as other detector effects such as misalignments and errors in the magnetic field map. The signals were then extracted using the following four mass distributions: where X indicates the missing particle, labeled as where X indicates the missing particle, labeled as MM(K + K + π − ). 3. Invariant mass of the (Λ + π − ) system, labeled as M(Λ+π − ), and where the known Λ mass, 1115.683 GeV [44], was combined with the missing threemomentum of the K + K + π − system to define the Λ four-momentum vector. 4. Invariant mass reconstructed from the fourmomentum difference of the Ξ − and π − system, labeled as M(Ξ − − π − ), and where the known Ξ − mass, 1321.71 GeV [44], was combined with the missing three-momentum of the K + K + system to define the Ξ − four-momentum vector.
The mass distributions for events passing cuts on event timing, event vertex location, and detected particle mass are shown by the data points with error bars in Fig. 2.
Clear signals for the Λ and Ξ − are seen. Instead of cutting on individual mass distributions, each of the above quantities was scaled by the reciprocal of their individually associated 3σ width, and treated as orthogonal displacements in a four dimensional space. A composite cut was then placed on the volume of the hypersphere that was constructed from the scaled displacements. The width σ, of each mass distribution was measured by fitting it with a Gaussian plus a polynomial to model the signal and background, as shown by the fits in Fig. 2. The hypersphere coordinates were defined as, , where σ n denotes the Gaussian width of the associated quantity as displayed in Fig. 2. A cut on the hypersphere radius r represents a simultaneous cut on all four mass quantities, where a 3σ cut corresponds to taking events within the hypervolume defined by r < 1. This cut, as opposed to simply rectangular cuts on the masses, allowed the best signal to background ratio, even though x i 's are not totally independent. The final data sample of 5143 events are shown in the filled histograms in Fig. 2.
The Ξ − polarization is related to the angular distribution of the decay π − as measured in the rest frame of the Ξ − by [45] where θˆi π is the pion angle relative to the i = x, y, or z axes in the Ξ − rest frame, N is the total number of events in the I(cos θˆi π ) distribution, P Ξ i is the i-component of the Ξ − polarization, and α is the Ξ − weak-decay asymmetry or analyzing power with α = −0.458±0.012 [34].
The axes are defined in the Ξ − rest-frame (Fig. 3) aŝ where p γ and p Ξ are the photon and cascade momentum vectors, respectively, both in the center-of-momentum frame of the beam-plus-target system. The spin observables P, C x , and C z are connected to the recoil polarization P Ξ through, where P is the degree of photon-beam polarization. The induced polarization, P, can be extracted from the forward-backward asymmetry, A y , of the pion angular distribution. This method has the advantage of the cancelation of detector-acceptance effects, which follows from the fact that the polarization axisŷ points isotropically in the lab frame. The asymmetry is defined as, where N + y and N − y represent the number of events with cos θ y π as positive and negative, respectively. The asymmetry is related to the induced Ξ − polarization by The double polarization observables C x and C z characterize the transferred polarization of the photon to the Ξ − and are extracted from the photon-helicity asymmetry, where N + hel and N − hel are the number of events associated with positive and negative photon-beam helicity states, Figure 4: Above shows the beam helicity asymmetries across x and z for the Ξ − decay, the slopes of which, along with the dilution factor, D, are used to calculate C x and C z . The events displayed include all angles between Ξ − and the z-axis but are limited to one photon energy bin.
respectively. The transferred polarization is related to the photon-helicity asymmetry by −A(cos θˆi π ) |P |α = C i cos θˆi π .
The value and uncertainty of C i can thus obtained from the slope of A cos θˆi π . Examples of the linear fits used to extract C x and C z are shown in Fig. 4. In the asymmetry defined in Equation 7, systematic effects such as detector acceptance mostly cancel, since they occur irrespective of the photon helicity. It was found that overall around 15% of the events surviving the final cuts were unpolarized background events. The fraction of these events were estimated in each kinematic bin by evaluating the background subtracted yield through a Gaussian fit with a polynomial background. These events were found to have polarizations consistent with zero, thus reducing the measured polarization by the dilution factor, where f BG is the fraction of background events in each sample. In order to recover the true polarization, the measured polarization observables in each bin were divided by the corresponding dilution factor, the values of which were found to be between 0.82 and 0.91. Aside from the dilution factor, three main sources of systematic uncertainty contributed to the overall uncertainties in the measurements. For one, systematic effects due to acceptance-related factors, including the selection of the fiducial region of the detector, were estimated by comparing the final results obtained with and without these cuts, and were found to be, integrating over all kinematic bins, δ acc P = 0.022, δ acc C x = 0.01 and δ acc C z = 0.052. Additionally, uncertainty in the degree of photon-beam polarization, which in turn resulted from the uncertainty in the primary electron beam polarization, contributed a relative scale-type uncertainty of δ P · C i /C i = 0.03. Finally, the uncertainty in the analyzing power of the cascade, which is ±0.012 [34], leads to a relative scale-type uncertainty of δ α P/P = δ α C i /C i = 0.026. For both the induced and transferred polarization measurements, the statistical uncertainty dominates the cumulative systematic uncertainty.

Results & Comparison With Theory
In the extraction of P, data were binned into nine regions defined by three bins of the cascade angle between the photon and target momenta in the c.m. frame with event-weighted average values of cos θ Ξ = −0.79, −0.41, and 0.19, and three bins of photon energy with event-weighted averages of E γ = 3.47, 4.09, and 4.88 GeV. Since the extractions of C x and C z require more events to achieve the same statistical uncertainty as P, these variables were binned into only three regions of cos θ Ξ and summed over 2.8 ≤ E γ ≤ 5.5 GeV, or conversely, binned into three regions of E γ and summed over −1 ≤ cos θ Ξ ≤ 1. The P results are given in Table 1 and the C x and C z results are given in Table 2, as well as shown in Figs. 5, 6, and 7. These results can be found in Ref. [46]. E γ (GeV) cos θ Ξ P δ stat P δ sys P δ total P δ scl P/P 3. For comparison, the polarization predictions of the three phenomenological model variants put forth by Refs. [28,29] to help explain the differential cross sections reported by Ref. [27], overlay our results in Figs. 5, 6, and 7. All three model variants share the same framework, in which cascade photoproduction E γ (GeV) cos θ Ξ C x δ stat C δ sys C δ total C δ scl C/C 3.   2030), which has spin-7/2, were introduced in Ref. [29] (dotted green).
The predicted values of P and C x follow fairly flat curves, that when determined over the entire angular and/or energy range, integrate to nearly zero. Conversely, the predicted values of C z are positive and sizable over the kinematic range and thus do not integrate to zero on any interval.
As shown in Figs. 5, 6, and 7, our measurements are generally well described by the pseudoscalar (solid red) and the 2011 pseudovector (dotted green) models but not the 2006 pseudovector model (dashed blue). We have performed a statistical comparison of the three model variants to 15 independent data points, 9 of which come from the induced polarization, P, in the unintegrated binning scheme in Table 1, while the other 6 data points come from the transferred polarization, C x and C z , summed over E γ . The agreement between the data and the pseudoscalar variant is good, with a χ 2 = 13.0. The 2006 variant of the pseudovector model has χ 2 = 33.0 and is therefore excluded by the data with ∼ 99% confidence. The 2011 variant of the pseudoscalar model (dotted green) has χ 2 = 17.4. Similar results are found when comparing the model to the cos θ Ξ integrated transferred polarization results. However it is import to point out these models were tested against the cross sections measurements up to around 4 GeV. Above that, it is possible that other mechanisms not accounted for such as the Regge trajectories and other higher-mass hyperons might need to be included.
Finally, it is worth pointing out that the photoproduced Λ was observed [8] to exhibit nearly 100% po- Figure 5: P (top), C x (middle) and C z (bottom) as a function of E γ and summed over cos θ Ξ . The error bars represent the total uncertainty. The legend specifies pseudoscalar (ps) or pseudovector (pv) coupling, as well as the journal of publication for the associated model. larization by evaluation of R = C 2 x + C 2 z + P 2 . This quantity for the Ξ − , integrating our results over all bins, is 0.30 ± 0.14, which is non-zero but significantly smaller than the Λ counterpart.

Conclusion
To summarize, we have made the first polarization measurements for the Ξ − in photoproduction by measuring the induced polarization, P, as well as transferred polarization, C x and C z , using a circularly polarized photon beam. We have found that the total integrated Ξ − polarization departs from zero by 2σ, but is significantly smaller than in the analogous case for Λ photoproduction. The results have been compared, and show general agreement with the predictions of a phenomenological model of cascade photoproduction involving intermediate hyperon resonances that are produced, predominantly in the t-channel, via relativistic pseudoscalar meson exchange. The results strongly disfavored a model variant that includes significant contributions from the Σ(2030) 7 2 + . While precisely distinguishing between current and future model variants to determine the role of high-spin excited hyperons and the contributions from scalar versus vector exchange mechanisms will be left to future experiments at CLAS12 and GlueX [47], we have made the first step toward a detailed understanding of Ξ − photoproduction.

Acknowledgments
We thank K. Nakayama for many fruitful discussions in which he provided his insight and support. We acknowledge the outstanding efforts of the staff of the Accelerator and the Physics Divisions at Jefferson Lab that made this experiment possible. This work was supported in part by the U.S. Department of Energy, the National Science Foundation, the Italian Istituto Nazionale di Fisica Nucleare, the French Centre National de la Recherche Scientifique, the French Commissariatà l'Energie Atomique, the National Research Foundation of Korea, the UK Science and Technology Facilities Council (STFC), and the Physics Department at Moscow State University. The Jefferson Science Associates (JSA) operates the Thomas Jefferson National Accelerator Facility for the United States Department of Energy under contract DE-AC05-06OR23177. The FIU group is supported by the U.S. Department of En- Figure 7: P as a function of cos θ Ξ for three E γ bins as indicated. Error bars and curves are the same as in Fig. 5. ergy, Office of Nuclear Physics, under contracts No. de-sc0013620.