K⁺Σ⁰ photoproduction at forward angles

Similarly to the K⁺Λ photoproduction described here, a wealth of polarisation observables have been measured for K⁺Σ. The interpretation in terms of PWAs and phenomenological models is more complex however, due to the isospin I = 3/2 of the Σ. This allows also ∆ states to contribute in the s-channel in contrast to only N*s in the Λ case.

A striking feature observed in the charge conjugate K⁰_SΣ⁺ channel at very forward angles is the cusp-like structure at the K* threshold [1]. If this indeed was driven by a box process as shown in Fig. 1 or a corresponding triangle, then similar effects may occur in the K⁺Σ⁰ channel. To understand this, the hitherto unmeasured very forward K+ angular region is essential. This kinematic regime is also important for PWAs, since higher spin intermediate states are expected to generate modulations at the extreme angles. For both, PWAs and phenomenolgical models, this region is also crucial in constraining the dominant t-channel mechanisms contributing to the reaction. An obstacle for PWAs is the inconsistency between existing data sets of the order of 25 – 30 % deviation in forward K⁺ directions.

3_K-Sigma_FeynmanForKSigma_Revised-eps-converted-to.pdf-1.png

Fig. 1: Possible process in (KΣ)⁰ photoproduc-tion in the vicinity of the K* threshold(s).

With the predecessor project we measured the γp → K⁺Σ⁰ reaction from threshold to cm-energies of W≅2 GeV. Data were taken over 22 days using an 3.2 GeV electron beam on a 6 cm long liquid hydrogen target. K⁺ were detected in the forward spectrometer as described above. Of particular importance is the single γ originating from the Σ⁰ decay. Boosted into the rest frame of the parent Σ⁰ the characteristic energy of 74 MeV can be efficiently observed in the BGO ball and utilized to tag the Σ⁰ decay.

Fig. 2: γp → K⁺Σ⁰ differential cross section for cos θ^K_cm > 0.9. Black circles represent BGOOD data. Systematic uncertainties are indicated on the abscissa (shaded blue: overall scaling uncertainty, shaded red: point-to-point uncertainty, grey: total). The Bonn-Gatchina PWA solutions [2] with and without the inclusion of our new data are the magenta and cyan lines, respectively.
Left panel: Whole forward region in comparison to previous experiments (CLAS: Dey et al. [3] (blue squares) and Bradford et al. [4] (red triangles), SAPHIR: Glander et al. [5] (green circles), Sumihama et al. (LEPS) [6] (yellow diamonds), Shiu et al. (LEPS) [7] (yellow stars)). Note the CLAS angular intervals are cos θ^K_cm ≅0.95 ...0.85 as more forward directions are inaccessible.
Right panel: Forward region of left part split into 5 angular bins for BGOOD. Angular ranges and transverse momentum p_T (c.f. text) labelled inset.

Results for the forward differential cross section are shown in Fig. 2. In comparison (c.f. Fig. 2 left) our new data provide the highest statistics from threshold to W = 1970 MeV, enabling a discrimination between the conflicting previous analyses. In this forward direction we agree with the older CLAS data set of Bradford [4]. The CLAS data of Dey [3] is higher by approximately 20 % and the SAPHIR [5] somewhat lower. The previous data sets are consistent with a drop at W ≅ 1900 MeV. In PWAs and isobar
models [8–11] the region below was regarded as an enhancement associated with D₁₃(1895), S₃₁(1900), P₃₁(1910) and P₁₃(1900), but with no firm agreement. Forward acceptance and resolution of the BGOOD experiment are sufficient to divide the forward region into five intervals in cos θ^K_cm of 0.02 each. With this we now resolve a cusp-like structure. Fig. 2 (right) demonstrates this becomes more pronounced in very forward directions. For cos θ^K_cm > 0.98 the reduction is approximately 70 % over a 30 MeV range. It is less than 20 % at the most backward interval of cos θ^K_cm < 0.92.

Mostly constrained by the CLAS data, the Bonn-Gatchina PWA solution BG2019 [2] gives a reduced χ2 ≅ 6 when compared to the new BGOOD data. After including this data and optimisations of the couplings [12], a marked improvement to χ2 ≅ 2.1 was achieved, with no significant changes to the fit at more backwards angles. Additional s-channel contributions were iteratively included to test this. A previously unobserved ∆(1917) with J = 5/2⁻ and a narrow width of 59 MeV gave the best fits, only influencing the most forward directions and not significantly affecting the description of the CLAS data.

These changes to the PWA solution demonstrates how important it is to cover the kinematic regime of the BGOOD experiment. Nevertheless, it is certainly premature to draw firm conclusions regarding the ∆(5/2⁻) without indications for it from other reaction channels. It could also mimic meson-baryon interaction effects in this specific photoproduction reaction of the type of triangle and box diagrams discussed above, as a number of thresholds are close by. For example, due to attractive I = 1 S-wave interactions of the baryon decuplet with the octet of pseudoscalar mesons, pronounced structures had been expected in the ΣK channel at the Σ*(1385)K threshold [13]. The interplay of intermediate resonances and meson-baryon interaction dynamics should specifically affect the t-dependence. The t-dependence of the γp → K⁺Σ reaction for cos θ^K_cm > 0.9 is shown in Fig. 3. The left diagram illustrates in sample bins of W how the function

dσ⁄dt = dσ⁄dt _{t=t_min}e^S|t−t_min| (1)

was fitted to the data (red lines). For a dominating t-channel process a dependence falling with t would be expected, flat or increasing with no maximum at tmin for predominantly s-channel.
Fig. 3 right shows the slope parameter, S, extracted from the fits. It is predominantly positive, but with a pronounced structure of slightly negative values in the region of the cusp.

Fig. 3: t-dependence of the γp → K⁺Σ for cos θ^K_cm > 0.9. Black points represent BGOOD data. Only statistical errors shown. Left panel: dσ/dt versus |t −t_min| for intervals of cm energy, W, labelled inset. The red line is Eq. 1 fitted to the data.
Right panel: slope parameter, S, versus W.

This is indicative of a change in the reaction mechanism as would be expected if an initially resonance driven process was modified through t-channel exchange within a certain energy region. A possible origin could be a box mechanism similar to Fig. 1 or a triangle process like this. Both will contribute only in the narrow energy interval where, according to the Coleman-Norton theorem, the internal lines can be almost on mass shell. It is interesting to note the previous measurements of K⁺Σ⁰ invariant mass distributions, produced via coherent diffractive proton-carbon scattering at small transverse momentum p_T (corresponding to small t in photoproduction!) [14]. Preliminary results indicated a peak close to 2 GeV/c², which was interpreted as K*Σ configurations of a pentaquark or molecular-type ‘exotic’ state of hidden strangeness. In photoproduction strong distortions in the vicinity of the K* threshold were expected, however there was no significant evidence in the existing photoproduction at the time (1997) [15].

Due to the forward acceptance and resolution of BGOOD it is straightforward to extrapolate the cross section to tmin which corresponds to θ^K_c = 0. This is shown in Fig. 4 where the cusp-like structure becomes particularly pronounced. The energy regime of W ≅ 1.9...2 GeV is of particular interest, due to the thresholds indicated in Fig. 4 and, associated with this, predictions and earlier experimental indications of meson-baryon or pentaquark quasi bound states.

A X(2000) pentaquark candidate was suggested by data of the Sphinx collaboration [16] on diffractive K⁺Σ⁰ production. The signal only became apparent when it was required that the K⁺ (or Σ⁰) transverse momentum p_T was smaller than 141 MeV/c. Due to the extreme forward acceptance of the new BGOOD dataset it is in a similar kinematic regime, and the corresponding p_T at the cusp is labelled for each cos θ^K_cm interval in Fig. 2 (right panel). p_T is about 1/3 in the most forward interval than what could be accessed by CLAS and becomes comparable of the Fermi momentum of the deuteron. The quickly changing cross section with respect to p_T might suggest an extended, loosely bound system where the constituents travel parallel at very small transverse momentum. The width of 91 MeV/c² proposed from the Sphinx analysis ensures that the X(2000) significantly overlaps with the observed cusp.

Indicated in Fig. 4 are predicted KKp and φp bound states [50,51]. The KKp state mass of 1920 MeV is exactly at the cusp, and the width of approximately 100 MeV comparable with the width of the cusp. The predicted ΦN state is expected at a mass of approximately 1950 MeV, immediately after the cusp. Ref. [20] suggested to experimentally produce it using a gold target where, due to Fermi motion, the Φ could have sufficiently low relative momentum to one of the nucleons to form the bound system. At the cusp at W = 1900 MeV the 3-momentum component of t is very similar, between 500 to 550 MeV/c, to the momentum at the maximum amplitude of the bound state formation, c.f. Fig. 4 in Ref. [20].

Fig. 4: γp → K⁺Σ⁰ differential cross section dσ/dt extrapolated to t_min versus W (filled black circles). Data from the CLAS collaboration for the K⁺Λ(1405) and K⁺Σ⁰(1385) final states are included, which were estimated from ref. [17] (red squares and blue triangles, respectively). The magenta diamonds represent the Φp cross section from LEPS [18]. The colored vertical dashed lines indicate the respective thresholds, with the addition of the K⁺K⁻p threshold marked in black. The predictions of the KKN [19] and ΦN [20] bound states are shown as the cyan and green lines at arbitrary scale.

Ref. [21] predicted a hidden-strangeness pentaquark consisting of a bound Σ(1385)K system. It is calculated to have a mass of 1873 MeV and binding energy of 7.4 MeV and thus lying just below the observed cusp. Also shown in Fig. 4 are cross section data for K⁺Λ(1405), K⁺Σ(1385), and Φp at t_min photoproduction. All those channels have thresholds close to the cusp. There appears a similar behaviour of the KΣ(1385) channel compared to K⁺Σ⁰, exhibiting a pronounced drop in strength directly at threshold at similar W, and a smooth transition with the K⁺Λ(1405) and Φp channels. Qualitatively one might be tempted to argue that a conserved quantity of ss quark pairs is distributed across the different channels and bound states.

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