K⁰sΣ⁰ photoproduction off the neutron at the K* threshold

This is the smoking gun experiment for hidden strangeness states to exist [1] similar to the pentaquark states observed by LHCb [2] in the hidden charm sector. Data were taken using an Emax = 2.9 GeV tagged photon beam incident on 11 cm long liquid deuterium and hydrogen targets with integrated photon fluxes from threshold to Ecm = 2.4 GeV of 6.39 and 5.78 ×1012, respectively. K0S candidates were identified in the BGO ball via the decay K⁰S →π⁰π⁰ →(γγ)(γγ). The invariant masses of the two-photon pairs were required within 30 MeV of the π⁰ mass. As in the previous analyses, the Σ⁰ was tagged through the characteristic photon of the Σ⁰ →Λγ decay. Two additional criteria were used to isolate the reaction channel: the missing mass from the K⁰S must be consistent with the Σ⁰ mass, and the detection of exactly two charged particles must match the kinematically allowed region of the decay Λ →π⁻p.

The deuteron data set contains the desired reaction off the neutron with additional background both off the neutron and proton. The background off the proton was subtracted using the hydrogen data set with the same selection criteria applied, and scaled according to relative luminosities. To account for Fermi motion, the 4-momentum of the target proton (used to determine the missing momentum to K⁰S candidates) was smeared according to the nucleon momentum distribution in deuterium [3]. Fig. 1 shows the 2π⁰ invariant mass distributions obtained from deuterium and hydrogen targets. A peak consistent with the K⁰S mass is visible in the deuterium and, especially, the hydrogen subtracted data. Compared to hydrogen there is additional background which is dominantly associated with the neutron reactions γn → 3π⁰n and γn → ηn. To fit this remaining background two methods were used. The first used simulated phase space distributions, referred to as PS. The second used real data distributions (RD) with selection criteria relaxed to provide a distribution which only described the background without signal. In both cases the signal shape was phase space generated.

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Fig. 1: Two π⁰ invariant mass distributions for deuterium (cyan) and hydrogen (black) data sets. The hydrogen data is Fermi broadened and luminosity scaled. The hydrogen-subtracted deuterium spectrum is shown in blue.

ROOFIT [4] was again used to fit the data. Fig. 2 shows fits using the PS background description. The differential cross sections extracted for the reaction γn → K⁰SΣ⁰ as a function of cm-energy W and for four angular bins covering −0.7 <cos θKcm < +0.5 are shown Fig. 3. In the overlap region they are consistent with a recent MAMI-A2 measurement [5] which is however limited in energy. At backward angles the energy dependence is flat with a cross section of dσ/dΩ ≅0.05 μb/sr. It is rising to more forward angles and, in the most forward bin a peak develops at W = 2 GeV, i.e. indeed at the K* threshold. This is consistent with the form of the energy dependent peak predicted, albeit in Ref. [1] for the total cross section. We observe the strength in forward directions. The slight shift in energy between data and predicted peak can be easily accommodated by minor adjustments of resonance parameters [6]. In addition to the cusp in K⁺Λ(1405) photoproduction discussed here, this result is taken as a further possible indication that the mechanism of vector meson-baryon interactions suggested in Ref. [1] could describe the formation of multi-quark configurations in both the hidden c and s sectors. For conclusive evidence of the peak to exist, it is necessary to significantly improve statistical precision for the K⁰SΣ⁰ channel.

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Fig. 2: Example fits to the 2π⁰ invariant mass spectrum after subtraction of the scaled hydrogen yield. Shown is the angular region 0.2 < cos θKcm < 0.5 in 10 cm-energy bins.
The centre energy of each bin is labelled in the top right corner. The lines represent fits of signal (green), and the two background channels γn →3π⁰n (light blue) and γn →ηn (gray). The red line indicates the sum of signal and backgrounds. The residuals are plotted at the bottom of each fit.
Fig. 3: Differential cross section of γn → K⁰SΣ⁰ as a function of W in four angle bins labelled inset and for RD (red triangles) and PS (black circles) background descriptions. Error bars are purely statistical. Systematic errors are shown as bars on the abscissa (gray: scaling errors, red: fitting, green: quadratic sum). The red line in the most foraward angular bin is the prediction of Ref. [1] for the total cross section, arbitrarily scaled. Blue data is from Ref. [5].
[1] A. Ramos and E. Oset, Phys. Lett. B 727 (2013) 287
[2] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 115 (2015) 072001, e-print: 1507.03414 [hep-ex]
[3] M. Lacombe et al., Phys. Rev. C 21 (1980) 861
[4] Toolkit for Data Modeling with ROOT (https://root.cern.ch/roofit)
[5] C.S. Akondi et al., Eur. Phys. J. A 55 (2019) 202
[6] A. Ramos and E. Oset, priv. comm. (2020)
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