The Story of Σ Hypernuclei-A Modern Fable

The reality of Σ hypernuclei has been the subject of intense concern among experimenters and theoreticians for more than 20 years. The possible existence of Σ hypernuclei was first suggested by by a pioneering experiment on a ⁹Be target at the CERN PS. There were reported to be two narrow (Γ < 8 MeV) peaks in the continuum region. This finding was quite unexpected since the widths of Σ states were believed to be large due to the strong conversion process. It is obvious that if such relatively long-lived systems were confirmed unambiguously by experiment, their masses and widths provide important constraints on the ΣN effective interaction and its relation to the ΛN and NN interactions. Since the Σ carries isospin, the role of isospin and isospin conservation in hadronic reactions could be explored. This report stimulated a number of subsequent experiments at the BNL-AGS and KEK, along with further experiments with a specially created short kaon beam at the CERN PS. Experimental data were reported for different targets at different momenta and at different conditions. Various tagging techniques were employed to suppress backgrounds, but always at the expense of a reduction in statistical quality. Because of problems with resolution and statistics, contradictions among the different sets of data resulted more often in clouding the issues than clarifying them. Thus, up until a few years ago, there was no statistically clear confirmation of this surprising finding. In the last few years, however, a series of definitive experiments has been performed at the BNL-AGS in an effort to resolve the discrepancies and settle the controversy. Besides repeating the initial experiment on Be, a target of ⁶Li was run. The earlier stopped kaon data on ⁴He was repeated in an in-flight experiment, and the suggestion of a Σ bound state, with virtually pure isospin, confirmed. We now have a better understanding of the role of isospin in the nucleon-hyperon interaction and the importance of three body forces in hypernuclei. According to that understanding, it is unlikely that Σ states for A > 5 will ever be seen. In this review, a critique of the past BNL experiments is presented and conclusions on the status of the Σ database drawn. As it is with the fables of old, this modem story also has a moral and it can be derived by paraphrasing and combining two old ones: "Seek and ye shall find; but beware, lest what ye find be only in the eye of the beholder."