Examination of the nature of the ABC effect
Introduction
Recently it was shown that there is a resonance pole at in the – coupled partial waves based on a SAID partial-wave analysis, which included new data from COSY on the analyzing power of np scattering [1], [2], [3], [4]. This finding matches perfectly with the resonance structure observed at with a width of 70 MeV in the total cross section of the double-pionic fusion reactions and [5], [6], [7]. The results from the WASA-at-COSY for the reaction have meanwhile found support by preliminary results from HADES [8].
Having revealed the pole in the np scattering amplitudes means that this resonance structure constitutes an s-channel resonance in the system of two baryons. It has been denoted since then by following the nomenclature used for nucleon excitations.
Follow-up measurements of the non-fusion reactions [9] and [10] with the WASA detector at COSY and [11] with the HADES detector at GSI showed that also these reactions, which are partially of isoscalar character, show the resonance in agreement with expectations based on isospin coupling.
In addition, WASA measurements revealed that is also present in the double-pionic fusion reactions to the helium isotopes , , and [12], [13], [14], [15]. This means that obviously is stable enough to survive also in a nuclear surrounding. This conclusion is in agreement with the appearance of a dilepton enhancement (DLS puzzle) in heavy-ion collisions [16].
Section snippets
ABC effect
In 1960 Abashian, Booth and Crowe [17] found out that the ππ-invariant mass spectrum in the double-pionic fusion reaction exhibits a pronounced low-mass enhancement. Subsequent measurements showed that this enhancement also persists in the fusion reactions to d and 4He [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], if the produced pion pair is of isoscalar nature. Since there was no plausible explanation for this effect, it got named after the initials of the authors
Hypotheses for its explanation
From the Dalitz plots of the double-pionic fusion reactions [5], [6], [7], [12], [14] we know that decays predominantly via the ΔΔ system in the intermediate state – with the two Δs being in relative s-wave. This is in accordance with meanwhile numerous theoretical work about this resonance [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39]. It also is in agreement with the measured branchings of the decay into the diverse channels [40].
Therefore it seems likely
Conclusions
We have discussed several possible reasons for the ABC effect. Most of these hypotheses can be tuned to reproduce at least qualitatively the measured low-mass enhancements in the spectra of double-pionic fusion reactions. The non-occurrence of the ABC effect in the non-fusion reaction has been used as a further constraint to filter out viable solutions.
Most natural and straightforward appears the explanation of the ABC effect as a direct consequence of the vertex function in the
Acknowledgements
We acknowledge valuable discussions with V. Baru, A. Gal, V. Grishina, C. Hanhart, G. Kälbermann, V. Kukulin, E. Oset, G.J. Wagner and C. Wilkin. This work has been supported by DFG (CL 214/3-1) and STFC (ST/L00478X/1).
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