Updating the effective range expansion of low-energyN $$\bar N$$ -scattering

Abstract

Low energy N?4 scattering is reanalyzed using the new data on annihilation cross-sections from CERN [1], the tip-absorption measurement from BNL [-2] and the annihilation width of the 2p state in antiprotonic hydrogen [-3]. Imposing the condition that the imaginary part of the effective range is negative we find low energy scattering parameters which interpolate between the existing ITEP [4] and CERN/Heidelberg [5] values. PACS: 13.75.-n; 13.75.cs Experiments in low energy NbT-scattering have developed greatly since the operation of the LEAR facility at CERN has started. Besides the NN and the ~N interactions antinucleon-nucleon scattering is the third test of our limited understanding of hadronic interactions. A comparison of N/V-intermediate range potentials with NN-potentials is perhaps the only chance to find the range where the meson-exchange picture breaks down and subnucleonic constituent interchange takes over. Unfortunately the strong NN-annihilation masks such a simple picture and only careful comparison to the data will clarify the situation.In this paper we follow up a model independent analysis of the low energy NiV interaction with the effective range expansion [4,5]. Previously there have been two quite different solutions obtained from the data with pc<300 MeV/c. The CERN/Heidelberg fit [5] used more experimental data than the ITEP fit [4]. But this alone cannot explain the discrepancy. In the ITEP fit the effective range is restricted to be real, whereas in the CERN/Heidelberg fit it is unconstrained besides the condition that each partial wave amplitude is unitary in the considered momentum range. The argument for * Supported by the BMFT-grant 06 HD 756 ** Institute for Theoretical and Experimental Physics (ITEP), Moscow, USSR *** Saha Institute of Nuclear Physics, Calcutta, India a real effective range in the ITEP fit was that there are no important annihilation thresholds close to the NN threshold. Then the phase space in the annihilation thresholds close to the NN threshold. Then the phase space in the annihilation channel changes only by about 10% within the interval of the incident i0 momentum 0 <PL < 300 MeV/c and the imaginary part of the effective range M-matrix should vary little with energy. More recently, however, the ITEP group [6] proposed a model of N/V interaction with a confined doorway quark channel which mediates between elastic NN channel and annihilation. This model gives analytical values for the lowenergy parameters and in particular an effective range with a negative imaginary part of the same magnitude as the real part. Thus the effective range is connected to the dynamics of the annihilation process and it may be complex.It can easily be shown that a sufficient condition to guarantee unitarity is Im r < 0. For example in case of s-wave scattering with absorption one hasBecause of Im a > 0, a negative imaginary r gives a consistently negative imaginary part in the denominator and 4~z consequently a positive cross section a1 = o = ~-Im F~ = o.In addition to the theoretica...

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