Extraction of scattering lengths from final-state interactions

Abstract

A recently proposed method, based on dispersion theory, that allows the scattering length of a hadronic two-body system to be extracted from corresponding final-state interactions is generalized to the situation where the Coulomb interaction is present. The steps required in a concrete practical application are discussed in detail. In addition a thorough examination of the accuracy of the proposed method is presented and a comparison is made with results achieved with other methods such as the Jost-function approach based on the effective-range approximation. Deficiencies of the latter method are pointed out. The reliability of the dispersion theory method for also extracting the effective range is investigated.

High resolution study of the Λp final state interaction in the reaction p+p→K++(Λp)

“…Also, the fit indicates that the reaction p + p → K + + (Λp) is dominated by the singlet contribution, however, this result should be considered with respect to the theoretical uncertainties of the Jost-function approach [19]. A direct determination of the singlet and triplet contributions requires polarization measurements as proposed in [18].…”

“…The recently proposed dispersion-integral method [18,19] differs from the Jostfunction approach by restricting the dispersion integral over the scattering phase shift to a finite upper limit. In a further investigation we will analyze our data using different approaches.…”

“…We note that a possible theoretical uncertainty of the Jost-function approach may be in the order of 0.4 fm for the scattering length and even more for the effective range as suggested by the analysis of pseudodata [19]. This aspect will be discussed in a further paper.…”

“…The FSI enhancement close to the Λp threshold was later analyzed [16] in terms of the inverse Jost function and the effective range approximation [17]. Recently a new method based on dispersion theory was developed [18,19] in order to extract the scattering length and the effective range and to estimate the theoretical error.…”

Thepp→pΛK+andpp→pΣ0K+Xie1, Chen2, Oset3 2011Phys. Rev. C8080View full textAdd to dashboardCite

“…More recently the issue of the FSI in these reactions has been retaken in Refs. [5,6] using dispersion relations, and a further experimental research has given more support to the role of the Λp FSI in these reactions [7]. A further incursion into the problem looked for angular distribution as further observable that supported the importance of the Λp FSI [8].…”