How to extract theΛNscattering length from production reactions

Abstract

A dispersion integral is derived that allows one to relate directly (spin dependent) ΛN invariant mass spectra, measured in a large-momentum transfer reaction such as pp → K + pΛ or γd → K + nΛ, to the scattering length for elastic ΛN scattering. The involved systematic uncertainties are estimated to be smaller than 0.3 fm. This estimate is confirmed by comparing results of the proposed formalism with those of microscopic model calculations. We also show, for the specific reaction pp → K + Λp, how polarization observables can be used to separate the two spin states of the ΛN system.

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 result |a s | > |a t | indicates that the Λp interaction is more attractive in the singlet state than in the triplet state.…”

“…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.…”

“…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.…”

Near threshold enhancement of thepp¯mass spectrum inJ/Ψdecay

“…However, the prescription of Watson-Migdal is only valid for interactions that yield a rather large scattering length, like the 1 S 0 N N partial wave where the scattering length a is in the order of 20 fm, and even then only for a relatively small energy range, as was pointed out in several recent papers [42][43][44]. Therefore, in the present case, where the scattering lengths are in the order of 1 fm one should be cautious with the interpretation of results obtained from applying Eq.(5).…”

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].…”