Resonant formation ofΛ(1405)by stopped-K−absorption in the deuteron

Abstract

To solve the current debate on the position of the quasibound K − p state, namely, " (1405) or * (1420)," we propose to measure the T 21 = T π←KN π invariant-mass spectrum in stopped-K − absorption in the deuteron, since the spectrum, reflecting the soft and hard deuteron momentum distribution, is expected to have a narrow quasifree component with an upper edge of M = 1430 MeV/c 2 , followed by a significant "high-momentum" tail toward the lower mass region, where a resonant formation of (1405) of any mass and width in a wide range will be clearly revealed. We introduce a "deviation" spectrum as defined by DEV = OBS (observed or calculated) / QF (nonresonant quasifree), in which the resonant component can be seen as an isolated peak free from the QF shape.

Theoretical analysis ofΛ(1405)→(Σπ)0mass spectra produced inp+<

“…For this purpose we have to treat the (1405) structure with the AY model and the Chiral model on equal footing to be compared with experimental data. To resolve this issue, observations of M( π) spectra associated with resonant formation of * in the stopped-K − absorption in 3,4 He [17] and also in d [18] have been proposed. Whereas old bubble-chamber experiments of stopped K − in 4 He [19] indicated a preference of (1405) over (1420) [8,18], a much more precise experiment with a deuteron target is expected at J-PARC [20].…”

The investigation ofΛ(1405) state in the stoppedK−reaction on deuterium

“…On the other hand, a very recent theoretical analysis [12] has clarified that the (Σπ) 0 invariant mass spectra after K − absorption in 4 He, 3 He and d do reflect resonant formation of Λ(1405) (or Λ(1420)) via the spectator process by the projection onto well-known Fermi momentum distribution in the target nuclei, and the mass and width of Λ(1405) have been actually determined to be MeV from a statistical analysis of an old bubble chamber data on 4 He [13]. Furthermore, it was pointed out that the target of d, as the calculated spectra are shown in figure 4, is even more interesting, because the "quasi-free" shape of M (Σπ) 0 is narrow enough because of the low internal momentum of the spectator n to observe a resonant Λ(1405) as a separate peak on a distant tail which is expected from the high-Fermimomentum component of realistic deuteron wave function [14].…”

“…In both calculations, the width of 40 MeV is assumed. Bottom: Expected sensitivity of the mass and the width of Λ * for various cases, assuming ∼40% of expected statistics [14].…”

Neutron spectra from the low-energy $\boldsymbol{K^{-} + d \to \pi + \Sigma + n}$ reaction and the shape of the $\boldsymbol{\Lambda(1405)}$ resonance

“…In principle, the numerator of (2) should correspond to the full spectrum of K − + d → π + + n reaction P full , containing both three-body kinematical and dynamical effects. However, the authors of [2] used their own approach for calculation of the numerator, which, in fact, corresponds to the zero-order iteration of the Faddeev equations, generally called single scattering approximation. Since in this case the transition operator is replaced by a two-body T-matrix, the corresponding spectrum P single contains three-body kinematics, but only two-body dynamics.…”

“…It turned out, that the effect of all the above factors remains within a few per cent. Recently, a method of eliminating the disturbing kinematical effects in order to reveal the dynamical ones was proposed [2]. The authors suggested to consider the deviation spectrum…”