S-matrix poles and phase shifts forNΔ scattering

Abstract

Threshold behavior of S-wave phase shifts is studied for Nh, scattering with a nearby S-matrix pole. The phase 8n& for pp ('D~) Nh ('S~) obtained by experiments for pp nptt+ are explained on the basis of the pole of unstable bound state type or broad dibaryop, (M =2144 MeV, I = 1, J =2+), by taking into account instability of the 6, NN final-state interaction for Nh, npn+ and a factor i due to p-wave pion emission. This pole explains also the '02 phase parameters for pp pp around 2144 MeV in Es. PACS number(s): 21.30.+y, 13.75.Cs, 14.20.Pt Dibaryons have been suggested by a number of analyses of the pp scattering data [1-3]. Recently, Shypit etal. have reported results of a partial-wave analysis (PWA) for p' p'nx+p with a conclusion against the existence of dibaryons [4,5]. A criticism of this analysis has been given by Ryskin and Strakovsky [6] and by Lee [7]. As the PWA is the only source of detailed information on Nh scattering, we will examine the reported phase solution and try to explain it on the basis of an S-matrix pole of an NA bound state type or broad dibaryon. The case for an 1Vh, resonance will be discussed separately.The reaction pp npx+ contains two dominant processes, pp('D2) NA('S2) and pp( P~) NS( S~), in the low-energy region. Here, S stands for a zN S wave.In the following, we will mainly consider the first process and try to find the reason why the S-wave Nh, phase shift of Ref.[4] (SHY-88) is -30'-40' near the NA threshold and falls off with energy. We will present a simple S-matrix formalism to observe the threshold behavior of an S-wave phase shift for unstable particle scattering when a nearby S-matrix pole of bound or virtual state type exists. We will then study important effects on the phases for pp npx+ not taken into account in SHY-88 and Ref.[5] (SHY-89): the NN final-state interaction (NN FSI) and the problem of a factor i due to p-wave pion emission. Our main results will be given, we will discuss effects of the NN FSI peak cut and zd channel, and another treatment of NN FSI will be given.The phase shift btvtt, for NA('Sq) NA( S2) near the threshold. We first discuss S-wave Nh scattering without coupling to pp. We define the 5 momentum p relative to N by smearing in mass m * the relative momentum k(s, m*) of the A considered as stable and having the mass m* with a weight p (m ) of the Breit-Wigner type normalized to 1. In the narrow width approximation, we obtain p=k(s, Mq -iI q/2) =k+ikt with (k, kt)

Examination of the nature of the ABC effect

“…Refs. [61][62][63][64][65][66][67][68][69][70][71][72]. Since in this route D 12 and the associated pion have to be in relative p-wave, in order to fulfill the angular momentum requirements of D 03 , this decay route is practically indistinguishable from the route D 03 → ∆∆ → dππ, i.e.…”

Encounters with dibaryons - have they finally become true?

“…In a series of papers [38,39] Hoshizaki concluded that interpretations in terms of a NΔ virtual-state pole or a threshold cusp are invalid, rather it constitutes a S -matrix pole at (2144 -i55) MeV. But still we are left with the problem that these values do not deviate significantly from what is expected for a conventional Δ excitation by t-channel meson exchange between the two nucleons.…”

Pion assisted dibaryons: the d*(2380) resonance

“…The D 12 dibaryon of Table 1 shows up clearly in the Argand diagram of the NN 1 D 2 partial wave which is coupled above the NNπ threshold to the I = 1 s-wave NΔ channel. Its S -matrix pole position W = M − iΓ/2 was given by 2148−i63 MeV in NN phase shift analyses [7] and by 2144−i55 MeV in dedicated pp ↔ npπ + coupled-channels analyses [8]. Values of D 12 and D 21 pole positions from our hadronic-model three-body πNN Faddeev calculations [5,6] described in the previous subsection are listed in Table 2.…”