Low energyK¯Ninteractions and Faddeev calculation of theK−dscattering length in isospin and particle

Abstract

KN interactions are investigated via an effective non-linear chiral meson-baryon Lagrangian. The adjustable parameters are determined by a fitting procedure on the K − p threshold branching ratios and total cross-section data for p lab K ≤ 250 MeV/c. We produce predictions for the Σπ mass spectrum, and scattering lenghts a K − p , an(K − n → K − n), a 0 n (K 0 n → K 0 n), and aex(K − p → K 0 n). The KN amplitudes thus obtained, as well as those for other two-body channels (πN , N N , and Y N ) are used as input to predict the scattering length A K − d , for which we have devised a relativistic version of the three-body Faddeev equations. Results for all two-and three-body coupled channels are reported both in isospin and particle bases. All available KN data are well reproduced and our best results for the K − p and K − d scattering lenghts are a K − p = (−0.90 + i0.87) fm and A K − d = (−1.80 + i1.55) fm.

s-wave pion nucleon scattering lengths fromπN, pionic hydrogen, and deuteron data

“…As Table I shows, the deuteron scattering length is particularly sensitive to b 0 . This is due to the impulse approximation that cancels in the limit b 0 → 0, but contributes significantly for b 0 = 0 as the results for the phenomenological Hamiltonian (14) in Table I demonstrate. The data from pionic hydrogen, a π − p→π − p and a π − p→π 0 n , on the other hand, provide exact restrictions on the isovector scattering length b 1 .…”

“…The determination of the pion deuteron scattering length from the elementary ones is one of the problems which has attracted much attention [7,8,9,10,11] in the past, but has also stimulated more recent studies [6,12,13,14,15,16]. In ref.…”

Constraints on the S=-1 meson-baryon interaction at NLO

“…As we see, the WT term depends only on one parameter -the pion decay constant f , which is well known experimentally, f π = 92.4 MeV. However in UχPT calculations this parameter is usually taken to be larger than the experimental value, ranging from f = 1.15 f π to f = 1.36 f π [7][8][9][10][11][12][13][14][15][16][18][19][20][21], meaning to be a sort of average over the decay constants of the mesons involved in the various coupled channels. We will leave it as a free parameter of our fits.…”

“…From the studies of the meson-baryon interaction in s-wave approximation [8][9][10][11][12][13][14][15][16][18][19][20][21], it can be concluded that the significant term that allows one to get a good agreement with the experimental data is the Weinberg-Tomozawa (WT) one, which is of order O(p 2 ), and the addition of other terms such as the direct and crossed Born terms (O(p 2 )) as well as the NLO terms (O(p 4 )) only play a finetuning role. The corresponding diagrams are represented in figure 1.…”

Kaonic deuterium and low-energy antikaon-nucleon interaction

“…Three-body Faddeev calculations of kaonic deuterium have their own history -see for example Ref. [7]. Recent advanced Faddeev computations [8,9] use separable potentials constrained by the SIDDHARTA kaonic hydrogen data and have evaluated the 1s K − d atomic state assuming isospin symmetry for theK and nucleon doublets.…”