ΛNNandΣNNsystems at threshold

Abstract

We calculate the hypertriton binding energy and the d and d scattering lengths using baryon-baryon interactions obtained from a chiral constituent quark model. We study consistently the N N and NN systems by analyzing the effect of the ↔ conversion. Our interactions correctly predict the hypertriton binding energy. The (I, J ) = (0, 3/2) N N channel is also attractive and it might have a bound state. From the condition of nonexistence of a (0,3/2) N N bound state, an upper limit for the spin-triplet N scattering length is obtained. We also present results for the elastic and inelastic N and N cross sections. The consistent description of the N scattering cross sections imposes a lower limit for the corresponding spin-triplet scattering lengths. In the NN system the only attractive channels are (I, J ) = (1, 1/2) and (0, 1/2), the (1, 1/2) state being the most attractive one.

ΛNNandΣNNsystems at threshold. II. The effect ofDwaves

“…In Ref. [4] we found that our model with only S waves is able to predict correctly the binding energy of the hypertriton, which is a bound state in the channel (I, J ) = (0, 1/2). We also found that the channel (I, J ) = (0, 3/2) will develop a bound state if the triplet N scattering length a 1/2,1 is larger than 1.68 fm.…”

“…Recently, a more elaborate description of the model was developed in Ref. [4], in which the N N system was also studied.…”

“…[4] we studied the N N and NN systems at threshold by solving the Faddeev equations of the coupled N N -NN system in the case of pure S wave configurations for the channels (I, J ) with I = 0, 1, 2 and J = 1/2, 3/2. However, since the hyperon-nucleon and nucleon-nucleon interactions contain sizable tensor terms, there is a coupling between the = 0 and = 2 baryon-baryon channels and between the hyperon-nucleon-nucleon channels with = 0 and λ = 0 to the channels with = 2 and λ = 2.…”

“…[3,4] we considered all configurations in which the baryon-baryon subsystems are in an S wave and the third particle is also in an S wave with respect to the pair. However, to construct the two-body t matrices that serve as input to the Faddeev equations, we considered the full interaction including the contribution of the D waves and of course the coupling between the N and N subsystems (which is known as the truncated t-matrix approximation [6]).…”

“…In the next section we will resume the basic aspects of the two-body interactions and present the generalization of the Faddeev equations of Ref. [4] for arbitrary orbital angular momenta. In Sec.…”