Isospin breaking from diquark clustering

Abstract

Although SU(2) isospin symmetry is generally assumed in the basic theory of the strong interaction, a number of significant violations have been observed in scattering and bound states of nucleons. Many of these violations can be attributed to the electromagnetic interaction but the question of how much of the violation is due to it remains open. A schematic model based on clustering of quarks in the interior of the confinement region of the two-nucleon system is introduced and evaluated. In this model the Coulomb interaction is the source of all isospin breaking. It draws on a picture of the quark density based on the diquark-quark model of hadron structure which has been investigated by a number of groups. The model produces three isospin breaking potentials connecting This illustrative model suggests that the breaking seen in the low-energy NN interaction may be understood in terms of the Coulomb force between members of diquark clusters. It allows the prediction of the charge symmetry breaking interaction and the $nn$ scattering length from the well measured $np$ singlet scattering length. Values of the $nn$ scattering length around $-18$ fm are favored. Since the model is based on the quark picture, it can be easily extended, in the SU(3) limit, to calculate isospin breaking in the strange sector in the corresponding channels. A natural consequence of isospin breaking from diquark clustering is that the breaking in the strange sector, as measured by the separation energy difference between $_{\Lambda}^4$H and $_{\Lambda}^4$He, is several times larger than that seen in the comparison of three-nucleon mirror nuclei as observed experimentally.Comment: 29 pages 12 figure

Ernest Henley’s isospin and the ensuing progress

“…The work of Ref. [57] initiates a model of nucleon-nucleon scattering that is consistent with scattering lengths. This is then used to compute the A = 3 binding energy difference, using a wave function that is expressed in terms of nucleon coordinates However, it is well known that using any potential that accounts for the scattering length difference will account for the A = 3 binding energy difference.…”

“…Thus the computed agreement for A = 3 provided in this reference provides no (nada, nil, rien de tout) evidence for the particular Coulomb mechanism used to create the potential. Furthermore, the claim of [57] that the Coulomb interaction is exclusively responsible for the nucleon-nucleon scattering length differences is incomplete. There are other mechanisms that are non-zero.…”

“…A recent paper [57] uses a model in which "the Coulomb interaction is the source of all isospin breaking". The basic idea of this work is that at short center-of -mass separations between two nucleons "the six quarks intermixed give more possibilities for correlations among them leading to additional Coulomb-energy."…”