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arXiv · hep-lat/0610070

Baryon-Baryon Bound States From First Principles

Paulo A. Faria da Veiga·Michael O'Carroll
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Abstract

We determine baryon-baryon bound states in 3+1 dimensional ${\rm SU}(3)$ lattice QCD with two flavors, $4\times 4$ spin matrices, and in an imaginary time formulation. For small hopping parameter, $κ>0$, and large glueball mass (strong coupling), we show the existence of three-quark isospin 1/2 particles (proton and neutron) and isospin 3/2 baryons (delta particles), with asymptotic masses $-3\lnκ$ and isolated dispersion curves. We only consider the existence of bound states of total isospin $I=0,3$. Using a ladder approximation to a lattice Bethe-Salpeter equation, baryon-baryon bound states are found in these two sectors, with asymptotic masses $-6\lnκ$ and binding energies of order $κ^2$. The dominant baryon-baryon interaction is an energy-independent spatial range-one potential with an ${\cal O}(κ^2)$ strength. There is also attraction arising from gauge field correlations associated with six overlapping bonds, but it is counterbalanced by Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a quark, antiquark exchange with {\it no} meson exchange interpretation; the repulsive or attractive nature of the interaction does depend on the isospin and spin of the two-baryon state.

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BibTeXRIS

Paulo A. Faria da Veiga, Michael O'Carroll. 2006-10-10. Baryon-Baryon Bound States From First Principles. https://arxiv.org/abs/hep-lat/0610070

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