Meson-meson bound states in (2+1)-dimensional strongly coupled lattice QCD model.
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2004
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We consider bound states of two mesons ~antimesons! in lattice quantum chromodynamics in an Euclidean
formulation. For simplicity, we analyze an SU~3! theory with a single flavor in 211 dimensions and twodimensional
Dirac matrices. For a small hopping parameter k and small plaquette coupling g0
22, such that 0
,g0
22!k!1, recently we showed the existence of a ~anti!mesonlike particle, with an asymptotic mass of the
order of 22 lnk and with an isolated dispersion curve—i.e., an upper gap property persisting up to near the
meson-meson threshold which is of the order of 24 lnk. Here, in a ladder approximation, we show that there
is no meson-meson ~or antimeson-antimeson! bound state solution to the Bethe-Salpeter equation up to the
two-meson threshold. Remarkably the absence of such a bound state is an effect of a potential which is
nonlocal in space at order k 2, i.e., the leading order in the hopping parameter k. A local potential appears only
at order k 4 and is repulsive. The relevant spectral properties for our model are unveiled by considering the
correspondence between the lattice Bethe-Salpeter equation and a lattice Schro¨dinger resolvent equation with
a nonlocal potential.
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VEIGA, P. A. F. da; O'CARROLL, M. L.; FRANCISCO NETO, A. Meson-meson bound states in (2+1)-dimensional strongly coupled lattice QCD model. Physical Review D, v. 69, n.097501, p. 1-4, 2004. Disponível em: <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.69.097501>. Acesso em: 20 jul. 2017.