BB intermeson potentials in the quark model

Abstract

In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V BB (r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two B * B * channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude *

Possible molecular states in B(*)B(*) scatterings

“…In the constituent interchange model developed by Barnes and Swanson [34,35], the meson-meson scattering amplitude is calculated by the (anti)quark-(anti)quark interactions by assuming the one-gluon-exchange (OGE) color Coulomb interaction, spin-spin interaction, and linear scalar confinement interaction. In the coordinate space, the effective interaction Hamiltonian is…”

“…The unitary amplitude is obtained using the K-matrix method by unitarization of a Born approximation of the amplitude. The valence quark interchange model by Barnes and Swanson is adopted to provide the Born approximation of the meson-meson scattering amplitude [11,34]. Then, the unitarization of partial-wave amplitudes are derived and the poles of unitarized scattering amplitudes could be extracted by analytically continuing the energy to the complex plane.…”

AreY(4260)andZ2+(4250)Ding1 2009Phys. Rev. D

“…Following this systematic procedure, we can convert a general T-matrix into an equivalent potential operator. In this work, we obtain the local potential by Fourier transforming the leading terms T (0) (q) of the scattering amplitude T f i , which is common in potential model [37,38]. Since the propagators are off-shell, we introduce form factor at each vertex when writing out the scattering amplitude, the usual form factor is expressed as [39,40] …”

Quasi-nuclear and quark model baryonium: historical survey

“…Such a state is called an "hadronic molecule". There has been many discussions on such molecules [32][33][34][35][36][37][38][39][40], KK, DD or BB * . In particular, pion-exchange, due to its long range, plays a crucial role in achieving the binding of some configurations.…”