Heavy meson masses via Dick interquark potential

Details Heavy meson masses via Dick interquark potential Heavy meson masses via Dick interquark potential

2001-01-06

arxiv.org/abs/hep-ph/0101056v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, Latex

Scientific paper

We study Dick quark-antiquark potential (up to a color factor) $V_D(r)={-\alpha_s \over r} + gf \sqrt{N_c \over {2(N_c-1)}} \ln[exp(2mr)-1]$ in the heavy meson sector. This potential emerges from an effective dilaton-gluon coupling inspired from string theory and proves to be linearly rising at large distances which ensures quark confinement. The semi-relativistic wave equation which appears in the theory of relativistic quark-antiquark bound states is used. This equation is cast into a constituent second order Schr\"{o}dinger-like equation with the inclusion of relativistic corrections up to order $(v/c)^{2}$ in the quark speeds. The resulting equation is solved for Dick potential via the Shifted-$l$ expansion technique (SLET). The obtained results show that the spin-averaged energy levels of heavy-mesons are well explained and agree with other potential models or QCD sum rules predictions. Moreover, as a by-product, our analysis assign to the dilaton a mass around 56.9 MeV lying within the range of many theoretical scenario of dilatonic mass.

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