Effective string theory inspired potential and meson masses in higher dimension

Abstract

Nambu–Goto action in classical bosonic string model for hadrons predicts quark-antiquark potential to be (Lüscher and Weisz. JHEP 07, 049 (2002). doi: 10.1088/1126-6708/2002/07/049 ) V(r) = −(γ/r) + σr + μ0. In this report we present studies of masses of heavy flavour mesons in higher dimension with our recently developed wave functions obtained following string inspired potential. We report the dimensional dependence of the masses of mesons. Our results suggest that as the meson mass increases with the number of extra spatial dimensions, it will attain the Planck scale (∼1019 GeV) asymptotically at an astronomically large spatial dimension (we call it Planck dimension) DPlanck ∼ 1011, which sets the limit of applicability of Schrodinger equation in large dimension.